The Economics of Innovation (Critical Concepts in Economics)

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THE OF INNOVATION Edited by Cristiano Antonelli

CRITICAL CONCEPTS IN ECONOMICS

.1

-

T H E ECONOMICS O F INNOVATION

THE ECONOMICS O F INNOVATION Critical Concepts in Economics

Edited by Cristiano Antonelli Volume I Innovation and Growth: The Classical Legacies

Routledge Taylor &Francis Group L O N D O N A N D NEW YORK

First published 2008 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN, U K Simultaneously published in the USA and Canada by Routledge 270 Madison Avenue, New York, NY 10016 Routledgc~is an imprint qf the Tuylor & Francis Group, an informu business

Editorial material and selection 0 2008 Cristiano Antonelli; individual owners retain copyright in their own material Typeset in 10112pt Times N R M T by Graphicraft Limited, Hong Kong Printed and bound in Great Britain by TJI Digital, Padstow, Cornwall All rights reserved. N o part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known o r hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cutuloguing in Publication Datcr A catalogue record for this book is available from the British Library Lihrury of Congress Cataloging in Publication Dutu A catalog record for this book has been requested

ISBNIO: 0-415-42677-4 (Set) ISBNIO: 0-415-42678-2 (Volume I ) ISBN 13: 978-0-41 5-42677-0 (Set) ISBN13: 978-0-415-42678-7 (Volume I ) Publisher's Note References within each chapter are as they appear in the original complete work

CONTENTS

Acknowledgements Chronological table of reprinted urticles and chapters

General Introduction

VOLUME I INNOVATION AND GROWTH: T H E CLASSICAL LEGACIES Technical change and the aggregate production function ROBERT M. SOLOW

Adam Smith on the division of labour: two views or one? NATHAN ROSENBERG

The level of inventive activity JACOB SCHMOOKLER

Economic experiments NATHAN ROSENBERG

The direction of technological change: inducement mechanisms and focusing devices NATHAN ROSENBERG

Two propositions in the theory of induced innovations WILLIAM FELLNER

Induced technical change: evolution of thought H A N S P. BINSWANGER

Why do new technologies complement skills? Directed technical change and wage inequality DARON ACEMOGLU

xiii xv

CONTENTS

9 A new view of technological change ANTHONY B. ATKINSON AND JOSEPH E. STIGLITZ

10 The origins of endogenous growth PAUL M . ROMER

11 A model of growth through creative destruction PHILIPPE AGHION AND PETER HOWITT

12 Growth theory from an evolutionary perspective: the differential productivity puzzle RICHARD R. NELSON AND SIDNEY G . WINTER

13 General purpose technologies: 'engines of growth'?

271

TIMOTHY F. BRESNAHAN AND M. TRAJTENBERG

14 What requires explanation? RICHARD G . LIPSEY, CLIFF BEKAR AND KENNETH CARLAW

15 The dynamo and the computer: an historical perspective on the modern productivity paradox PAUL A. DAVID

VOLUME I1 INNOVATION AND COMPETITION: T H E SCHUMPETERIAN LEGACY Acknowledgements

16 Innovation in large and small firms: an empirical analysis

vii

1

ZOLTAN J. ACS AND DAVID B. AUDRETSCH

17 Entrepreneurial enterprises, large established firms and other components of the free-market growth machine

20

WILLIAM J. BAUMOL

18 The simple economics of basic scientific research RICHARD R. NELSON

19 A statistical analysis of corporate technological leadership historically JOHN CANTWELL AND BIRGITTE ANDERSEN

51

CONTENTS

Appropriation of returns from technological assets and the values of patents and R&D in Japanese high-tech firms SHOKO HANEDA AND HIROYUKI ODAGIRI

Research and development resource allocation under rivalry F. M. SCHERER

Industrial structure and the nature of innovative activity PARTHA DASGUPTA AND JOSEPH STIGLITZ

The role of supply factors in the diffusion of new process technology P. STONEMAN AND N. J. IRELAND

Investment and adoption in advanced telecommunications CRISTIANO ANTONELLI

Technology adoption in the presence of network externalities MICHAEL L. KATZ AND CARL SHAPIRO

Diffusion as a process of creative adoption CRISTIANO ANTONELLI

Sectoral patterns of technical change: towards a taxonomy and a theory KEITH PAVITT

Schumpeterian patterns of innovation F R A N C 0 MALERBA AND LUIGI ORSENIGO

Innovation: mapping the winds of creative destruction WILLIAM J. ABERNATHY AND KIM B. CLARK

Architectural innovation: the reconfiguration of existing product technologies and the failure of established firms REBECCA M. HENDERSON AND KIM B. CLARK

VOLUME I11 INNOVATION AND KNOWLEDGE: T H E ARROVIAN LEGACY Acknowledgements 31 Karl Marx on the economic role of science NATHAN ROSENBERG

vii

CONTENTS

32 Economic welfare and the allocation of resources for invention K E N N E T H J. A R R O W

33 Toward a new economics of science P A R T H A D A S G U P T A A N D P A U L A. D A V I D

34 Patents and R&D at the firm level: a first report A R I E L PAKES A N D Z V I G R I L I C H E S

35 Innovativity: a comparison across seven European countries P I E R R E M O H N E N , JACQUES MAIRESSE A N D MARCEL DAGENAIS

36 Technological opportunity and spillovers of R&D: evidence from firms' patents, profits, and market value A D A M B. JAFFE

37 The search for R&D spillovers ZVI GRILICHES

38 The new economics of innovation, spillovers and agglomeration: a review of empirical studies M A R Y A N N P . FELDMAN

39 Learning by firms and incremental technical change F R A N C 0 MALERBA

40 Classificatory notes on the production and transmission of technological knowledge KENNETH J. ARROW

41 Imitation costs and patents: an empirical study E D W I N MANSFIELD, MARK S C H W A R T Z A N D SAMUEL W A G N E R

42 Absorptive capacity: a new perspective on learning and innovation WESLEY M. C O H E N A N D D A N I E L A. L E V I N T H A L

43 The role of knowledge in R&D efficiency R I C H A R D R. NELSON

44 The use of knowledge in society F. A. HAYEK

45 The dominant role of users in the scientific instrument innovation process E R I C VON H I P P E L

CONTENTS

46 Profiting from technological innovation: implications for integration, collaboration, licensing and public policy D A V I D J . TEECE

47 The changing technology of technological change: general and

abstract knowledge and the division of innovative labour ASHISH ARORA A N D ALFONSO GAMBARDELLA

48 The emergence of technology systems: knowledge production

and distribution in the case of the Emilian plastics district P I E R PAOLO P A T R U C C O

49 Licensing tacit knowledge: intellectual property rights and

the market for know-how ASHISH ARORA

50 University versus corporate patents: a window on the

basicness of invention MANUEL TRAJTENBERG, REBECCA HENDERSON A N D ADAM JAFFE

51 Learning, internal research, and spillovers JAMES D. ADAMS

52 Networks of innovators: a synthesis of research issues C . FREEMAN

53 National innovation systems: why they are important, and how they might be measured and compared PARIMAL PATEL A N D K E I T H P A V I T T

54 The venture capital revolution P A U L GOMPERS A N D JOSH LERNER

55 The business governance of localized knowledge: an information economics approach for the economics of knowledge C R I S T I A N O ANTONELLI

CONTENTS

VOLUME IV INNOVATION AND COMPLEXITY: T H E MARSHALLIAN LEGACY

Acknowledgements

56 Hybrid corn: an exploration in the economics of technological change ZVI GRILICHES

57 A dynamic model of process and product innovation JAMES M. UTTERBACK A N D WILLIAM J . ABERNATHY

58 Technology diffusion and the rate of technical change L U C SOETE A N D ROY TURNER

59 Rational decision making in business organizations HERBERT A. SIMON

60 A failure-inducement model of research and development expenditure: Italian evidence from the early 1980s CRISTIANO ANTONELLI

61 In search of useful theory of innovation R I C H A R D R . NELSON A N D SIDNEY G. W I N T E R

62 The organisation of capabilities BRIAN J . LOASBY

63 Technological paradigms and technological trajectories: a suggested interpretation of the determinants and directions of technical change GIOVANNI DOSI

64 Innovation, diversity and diffusion: a self-organisation model GERALD SILVERBERG, GIOVANNI DOSI A N D LUIGI ORSENIGO

65 On the complexities of complex economic dynamics J . BARKLEY ROSSER J R .

66 From simplistic to complex systems in economics J O H N FOSTER

67 Complexity and empirical economics

vii

CONTENTS STEVEN N . D U R L A U F

68 Why are institutions the 'carriers of history'?: path dependence and the evolution of conventions, organizations and institutions P A U L A. DAVID

69 Competing technologies, increasing returns, and lock-in by historical events W . BRIAN A R T H U R

70 Clio and the economics of QWERTY P A U L A. DAVID

71 Some fundamental puzzles in economic historyldevelopment DOUGLASS C . NORTH

72 Punctuated equilibria and technological progress JOEL MOKYR

73 Adaptive economic growth J . STAN METCALFE, J O H N FOSTER A N D RONNIE RAMLOGAN

74 The economics of path-dependence in industrial organization CRISTIANO ANTONELLI

75 The system dynamics of collective knowledge: from gradualism and saltationism to punctuated change CRISTIANO ANTONELLI

76 Complex landscapes in economic geography P A U L KRUGMAN

77 Foresight, complexity, and strategy DAVID LANE A N D ROBERT MAXFIELD

78 Increasing returns: historiographic issues and path dependence KENNETH J . A R R O W

Index

ACKNOWLEDGEMENTS

The publishers would like to thank the following for permission to reprint their material: MIT Press for permission to reprint R. M. Solow, 'Technical change and the aggregate production function', Review of Economics and Statistics 39, 3, 1957, pp. 312-20. O 1957 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Blackwell Publishing for permission to reprint N. Rosenberg, 'Adam Smith on the division of labour: Two views or one?', Economicu 32, 126, 1965, pp. 127-39. MIT Press for permission to reprint J. Schmookler, 'The level of inventive activity', Review ofEconomics and Statistics 36, 2, 1954, pp. 183-190. O 1954 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Oxford University Press for permission to reprint N. Rosenberg, 'Economic experiments', Industrial and Corporate Change 1, 1, 1992, pp. 181-203. The University of Chicago Press for permission to reprint N. Rosenberg, 'The direction of technological change: Inducement mechanisms and focusing devices', Economic Developnzent and Cultural Change 18, 1, 1969, pp. 1-24. Blackwell Publishing for permission to reprint W. Fellner, 'Two propositions in the theory of induced innovations', Economic Journal 71,282, 1961, pp. 305-08. Hans P. Binswanger, 'Induced Technical Change: Evolution of Thought' in Hans P. Binswanger and Vernon W. Ruttan (eds), Induced Innovution: Technology Institutions and Development, pp. 13-43 O 1978 The Johns Hopkins University Press. Reprinted with permission of The Johns Hopkins University Press. MIT Press for permission to reprint D. Acemoglu, 'Why do new technologies complement skills? Directed technical change and wage inequality', ...

Xlll

ACKNOWLEDGEMENTS

Quarterly Journal of Economics 113, 4, 1998, pp. 1055-89. 0 1998 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.

Blackwell Publishing for permission to reprint A. B. Atkinson and J. E. Stiglitz, 'A new view of technological change', Economic Journal 79, 315, 1969, pp. 573-78. The American Economic Association and P. M. Romer for permission to reprint P. M. Romer, 'The origins of endogenous growth', Journal of Economic Perspectives 8, 1, 1994, pp. 3-22. The Econometric Society for permission to reprint P. Aghion and P. Howitt, 'A model of growth through creative destruction', Econometrica 60, 2, 1992, pp. 323-51. The American Economic Association and R. R. Nelson and S. G. Winter for permission to reprint R. R. Nelson and S. G. Winter, 'Growth theory from an evolutionary perspective: The differential productivity puzzle', American Economic Review 65, 2, 1975, pp. 338-44. Elsevier for permission to reprint T. F. Bresnahan and M. Trajtenberg, 'General purpose technologies: "Engines of growth"?', Journal of Econometrics 65, 1995, pp. 83-108. Copyright O Elsevier, 1995. MIT Press for permission to reprint R. Lipsey, C. Bekar and K. Carlaw, 'What requires explanation?', in E. Helpman (ed.), General Purpose Technologies and Economic Growth, 1998, pp. 15-54. The American Economic Association and P. A. David for permission to reprint P. A. David, 'The dynamo and the computer: An historical perspective on the modern productivity paradox', American Economic Review 80, 2, 1990, pp. 355-361.

Disclaimer The publishers have made every effort to contact authorslcopyright holders of works reprinted in The Economics of Innovation: Critical Concepts in Economics. This has not been possible in every case, however, and we would welcome correspondence from those individualslcompanies whom we have been unable to trace.

xiv

c:

X

William Fellner

1969 Anthony B. Atkinson and Joseph E. Stiglitz The direction of technological change: 1969 Nathan Rosenberg inducement mechanisms and focusing devices

1969 Kenneth J. Arrow

1967 F. M. Scherer

1965 Nathan Rosenberg

1962 Kenneth J. Arrow

196 1

1959 Richard R. Nelson

Adam Smith o n the division of labour: two views or one? Research and development resource allocation under rivalry Classificatory notes on the production and transmission of technological knowledge A new view of technological change

Hybrid corn: a n exploration in the economics of technological change Technical change and the aggregate production function The simple economics of basic scientific research Two propositions in the theory of induced innovations Economic welfare and the allocation of resources for invention

1957 Zvi Griliches

Economic Development and Cultural Change, 18:1, 1-24

Economic Journal, 79:3 15, 573-78

American Economic Review, 59:2, 29-35

Quarterly Journal of Economics, 8 1:3, 359-94

R. R. Nelson (ed.), The Rate and Direction of Inventive Activity: Economic and Social Factors, Princeton: Princeton University Press for NBER, 609-25 Economics, 32:126, 127-39

Economic Journal, 7 1:282, 305-08

Review of Economics and Statistics, 39:3, 312-20 Journal of' Political Economy, 67:3, 297-306

American Economic Review, 35:4, 519-30 Review of Economics and Statistics, 36:2, 183-90 Econonzetrica, 25:4, 501-22

The use of knowledge in society The level of inventive activity

1945 F. A. Hayek 1954 Jacob Schmookler

1957 Robert M. Solow

Source

Author

Title

Date

Chronological table of reprinted articles and chapters Vol. Chap.

Date

Partha Dasgupta and Joseph Stiglitz Ariel Pakes and Zvi Griliches Edwin Mansfield, Mark Schwartz and Samuel Wagner Giovanni Dosi

Herbert A. Simon

Richard R. Nelson and Sidney G. Winter Hans P. Binswanger

James M. Utterback and William J . Abernathy Eric von Hippel

Richard R. Nelson and Sidney G. Winter

Technological paradigms and technological trajectories: a suggested interpretation of the determinants and directions of technological change

Rational decision making in business organizations Industrial structure and the nature of innovative actvity Patents and R&D a t the firm level: a first report Imitation costs and patents: an empirical study

Induced technical change: evolution of thought

The dominant role of users in the scientific instrument innovation process In search of useful theory of innovation

Reseurch Policy, 11, 147-62

Economic Journal, 91:364, 907-18

Economic Letters, 5 , 377-81

Economic Journal, 90:358, 266-93

H. P. Binswanger and V. W. Ruttan (eds), Induced Innovation: Technology Institutions and Development, Baltimore: Johns Hopkins University Press, 13-43 American Economic Review, 69:4, 493-512

Research Policy, 6, 36-76

Research Policy, 5, 21 2-39

Karl Marx on the economic role of Journal of Political Economy, 82:4, 7 13-28 science American Economic Review, 65:2, 338-44 Growth theory from an evolutionary perspective: the differential productivity puzzle A dynamic model of process and product Omega, 3:6, 639-56 innovation

Nathan Rosenberg

Source

Title

Author

Chronological Table continued

1

Chap.

Wesley M. Cohen and Daniel A. Levinthal Paul A. David

W. Brian Arthur

Gerald Silverberg, Giovanni Dosi and Luigi Orsenigo Cristiano Antonelli

Michael L. Katz and Carl Shapiro David J. Teece

Luc Soete and Roy Turner William J. Abernathy and Kim B. Clark Paul A. David Adam B. Jaffe

Richard R. Nelson P. Stoneman and N. J. Ireland Keith Pavitt

The dynamo and the computer: an historical perspective on the modern productivity paradox

A failure-inducement model of research and development expenditure: Italian evidence from the early 1980s Competing technologies, increasing returns, and lock-in by historical events Absorptive capacity: a new perspective on learning and innovation

The role of knowledge in R&D efficiency The role of supply factors in the diffusion of new process technology Sectoral patterns of technical change: towards a taxonomy and a theory Technology diffusion and the rate of technical change Innovation: mapping the winds of creative destruction Clio and the economics of QWERTY Technological opportunity and spillovers of R&D: evidence from firms' patents, profits, and market value Technology adoption in the presence of network externalities Profiting from technological innovation: implications for integration, collaboration, licensing and public policy Innovation, diversity and diffusion: a self-organisation model

I1 IV II IV 111 I1

Research Policy, 13, 343-73 Economic Journal, 94:375, 612-23 Research Policy, 14, 3-22 American Economic Review, 75:2, 332-37 American Economic Review, 76:5, 984-1001

of' Political Economy, 94:4l, 822-41

111

Administrative Science Quarterly, 35:1, 128-52

I

IV

Economic Journal, 99:394, 11 6 31


IV

IV

Economic Journal, 98:393, 1032-54 Journal of Economic Behavior and Organization, 12, 159-80

I11


Journal

111 I1

Quarterly Journal of Economics, 97:3, 453-70 Economic Journal, 93, 66-78

". -.

i.

5

Author

1994 Partha Dasgupta and Paul A. David 1994 Paul A. David

1994 Ashish Arora and Alfonso Gambardella

1993 Cristiano Antonelli

1992 Nathan Rosenberg

1992 Franco Malerba

1992 Philippe Aghion and Peter Howitt 1992 Zvi Griliches

1991 C. Freeman

1990 Joel Mokyr

1990 Rebecca M. Henderson and Kim B. Clark

Date


Why are institutions the 'carriers of history'?: path dependence and the evolution of conventions, organizations and institutions

Investment and adoption in advanced telecommunications The changing technology of technological change: general and abstract knowledge and the division of innovative labour Toward a new economics of science

Learning by firms and incremental technical change Economic experiments

Administrative Science Quarterly, 35, 9-30

Architectural innovation: the reconfiguration of existing product technologies and the failure of established firms Punctuated equilibria and technological progress Networks of innovators: a synthesis of research issues A model of growth through creative destruction The search for R&D spillovers

Structural Change and Economic Dynamics, 5:2. 205-20


Industrial and Corporate Change, 1:1, 181-203 Journal of Economic Behavior and Organization, 20, 227-45 Research Policy, 23, 523-32

Scandinavian Journal of Economics, 94, S29-S47 Economic Journal, 102:413, 845-59

Econometrica, 60:2, 323-51



Source

Title

Vol.

Chap.

x

5.

Some fundamental puzzles in economic historyldevelopment Why d o new technologies complement skills? Directed technical change and wage inequality

1998 Daron Acemoglu

economic^ of Innovation and New Technology, 4:3, 21 1-34 Internatzonal Journal of Industrial Organization, 15, 643-75 W. B. Arthur, S. N. Durlauf and D. A. Lane (eds), The Economy us an Evolving Complex System II, Santa Fe: Westview Press, 169-98 W. B. Arthur, S. N. Durlauf and D. Lane (eds), The Economy as an Evolving Complex System II, Santa Fe: Westview Press, pp. 223-37 Quarterly Journcd of Econoniic~,1 13:4, 1055-89

economic.^ of' Innovution and New Technology. 5. 19-50

University versus corporate patents: a window on the basicness of invention A statistical analysis of corporate technological leadership historically The economics of path-dependence in industrial organization Foresight, complexity, and strategy

Cambridge Journal of Economics, 19, 47-65

Journal of Econometrics, 65, 83-108

Journal of Economic Perspectives, 8: 1, 3-22 Economics of Innovation and Neb+ Technology, 4, 41-59

Economics of Innovation and New Technology, 3, 77-95

American Economic Review, 84:2, 412-1 6

Schumpeterian patterns of innovation

Complex landscapes in economic geography National innovation systems: why they are important, and how they might be measured and compared The origins of endogenous growth Licensing tacit knowledge: intellectual property rights and the market for know-how General purpose technologies: 'engines of growth'?

1997 Douglass C. North

1997 David Lane and Robert Maxfield

1995 Timothy F. Bresnahan and M. Trajtenberg 1995 Franco Malerba and Luigi Orsenigo 1995 Manuel Trajtenberg, Rebecca Henderson and Adam Jaffe 1996 John Cantwell and Birgitte Andersen 1997 Cristiano Antonelli

1994 Paul M. Romer 1995 Ashish Arora

1994 Parimal Pate1 and Keith Pavitt

1994 Paul Krugman

x

X

Author

Kenneth J. Arrow

Paul Gompers and Josh Lerner 2004 William J. Baumol

2001

2000

1999 J. Barkley Rosser Jr.

1999 Maryann P. Feldman

1998 Brian J. Loasby

1998 Richard G. Lipsey, Cliff Bekar and Kenneth Carlaw 1998 Zoltan J. Acs and David B. Audretsch 1998 Shoko Haneda and Hiroyuki Odagiri

Date


Entrepreneurial enterprises, large established firms and other components of the free-market growth machine

The new economics of innovation, spillovers and agglomeration: a review of empirical studies On the complexities of complex economic dynamics Increasing returns: historiographic issues and path dependence The venture capital revolution

Journal of Economic Perspectives, 13:4. 169-92 European Journal of the History of Economic Thought, 7:2, 171-80 Journal of Economic Perspectives, 15:2, 145-68 Small Business Economics, 23, 9-21

Journal of Economic Behavior and Organization, 35, 139-60 Economics of Innovation and New Technology, 8, 5-25

Economics of Innovation and New Technology, 7:4, 303-21

E. Helpman (ed.), General Purpose Technologies and Economic Growth, Cambridge, MA: MIT Press, 15-54 American Economic Review, 78:4, 678-90

What requires explanation? Innovation in large and small firms: an empirical analysis Appropriation of returns from technological assets and the values of patents and R&D in Japanese high-tech firms The organisation of capabilities

Source

Title

I1

I11

IV

IV

111

17

54

78

65

38

62

20

I1

IV

16

14

Chap.

I1

I

Vol.

J. Stan Metcalfe, John Foster and Ronnie Ramlogan Pierre Mohnen, Jacques Mairesse and Marcel Dagenais Cristiano Antonelli

Cristiano Antonelli

Cristiano Antonelli

James D. Adams

Pier Paolo Patrucco

Steven N. Durlauf John Foster

Economics uf Innovation and New Technology, 15:4/5, 391-41 3 Journal of Econornic Behavior and Organizuton, 62, 21 5-36

Innovativity: a comparison across seven European countries The system dynamics of collective knowledge: from gradualism and saltationism to punctuated change

Industry and Innovation, 13:3, 227-61

Economics of Innovation and New Technology, 15, 5-36 Journal of Technology Tran.Cfer, 3 1 , 2 11-26



Economic Journal, 115, F225-43 Cambridge Journal of Economics, 29, 873-92

Complexity and empirical economics From simplistic to complex systems in economics The emergence of technology systems: knowledge production and distribution in the case of the Emilian plastics district Learning, internal research, and spillovers Diffusion as a process of creative adoption The business governance of localized knowledge: an information economics approach for the economics of knowledge Adaptive economic growth

INTRODUCTION The foundations of the economics of innovation Cvistiano Antonelli

During the last forty years, the economics of innovation has emerged as a distinct area of enquiry at the crossing of the economics of growth, industrial organization, regional economics and the theory of the firm, and has become a well-identified area of competence in economics specializing not only in the analysis of the effects of the introduction of new technologies, but also, and mainly, in understanding technological change as an endogenous process. As a result of the interpretation, elaboration and evolution of different fields of analysis in economic theory, innovation is viewed as a complex, path-dependent process characterized by the interdependence and interaction of a variety of heterogeneous agents, able to learn and react creatively with subjective and procedural rationality. After the discovery of the residual, the traditional assumptions about the exogeneity of technological change proved to be quite embarrassing and pushed economics to provide and elaborate an endogenous explanation: too large is the share of unexplained growth. Neoclassical economics provided an elaborated and sophisticated framework to understand the conditions for static efficiency. In such a context, growth and development are the consequences of exogenous changes in the shape of utility functions, in the characteristics of the technology, and in the demographic conditions as well as the supply of natural resources. This theory does not address the actual causes of growth and change. It is limited to analysing the complementary conditions in terms of rates of growth in the supply of labour and savings that make it possible to take advantage of the effects of 'technology push' falling from heaven like manna and for exogenous growth to take place. The effort to provide an endogenous explanation of technological change has been nurtured by the sequential and yet overlapping articulations and reinterpretations of different approaches that have been progressively built in a process of reconsideration and reappraisal of the dynamic legacies that had stressed the role of endogenous dynamics, but had been left aside by mainstream theorizing.

INTRODUCTION

Four wide-rangingheuristic frameworks can be identified: the classical legacies of Adam Smith and Karl Marx, the Schumpeterian legacy, the Arrovian legacy, and the biological suggestions stimulated by the Marshallian legacy eventually articulated in the evolutionary approaches leading to complexity. These four approaches have a clear focus. The classical legacies have been especially useful in understanding the contribution of innovation and technological change to economic growth, mainly at the aggregate level. The induced approach to technological change and the role of learning are the core contributions of this line of analysis. The Schumpeterian legacy has provided the basis of enquiry into the relationships between innovation and competition in the marketplace with important implications for the theory of the firm and the theory of the markets. The Schumpeterian approach has focused on the role of innovation as a competitive tool, and on both the corporation and entrepreneurship as the driving factors. The Arrovian legacy has made it possible to explore the economics of knowledge with its powerful implications for the theory of organization and regional economics. Finally, biological grafting based on the Marshallian legacy and evolutionary approaches, lately reinvigorated by complexity thinking, has paved the way to understanding the path-dependent dynamics and systemic interdependencies that characterize technological and structural change. The approaches have evolved in parallel in the second half of the twentieth century with a process of specialization and consolidation of their respective areas of expertise. Yet an increasing number of lateral and horizontal contributions have been made, feeding a process of increasing convergence and integration. As a result, a rich web of overlapping stratifications has gradually been growing. In order to highlight the origins and the evolution of the economics of innovation, a matrix of analytical tools can be elaborated. The basic line of understanding is found along the diagonal, where each field matches its own basic approach. Much interest, however, is found in cells around the diagonal, where an increasing number of cross contributions can be identified. The result of the process is an increasing complementarity and compatibility among the four approaches into the new frame provided by the economics of complexity. Table 1 synthesizes the matrix of notions and concepts elaborated in the economics of innovation. It shows how the different analytical trails have contributed to the evolution of the field. In so doing it provides a guide to the four volumes here. The classical, Schumpeterian, Arrovian and Marshallian approaches share a basic departure from standard economics: the attribution to economic agents with the capability to change their production and utility functions. A few common threads also emerge across them. First, the basic notion of learning is eventually articulated in terms of creative reaction, and the context within which learning takes place receives increasing attention. The heterogeneity of learning and interaction conditions emerges as a second

Division of labour -Demand-pull Inducement Creative destruction

-Residual Learning by doing Learning by using N e w growth theory

-Technological trajectories -Technological paths

THE CLASSICAL LEGACIES

THE SCHUMPETERIAN LEGACIES

THE ARROVIAN LEGACY

THE MARSHALLIAN LEGACY: EVOLUTION AND COMPLEXITY

INNOVATION AND GROWTH

Table I The innovation matrix

Dynamic efficiency -Sectoral patterns Technological regimes -Creative adoption

General-purpose technologies -Technological systems

-Localized technological change P a s t dependence -Positive feedbacks P a t h dependence -Generative relationships

-Knowledge as an economic good -Knowledge spillover -Industrial districts -Knowledge asymmetries -Knowledge governance -Localized technological knowledge -Distributed knowledge -Innovation networks -Knowledge as an input and an output -Competence

-Knowledge as a production factor Knowledge quasi-rents Spillover

L i f e cycle Epidemic diffusion -Replicator dynamics

-Industrial specialization

Learning -Collective knowledge G a l e s of innovation -R&D Technology push -Technological opportunities

INNO V A TION WITHIN EVOL VING SYSTEMS

I N N 0 VATION AND KNOWLEDGE

Creative reaction -The Schumpeterian hypothesis -Entrepreneurship Monopolistic competition Structure-conductperformance D o m i n a n t design Network externalities

INNOVATION AND COMPETITION

INTRODUCTION

common thread. The effects of historic time, both at the system level and at the agent level, are acknowledged. The conduct of each agent is shaped by the effects of the past and yet they are credited with the capability to alter the trajectories of their activities by means of the generation of new technological knowledge and the introduction of technological innovations. The dynamics of feedback is finally appreciated in the different contexts: the introduction of innovations changes the structure of the system and this in turn affects the conduct of agents, including the introduction of other innovations. The shared understanding of the working of the economic system as a complex dynamic process is possible as soon as the systemic properties that belong to economics as a science are extended so as to include the possibility for agents and subsystems to internally generate new technological knowledge and hence new production technologies and new preferences. What is more, it is not difficult to do this, for most of standard microeconomics can be retained and properly implemented at the agent level: heterogeneous agents do attempt to optimize within the strong limitations of their subjective conditions. The aggregate outcome of their action however is far from a general equilibrium steady state, and rather a process of continual change. This view can be considered the result of the integration of the four approaches and of the four fields of investigation into one broader analytical platform provided by complexity economics. With respect to Table 1 we see that, especially at the bottom right of the diagonal, the borders of the cells themselves are more and more blurred as systematic overlapping across fields of investigation and traditions of analysis take place. Economics of innovation emerges as a distinctive field of investigation with a broad array of complementary concepts articulated within convergent and consistent fields of specialization. The aim of the four volumes here is to provide an interpretative framework able to identify the main contributions of the economics of innovation and to track the emergence of the view that innovation is a path-dependent, collective process that takes place in a localized context if, when and where a sufficient number of creative reactions are made in a coherent, complementary and consistent way. As such innovation is one of the key emergent properties of an economic system viewed as a dynamic complex system (Antonelli, 2008).

Volume I: Innovation and growth - The reappraisal of the classical legacies The discovery of the residual

The discovery of the residual coincides with the birth of economics of innovation. In neoclassical economics, technological change is exogenous.

INTRODUCTION

Occasionally technological shocks perturbate the equilibrium conditions of the system: firms are not supposed to be able to intentionally change their technologies. Volume I looks at the key steps in the departure from this obsolete position. The empirical investigations of Robert Solow in this volume (Chapter 1) and Moses Abramovitz (1956) show that over 50% of the growth of output in the US economy between the end of the nineteenth century and the first part of the twentieth century cannot be reconciled with the growth of inputs. Technological change should be credited for its astonishing contribution to economic growth. Equilibrium economics is able to explain only a fraction of the economics system. It is this evidence that presents a challenge. The basic puzzle remains the problematic core of this area of specialization. How innovations come to the marketplace, how novelty takes place in our understanding of the economic and technological interplay, how and why total factor productivity grows, how firms and economic agents in general generate and react to the introduction of novelty, are the key questions. The birth of economics of innovation as a specific area of enquiry and investigation in the broader context of the increasing specialization of economics can be considered the ultimate result of the analysis of growth of output and labour productivity, ceteris paribus input levels, when and if increasing returns do not take place. The volume brings together the founding stones of classical analysis on the endogenous determinants of technological change and the more recent approaches elaborated after the discovery of the residual. As will be shown below, it was the writings of Adam Smith and Karl Marx that provided the key points of departure to the economics of technical change and at the same time made clear how the economics of innovation and new technology cannot be separated by the need to elaborate the tools for an economic understanding of the continual transformations that characterize growth and change. As the Classical School stresses, technological change is but an inseparable and indispensable aspect of economic growth. Adam Smith and the demand-pull hypothesis

In the effort to grasp the determinants of the early stages of the first industrial revolution, Adam Smith contributed the basic elements of the demand-pull approach. The division of labour is determined by the extent of the market. All increases in the extent of the market can lead to an increase in the division of labour and hence in specialization. Specialization in turn is the base for dedicated learning and the eventual introduction of innovations. Innovations increase the efficiency of labour and hence the extent of the market. As Nathan Rosenberg notes in Chapter 2, Smith laid down the foundations for the analysis of technological change as an

INTRODUCTION

endogenous and self-feeding process. Allyn Young (1928) and Nicholas Kaldor (1972) have developed this approach further, and shown the irrelevance of equilibrium economics when the dynamics of technological change is understood. Smith provided the most impressive and clear account of the essential role of technological knowledge and technological change as endogenous factors in explaining the dynamic character of the economic process. The first four books of An Enquiry into the Nature and Causes of the Wealth of Nations, the founding stone of economics, are devoted to exploring the economic process and its determinants, and the first lines are devoted to the relationship between productivity and the division of labour. According to Smith, the growth in productivity is a consequence of the division of labour: 'The greatest improvement in the productive powers of labor, and the greater part of the skills, dexterity, and judgment with which it is any where directed, or applied, seem to have been the effects of the division of labor' (Smith, 1776: 13). The division of labour has a clear causal role in Smith's view of the origins of the accumulation of competence and knowledge. More specifically, Smith elaborated a sequence according to which the division of labour is the cause of an increase in competence. The generation of new knowledge builds on the increase in competence, and technological innovations are the result of this process. Smith fully articulated a bottom-up theory of technological knowledge. Learning by doing and learning by using are at the origin of inventions that eventually make possible the introduction of new and improved machineries. According to Smith, the professional competence of workers is acquired and implemented by means of learning processes that, ultimately, because of the division of labour, are the cause of the skills of workers. However, learning by doing and by using processes, internal to each firm, are not the sole factors in the accumulation of new knowledge. An important role is also played by the producers of machines and by scientists. The division of labour in conclusion, enters the workings of science and becomes a powerful factor in the organization and efficiency of scientific progress. A reading of Smith confirms the key role of the economics of knowledge in the understanding of the economic process shaped by continual development based on the introduction of new technologies. Indeed, one finds in Smith the early foundations of the economic understanding of the mechanisms at work in the generation of technological knowledge. Smith in fact provides a comprehensive analysis where technological knowledge is regarded as the eventual result of at least three processes: a) a bottom-up process by means of learning by doing and learning by using; b) the specialized activity of 'philosophers' in a top-down process; and c) the interactions with suppliers of machinery and intermediary inputs.

INTRODUCTION

Building on these bases, the dynamic engine of Smith is in place. The division of labour is the consequence of the extent of the market and is the cause of the increase of technological knowledge, hence of inventions and eventually technological innovations. Technological innovations in turn lead to an increase in productivity. The increase in productivity leads to an increase in the demand and hence of the extent of the market. Thus the analysis of Smith comes full circle. Alfred Marshall followed the line of enquiry elaborated by Smith and acknowledged the dual relationship between the division of labour and the introduction of new technologies. Technological change and specialization are two sides of the same process. Allyn Young, following Marshall, probably contributed more to focusing attention on the key role of endogenous dynamics in the work of Smith. According to Young, the interaction between technological and structural change is fed by the dynamics of the division of labour. Specialization, accumulation of competence, the introduction of new technologies and increases in the extent of the market is change are all steps towards progressive and cumulative change. Young here captures the critical role of technological change, as both the product and the cause of increasing functional differentiation and complementarity within the economic system, in economic growth. He lays down the first elements of a system dynamic approach to understanding economic growth. Economic systems in fact are viewed as complex and dynamic adaptive organizations composed by autonomous and yet interrelated and interdependent units that change over time. Nicholas Kaldor digs even deeper and fully recognizes the essential contribution of Smith to building a dynamic theory of the economic process where technological change and technological knowledge pulled by the interplay between the beneficial effects of the division of labour and the extent of the market take centrestage. Cumulative technological change takes place, in out-of-equilibrium conditions, in an economic system where and when firms are viewed not as passive users of given technologies only able to select the techniques more appropriate to a given set of relative prices, but as agents able to change and generate their own technologies. Building on Smith, in Chapter 3 Jacob Schmookler provides empirical support to the hypothesis that demand growth pulls the increase of technological knowledge, hence of inventions and eventually technological innovations. Nathan Rosenberg and David Mowery (1979) provide an outstanding account of the pervasive role of the demand-pull hypothesis within the post-Keynesian approach. Kavl Mavx and induced technological change

Building on a superb command of the historical processes that characterized the first industrial revolution, Marx contributed the first elements of a theory

INTRODUCTION

of endogenous technological change as the result of the intentional process of augmented labour substitution. When wages increase, capitalists are induced to introduce new capital-intensive technologies that help to reduce the pressure of unions and increase the total efficiency of labour. The analysis of technological change plays a key role in Marx's master work Capital (1867, 1976). As Nathan Rosenberg point out in Chapter 4, Marx shows how technological change is the basic tool by which at the same time capitalists increase both profits and the extraction of surplus value from the production process. Marx stressed the dual role of technological change. On the one hand technological change makes it possible to reduce the price of goods in the marketplace. On the other, technological change makes it possible to increase the extraction of surplus value (Rosenberg, 1976). The competitive process among capitalists feeds the former. The exploitation of labour by capitalists as a class is the result of the latter. In Chapter 5, Nathan Rosenberg provides an admirable account of the dynamics of the innovative process in the Marxian approach. The attempt to contrast the decline in the profitability of each firm, stemming from the increase in wages, is the direct incentive for the innovative action of each capitalist that leads to the generation and introduction of technological innovations embodied in new machines. The competitive pressure in the markets for products, among capitalists, adds momentum to the dynamics of the process. Marx paid much stronger attention to process innovations than to product innovations: hence at the system level the innovative process has the aggregate effect of substituting capital for labour. The decline in the number of workers is relative, but not absolute. After the absorption of temporary unemployment, wages increase again, and capitalists are again induced to introduce new process technologies that reduce the labour intensity of the production process. Specifically, a distinction has to be made between models of induced technological change, which focus on the changes in factor prices, and models of induced technological change, which stress the static conditions of factor markets. In the first approach, following John Hicks and Karl Marx, firms are induced to change their technology when the price of a production factor increases (Hicks, 1932). According to Hicks, the change in factor prices acts as a powerful inducement mechanism that explains both the rate and the direction of the introduction of new technologies. The change in factor prices in fact induces firms to introduce new technologies to reduce the cost of the factor that has become more expensive. The introduction of new technologies complements the standard substitution process, i.e. the technical change represented by the selection of new techniques, defined in terms of factor intensities, on the existing isoquants. In this case, as Fellner elaborates in Chapter 6, technological change is considered an augmented form of substitution: technological change complements technical change.

INTRODUCTION

As the debate summarized by Hans Binswanger in Chapter 7 shows, this approach to induced technological change differs from the static Kennedy-von Weizsacker-Samuelson approach, according to which firms introduce new technologies in order to save on the production factors that are relatively more expensive. Here the levels of factor price matter instead of the rates of change. This approach has revealed a major limitation of the former. From simple algebraic calculation it is in fact clear that firms have an incentive to introduce labour-intensive technologies, in labour-abundant and capital-scarce regions and countries, even after an increase in wages. The Kennedy-von Weizsacker-Samuelson approach, however, is severely limited from the dynamic viewpoint. It is no longer clear when and why firms should innovate. Consistently only the direction of technological change can be induced, rather than the rate. Both approaches, as is well known, have often been criticized using Salter's argument, according to which firms should be equally eager to introduce any kind of technological change, either labour- or capital-intensive, provided it enables reduced production costs and increased efficiency. It is interesting to note that the analysis of the role of relative factor endowments in explaining the direction of technological change has recently been revived, by Daron Acemoglu in Chapter 8, to explain the bias towards new information and communication technologies in terms of skill intensity (see also Acemoglu, 2002). Learning as the engine of growth

The first attempt to deal with the residual in the neoclassical framework was provided by Kenneth Arrow using the notion of learning. Arrow (1962) laid the foundations for a theory of economic growth based on learning processes that make possible the generation of new knowledge and, eventually, the introduction of new technologies. Agents, as well as firms, are now credited with the capability to learn. Learning is the result of repeated actions over time and reflective thinking. Learning has strong cumulative features and as such leads to dynamic increasing returns where cost reduction is associated with time rather than sheer size of production. This is consistent with the orthodoxy only as long as it applies to the representative agent: learning should be ubiquitous and symmetric across agents in the system. The evidence, however, shows that the distribution of the residual is highly uneven across regions, industries, firms and, especially, historic phases. Nevertheless, the rediscovery of the notion of learning originally introduced by Smith is especially fertile in many different directions. In Chapter 9, Anthony Atkinson and Joseph Stiglitz develop the analysis of learning and appreciate the role of technical constraints in shaping the process: learning is possible only in the limited spectrum oftechniques where firms have been practising. Hence technological change is localized (Antonelli, 1995).

INTRODUCTION

The new growth theory

The theory of learning provides the basis for important efforts to integrate the analysis of technological change into an equilibrium context of analysis: the new growth theory. The new growth theory builds on three important acquisitions of economics of knowledge: a) the distinction between generic and tacit knowledge, and the related notion of technological knowledge as a quasi-public good because of quasi-appropriability; b) the understanding of technological externalities and the dynamics of spillover; and c) the notion of monopolistic competition as a result of the introduction of new products. According to the analysis of Paul Romer synthesized in Chapter 10, economic growth relies on collective access to generic knowledge, which flows in the air. Romer distinguishes between generic technological knowledge, which is germane to a variety of uses, and specific technological knowledge that is embodied in products and as such has strong idiosyncratic features. Specific knowledge can be appropriated; generic knowledge instead retains the typical features of the Arrovian public good. Innovators generate generic knowledge while engaged in the introduction of new specific knowledge embodied in new products and new processes. The production of specific knowledge takes advantage of the collective availability of generic knowledge. The spillover of generic knowledge helps the generation of new specific knowledge by third parties and yet does not reduce the incentives to the generation of new knowledge for the strong appropriability of the specific applications. The new growth theory has been further enriched with the grafting of the Schumpeterian notion of creative destruction implemented in Chapter 11 by Philippe Aghion and Peter Howitt. Monopolistic competition characterizes the markets for products and provides a coherent context for a close variety of products, drawing from the same pool of generic knowledge, to coexist. While the new growth theory has been able to adopt and adapt to much of the progress put forward by the economics of innovation, it misses the core of the analysis. The actual determinants of the partial excludability and appropriability of the new knowledge and, more specifically, the ratio of the generic component of the new knowledge, with respect to the idiosyncratic one, are not investigated. Hence the definition of the incentives to the generation of new knowledge on the one hand, and the actual contribution of the spillovers of generic knowledge to the generation of new knowledge on the other, remains unclear. Moreover, the evolutionary outcome of the

a pait of a broader process of heterogeneous interactions between the effects and the determinants of technological and structural changes, which takes place in a disequilibrium context (Day, 1983).

I

INTRODUCTION

Technological paths and general-purpose technologies The long-term analysis of economic growth shows the persistency of factor intensity presumably explained by elastic barriers based on local irreversibilities and switching costs that prevent firms adjusting to the changing levels of relative input costs. However, when significant changes in the relative costs of production factors take place firms react with the introduction of new technologies. The ground-breaking analysis of Paul David (1975) lays down the foundations of much of contemporary economics of technological change intertwined with the historic analysis of structural change. The Schumpeterian notion of innovation as the basic competitive tool provided by Richard Nelson and Sidney Winter in Chapter 12 makes it possible to mimic with simulation techniques the working of a system where myopic firms follow innovative routines in order to compete beyond maximization rules along technological trajectories, and in so doing generate growth. The notion of general-purpose technology introduced by Tim Bresnahan and Manuel Trajtenberg in Chapter 13, and further elaborated in Chapter 14 by Richard Lipsey, Cliff Bekar and Kenneth Carlaw stresses the systemic character of technological change. New general-purpose technologies, are the result of the complementarity and interdependence of a variety of technological innovations being sequentially introduced, and are characterized by high levels of fungibility as they can be applied to a great variety of production processes. The analysis of the role of the structural characteristics of economic systems in general, and specifically of the role of the structure of relative prices, as determined by the endowment of basic inputs, and of the dynamics of industries and sectors as factors shaping the rate and direction of technological change, provides a historical context into which the analysis of the interplay between technological and structural change makes a step forward. Developing the localized technological change approach, Antonelli (2003) argues that because there are irreversibilities, limited knowledge and local learning, the introduction of new technologies is induced by the disequilibrium conditions brought about in each system by all changes in relative factor prices. The direction of technological change in terms of its specific form of bias and how it is introduced and adopted, however, reflects the specific conditions of local factor markets. Well-defined long-term technological paths emerge in each region and depend on the selection process in product markets. The more rigid and idiosyncratic, the endowment of production factors and the system of relative prices, the more specific the technological path of each region is likely to be. The analysis of the asymmetric effects of the introduction and diffusion of new technologies and of the structural determinants of the rate and the direction of technological change enables Paul David in Chapter 15 to

INTRODUCTION

identify the path-dependent interplay between structural and technological change. Technological change is now viewed as a process able to alter the characteristics of the system and yet itself the product of the characteristics of the system at each point in time. The application of the new generalpurpose information and communication technology in the US does not materialize in terms of productivity, and is better understood in terms of system transition.

Volume 11: Innovation and competition The Schumpeterian legacy Volume I1 explores the lasting legacy of the works of Joseph Schumpeter, from his first book, The Theory of Economic Development (191 1 and 1934), to his key article 'The instability of capitalism' in the Economic Journal (1928), from Business Cycles (1 939) and Capitalism, Socialism and Democracy (1942), to his key contribution in the Journal of Economic History, 'The creative response in economic history' (1947). The work of Schumpeter is at the heart of the economics of innovation. He has provided the basic tools of the economics of innovation with definition of innovation; the distinction between invention, innovation, imitation and diffusion; the understanding of the concentration of innovation in time and space with the notion of gales of innovations; the analysis of the key role of the corporation as the appropriate institution for fostering the rate of introduction of innovations; and an understanding of the crucial role of credit to fund both the generation and introduction of new technologies. Every student of economics of innovation is aware of the Schumpeter's ground-breaking contribution to the economics of innovation and technological change, thus an extensive and comprehensive analysis of his many contributions to this approach here would risk being repetitive (Rosenberg, 1994). Schumpeter, however, was not only the founding father of economics of innovation, but also, and mainly, one of the key contributors to an economics of complexity where agents are credited with the competence to generate new knowledge and change their technologies. Technological change and economic change cannot be separated, and are the two inseparable features of the process of creative destruction that characterizes economic development. For Schumpeter, innovation, as opposed to invention, is the distinctive feature of the competitive process. Competition takes place by means of the introduction, adoption and diffusion of innovation, rather than by means of quantity and price adjustments. At the same time, competition among firms is the engine that drives them to introduce innovations. By means of the introduction of new products, new processes, new organizations, new inputs and the identification of new markets, firms acquire a transient competitive advantage that feed extraprofits. Eventually their innovations will be

INTRODUCTION

imitated and perfect competition might be restored. However, firms can contrast the decline of profitability linked to the imitation of their innovations and the ensuing reduction of monopolistic power by introducing further innovations. Creative destruction is an endless process. Schumpeter thus traced the basic guidelines to venture into an economics where change and novelty are continual, and essential, features of an endogenous process (Antonelli, 1999). Much attention has been given to the evolution of the thinking of Schumpeter on the drivers of technological change in economic development. A divide between the 'first' and the 'second' Schumpeter has been identified. The first Schumpeter, that is the tradition based on the Theorie der Wirtschaflichen Entwicklung originally published in German in 1911, pays attention to entrepreneurship as the driving mechanism. Entrepreneurs who create new firms to enter markets are the primary source of technological innovations. The provision of credit by far-sighted bankers able to spot new ways of doing business is the complementary condition. The combination of both is at the origin of the perpetual unrest of the economy. The key role attributed to entrepreneurship and its strong characterization in anthropological and sociological terms has raised some concerns about the economic endogeneity of innovation. In the first Schumpeter, entrepreneurs are indeed the essence of capitalist development, but their emergence is mainly characterized as the result of sociological forces. The second Schumpeter is based on his 1942 book Capitalism, Socialism and Democracy. Here the driving role of the large corporation as the engine for the introduction of innovations is highlighted. The well-known Schumpeterian hypothesis is based on this second book: the monopolistic power, stemming from barriers to entry in existing product markets, of large corporations reduces the risks of imitation, feeds the accumulation of extraprofits, hence increases the incentives to fund risky research activities, and favours the working of internal financial markets where the resources extracted by extraprofits can better match the competences of skilled managers. The large corporation appears as the institutional device that makes it possible to combine resources, incentives and competence to generate new technologies so as to increase the efficiency of the innovation process at the firm level and substitute external financial markets in the key role of the effective provision and correct allocation of funds to innovation with competent bureaucracies at the system level. A divide between static and dynamic efficiency arises: static inefficiency, stemming from monopolistic power, is compensated by dynamic efficiency, stemming from faster rates of introduction of new and superior technologies. The second Schumpeter, however, also expresses some concern about the long-term viability of competitive mechanisms based on innovations due to the increasing routinization of activities leading to the introduction of innovations within the large corporation. Innovation here is fully endogenous, but 'routinized' within bureaucratic procedures. A large

INTRODUCTION

empirical literature has tested both hypotheses and proved their consistency, stressing the different role of large and small firms according to different types of industrial structures and phases of technological regimes. While there has been much debate on the differences highlighted in the evolution of Schumpeter thought from the entrepreneurial emphasis of his first book, The Theory of Economic Development, to the view elaborated in Capitalism, Socialism and Democracy, the consistency of the theory implemented in the two key journal articles of 1928 and 1947 deserves new attention and appreciation. In 'The instability of capitalism', the 'two Schumpeters' are well integrated and coexist consistently. It thus seems appropriate to pay more attention to this contribution. Here, in fact, the theoretical distance between the dynamic analysis of the economic process, based on the understanding of the central role of technological change in market competition, and the Walrasian analysis of the general equilibrium, is especially clear. Innovation, as distinct from invention, is not only endogenous but the intrinsic element of the capitalistic economy. Innovation cannot be regarded as an external economy because this is the distinctive feature of the competitive process. In his analysis of the role of creative reaction in economic history, Schumpeter fully elaborates the view that firms and agents in general are induced to react to the changing conditions of both product and factor markets in a creative way with the introduction of innovations, both in technologies and organizations, and by changing their products and processes: What has not been adequately appreciated among theorists is the distinction between different kinds of reaction to changes in 'condition'. Whenever an economy or a sector of an economy adapts itself to a change in its data in the way that traditional theory describes, whenever, that is, an economy reacts to an increase in population by simply adding the new brains and hands to the working force in the existing employment, or an industry reacts to a protective duty by the expansion within its existing practice, we may speak of the development as an adaptive response. And whenever the economy or an industry or some firms in an industry do something else, something that is outside of the range of existing practice, we may speak of creative response. Creative response has at least three essential characteristics. First, from the standpoint of the observer who is in full possession of all relevant facts, it can always be understood ex post; but it can practically never be understood ex ante; that is to say, it cannot be predicted by applying the ordinary rules of inference from the pre-existing facts. This is why the 'how' in what has been called the 'mechanisms'

INTRODUCTION

must be investigated in each case. Secondly, creative response shapes the whole course of subsequent events and their 'long-run' outcome. It is not true that both types of responses dominate only what the economist loves to call 'transitions', leaving the ultimate outcome to be determined by the initial data. Creative response changes social and economic situations for good, or, to put it differently, it creates situations from which there is no bridge to those situations that might have emerged in the absence. This is why creative response is an essential element in the historical process; no deterministic credo avails against this. Thirdly, creative response - the frequency of its occurrence in a group, its intensity and success or failure - has obviously something, be that much or little, to do (a) with quality of the personnel available in a society, (b) with relative quality of personnel, that is, with quality available to a particular field of activity relative to the quality available, at the same time, to others, and (c) with individual decisions, actions, and patterns of behavior. (Schumpeter, 1947: 149-50) Finally, in the Schumpeterian approach firms do more than adjusting prices to quantities and vice-versa: firms innovate. At the same time innovation is no longer viewed as the result of the ingenuity of entrepreneurs only (outsiders who enter the marketplace by means of new products or processes): incumbents innovate as well, and do so in order to face unexpected changes in the economic environment. With the notion of creative response, innovation becomes fully endogenous to the economic system. The dynamic efficiency of a system, as measured by the capability to increase its overall efficiency by means of the introduction of technological and organizational innovations, becomes the new key parameter to assess actual welfare. In this context, the analysis carried out in Business Cycles, where the collective character of the innovation process, the interdependence among innovators, and the complementarity of new technologies within the gales of innovations are highlighted, and the intertwined co-evolution of economic institutions, industrial structures, economic architectures of interactions and exchanges and consumer preferences along with the innovative process is historically substantiated, paves the way to a richer understanding of the systemic and inherently complex character of innovation dynamics (Antonelli, 2001). Innovation and entuepueneuvship Following Schumpeter Mark 1 - the literature inspired by The Theory of Economic Development the supply of entrepreneurs able to spot new technological opportunities and to understand the possible technological and economic applications of new scientific breakthrough is considered an -

INTRODUCTION

important factor in understanding the pace of introduction of new technologies and their specific economic and technological characteristics. This approach praises the role of new firms as vectors of new technologies and suggests that only high birth levels of new firms can sustain rates of technological change. Large empirical evidence to support the hypothesis has been provided by Zoltan Acs and David Audretsch in Chapter 16. Analysis of the institutional and economic conditions that favour entrepreneurship, and the entry of new innovative firms in the marketplace generally, becomes an important area of investigation. Entrepreneurship in this context supplies evidence of the key role of meta-economic factors in assessing the rate and direction of technological change. Expanding this line of enquiry, in Chapter 17 William Baumol highlights the role of the social organization of economic, institutional and social mechanisms of identification and the valorization of the 'given' supply of creative talents distributed at random in any economic system. The larger the number of creative talents each system is able to identify and valorize, the larger is the dynamics of growth in output and efficiency in the economic system. Here creative talents are an exogenous characteristic distributed at random, but the filtering mechanisms elaborated within the economic system are endogenous. Innovation and the corporation

The so-called Schumpeterian hypothesis sketched in Capitalism, Socialism and Democracy articulates the approach that large firms are necessary for high rates of technological advance to take place. Barriers to entry and monopolistic competition provide to corporations ex-ante appropriability, reducing the risks of leakage and imitation. In turn, large price-cost margins and competence provide corporations with the opportunity to match internal financial resources with dedicated information and competent decision-making so as to fund new and promising research activities. Here, the large firm takes on a central role and appears the locus of accumulation of sticky technical knowledge and hence technological progress. As Richard Nelson shows in Chapter 18, the funding and performance of research and development (R&D) activities become an integral part of the conduct of large corporations. In this context, Alfred Chandler (1977, 1990) provides the foundations of the resource-based theory of the firm with emphasis placed on the characteristics of the corporation as the institutional locus for fostering learning processes, the accumulation of technological knowledge and economic competence. Edith Penrose (1959) stresses the strategic efforts of corporations to exploit technological knowledge generated by means of systematic learning processes with the identification, creation and valorization of idiosyncratic production factors.

INTRODUCTION

A rich empirical literature investigates the relations between the characteristics of corporations, their conduct, their innovation strategies and their performances. In Chapter 19, John Cantwell and Birgitte Andersen provide evidence on the extent to which technological leadership lasts over time. Shoko Haneda and Hiroyuki Odagiri confirm with the evidence gathered in Chapter 20 that technological assets are positively related to the ratio of the stock exchange value to the book value of corporations (the so-called Tobin's q). Innovation and market structure

The Schumpeterian approach to innovation as an essential component of the competitive process is consistent with the Marshallian interpretation of the competitive process. Variety and selection are essential elements of the Marshallian notion of competition. Firms, diverse in terms of size, location and efficiency, confront each other in the product marketplace and are sorted out by the workings of the competitive process. Entry and exit feed the dynamics of the process. Here, each firm is confronted with a continual redefinition of its relative market context and must face the competitive threat brought about by firms that are able to produce at lower costs, either because of access to cheaper production factors or more effective production technologies. In the Marshallian competition, the duration of the adjustment process to an eventual equilibrium is endless and firms experience prolonged out-of-equilibrium conditions in which they can earn transient yet heterogeneous profit levels. The Schumpeterian legacy has been especially fertile in articulating the key relationship between rivalry and intentional innovation, and has allowed exploration of the causal relations between barriers to entry, levels of markups, market structure and incentives to introduce new technologies as articulated by Mike Scherer in Chapter 21. Scherer (1970) implements the structure-conduct-performance framework, drawn from industrial organization, within the notions of technological opportunities - defined as the opportunity to introduce technological innovations impinging on exogenous scientific breakthrough - as a key aspect of the industrial structure, and innovation as one of the main conducts of firms. The enriched structureconduct-performance framework has made it possible to gather empirical evidence that confirms that the size distribution of firms, the levels of concentration and the forms of competition among firms do indeed affect the rates of introduction of innovations and their characteristics. The rich survey by Morten Kamien and Nancy Schwartz (1975) provides a detailed review of this literature. In Chapter 22, Partha Dasgupta and Joseph Stiglitz provide an original framework to understand how the tools of oligopolistic rivalry make it possible identity the 'equilibrium' amount of R&D expenditure within an

INTRODUCTION

industry, but fail to grasp the determinants of the actual amount of innovations that research and development expenditures can yield. This line of enquiry fails to appreciate the key elements of the aggregate dynamics by means of which individual research efforts interact and eventually translate into innovation. A substantial gap emerges between the understanding of the amount of research efforts and the identification of the actual amount of innovations introduced and put to use, at both the firm and the system levels. The study of the processes of the delayed adoption of innovations, i.e. of the diffusion of innovations, rather than of their early introduction, provides a rich and fertile context of empirical and theoretical application of the Schumpeterian framework. The time patterns of entry of firms and hence the evolution of industrial demography, concentration, profitability and rates of growth of both firms and industries is analysed within the Schumpeterian sequence of early monopolistic power followed by imitative entry and finally competition. Diffusion matters on both the demand and the supply side. As Paul Stoneman and Norman Ireland show in Chapter 23, new technologies are adopted only if and when they fit specific product and factor markets conditions: some agents will never adopt a new technology and the identification of the determinants of such non-adoption becomes relevant. Adopters are no longer viewed as passive and reluctant perspective users, but rather as ingenious screeners who assess the scope for complementarity and cumulability of each new technology with their own specific needs and contexts of action. Profitability of adoption is the result of a process rather than a given fact. Technology diffuses when it is applied to diverse conditions of use. The intrinsic heterogeneity of agents applies in fact not only to their own technological base, but also to the product and factor markets in which they operate. The vintage structure of their fixed costs and tangible and intangible capital is portrayed, in Chapter 24 as major factors of differentiation and identification of the specific context of action, with respect to both technological change and market strategy. The flow of investments is determinant in assessing the rates of adoption: firms and countries with low investment rates have fewer chances to adopt new capital goods. Lower levels of penetration of new capital goods reduce the competitive edge of firms and hence their rates of growth and subsequently their rates of investment. In this case typical positive feedback occurs: fast rates of investment favour the diffusion of innovations that feed faster rates of growth and hence higher rates of investment. The economics of complexity sneaks in. In Chapter 25, Michael Katz and Carl Shapiro stress the role of the changing conditions of usage in the diffusion of innovations. Important changes in the profitability of adoption may take place on the demand side because of the effect of network externalities, i.e. the preference of consumers for a new good is influenced by the number of adopters.

INTRODUCTION

Within the context of the economics of localized technological change, Chapter 26 blurs the distinction between innovation and diffusion: adoption is viewed as a complementary component of a broader process of adjusting the technology when unexpected events in the product and factor markets push firms towards a creative reaction. When the stock of adoptions exerts a suitable combined effect on the gross profitability of adoption and on the costs of adoption, such that the net profitability of adoption and hence the rates of new adoption follow a quadratic path, the dynamics of creative adoption can engender an s-shaped diffusion process. Keith Pavitt, in Chapter 27, accommodates and operationalizes the variety of paths of technological change across sectors and technologies. In so doing he implements the neo-Schumpeterian structure-conductperformance approach elaborated by Scherer and paves the way to the notion of 'technological regimes' implemented by Franco Malerba and Luigi Orsenigo in Chapter 28 so as to further expand the notion of industrial structure and include the characteristics of knowledge in terms of appropriability and cumulability. Similar efforts are made by Steven Klepper to update the notion of product cycle and include the rates of entry and exit and the critical phases of industrial shake-out that follow the introduction of an innovation. Incumbent innovators can take advantage of previous innovations in many ways: early competitive advantage makes it possible to fund new research; acquired competence and technological knowledge are useful inputs for further innovations; barriers to entry based on market shares and size delay imitation; and technological advance feeds diversification and entry in new industries (Klepper and Graddy, 1990). An important contribution is made with the notion of dominant design elaborated in Chapter 29 by William Abernathy and Kim Clark. The dominant design is the result of a new interpretation of the innovation process. It provides an alternative route to the traditional sequence between the transient monopolistic power stemming from the introduction of an innovation, eventually followed by a few imitators leading to oligopoly and monopolistic competition. After the introduction of a variety of rival technologies by many rival firms, a selection process takes place and a few leading firms, able to elaborate the dominant design, emerge out of the competition with a consistent competitive advantage. Monopolistic rents emerge at the end of the selection process and may last. The diffusion of a new technology is no longer seen as the outcome of the adaptive adoption of a new single technology, but rather of the choice of one new technology among many. Diffusion is the result of the selection of a dominant design out of an original variety of different technological options. New ideas can be implemented and incrementally enriched, so as to eventually become profitable innovations, only when appropriate coalitions of heterogeneous firms are formed both on the demand and the supply side.

INTRODUCTION

Technological choices concerning the introduction of product and process innovations, the adoption of new technologies provided by suppliers and the imitation of competitors are mingled with market strategies such as specialization, outsourcing, diversification, entry and exit, merger and acquisitions and internal growth. In a continual trial in the marketplace, firms experiment their changing mix of technological and market conduct. At the aggregate level the result is the market selection of new and better technologies, often characterized by strong systemic complementarities. As Rebecca Henderson and Kim Clark point out in Chapter 30, the structure of interactions and the changing coalitions between different groups of players in overlapping yet specific technological arenas shape the rate and direction of technological change in general. In this context the shake-out of the system may favour the emergence of new industrial architectures where firms and technologies find a new contextual location.

Volume 111: Innovation and knowledge: The Arrovian legacy Knowledge as a production factor Volume I11 explores the many facets of the economic analysis of knowledge as an economic good, both as an input or production factor and as an output of an intentional process of creation. The economics of knowledge owes much to the classical legacy of Marx, as Nathan Rosenberg recalls in Chapter 31. The systematic application of scientific knowledge to the production process becomes, in Marx, the distinctive feature of capitalism. First, the collective character of technological knowledge is clearly grasped. Technological knowledge consists in a complex system of machines, skills and workers all characterized by distinctive elements of complementarity, interoperability and necessary compatibility. Second, technological and scientific knowledge are characterized by the strong elements of non-exhaustibility and limited appropriability. Their application, however, requires dedicated competence and resources that have a strong idiosyncratic character. In order to keep the process in motion, technological knowledge is constantly reproduced and expanded. In the Grundrisse (1857-58), Marx's analysis of the central role of science in the capitalist process reveals extraordinary levels of clarity and insight. Technological change is fully endogenous to the economic system. More specifically, Marx argues that the levels of endogeneity of technological change are themselves an indicator of the advance of an economic system. The notion of knowledge as an endogenous productive force is clearly identified by Marx. Actually, the levels of endogeneity of knowledge, as a distributed economic force shared by a myriad of agents, fed by the combination of learning processes that lead to the accumulation of competence and tacit knowledge with scientific processes of deduction, and transformed

INTRODUCTION

into a means of accumulation of capital pushed by profit maximization (the general intellect), become a measure of the advance of capitalism as a social system. Alfred Marshall further elaborates the dynamic approach along the lines of the analysis paved by Marx and Smith, and makes explicit that knowledge is a key component of capital and itself a production factor. Marshall also identifies the collective character of technological knowledge as a process where a variety of agents, co-localized within the industrial districts, contribute complementary bits of knowledge. Knowledge externalities play a key role in providing firms with essential inputs for the generation of new knowledge (Antonelli, 2001). Finally, Marshall accommodates, within competitive markets, the heterogeneity of firms and explains this in terms of the different levels of knowledge and competence possessed by each firm. Quasi rents are the direct remuneration of the stock of knowledge and competence that each firm has been able to accumulate and valorize.

Knowledge as an economic good Building on these foundations, Chapter 32, by Kenneth Arrow, makes an important step forward, focusing on the analysis of knowledge as an economic good per se, no longer embedded either in capital products or organizations. Prior to this, knowledge was not regarded as a separate item. The analysis of knowledge as an economic good made it possible to grasp the causes of the radical failure of the marketplace to perform its traditional functions and the ensuing risks of the under-production of knowledge in market systems. The results of the new approach are ground breaking. Knowledge is the basic intermediary input for the increase of efficiency, and the incentive, in terms of social desirability to the production of knowledge, is huge, as any economic system would dedicate most of its resources to the generation of new knowledge as a way of increasing efficiency in the production of all the other goods. However, because of the major limitations of knowledge as an economic good in terms of non-appropriability, non-excludability, nonrivalry in use, non-exhaustibility and non-divisibility, the private profitability of knowledge-generating activities is well below social desirability. Moreover, because of the high levels of uncertainty both in generation and appropriation, economic systems are unable to fund the correct amount of resources for the generation of new knowledge and therefore to increase the production of goods via the increase in the general efficiency of the production process. Hence dynamic inefficiency adds to static efficiency: the markets for knowledge, as a standalone good, are inefficient and therefore the necessary levels of division of laboir and specialization cannot be achieved. A radical market failure is the direct consequence of the characteristics of

INTRODUCTION

knowledge, as an economic, private and unbundled good. The failure of markets for knowledge is twofold: it takes place in the markets for knowledge as an output, and in the markets for financial resources necessary to undertake its generation. In Chapter 33, Partha Dasgupta and Paul David implement the attribution to scientific knowledge of the characteristics of a public good and legitimate a division of labour between firms and universities. The latter are responsible for the production and distribution of scientific knowledge as a public good. The State's role in this situation was that of an indispensable intermediary that collected the taxes necessary to finance university research. Scientific inventions are mainly perfected and improved in the academic institution. The university is a well-defined institution that has emerged through centuries of implementation. Scientific knowledge is therefore the output of a highly idiosyncratic ethos and dedicated incentives where reputation-seeking behaviour substitutes standard profit-maximization. Scientific knowledge produces effects in terms of technological opportunities. Firms in fact are expected to be able to collect and implement the stimulus that was set off by new scientific discoveries, and will eventually take advantage of the provision of new scientific breakthroughs and use them as the basis for the actual generation of technological innovations. Ariel Pakes and Zvi Griliches, in Chapter 34, confirm that, at the firm level, technological knowledge, as measured by patent statistics, can be considered an output in a knowledge-production function where R&D activities are the main inputs. The empirical evidence gathered and analysed in Chapter 35 by Pierre Mohnen, Jacques Mairesse and Marcel Dagenais confirms, however, that the local context of activity has strong influences on the effects of R&D activities. In Chapter 36, Adam Jaffe identifies the contribution of external knowledge that spills from the research efforts of other firms and public research laboratories and can be used in the production of new knowledge by other parties. Zvi Griliches, in Chapter 37, contributes the methodology to appreciate the contribution of knowledge spillovers to the knowledge generation process. Maryann Feldman reviews the large literature on the geography of knowledge spillovers and shows, in Chapter 38, how the rediscovery to knowledge spillovers leads to the revival of the Marshallian analysis of externalities. Regional economics contribute the analysis of spillovers with a substantial understanding of the role of geographic proximity in favouring access to external knowledge with positive effects on the productivity of resources invested internally in R&D expenditures. The Arrovian view of knowledge as a quasi-public good is contrasted by a radical change in perspective that stresses the role of learning by doing and learning by using as the basic engine of accumulation of knowledge. New technological knowledge stems from such learning processes and especially from efforts to convert tacit knowledge into new procedures that can

INTRODUCTION

be partly shared and transferred (Stiglitz, 1987). The new bottom-up understanding of the discovery process contrasts the traditional top-down approach to the origin of technological innovations. The analysis of the accumulation of technological knowledge plays a key role in this context. Franco Malerba highlights in Chapter 39 the importance of tacit knowledge, embedded in the organization of innovators and especially in their learning procedures, in reducing the capability of perspective imitators to absorb the new knowledge and to favour higher levels of appropriability. Infovmation economics for the economics of knowledge

The distinction introduced by Kenneth Arrow in Chapter 40 between information economics and economics of knowledge provides basic guidance to implement the economics of knowledge. An array of tools elaborated by the economics of information - such as agency theory, transaction costs analysis, signalling theory and economics of contracts is applied successfully to understanding the generation and dissemination and use of knowledge. The costs of imitation and absorption of external knowledge are gradually identified. In Chapter 41, Edwin Mansfield, Mark Schwartz and Samuel Wagner explore empirically the notion of knowledge appropriability. And in Chapter 42, Wesley Cohen and Daniel Levinthal elaborate the key notion of absorption costs and stress that an active role of users and imitators is necessary in order to fully take advantage of the potential benefits of knowledge spillovers. In Chapter 43, Richard Nelson shows that, next to the amount of resources invested in the production of knowledge, the efficiency of the internal production of knowledge is a central issue, and highlights the key role of learning processes and, more importantly, of external knowledge as a source of inputs. In this second step the debate shifts towards the basic issue of the intrinsic complementarity and interdependence, at the technological, industrial and regional levels, among the agents in the accumulation of new technological knowledge and economic competence and subsequently in the introduction and adoption of new technologies. Knowledge is now viewed both as the output of a specific research and learning process, and as the input for other activities leading to the generation of new knowledge. Here again the dynamics of positive feedback is at work: the output of one part of the system is the input for another, and yet such interactions are mediated by the price mechanism only to a limited extent complexity economics is again closer. The Hayekian notion of distributed knowledge, dispersed and fragmented in a myriad of economic agents, elaborated in Chapter 44, provides the foundations for the new understanding. Only when a complementary set of knowledge fragments is brought together within a context of consistent interactions, can successful innovations be introduced and adopted: -

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INTRODUCTION

technological knowledge is the product of a collective activity. Chapter 45, by Eric Von Hippel, paves the way to an array of empirical analyses on the key role of user-producer interactions as basic engines for the accumulation of new technological knowledge and the eventual introduction of new technologies are important at this stage. At the same time, the appreciation of the key role of internal learning leads us to understand how technological knowledge is characterized by considerable stickiness (Lundvall, 1988; Von Hippel, 1998). In Chapter 46, David Teece shows how the analysis of transaction, agency and communication costs provides basic guidance to elaborate an integrated framework able to understand the matching between types of knowledge and modes and mechanisms of knowledge governance both in generation and exploitation (March, 1991). Ashish Arora and Alfonso Gambardella provide empirical evidence, in Chapter 47, on the array of institutional arrangements that make possible knowledge transactions calling attention to the enforcement of appropriate contracts, exchanges of hostages within technological clubs and long-term, repeated interactions. In Chapter 48, Pier Paolo Patrucco shows that communication costs play a key role in assessing the actual capability of firms to access relevant external knowledge and contribute the emergence of new technological systems. Proximity of firms to universities and public research centres in general becomes a major source of access to external knowledge provided some effort is made to absorb the knowledge available in the local knowledge commons. As the path-breaking analysis elaborated in Chapter 49 by Ashish Arora shows, the tools of the economics of information can be successfully applied to analysing the economics of knowledge. Knowledge interactions and transactions are possible provided that appropriate institutional settings are elaborated so as to overcome the problems of typical information asymmetries, transaction costs, and principal agents that arise with intangible goods. The generation and introduction of technological innovations are now viewed as the result of complex alliances and compromises among heterogeneous groups of agents. Agents are diverse because of the variety of competencies and localized kinds of knowledge they build on. Alliances are based on the valorization of weak knowledge indivisibilities and local complementarities among technological different kinds of knowledge (Link and Scott, 2002). Manuel Trajtenberg, Rebecca Henderson and Adam Jaffe provide clear evidence in Chapter 50 of how the convergence of the efforts of a variety of innovators, including corporations and universities, each of which has a specific and yet complementary technological base, can lead to the successful generation of a new technology. Here the Schumpeterian notion of gales of innovations that characterize business cycles revives and reveals its heuristic strength (Schumpeter, 1939).

INTRODUCTION

Once more the dynamics of positive feedback emerges as the key factor. Now, however, it is clear that positive feedback can take place only when an appropriate architecture of network relations is formed. In Chapter 51 James Adams highlights the appreciation of the critical role played by the architecture of network relations especially between corporations and public research centres marks an important step towards the foray of complexity economics. Chapter 52, by Chris Freeman, stresses the systemic features of the process of generation and usage of technological knowledge. The contributions of Chris Freeman and Pari Pate1 and Keith Pavitt (Chapter 53) show how knowledge complementarity, weak divisibility and interdependence among learning agents, firms and public research centres become central to understanding the attributes of specific national innovation systems articulated in technological, industrial and regional subsystems characterized by networks of interaction and communication into which the dissemination and access to technological knowledge takes place. The new understanding about the asymmetry between debt and equity in the provision of funds for research activities paves the way to a revolution in financial markets. Equity finance has an important advantage over debt in the provision of funds for innovative undertakings because it can participate within the bottom tail of the highly skewed distribution of positive returns stemming from the generation of new knowledge and the introduction of new technologies. This has important consequences both in terms of the reduction of both the risks of credit rationing and the costs of financial resources for research activities. Lenders, in fact, need to charge high interest rates in order to compensate for the risks of failure and to sort out a large portion of new research activities to avoid as many 'lemons' as possible. Equity investors instead find an equilibrium rate of return at much lower levels because they can participate within the huge profits of a small fraction of the new ventures. As Paul Gompers and Josh Lerner argue in Chapter 54, the fraction of lemons that equity can support is much larger than that of debt; as a consequence, financial equity by means of venture capital can provide a much larger amount of funding for research activities. The creation of technological platforms centred on new key technologies by means of the cooperation of rival innovators favours upstream the convergence of technologies, and increases downstream the scope for both the widespread diffusion of applications and the introduction of incremental enrichments. This type of systemic approach to innovation reappraises the relationship between services and manufacturing as complementary activities, and overcomes previous understanding rooted in the divide between the two. The empirical analyses reviewed by Cristiano Antonelli in Chapter 55 within the frame of economics of information, show that technological knowledge is a highly heterogeneous dynamic process characterized by varying

IN T R 0 D U C T I 0 N

levels of appropriability, tacitness and indivisibility that take the forms of cumulability, complexity, fungibility and stickiness. The heterogeneity of knowledge leads to different modes of knowledge governance, articulated in a variety of hybrid forms ranging from coordinated transactions and constructed interactions to quasi-hierarchies, which can be found between the two unrealistic extremes of pure markets and pure organizations.

Volume IV: The Marshallian legacy Innovation and complexity

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Volume IV identifies the different analytical trails that converge towards the notion of innovation as an emergent property of a complex evolving system. In this approach innovation is the result of a path-dependent and collective process that takes place in a localized context if, when and where a sufficient number of failure-induced creative reactions are made in a coherent, complementary and consistent way. This approach is the result of the integration within the new emerging paradigm of complexity of three different strands of analysis: a) the early biological grafting; b) the new epistemology based on notions of tacit knowledge, bounded and procedural rationality; and c) evolutionary approaches and the economics of complexity. Biological gvafting

Alfred Marshall was the first to note that biology is the Mecca of economics. Indeed, biology provided important suggestions and stimulation to the early economics of innovation. In the Principles, Marshall is able to blend the legacy of Smith with the neoclassical approach, grasping the dynamic complexity of structural change, as articulated in the interaction between specialization and technological change leading to a growing heterogeneity of firms in a context characterized by variety and complementarity: The development of the organism, whether social or physical, involves an increasing subdivision of functions between its separate parts on the one hand, and on the other a more intimate connection between them. Each part gets to be less and less self-sufficient, to depend for its wellbeing more and more on other parts, so that any disorder in any part of a highly-developed organism will affect other parts also. This increased subdivision of functions, or 'differentiation,' as it is called, manifests itself with regard to industry in such forms as the division of labour, and the development of specialized skill, knowledge and machinery: while 'integration,' that is, a growing intimacy and firmness of the connections between the separate

INTRODUCTION

parts of the industrial organism, shows itself in such forms as the increase of security of commercial credit, and of the means and habits of communication by sea and road, by railway and telegraph, by post and printing-press. (Book VIII, I, 4 3 and 4) A first relevant basket of important research programmes favoured by biological grafting is the analysis of the delays in the adoption of given technological innovations. The economics of the diffusion of new technologies is conceived of as the study of the factors that account for the distribution over time of the adoption of identifiable successful innovations. A new technology is introduced after a scientific breakthrough and yet it takes time for all perspective users to adopt it. The successful and still widening application of the epidemic methodology emerges in this context. The time distribution of adoptions can be conceived of as the result of the spread of the contagious information about the profitability of the new technology. Proximity in geographical, industrial and technical space matters here in that it provides reluctant and sceptical, risk-adverse adopters with the opportunity to assess the actual profitability of the new technology and hence to adopt it. In the superb Chapter 56, Zvi Griliches grafts epidemiology into economics of innovation, providing a new analytical tool and a fertile context for empirical analysis where contagion is assimilated to diffusion assuming that agents are heterogeneous and the engine of the dynamics is based on the spread of information. Stan Metcalfe (1981) provides a significant improvement to epidemic diffusion: next to epidemic contagion on the demand side, changes in supply also account for the distribution over time of adoptions. In so doing, Metcalfe reintroduces the basic laws of standard economics into the epidemic framework and shows the relevance of their dynamic interplay. A sequence of logistic diffusion paths takes place when relevant changes on the supply side affect the spread of the epidemic contagion in new categories of perspective adopters. The second relevant biological graft into economics of innovation is provided by the life cycle metaphor. The life cycle metaphor has been around in the theory of the firm ever since the Marshallian forest's trees. A shift takes place when the sequence of birth, adolescence, maturity and obsolescence is applied to framing the steps in the life of a new product instead of a new firm. After introduction, the life of new products is characterized by a number of systematic events. According to the product life cycle approach a consistent pattern can be identified in the typology of innovations being introduced, in the evolution of the demand, in the industrial dynamics and in the characteristics of the growth of the firm. In Chapter 57, James Utterback and William Abernathy successfully apply the life cycle metaphor to technological innovations: a) The distinction

INTRODUCTION

between major innovations and minor ones is articulated and a sequence is identified between the introduction of a major innovation and the eventual swarm of minor, incremental ones; b) a sequence between product and process innovations is identified. After the introduction of a new product, much research takes place in the effort to improve the production process. In Chapter 58, Luc Soete and Roy Turner explore the details of the selection process in biology and apply the notion of replicator to grasping the sequential features of industrial dynamics along the trajectory. Stan Metcalfe (1997) has shown the fertility of the replicator in understanding how innovators can earn extra profits, fund their growth and acquire larger market shares. The analysis of the diffusion of innovation is intertwined with the study of the selection mechanism in the marketplace. Firms that have been able to introduce new technologies are also able to increase their growth and their market shares. Rationality and change

Two important contributions drawn directly from the philosophy of science and early cognitive science characterize the emergence of technological trajectories as the new heuristic metaphor and a research agenda. The distinctions introduced between tacit and codified knowledge and bounded and procedural rationality, as opposed to Olympian rationality, can be considered the founding blocks. According to Michael Polanyi (1969): 'Knowledge is an activity which would be better described as a process of knowing' (Polanyi, 1969: 132), rather than a good, and agents often know more than they are able to spell in a codified and explicit way. Tacit knowledge is embedded in the idiosyncratic procedures and habits elaborated by each agent. It can be translated into a fully codified knowledge only by means of systematic and explicit efforts. An important implication of the distinction between tacit and codified knowledge consists in fact in the increase in the 'natural' appropriability of technological knowledge. In Chapter 59 Herbert Simon makes two important contributions here. In the first he introduces the notion of bounded rationality in order to stress the limitations of traditional assumptions about the Olympian rationality of 'homo oeconomicus'. Bounded rationality quickly became a building block for the new emerging economics of information: the acquisition of information and the generation of signals are costly and economics needs to care about them. Subsequently, however, Simon elaborated the distinction between substantive and procedural rationality. The introduction of the notion of procedural rationality has far-reaching consequences as it introduces the notion of sequential decision-making. Agents cannot achieve substantive rationality for the burden of the wide range of activities necessary for

INTRODUCTION

gathering and processing all the relevant information. Agents can elaborate procedures to evaluate at each point in time and space the possible outcomes of their behaviour, but within the boundaries of a limited knowledge and using satisfying criteria as opposed to maximization rules. The notion of procedural rationality introduced by Simon marks a major contribution to the economics of innovation. Olympian rationality is at odds with a context characterized by radical uncertainty where nobody actually knows the outcome of a research project and even less so the next direction of the technological changes being introduced. Indeed, the very notions of future prices and future markets cannot even be considered when technological change is taken into account. In such a context only sequential decision-making based on limited information and limited knowledge is possible. The application of the notion of procedural rationality to the economics of innovation leads to a new appraisal of the role of the creative reaction as the new understanding of the basic inducement of innovation. Chapter 60 implements and elaborates the Schumpeterian notion of creative reaction as the qualifying aspect of the behaviour of innovative agents: agents innovate when their expectations are deceived and their performances fall below subjective levels of aspiration. Creative reaction is a part of the satisfying behaviour of economic agents afflicted by bounded rationality but able to rely on their procedural rationality and to learn, and hence to generate new knowledge and to modify their conditions. Evolutionary approaches: Routines and trajectories

The real problem facing economics of innovation is to provide an economic context within which to understand the behaviour of economic agents facing radical uncertainty and the multiple possible outcomes of their choices. A broader notion of rationality is needed as well as a more articulated understanding of the complexity of social interactions, beyond the standard price-quantities adjustments selected in a context of perfect foresight. Richard Nelson and Sidney Winter (Chapter 61) apply fruitfully the notions of tacit and codified knowledge and the implications of bounded and limited rationality to the theory of the firm with the notion of routines. Brian Loasby shows in Chapter 62 that routines provide a clue to understanding growth as the result of the innovative behaviour of myopic agents able to accumulate knowledge and to convert it into competence. In Chapter 63, Giovanni Dosi implements the notion of trajectories and applies it both to understanding the dynamics of innovation with respect to the sequence of well-defined technologies and to the sequence of innovations introduced by well-identified firms and, eventually, economic systems such as regions, industries and even countries. The analysis of trajectories appears especially promising at the firm level and in the analysis of the

INTRODUCTION

competitive process. First-comers reap substantial competitive advantages and build barriers to entry based on their technological knowledge. Longlasting extraprofits provide financial resources to fund the incremental implementation of internal learning by doing and accumulated competence. The notion of technological trajectory builds on the achievements made in terms of product life cycle and makes possible a spring of cumulative research in the discipline, including the notion of technological convergence introduced by Rosenberg (1963) to stress the dynamic blending of technologies and their generative relations. Empirical research makes it possible to identify a variety of trajectories. When a variety of trajectories in a variety of technologies and firms is identified, a number of basic questions arise: why some trajectories are 'steeper' than others; why some trajectories 'last' longer than others; why some firms fail to innovate; and why some industries are less able than others to build their own trajectories. In Chapter 64, Gerald Silverberg, Giovanni Dosi and Luigi Orsenigo elaborate the analysis of the possible outcome stemming from multiple interactions among a variety of trajectories applied both to firms and technologies. Agreement on the trajectory metaphor disappears quite rapidly when its strong deterministic bent is fully revealed. This trajectory metaphor seems to revive the old temptation to use ad-hoc technological determinism to explain social and economic changes as a process of sequential alignment dictated by technology. Paradigmatic crises arise as factors of discontinuity. New trajectories are generated and old ones decline. The origin of such changes and the emergence of new technological paradigms, however, remain unclear but for the implicit reference to the notion of technological opportunities and their eventual exhaustion. The ultimate origin of technological change remains exogenous and a strong deterministic character is now added. In this context, characterized by the decline of the heuristic power of the notion of trajectory and evolutionary frames, increasing attention is paid to the role of historic time. The evidence, provided by economic historians and historians of technology, makes clear the key role of technological cumulability and irreversibility, localized learning and local externalities (Dosi, 1988; Freeman, 1994). More generally, it becomes evident that while evolutionary thinking provides a reliable and fertile approach to explain the selection process, it is less able to provide an explanation for the emergence of novelty and the regeneration of variation. Evolutionary thinking is not always able to disentangle from a framework where variations and occasional mutations are mainly the blind product of random processes determined by genetic recombination and drift, hence an appreciation of the role of the intentional components of decision making, both in the generation of technological knowledge and in the introduction of innovations, seems necessary. The

INTRODUCTION

analysis of the role of the mutual interactions between the purpose-oriented and creative reaction of each agent and the changing conditions of the system, including the innovations being introduced by other agents, emerges as the approach by which technological change can be understood as an endogenous process. Towards an economics of complexity

Complexity is emerging as a new unifying theory to understand endogenous change and transformation across a variety of disciplines, ranging from mathematics and physics to biology. Complexity favours the systemic approach in that the outcome of the behaviour of each agent and of the system into which each one is embedded can only be understood as the result of the interaction between micro and macro dynamics. Complexity builds on a number of basic assumptions: Heterogeneous agents. Agents are characterized by distinctive and specific characteristics as well as being intrinsically heterogeneous. Location matters. Location in a multidimensional space, in terms of distance among agents and their density, matters and influences both behaviour and performance. Local knowledge. Each agent has access only to local information and local knowledge, i.e. no agent knows what every other agent knows. Local context of interaction. Agents are localized within networks of relations, including transactions and feedbacks, which are specific subsets of the broader array of interactions that define their behaviour. Cwtivity. Agents are creative, i.e. agents can follow some rules, but they can also change the rules. They do this in response to given feedbacks, according to their own specific characteristics and the features of local endowments, including the network of transactions and interactions into which they are embedded. Systemic interdependence. The outcome of the behaviour of each agent is strictly dependent on the web of interactions that take place within the system. Hence at each point in time, the topology of the system, i.e. how the characteristics and structural interactions of the agents in their relevant multidimensional spaces are distributed, plays a key role.

Complex systems are characterized by non-ergodicity, phase transition and emergent properties. When non-ergodicity applies a little shock at a particular point in time, this affects the long-term dynamics of a system. Phase transitions consist in qualitative changes that can be determined by small changes in the parameters of the system. Emergent properties are properties of a system that apply at a specific level of aggregation of a system.

As Barkley Rosser and John Foster show respectively in Chapters 65 and 66, the merging of the theory of complexity and economics contributes to the building of an economic theory of complexity based on non-ergodicity, phase transition and emerging properties. The integration of the rich and elaborated competence of economics in dealing with systemic analysis, although in a static context, can draw on complex system dynamics, especially when the role of historic time, and the intentional behaviour of rent-seeking agents, are taken into account, and when an understanding of the economics of innovation is integrated. According to the analysis of Steven Durlauf in Chapter 67, the notion of path dependence is the specific form of complex dynamics applied to understanding economic systems as evolving systems makes it possible to integrate into a single and coherent framework a number of relevant and complementary contributions. Path dependence provides a unique and fertile analytical framework which is able to explain and assess the ever-changing outcomes of the combination of and interplay between factors of continuity and discontinuity, growth and development, hysteresis and creativity, routines and 'free will', which all characterize economic action in a dynamic perspective that is also able to appreciate the role of historic time. According to the analysis articulated by Paul David in a long sequence of contributions dating back to 1975 and put forward in Chapter 68, path dependence is an attribute of a special class of dynamic processes. A process is path dependent when it is non-ergodic and subject to multiple attractors: 'Systems possessing this property cannot shake off the effects of past events, and do not have a limiting, invariant probability distribution that is continuous over the entire state space' (David, 1992: 1; David 1988; David 1985; David, 1975). Indeed, historic analysis and much empirical evidence in economic growth and specifically in the economics of innovation and new technologies confirm that these characteristics apply and are most relevant to understanding the laws of change and growth of complex systems. Path dependence is the specific form of complex system dynamics most apt to understand the process and the outcomes of the interactions among myopic agents embedded in their own context and constrained by their past decision, yet endowed with creativity and able to generate new knowledge by means of both learning and intentional innovative strategies as well as through structural changes. The notion of ergodicity deserves careful examination. When a process is non-ergodic, initial conditions (and events that occur at early points along the path) typically exert strong effects on its development and on the final outcome. Past dependence, or 'historicity', is an extreme form of nonergodicity. Historic, as well as social and technological, determinism fully belongs to past dependence. Here, the characteristics of the processes that are analysed and their results are fully determined and contained in their

INTRODUCTION

initial condition. In the theoretical economics of innovation, this extreme (some would say degenerate) form of path dependence has often been assumed: the epidemic models of the diffusion of innovations and the notion of innovations 'locked in' a technological trajectory are typical examples of the deterministic representation of essentially stochastic technological and social phenomena. As such, these non-ergodic models are analytically informative but empirically uninteresting. The process takes place within a single corridor, defined at the outset, and external attractors cannot divert its route, nor can the dynamics of the process be altered by transient random disturbances in its internal operations. Path dependence differs from deterministic past dependence in that irreversibility arises from events along the path, and it is not only the initial conditions that play a role in selecting from among the multiplicity of possible outcomes. The analysis of a path-dependent stochastic system is based on the concepts of transient or 'permanent micro-level' irreversibilities, creativity and positive feedback. The latter self-reinforcing processes work both through the price system and by means of non-pecuniary externalities shaped by social, non-market interactions. The conceptualization of stochastic path-dependence can be considered to occupy the border region between a view of the world in which history is relevant only to establish the initial conditions but has no bearing on the developments of the process, and another where the dynamics unfold deterministically. Path dependence is the conceptualization of historical dynamics in which one 'accident' follows another relentlessly and unpredictably and yet the past narrows the scope of possible outcomes, shaping the corridor within which the dynamics takes place. It gives economists the scope to include historical forces without succumbing to naive historical determinism. At the same time it makes possible the reduction of the array of relevant spaces into which the system is likely to move at each point in time. The understanding of the historic forces of the dynamics of both individual agents and aggregate systems provides a clue to foresee, with some degree of indeterminacy, future developments of a dynamic process. In so doing path dependences allow the substitution of the deterministic fallacy of general equilibrium analysis with the stochastic understanding of long-term dynamic processes (Rosenberg, 1994). An important distinction emerges here between path-dependent innovation and path-dependent diffusion. The former takes place when the path along which the firm acts is determined by the irreversibility of its production factors and by the accumulation of competence and tacit knowledge based on learning by doing and learning by using. In this case the switching costs firms face influence the choice of the new technology when, because of changes in relative factor costs or in the levels of output, they try to change the levels of their inputs. The latter applies to the choice of the new technology as it is shaped by market conditions. Interdependence among users

INTRODUCTION

leads to increasing returns in adoption so that technologies that have been adopted by a large share of prospective users have a greater chance of winning out in the selection process and spreading throughout the rest of the system. The notion of path dependence elaborated by David (1975, 1988, 1992) belongs to the first case: firms are induced to follow a path of technological change by their internal characteristics. The notion of pathdependence adoption elaborated in Chapter 69 by Brian Arthur and Chapter 70 by Paul David applies to the choice of one new technology among many possible ones and clearly belongs to the second case: new technologies are sorted out by increasing returns to adoption at the system level. The distinction between internal and external path dependence is also crucial. In the first case the emphasis is on the role of factors internal to each firm in shaping their path of innovation and change. In the latter, much more attention is instead given to the role of external factors, including feedbacks (Arthur, 1999). According to Douglass North in Chapter 71, the introduction of innovations takes place as the result of disequilibrium conditions of the system and reproduces new disequilibrium conditions. Technological change is now the endogenous outcome of a disequilibrium condition that has little chance to converge towards a new equilibrium. In fact, equilibrium and technological change emerge as opposite extremes: equilibrium is possible when no technological change takes place, and vice-versa. Hence Joel Mokry can articulate in Chapter 72 the view that technological change is a form of systemic, dynamic, stochastic and finite increasing returns that lead to punctuated growth. Technological change in fact takes place when a number of highly qualified, necessary conditions apply. As Stan Metcalfe, John Foster and Ronnie Ramlogan document in Chapter 73, the successful introduction of technological change is the fragile result of a complex set of necessary and complementary conditions where firms adapt continually to the changing conditions of their environment. A strong common thread links the analyses developed with the notion of life cycle and technological trajectory and the notion of path dependence. Only the latter, however, provides a theory to understand why and how technological change takes place sequentially along axes defined in terms of complementarity and cumulability, both internal and external to each firm. From this viewpoint the technological path represents significant progress with respect to both the technological trajectory and the life cycle. Path dependence applies to each agent and at the system level: hence we can identify and articulate an individual and a systemic path-dependence. Individual path-dependence provides the tools to understand the combination of hysteretic, past-dependent factors such as the quasi-irreversibility of tangible and intangible production factors, stock of knowledge and competence, and localized learning, with the generative relationships and creative reactions that make possible, at each point in time, a change in

INTRODUCTION

the direction of the action of each agent, including the introduction of innovations. At the firm level the generation of knowledge shares the typical characteristics of a path-dependent process where the effects of the past, in terms of accumulation of competence, mainly based on processes of learning in a localized context and interaction with a given structure of agents, exert an influence and yet are balanced by the specific creativity that is induced by the changing conditions of the system. Chapters 74 and 75 provide a systematic account of recent advances in the economics of innovation towards the economics of complexity. Firms innovate when faced with changes in the expected state of the world as generated by changes in both product and factor markets. Innovation is induced by the mismatch between unexpected events that myopic agents cannot fully anticipate and the irreversible decisions that need to be taken at any point in time. Firms induced to innovate by irreversibility and disequilibrium in both products and factor markets search locally for new technologies. The direction of technological change is influenced by the search for new technologies that are complementary to existing ones. This is all the more plausible when the introduction of technological changes is made possible by the accumulation of competence and localized knowledge within the firm. In this context the introduction of innovations and new technologies is the result of a local search, constrained by the limitations of firms to explore a wide range of technological options. Procedural rationality pushes firms to limit the search for new technologies in the proximity of techniques already in use, upon which learning by doing and learning by using have increased the stock of competence and tacit knowledge. The rate of technological change in turn is influenced by the relative efficiency of the search for new technologies. This dynamics leads firms to remain in a region of techniques that are close to the original one and continue to improve the technology in use. Firms are better able to change their technologies when, as a result of effective communication systems, local externalities can turn into collective knowledge; when high levels of investments can help the introduction of new technologies; when an appropriate institutional system of interaction between the academic community, public research centres and the business community is in place; when industrial dynamics in product and input markets can induce localized technological changes that in turn affect the competitive conditions of firms; when stochastic processes help the creative interaction of complementary new localized kinds of knowledge and new localized technologies to form new effective technological systems; when the dynamics of positive feedback can actually implement the sequences of learning along technological paths, as well as the interactions between innovation and diffusion. Such a set of dynamic and systemic conditions has strong stochastic features and is available in finite conditions: the process is unlikely to go on indefinitely until all possible combinations have been exhausted.

INTRODUCTION

The architectures of the system into which firms are localized exert a key role in shaping the dynamics both at the aggregate and the individual level. The structure of interactions, the networks of cooperation and communication, the flows of technological externalities, the structure of the markets for products and processes and the forms of competition that prevail in each of them, the geographical distribution of firms, their density in regional and technological spaces, the forms of organization within and among firms, the institutional context are the meso-economic carriers of history and, as such, embody the memory of the system. They change through time, albeit at a slow rate, as a result of the dynamics of agents and of the aggregate. The meso-economic characteristics of the system act as a filter between the dynamics at the individual and the aggregate levels (Antonelli, 2008; Dopfer, 2005). According to Paul Krugman in Chapter 76, rugged landscapes in geographical, technological, knowledge, market and product space are at the same time the consequence and the determinants of complex dynamics. Path-dependent complexity makes it possible to pay attention to the structural characteristics of the system in terms of the distribution of agents in the different space dimensions, and to appreciate the architecture of the relations of communication, interaction and competition that take place among agents in assessing the rate and direction of technological change. Some architectures are clearly more conducive than others. Architectures themselves are, however, the path-dependent products of intentional choices of location and mobility of agents, aware of the effects of their location in such a multidimensional space on their chances to generate and introduce timely, new and appropriate technological innovations. Systemic pathdependence explores the mix of past dependent elements embedded in the structural characteristics of the system, such as endowments, industrial and economic structure, market forms and organization of the networks of communication and interaction in place, with changes to the architecture of the structure that collective action can introduce at each point in time, The appreciation and identification of the structural conditions that shape economic systems and are conducive to the introduction and diffusion of new technologies is one of the main results of this line of analysis. The structure of social, non-market interactions is endogenous to the system itself: the architecture of knowledge networks is heavily influenced by the strategies of firms seeking to improve their location within systems of interactions. The exploration of the endogenous formation of coalitions within scientific communities provides useful insights both to increase the efficiency of scientific undertakings and to implement dedicated tools for science and innovation policy (David and Keely, 2003; D'Ignazio and Giovannetti, 2006). In this context, the notion of the generative relationship introduced in Chapter 77 by David Lane and Robert Maxfield is very important. Generative relationships are:

INTRODUCTION

constructive positive feedbacks - that - have an obvious counterpart: as the structure of agentlartifact space undergoes ripple of changes, new agents and artifacts come into being and old ones acquire new functionalities, so identities change - and hence, old interpretations of identity bear an increasingly strained relationship with observable actions, the facts of the world. Different agents respond differently: some respond to the resulting ambiguity by generating new attributions to make sense of experienced novelty, and so attributional heterogeneity increases - increasing further the possibility that participants in other relationships will achieve sufficient attributional diversity to become generative actually. (Lane and Maxfield, 1997: 185) Generative relationships lead to the introduction of innovations, and innovations feed structural change in agentlartifact space. The process takes place through a 'bootstrap' dynamics where new generative relationships induce attributional shifts that lead to actions that in turn generate possibilities for new generative relationships. The structural characteristics of the system in terms of the distribution of agents in multidimensional spaces, of their networks of communication, relationship and interactions qualified by aligned directedness, heterogeneity, mutual directedness, permissions and action opportunities, are key elements for the sustainability of the process. The successful accumulation of new technological knowledge, the eventual introduction of new and more productive technologies and their fast diffusion are likely to take place in a self-propelling and spiralling process and at a faster pace within economic systems characterized by fast rates of growth where interaction, feedbacks and communication are swifter. In such special circumstances, the system can undergo a phase transition leading to the introduction of a new radical technological system. The circular relationship between structure and innovation, and the conduct ana performance of firms, are indeed influenced by the structure of the system as it stands at time t , but in turn they exert strong influences on the characteristics of the structure at time t + 1, with the introduction of innovations. A new structure is determined and in order to readjust to it, firms elaborate new strategies that include the introduction of further innovations. The understanding of this recursive relationship paves the way to grasping the basic elements of the continual and dynamic system of feedback between the conduct and performance of firms, the rate and direction of technological change and structural change with a growing awareness of its evolving and historic characteristics. As Kenneth Arrow suggests in Chapter 78, in these circumstances the generation of new technological knowledge and the introduction of new technologies can be viewed as the cause and the consequence of punctuated economic growth and dynamic increasing returns.

INTRODUCTION

Innovation is both the result and cause of out-of-equilibrium conditions. A clear continuity, ever since biological grafts into the trajectory and finally the systemic network approach, confirms that innovation can only be understood in an analytical context that accepts the integration of the analysis of firms and agents that are continually pushed away from potential equilibrium conditions and attempts to react to the unexpected conditions of both product and factor markets by means of the introduction of new products, new processes, new organizational modes and new markets.

Conclusion Economics of innovation is a distinctive area of specialization within economics, with a well-defined set of competences about the origins, causes, characteristics and consequences of the introduction of technological and organization changes in the economic system. At the same time, however, economics of innovation pretends to be one of the main pillars of the emerging economics of complexity. It is the result of a long process. The starting point is indeed the discovery of the large portion of unexplained economic growth that only technological change can be credited for. The attempt to provide an economic explanation for technological change able to integrate analysis of the effects and causes of the introduction of innovations has led to the rediscovery of a number of forgotten dynamic paths provided by the history of economic thought. The four wide-ranging heuristic frameworks identified are: the classical legacies of Adam Smith and Karl Marx, the Schumpeterian legacy, the Arrovian legacy, and the Marshallian legacy eventually implemented by evolutionary approaches leading to complexity. As soon as assumptions about the exogeneity of production (and utility) functions are relaxed and agents are considered both intelligent and endowed with a specific form of creativity that makes it possible to endogenously change the basic features of the utility and production functions and hence tastes, preferences, technologies and routines, the relevance of general equilibrium analysis declines. It is difficult to conceive a system of future prices that is able to take into account the introduction of all possible new technologies in a given time horizon. In fact, there is no longer a single attractor as firms are now credited with the capability of generating their own technological knowledge and changing their technologies, and not only varying either the quantity they produce or the prices they charge. Identification of the four lines of investigation is the result of the progressive matching between a specific legacy of the history of economic thought and a specific area of investigation considered in the history of economic analysis. The classical legacy provided the basic inputs to elaborate a theory of economic growth based on the intentional introduction of technological

INTRODUCTION

innovations. The Schumpeterian legacy proved fertile to analyse the role of innovation within oligopolistic rivalry and made it possible to appreciate the role of entrepreneurship as a basic engine for the continual introduction of new technologies. The Arrovian legacy provided the first elements eventually enriched in a fully fledged analysis of the economic characteristics of knowledge from an economic viewpoint. Finally, the Marshallian legacy has led to the emergence of an evolutionary approach, eventually articulated in new complexity theory, that makes it possible to understand the process of specialization and structural change, based on the interplay between heterogeneity, complementarity and competition that characterizes the innovation process. Each of the four approaches has a clear focus and a distinctive area of investigation. In the second part of the twentieth century they evolved in parallel with a process of specialization and consolidation of their respective areas of expertise. In a second step, however, an increasing number of lateral and horizontal contributions have been made. As a consequence, a quite consistent body of knowledge articulated in a portfolio of analytical tools has emerged out of the convergence of the four approaches with the progressive integration of the different fields of investigation. This seems to be the context in which the analysis of the conditions of dynamic efficiency can be considered so that it can become one of the key aims and scopes of contemporary work in economic theory. The merging of complex dynamic theory with a theory of the agent based on subjective optimization implemented by the necessary consideration for creative choices in a context characterized by intrinsic heterogeneity of firms, can be productive both for economics and for building a more articulated theory of complex system dynamics. Economic systems are more and more considered as complex dynamic mechanisms that are able to grow and have differentiated levels of dynamic efficiency. In turn, such levels of efficiency are the outcome of the behaviour of heterogeneous agents and of the structure of their relations, in that they have a differential capability to change the rules and the network of interactions. Hence they are able to generate new technological knowledge and to introduce new technologies. The notion of path dependence provides one of the most articulated and comprehensive frameworks from which to move towards an analysis of the conditions that make it possible to conceive the working of an economic system where agents are able to generate new technological knowledge, introduce new technological innovations and exploit endogenous growth. The notion of path dependence can be considered the analytical form of complexity most apt to understand the dynamics of economic systems where heterogeneous agents are characterized by some level of past dependence, as well as by local creativity, interdependence and limited mobility in a structured space that affects their behaviour but is not the single determinant.

INTRODUCTION

Path dependence is an essential conceptual framework that goes beyond analysis of static efficiency and enters the analysis of the conditions for dynamic efficiency. It applies to each agent, in terms of the quasi-irreversibility of their own endowment of tangible and intangible assets, networks of relations in both product and factor markets, stock of knowledge and competence, and to the system level in terms of general endowments of production factors, industrial and economic structure, and the architecture of the networks in place. The identification and articulation of individual and system pathdependence makes it possible to catch the basic laws of the continual interaction between the hysteretic effects of past dependence, both at the agent and at the system level, and the feedback dynamics that allows the intentional conduct of the creative agent to change both the course of their actions and the characteristics of the structured space. In so doing, path dependence retains the positive contributions of complex dynamic system methodology, and at the same time has the capability to overcome the intrinsic limitations stemming from its origins built on natural sciences where human decision-making is not considered. Indeed, the notion of path dependence is one of the main forays in the challenging attempt to apply the emerging theory of complexity to economics.

Acknowledgement I acknowledge the financial support of the Research Grants of the Dipartimento di Economia Salvatore Cognetti de Martiis of the University of Torino for the years 2006 and 2007.

References Abramovitz, M. (1956), Resources and output trends in the US since 1870, American Economic Review 46, 5-23. Acemoglu, D. (2002), Directed technical change, Review of Economic Studies 69, 781-810. Antonelli, C. (1995), The Economics of Localized Technological Change and Industrial Dynamics, Boston, MA: Kluwer Academic Publisher. Antonelli, C. (1999), The Microdynamics of Technological Change, London: Routledge. Antonelli, C. (2001), The Microeconomics of Technological Systems, Oxford: Oxford University Press. Antonelli, C. (2003), The Economics of Innovation, New technologies and Structural Change, London: Routledge. Antonelli, C. (2008), Localized Technological Change: Towards the Economics of Complexity, London: Routledge. Arrow, K. J. (1962), The economic implications of learning by doing, Review of Economic Studies 29, 155-73.

INTRODUCTION

Arthur, B. (1999), Complexity and the economy, Science 284, 107-09. Chandler, A. D. (1977), The Visible Hand: The Managerial Revolution in American Business, Cambridge, MA: Harvard University Press. Chandler, A. D. (1990), Scale and Scope: The Dynamics of Industrial Capitalism, Cambridge, MA: The Belknap Press of Harvard University Press. David, P. A. (1975), Technical Choice Innovation and Economic Growth, Cambridge: Cambridge University Press. David, P. A. (1988), Path-Dependence: Putting the Past into the Future o f Economics, Mimeo, Department of Economics, Stanford University. David, P. A. (1992), Path-Dependence in Economic Processes: Implications for Policy Analysis in Dynamical System Contexts, Italy: Fondazione Rosselli. David, P. A. and Keely, L. (2003), The endogenous formation of scientific research coalitions, Economics of Innovation and New Technology 12, 93-1 16. Day, R. H. (1983), The emergence of chaos from classical economic growth, Quarterly Journal of Economics 98, 201-13. D'Ignazio, A. and Giovannetti, E. (2006), From exogenous to endogenous economic networks: Internet applications, Journal of Economic Survey 20, 757-96. Dopfer, K. (ed.) (2005), The Evolutioncwy Foundations of Economics, Cambridge: Cambridge University Press. Dosi, G. (1988), Sources, procedures, and microeconomic effects of innovation, Journal of' Economic Literature 26, 1120-17. Freeman, C. (1994), The economics of technical change, Cambridge Journal of Economics 18, 463-514. Hicks, J. R. (1932), The Theory of' Wagcs, London: Macmillan. Kaldor, N. (1972), The irrelevance of equilibrium economics, Economic Journal 82, 1237-55. Kamien, M. I. and Schwartz, N. L. (1975), Market structure and innovation, Journal of Economic Literature 13, 1-37. Klepper, S. and Graddy, E. (1990), The evolution of new industries and the determinants of market structure, Rand Journal of Economics 21, 27-44. Link, A. N. and Scott, J. T. (2002), Explaining observed licensing agreements, Economics of Innovation and New Tec,hnology 11, 21 1-31. Lundvall, B. (1988), Innovation as an interactive process: From user-producer interaction to the national system of innovation, in G. Dosi, et a/. (eds), Technical Change and Economic Theory, London: Frances Pinter, pp. 349-69. March, J. C. (1991), Exploration and exploitation in organizing learning, Organisation Science 2, 71-87. Marshall, A. (1890), Principles of Economics, London: Macmillan (1920, 8th edn). Marx, K. (1867, 1976), Capital: A Critique of Political Economy, Harmondsworth: Penguin Books. Marx, K. (1857-58), Grundrisse: Foundations of the Critique of Political Economy, Harmondsworth: Penguin Books. Metcalfe, J. S. (1981), Impulse and diffusion in the study of technical change, Futures 13, 347-59. Metcalfe, J. S. (1997), Evolutionary Economics and Creative Destruction, London: Routledge. Mowery, D. and Rosenberg, N. (1979), The influence of market demand upon innovation: A critical review of some recent empirical studies, Research Policy 8, 102-50.

INTRODUCTION

Penrose, E. (1959), The Theory of the Growth of the Firm, Oxford: Oxford University Press. Polanyi, M. (1969), Knowing and being, in M. Grene (ed.), Knowing and Being: Essays, London: Routledge and Kegan Paul, pp. 123-207. Rosenberg, N. (1963), Technological change in the machine tool industry, 18401910, Journal of' Economic History 23, 414-43. Rosenberg, N. (1976), Marx as a student of technology, Monthly Review 28, 56-77. Rosenberg, N. (1994), Exploring the Black Box, Cambridge: Cambridge University Press, pp. 47-61. Scherer, F. M. (1970), Industrial Market Structure and Economic Performance, Chicago: Rand McNally & Co. Schumpeter, J. A. (191 1, 1934), The Theory of Economic Development, Cambridge, MA: Harvard University Press. Schumpeter, J. A. (1928), The instability of capitalism, Economic Journal 38, 36186. Schumpeter, J. A. (1939), Business Cycles, New York: McGraw-Hill. Schumpeter, J. A. (1942), Capitalism, Socialism and Democracy, New York: Harper and Brothers. Schumpeter, J. A. (1947), The creative response in economic history, Journal of Economic History 7, 149-59. Smith, A. (1776), An Inquiry into the Nature and Causes of the Wealth of' Nations, London Edition, 1976. Stiglitz, J. E. (1987): Learning to learn localized learning and technological progress, in P. Dasgupta, et al. (eds), Economic Policy and Technological Performance, Cambridge: Cambridge University Press, pp. 125-44. Von Hippel, E. (1998), Economies of product development by users: The impact of 'sticky' local information, Management Science 44, 629-44. Young, A. A. (1928), Increasing returns and economic progress, Economic Journal 38, 527-42.

TECHNICAL CHANGE A N D T H E AGGREGATE PRODUCTION FUNCTION* Robert M. Solow Source: Review of Economics and Statistics, 39:3 (1957). 312-20

In this day of rationally designed econometric studies and super-input-output tables, it takes something more than the usual "willing suspension of disbelief" to talk seriously of the aggregate production function. But the aggregate production function is only a little less legitimate a concept than, say, the aggregate consumption function, and for some kinds of long-run macro-models it is almost as indispensable as the latter is for the shortrun. As long as we insist on practicing macro-economics we shall need aggregate relationships. Even so, there would hardly be any justification for returning to this old-fashioned topic if I had no novelty to suggest. The new wrinkle I want to describe is an elementary way of segregating variations in output per head due to technical change from those due to changes in the availability of capital per head. Naturally, every additional bit of information has its price. In this case the price consists of one new required time series, the share of labor or property in total income, and one new assumption, that factors are paid their marginal products. Since the former is probably more respectable than the other data I shall use, and since the latter is an assumption often made, the price may not be unreasonably high. Before going on, let me be explicit that I would not try to justify what follows by calling on fancy theorems on aggregation and index numbers.' Either this kind of aggregate economics appeals or it doesn't. Personally I belong to both schools. If it does, I think one can draw some crude but useful conclusions from the results.

INNOVATION & G R O W T H

Theoretical basis I will first explain what I have in mind mathematically and then give a diagrammatic exposition. In this case the mathematics seems simpler. If Q represents output and K and L represent capital and labor inputs in "physical" units, then the aggregate production function can be written as:

The variable t for time appears in F to allow for technical change. It will be seen that I am using the phrase "technical change" as a short-hand expression for any kind of shift in the production function. Thus slowdowns, speed-ups, improvements in the education of the labor force, and all sorts of things will appear as "technical change." It is convenient to begin with the special case of neutral technical change. Shifts in the production function are defined as neutral if they leave marginal rates of substitution untouched but simply increase or decrease the output attainable from given inputs. In that case the production function takes the special form

and the multiplicative factor A(t) measures the cumulated effect of shifts over time. Differentiate (la) totally with respect to time and divide by Q and one obtains

aQ

K where dots indicate time derivatives. Now define w - --aaK Q

"

and

'a

the relative shares of capital and labor, and substitute in the aL Q above equation (note that aQlaK = A aflaK, etc.) and there results: wL =--

From time series of QIQ, w,, K I K , w, and LIL or their discrete year-to-year analogues, we could estimate AIAand thence A(t) itself. Actually an amusing thing happens here. Nothing has been said so far about returns to scale. But if all factor inputs are classified either as K or L, then the available figures always show w, and w, adding up to one. Since we have assumed that factors are paid their marginal products, this amounts to assuming the hypotheses of

TECHNICAL CHANGE & PRODUCTION FUNCTION

Euler's theorem. The calculus being what it is, we might just as well assume the conclusion, namely that F is homogeneous of degree one. This has the advantage of making everything come out neatly in terms of intensive magnitudes. Let QlL = q, KIL = k, w, = 1 - w;, note that 1j1q = QIQ - LIL etc., and (2) becomes

Now all we need to disentangle the technical change index A(t) are series for output per man hour, capital per man hour, and the share of capital. So far I have been assuming that technical change is neutral. But if we go back to ( 1 ) and carry out the same reasoning we arrive at something very like (2a), namely

It can be shown, by integrating a partial differential equation, that if

FIF is independent of K and L (actually under constant returns to scale only KIL matters) then (1) has the special form (la) and shifts in the production function are neutral. If in addition FIF is constant in time, say equal to a, then A(t) = e"' or in discrete approximation A(t) = (1 + a)'. The case of neutral shifts and constant returns to scale is now easily handled graphically. The production function is completely represented by a graph of q against k (analogously to the fact that if we know the unit-output isoquant, we know the whole map). The trouble is that this function is shifting in time, so that if we observe points in the (q,k) plane, their movements are compounded out of movements along the curve and shifts of the curve. In Chart 1, for instance, every ordinate on the curve for t = 1 has been multiplied by the same factor to give a neutral upward shift of the production function for period 2. The problem is to estimate this shift from knowledge of points PI and P,. Obviously it would be quite misleading to fit a curve through raw observed points like P I , P, and others. But if the shift factor for each point of time can be estimated, the observed points can be corrected for technical change, and a production function can then be found., The natural thing to do, for small changes, is to approximate the period 2 curve by its tangent at P, (or the period 1 curve by its tangent at PI). This estimate for A AIA, yields an3proximately corrected point P,,, and an namely 19,. But k,Pl, = q, - dqldkA k and hence &,< = 9, - q, - dqlak A k = A q - dqldk A k and A AIA = &,? lq, = A qlq - aqldk (klq) A klk = A qlq - w, A klk which is exactly the content of (2a). The not-necessarilyneutral case is a bit more complicated, but basically similar.

e,
0. This implies that the marginal product of capital remains unchanged when the capital-output ratio is unchanged. Harrod-neutral technical change will not be used much in this book. A good discussion of the concept can be found in James E. Meade, A Neoclassical Theory of Economic Growth (London: Unwin University Books, 1962), pp. 55-60. Wan, Economic Growth, p. 223. Nordhaus, "Some Skeptical Thoughts." Nordhaus has constructed a growth theoretical model of a planned economy in which the position of the frontier depends on the amount of labor allocated to a research activity that shifts the IPC neutrally and derives optimum allocation decisions for labor. William D. Nordhaus, "The Optimal Rate and Direction of Technical Change," in Essays in the Theory of Optimal Economic Growth, ed. Karl Shell (Cambridge: Massachusetts Institute of Technology Press, 1967). John Conslick also has developed an interesting alternative to the IPC. A productivity sector, to which both labor and capital are allocated explicitly, creates augmented labor and augmented capital increments. Additional allocations of capital and labor to the productivity sector shift the trade-off frontier between augmented capital and augmented labor neutrally. Conslick then postulates two saving ratios, one for capital s, and one for labor s,, which determine aggregate savings and capital-labor ratios in both the final goods and productivity sectors. These two savings ratios s, and s, and the ratio of creation of augmented capital to augmented labor b are assumed to be functions of the economy's aggregate capital-labor ratio. John Conslick, "A Neoclassical Growth Model with Endogenously Positioned Technical Change Frontier," Economic Journal 69 (1969): 348-62. In Conslick's model, "The allocation magnitudes s,, s, and b are allowed to vary only with the ratio KIL; this preserves degree-one homogeneity in the model, which is a quite conventional and almost essential assumption in a long-run growth model which is to have at least the possibility of a balanced asymptotic path. Some fairly weak assumptions about the form of the s,, s, and b functions will be introduced below. Nothing will be assumed about the precise origin of the functions. They may be the determinations of a central planner; they may be the reduced form of a competitive system; they may be something else." (ibid., pp. 351-2). This means that there is no microeconomic rationalization at all for the crucial allocation mechanisms in Conslick's model. Although his description of invention possibilities is very attractive, the model built with it represents implicit theorizing on the basis of assumptions whose only justification is mathematical convenience.

INDUCED TECHNICAL CHANGE

41 Nordhaus, Rate and Direction of Technical Change, pp. 64-5. 42 Wan, Economic Growth, pp. 219-20. 43 Nordhaus, "Some Skeptical Thoughts."

44 Samuelson, "Theory of Induced Innovation"; Drandakis and Phelps, "Model of Induced Invention." 45 Roy Radner, "A Behavioral Model of Cost Reduction," The Bell Journal o j Economics 6 , no 1. (Spring 1975): 196-215. 46 Ibid., p. 198. 47 Radner is interested primarily in the effect of various decision rules, which are simpler than the overall optimization. His model is perfectly capable of being generalized to the nonorthogonal case by postulating fractional allocation of a manager's time to the different input coefficients. However, Radner shows that the model then loses its behavioral aspects and becomes more like a full optimization model. Some of the generalizations he sketches in his paper are shared by the models of chapters 4 and 5. 48 William Fellner, "Empirical Support for the Theory of Induced Innovation," Quarterly Journal of Economics 85 (1971): 580-604. 49 Ibid., p. 582. 50 See Solow, "Some Recent Developments."

WHY D O NEW TECHNOLOGIES COMPLEMENT SKILLS? Directed technical change and

wage inequality* Daron Acemoglu Source: Quarterly Journal of Economics, 113:4 (1998), 1055-89

A high proportion of skilled workers in the labor force implies a large market size for skill-complementary technologies, and encourages faster upgrading of the productivity of skilled workers. As a result, an increase in the supply of skills reduces the skill premium in the short run, but then it induces skillbiased technical change and increases the skill premium, possibly even above its initial value. This theory suggests that the rapid increase in the proportion of college graduates in the United States labor force in the 1970s may have been a causal factor in both the decline in the college premium during the 1970s and the large increase in inequality during the 1980s.

I. Introduction In the 1970s college graduates earned 55 percent more than high school graduates. This premium fell to 41 percent in 1980, but then increased to 62 percent in 1995 [Autor, Katz, and Krueger 19981. One explanation for the rapid increase in the college premium in the 1980s is skill-biased technological change. According to this explanation, new technologies are by their nature complementary to skills, so there has always been some skill-biased technical change, and the recent past witnessed rapid introduction of new technologies, leading to an acceleration in skill-bias.' Empirical support for this view includes Autor, Katz, and Krueger [1998], who calculate that the relative supply of college equivalent workers (college graduates plus half of those with some college) increased by 2.73 percent per year between 1940 and 1970, and increased much faster between 1970 and 1995, by

I

DIRECTED TECHNICAL CHANGE & WAGE INEQUALITY

3.66 percent per year. In contrast, the college premium fell by 0.63 percent per year during the first period and increased by 0.92 percent per year between 1970 and 1995, indicating a much more rapid increase in the demand for college graduates during the last 25 years. The skill-biased change explanation leads to a number of questions, however. Why did skill-biased change accelerate soon after an unprecedented increase in the supply of skills during the 1970s? More striking, Katz and Murphy write, "for the 1963-87 period as a whole and most strongly for the 1980s, the groups with the largest increases in relative supplies tended to have the largest increases in relative wages" [1992, p. 521. Why is this? And related to these questions, why do new technologies complement skills? There are in fact many examples in the eighteenth and early nineteenth centuries of new technologies replacing rather than complementing skills, such as the spinning jenny, weaving machines, Jacquard's loom, printing cylinders, and later the assembly line (see Mokyr [1990]). Current technologies also are not skill-complementary by nature. Computers, for example, simplify some formerly complex tasks such as inventory control, and can be used by unskilled workers, as they often are in fast food restaurants and supermarkets. Motivated by this reasoning, this paper starts from the premise that new technologies are not complementary to skills by nature, but by design. I show that a natural model in which the direction of technical change is endogenous can explain why the demand for skills and the college premium first fell and then increased sharply following the large increase in the supply of skills, and also why as opposed to the skill-replacing technological advances of the eighteenth century, today most new technologies appear to be skill-complementary. Most technologies, once invented, are largely nonrival goods. They can be used by many firms and workers at low marginal cost. When there are more skilled workers, the market for skill-complementary technologies is larger. The inventor is therefore able to obtain higher profits, and more effort will be devoted to the invention of skill-complementary techn~logies.~ As a result, the impact of an increase in the supply of skills on the skill premium is determined by two competing forces: the first is the conventional substitution effect which makes the economy move along a downward sloping relative demand curve. The second is the directed technology effect, which shifts the relative demand curve for skills as shown in Figure I, because the increase in the supply of skills induces faster upgrading of skill-complementary technologies. A large increase in the supply of college graduates as in the late 1960s and 1970s first moves the economy along a short-run (constant technology) relative demand curve, reducing the college premium. The relative supply change also increases the size of the market for technologies complementary to skills, and induces a change in the direction of technical progress and a shift of the relative demand curve in Figure I. Suppose first that the

INNOVATION & GROWTH

College Premium

I

Short-run Relative

Y-

College Premium Short-run Response

I I I

... .. .... ... ............ ..... ...... . .... ..

o1

I

-

Shift in Relative Demand due to Directed Technical

I

WL

Shift in Relative Supply Figure I Directed technical change and dynamics of college premium.

substitution effect dominates the directed technology effect. In this case, the college premium first falls and then increases, but never above its initial level. In contrast, if the directed technology effect is sufficiently strong, the model predicts that in the long run the college premium should increase. This is the case drawn in Figure I and offers a more complete explanation for the changes in the U.S. college premium over the past 25 years. I will also show how this mechanism can account for a puzzling aspect of the recent changes in the structure of wages: the increase in residual wage inequality during the 1970s while the college premium was falling. The analysis in this paper therefore suggests that the unprecedented increase in the supply of college graduates during the 1970s may have been causal both for the technological developments and the changes in the structure of wages of the past two decades. Finally, since the proportion of skilled workers has increased substantially over time, this theory also suggests a natural reason why new technologies should be more skill-complementary today than two centuries ago, and accounts for the steady increase in the demand for skills in the face of the rapidly increasing supply of skills over the past century. There are other episodes in which a large increase in the supply of skills appears to have affected the direction of technical change. High school enrollment and graduation rates doubled in the 1910s, mostly due to changes in the location and curricula of schools and the decline in transport costs [Goldin and Katz 19951. The skill premium (white-collar wage relative to blue-collar wage) fell sharply in the 1910s. Yet, despite the even faster increase in the supply of high school skills during the 1920s, the skill premium leveled


off and started a mild increase. Goldin and Katz [I9951 conclude that the demand for high school graduates must have expanded sharply starting in the 1920s, presumably due to changes in office technology and higher demand from new industries such as electrical machinery, transport, and chemicals. Thought experiments with exogenous variation in skills illustrate the main ideas, but in the long run the supply of skills responds to changes in the skill premium. The model developed in this paper allows me to simultaneously endogenize the demand for and the supply of skills. When the directed technology effect dominates, an increase in the supply of college graduates again first depresses and then increases the college premium. But now it also encourages more workers to enroll in college, and induces an extended period of adjustment where the supply of skills and the productivity of skill-complementary technologies increase together. An analysis of the implications of international trade on wage inequality provides another application of this theory. The key observation is that trade affects the direction of technical change. If the United States starts trading with the Less Developed Countries (LDCs) and sells technologies to LDC firms, the size of the market for technologies complementary to unskilled labor increases and wage inequality declines, or at most increases by only a small amount. However, if due to lack of international property rights protection, it is not possible to sell new technologies to LDC firms, trade simply increases the relative price of the skill-intensive goods, inducing further effort in upgrading skill-complementary technologies. 1 show that in this case conventional calculations underestimate the impact of trade on wage inequality because they ignore the change in the direction of technical change induced by trade. This paper is related to the older literature on induced innovations, including theoretical work by Kennedy [1964], Ahmad [1966],and Samuelson [1965], empirical studies by Schmookler [I9661 and Hayami and Ruttan [1970], and historical work by Habakkuk [I9621 and David [1975]. These studies discuss the impact of factor prices on innovations. I treat factor prices as endogenous and point out the importance of market size. The market size effect-the fact that an increase in the number of skilled workers increases the size of the market for skill-complementary technologiesis crucial in deriving the main result of the paper, which is that a larger relative supply of a factor can lead to faster upgrading of technologies complementary to this factor. Previous papers would predict the opposite result because they do not feature the market size effect. My paper also builds on and extends the work of Romer [1990], Aghion and Howitt [I9921, and Grossman and Helpman [I9911 on endogenous technical change by including two types of workers, each using different technologies and allowing technological change to be directed. Finally, a number of recent papers also suggest that changes in the supply of skills may change

INNOVATION & GROWTH

the demand for skills. In Acemoglu [1996], when there is a sufficient fraction of workers who are skilled, firms find it profitable to create jobs specifically targeted for this group, and as a result, unskilled wages fall, and skilled wages increase. Krugman [I9971 has recently constructed a signaling model with some common features. Independent work by Kiley [I9971 considers an expanding varieties model and shows that an increase in the supply of skills can create skill-biased technical change and increase inequality. Walde [I9971 compares the technology choice of economies differing with regard to the skill level of their high school graduates. He shows that an economy with less skilled high school graduates may choose a technology which makes little use of high school skills and have a high skill premium. The plan of the paper is as follows. Section I1 analyzes the basic model and contains the most important results of the paper. Section I11 shows how the model can account for the increase in residual wage inequality during the 1970s while the college premium declined. Section IV endogenizes the relative supply of skills. Section V discusses the impact of international trade on the direction of technical change and wage inequality. Section VI concludes.

11. The basic model I first outline the standard part of the model and explain the main results informally. The formal model follows Aghion and Howitt [I9921 and Grossman and Helpman [1991], but allows the pace of technological improvements in skill-complementary and labor-complementary machines to differ. A. Preliminaries and outline

H skilled workers and L unskilled workers supply labor inelastically and have identical preferences over the unique consumption good y:

where ~ ~ (is2 the ) consumption of agent k at time T and r is the discount rate, and due to linear utility, it is also the interest rate. I will drop the time argument when this causes no confusion. The consumption good is produced from two complementary intermediate goods, or production processes, one using skilled and the other unskilled labor. The market for intermediate goods is competitive. I denote the total output of these intermediate goods by Y, and Y,, and the aggregate production of the consumption good is


where p I1, so the elasticity of substitution between Y, and Y,, is 141 - p). I normalize the price of the final good in each period to 1, and denote the prices of the two intermediate goods by p, and p,. Competitive pricing gives a standard relative demand equation for intermediate goods:

There are m, and m, firms in the two intermediate goods sectors, and for now, I normalize m, = m, = 1. Since later there will be constant returns to variable factors, the number of firms does not matter. The production of Y,, the skill-intensive good, requires skilled labor while the production of the labor-intensive good, Y,, requires unskilled labor. Namely, firm i in sector s has production function,

where s = 1, h, and n,(i) is the number of workers employed by firm i in sector s, p < 1, and A,(i) is the productivity of labor in this firm. The labor market is competitive and clears at every instant. Since firms in sector I only employ unskilled workers, and those in sector h only hire skilled workers, market clearing implies that jn,(i)di E N, = L and jn,(i)d rn N, = H . The profits of these firms, if any, are redistributed to consumers. Firm level productivity, A,(i), is determined by the technologies employed by the firm, and skilled and unskilled workers use different technologies. Leaving a detailed discussion to the next subsection, for now note that all firms in a sector face the same (strictly concave) problem, so in equilibrium A,(i) = A,, ' s = 1, h. and wages in terms of the final good are w, = P ~ , A , N ; " - ~for The skill premium-skilled wage w,,, relative to unskilled wage w,-is the main focus of this paper. Using (3), this skill premium o is3

The skill premium increases when skilled workers become more scarce; i.e.,

ao aHIL < 0. This is the usual substitution effect, and shows that for given technology, the relative demand curve for skill is downward sloping with elasticity 1 / ( 1 - pp). Moreover, when p E (0,1],

INNOVATION & GROWTH

that is, improvements in the skill-complementary technology increase the skill-premium. The converse is obtained when p < 0. The conventional wisdom is that the skill premium increases when skilled workers become more, not less, productive, which is consistent with p > 0. Most estimates reveal an elasticity of substitution between skilled and unskilled workers greater than 1 which also implies that p > 0.4Therefore, in the remainder of though the formal analysis does not the paper I focus on the case p E (0,1), depend on this parameter restriction. The main story of the paper can now be told informally. As shown in detail in the rest of this section, endogenous technical progress implies that

(6)

AJA, = f(p, HIL).

-

Namely, the relative productivity of skilled workers depends on the relative price of the skill-intensive good ( p p,lp,) and the relative supply of skilled The former effect is similar to the impact of factor prices on workers (HIL). technical change which was emphasized by the literature on induced innovations cited in the introduction. Intuitively, when a good becomes more expensive, technologies used in its production command a higher price, increasing the incentives to upgrade these technologies. Since an increase in HIL reduces p, this effect further depresses the skill premium in response to a rise in HIL. The innovation of this paper is the second term in f. The size of the market for skill-complementary technologies relative to the market size of technologies complementary to unskilled labor is proportional to HIL. An increase in HIL therefore makes the invention of a new technology complementing skills more profitable and increases AJA,, so

dA,IAI

aHIL

> 0.

The formal analysis below will establish that as long as p > 0, this second effect dominates the price effect. Therefore,

This is the essence of the directed technology effect: an increase in the relative supply of skilled workers leads to an improvement in the technologies used by skilled workers.


Since technology is given in the short run, an increase in HIL first leaves AhIAl(mostly) unchanged and reduces the skill premium. Then, the direction of technical progress changes due to the market size effect. As a result, the skill premium rebounds from its short-run low. Moreover, if the directed technology effect is sufficiently pronounced, the skill premium may rise above its initial level, as drawn in Figure I. The rest of this section models the R&D sector more formally, demonstrates that technical change takes the form summarized in equation (6), and analyzes the dynamic response of the skill premium to an increase in HIL.

B. Technological advances Firm level technology A,(i) is determined by the quality and quantity of machines used. There is a continuum j, E [0,1] of machines for each sector. The fact that each sector uses different machines is the sense in which skilled and unskilled workers use different technologies. The quantity of machine j that firm i in sector s uses is denoted by x,(i,j). Machines, the only form of capital in this economy, depreciate fully after use, which simplifies the analysis. I denote the currently available highest quality of machine j in sector s by q,(j). Incorporating the fact that outdated machines will not be used (which is true in equilibrium as shown below), the productivity of firm i takes the form:

Notice that (4) and (7) imply that production of Yj and Y, is subject to constant returns to scale. The presence of a continuum of machines in (7), rather than just one per sector, simplifies the analysis. First, it implies that innovators do not have to take their impact on factor prices into account. Second, it ensures that the growth rate of the economy is deterministic. Firms (producing y, and y,) purchase machines and labor to maximize static profits. Let us denote the price of machine of quality q,(j) by ~ , ( j ) . Since there are no adjustment costs, firm i's problem at all points in time is

The solution to this problem implies that the aggregate demand for machine j in sector s is X,(j ) = [psqs(j ) ~ ! l ~ j, )(] ' l P ,where Nj = H and Nl 5 L. Technological advances take place as in Aghion and Howitt 119921 and Grossman and Helpman [1991]. When there is an innovation for machine j, the quality of the machine increases by a factor h > 1. I further assume that

INNOVATION & GROWTH

h > (1 - p)-"-P'l! which is a simplifying assumption to be discussed in the next subsection. The R&D firm that innovates has a monopoly right over that particular vintage (e.g., it holds a perfectly enforced patent), so it can charge a profit-maximizing price and sell as many units of the newly discovered input as it wishes. The marginal cost of producing input qs(j) is q,(j), so it increases linearly with the quality of the machine. Innovations are the result of R&D carried out by research firms using only final output as factor of production. There is free entry into the R&D sector. If the total amount of R&D activity in technology j for sector s is z, then the probability of innovation in this technology is z@(z).The marginal cost of R&D effort for inventing a machine of vintage q,( j ) is Bq,y(j ) (in terms of the final good).5 z@(z)is nondecreasing, i.e., $(z) + z@'(z)2 0, and $(.) is everywhere smoothly decreasing, which implies decreasing returns to R&D effort (see the Appendix for the case of constant returns and lim,,@(z) = 0. to scale, @(z) = 1). Also, I impose lim,,,@(z) = These Inada type restrictions on $(.) ensure an interior solution and smooth dynamics.

-

C. Equilibrium R&D effort The aggregate demands for technology characterized above are isoelastic, so the profit-maximizing price is a constant markup over marginal cost: xs(j) = qs(j)l(l - P) for vintage q,(j). The assumption that h > (1 - p)-('-P)/P implies that even if the next best technology, 4s(j) = q,(j)lh, were sold at marginal cost, firms would prefer to buy q,(j) sold at the monopoly price, ensuring that the monopoly pricing policy is optimal (see Grossman and Helpman [1991]). Given monopoly prices, every firm in the relevant sector buys xs(i,j) = Xs(j) = [ ( I - P ) p , s ~ ~ ] Therefore, 'lP. the equilibrium productivity in sector s, (7), can be written as

where I have defined

for s = 1, h. Q, and Q, are the average qualities of machines used in the labor and skill-intensive sectors, and are the relevant measure of technological know-how and the key state variables of this economy. The value of owning the leading vintage of machine j of sector s is


where z,(j) is the current aggregate R&D effort to improve machine j in sector s and x,(j) = PX,(j)q,(j)l(l - P) is the flow profit. At the flow rate z,(j)+(zs(j)), the firm loses its monopoly position because there is an innovation, and the time derivative of V in (8) takes care of the fact that z,(j) may be time varying. Finally, free entry into R&D activities implies that

where the left-hand side is the marginal return to higher R&D effort directed at this machine, and the right-hand side is the marginal cost.6 An equilibrium in this economy requires that firms rent the profitmaximizing amounts of all inputs, innovators follow the profit-maximizing pricing policy, product, intermediate good, and labor markets clear, and there is no opportunity for any research firm to enter (or exit) and increase its profits. Equations (3), ( 5 ) , (8), and (9) ensure these conditions.

D. Chavactevizing the equilibrium Let us start with the balanced growth path (BGP) where all variables either grow at a constant rate or are time invariant. In particular, since V denotes the value of an existing frontier technology, we have v = 0. Then, equations (8) and (9) imply that in BGP

for all j E [0,1] and s = I, h. This equation states that innovation effort for machine j is higher when profits from technology sales, the left-hand side, are higher. The profits will be higher in turn when the price of the product is higher or when more workers use this technology. It also immediately follows from (10) that ~ , ~ (=j z, ) for all j. In other words, the BGP levels of effort for all skill-intensive (labor-intensive) technologies are the same, so we only have to determine two variables, z, and z,. Combining (10) for s = 1 and s = h, we see that z,/z,, relative research effort at skill-complementary technologies, is increasing in p ( ~ I ~ ) as P ,captured by the reduced-form equation f(p, HIL) above. The price effect has exactly the same intuition as before: when p, is high relative to p,, it is more profitable to invent skill-complementary technologies because their output is more expensive. Simple algebra using (3) and profit-maximizing technology choice gives the relative price p as a function of HIL:

INNOVATION & GROWTH

where v I (1 - (1 - P)p)-I. Therefore, an increase in HIL depresses p, and via the price effect, it induces the invention of more labor-complementary technologies. Counteracting the price effect is the market size effect, the second argument off in (6). When there are more skilled workers, the size of the market for skill-complementary technologies is larger. For p E (0,1], the market size effect is more p ~ w e r f u l . ~ To determine the dependence of technology on relative supplies more formally, note that there is a continuum of skill-intensive inputs, so z,@(z,) is exactly the rate of improvements. Hence ( 1 - l)z,@(z,) is the growth rate of Qh= jkq,(j)dj. Similarly, (h - l)z,@(z,)is the growth rate of Q,. For BGP we need QJQ, to be constant; therefore z, = z,. Equation (10) then implies that along the BGP

Intuitively, BGP requires that z, = z,, so the demand for skill-complementary technologies relative to labor-complementary machines should be independent of HIL, which implies (12). Combining (12) with (1 l), we see that in the BGP, the relative technology of skilled workers needs to satisfy

Equation (13) is an important result. Q,,/Q, is the equilibrium technology level of the skill-intensive sector relative to the labor-intensive sector, and depends on the relative abundance of the two types of labor. Since profits to innovation are proportional to market size, they are effectively proportional to the number of workers using the technology. Therefore, when HIL increases, innovation and R&D in the skill-intensive sector become more profitable, inducing Q,lQl to increase (as long as p > 0). This is the directed technology effect: the greater the fraction of skilled workers in the economy, the greater their productivity relative to unskilled workers. Another implication of (13) is that as the economy accumulates more skills, technical change responds by making new technologies more complementary to skilled labor. The fact that the demand for skills has increased steadily in the face of increasing supply of skills over the past century is therefore consistent with the approach in this paper. Also, interestingly, during the eighteenth and early nineteenth centuries, there was a large migration of unskilled workers from villages and Ireland to English cities (see Williamson [1990]). So this increase in the supply of unskilled workers might have played a role in inducing the creation of the well-known skill-replacing technologies of that period. Returning to the formal analysis, the BGP R&D effort level can now be determined from (lo), (12), and (13) by imposing z, = z , = z*, which gives8


Finally, using the analysis so far and (5), we have (proof in the Appendix): PROPOSITION 1. There is a unique balanced growth path (BGP) where both sectors and total output grow at the rate ( h - l)z*$(z*) with z* given by (14). Along the BGP, Qh/Q, is given by (13) and the skill premium is

where q = pp2/(1 - p)

-

(1

-

pp).

In the unique BGP there is a one-to-one relation between the relative supply of skilled workers and their relative wage. This relation can be either increasing or decreasing. The second term in q, -(1 - pp), is the usual substitution effect from equation (5). If technology were exogenous in this economy, i.e., if A,IA, (or Q,/Q,) were constant, the skill premium would be a decreasing function of HIL. When technology is endogenous, the increase in HIL changes the direction of technical progress, and leads to more R&D activity in the skill-complementary technologies. As a result, QJQ, increases, and the "short-run relative demand curve" shifts to the right as in Figure I. The long-run relative demand curve is therefore more elastic than the short-run demand curve.9 Moreover, if pp2/(1 - p), the directed technology effect, is large enough, q is positive, and the long-run relative demand curve for skills is upward sloping.1° In this case, an increase in the supply of skills leads to a higher relative price of skill in the long run. This "perverse" case is more likely to happen when p is close to 1 so that the skill-intensive and labor-intensive production processes (intermediate goods) are close substitutes, and when p is close to I so that there are only limited decreasing returns to labor within each sector. A different intuition for the possibly upward sloping relative demand curve is that there is an important nonconvexity in this economy. There is a fixed up-front cost of discovering new technologies, and once discovered, they can be sold to many firms at constant marginal cost. This nonconvexity (nonrivalry of technology use) implies that it is more profitable to improve technologies designed for a larger clientele. This is the essence of the directed technology effect. Interestingly, the size of this nonconvexity, B, does not matter for this result. Only when B = 0, the nonconvexity and hence our results disappear, but in this case the growth rate of the economy becomes infinity. To see the importance of the nonconvexity and market size for the results more clearly, one can consider a modified model where technological monopolists can only sell X units of their machines, where

INNOVATION & GROWTH

X < min { L , H ) .The rest of the market will then be filled by imitators who produce a unit of a machine of quality q at the marginal cost ql(1 - P) (so that all machines sell at the same price, and the profit-maximizing price for the monopolist is the same as above). This modification removes the market size effect because an increase in H does not increase the market size of skill-complementary technologies for the innovator. Following the same steps as above, we see that in this case (13) becomes Q,lQl = y'l"-P)(HI~)-'. So an increase in HIL only creates the price effect on technological improvements, and causes slower upgrading of skill-complementary technologies. The relative demand curve is always downward sloping in this case. The next proposition summarizes the equilibrium dynamics out of the BGP. Denoting the BGP level of Q J Q , given in (13) by Q*, we have (proof in the Appendix):

2. (a) Locally, there exists a unique transition path PROPOSITION converging to BGP, so that if Qh/Q,# Q*, then z , and z, jump, and Q,,IQ, monotonically adjusts to Q*. If Q,/Q, < Q*, then z , > z, along the transition path and vice versa. (b) Suppose that the elasticity of the function @, E&z), is nonincreasing in z. Then, for all Qh/Q,# Q*, there is a globally unique saddle path to BGP along which Qh/Qlmonotonically converges to Q*. If Q,/Q, < Q*, then z , > z, along the transition path and vice versa.

This proposition shows that the BGP is locally (saddle path) stable, and under a fairly weak assumption on the @ function, also globally stable. When Q,/Q, is below its BGP level, the economy invests more in skill-complementary technologies (z, > z,), raising Ql,/Ql toward the BGP.

E. The dynamic response to a relative supply shock The following result summarizes the dynamic response of the economy to an unanticipated relative supply shock (proof in the Appendix)." PROPOSITION 3. Consider an unanticipated increase from HIL to 6HIL starting from a BGP with skill premium o = o,. Immediately after the shift, the skill premium falls to a,,, where log a,, - log o, = -0 log 6 and 0 = (1 p)/(l (1 - P)p) > 0, and z,/z, jumps up. The new BGP skill premium o,, is such that log o,, - log o, = q log 6. -

-

Following the relative supply shock, the skill premium falls by 8 log 6. The short-run response is for given technological know-how because Q J Q , is a stock variable and changes slowly. In terms of Figure I in the Introduction,


this is a move along the short-run (constant technology) relative demand curve, causing a decline in the skill premium. As the economy adjusts to its new BGP, Q,lQ, increases, and the skill premium starts increasing from its short-term low. In terms of Figure I the constant technology relative demand curve shifts to the right. Therefore, an increase in the relative supply of skills creates a period of rising skill premium in response to the induced shift in the relative demand for skills. This result is not very surprising: an intuition based on the LeChatelier Principle suggests that the elasticity of substitution between skilled and unskilled workers should increase as other factors are adjusted [Samuelson 19471. In this paper the other factors are measures of technology, A, and A,, and in the case 17 < 0, the results confirm this intuition. In contrast, when 17 > 0, the model's predictions are more surprising and original. Because of the nonconvexity introduced by the market size effect, the increase in HIL has a large impact on A,IA,, and eventually raises the skill premium above its initial value. Proposition 3, especially in the case where 17 > 0, offers an alternative explanation for the behavior of the U.S. economy during the past 25 years. There was a large increase in the supply of skills in the 1970s. Between 1940 and 1970 the relative supply of college equivalent workers grew at the rate of 2.73 percent per year. In contrast, between 1970 and 1980 this relative supply grew almost twice as fast, at 5.19 percent per year (in other words by 52 percent in the course of ten years, see Autor, Katz, and Krueger [1998]). This is a very large change in the relative supply of skills preceding the rise in the college premium. Furthermore, these supply changes were at least partly "exogenous" rather than a simple response to anticipated higher returns to education in the future. Enrollment rates had been increasing since the mid-1950s, and this trend continued in the 1960s (see Freeman [1976], Figure 6, p. 35). The main reason for the increase in the proportion of college graduates in the labor force during the 1970s was the interaction of these higher enrollment rates with the large cohort sizes arriving in the market during the 1970s. In particular, the cohorts retiring in the 1970s had very few college graduates. For example, only 7.5 percent of those 55 years or older in 1970 were college graduates [Bureau of the Census 19711. In contrast, due to the enrollment trends dating back to the 1950s, 21.3 percent of those aged 30 to 34 in 1981, a cohort that entered the market between 1970 and 1980, had a college degree [Bureau of the Census 19831. Moreover, due to the baby boom, the entering cohorts were large relative to the labor force: in 1981 there were 38 million people between the ages of 25-34 as compared with 48.5 million people between the ages of 35 and 54 [Bureau of the Census 19831. Two other factors also contributed by increasing the enrollment rates further during the late 1960s and 1970s: (1) until almost the end of the war, the Vietnam era draft laws exempted males enrolled in college from military service. This induced many more young males to stay in college during the

INNOVATION & GROWTH

late 1960s in order to avoid the draft [Baskir and Strauss 19781; (2) government financial aid for college increased by a large amount during this era. For example, the total federal aid to college students that stood at approximately $2 billion in I963 increased to $14 billion in 1970-197 1 and then to $24 billion in 1975-1976 (all numbers in 1989-1990 dollars, see McPherson and Schapiro [1991]).12 My theory predicts that in response to this large increase in HIL, the college premium should fall first, and then increase due to the induced skill-biased technical change. This pattern matches the broad behavior of the U.S. college premium from 1970 to the present, and suggests an explanation for why the relative demand for college graduates increased much faster in the past 25 years than between 1940 and 1970 [Autor, Katz, and Krueger 19981." The model also predicts that after a large relative supply change, the growth rate of the economy should decline. During adjustment to the new BGP, z, increases, and z, falls, and because @(.)is decreasing-i.e., return to R&D is concave-the faster technological improvements in skillcomplementary technologies do not compensate for the slowdown in the productivity growth of unskilled workers. Therefore, a large increase in HIL not only changes the structure of wages, but also causes a productivity slowdown. Unfortunately, @(.),which determines the extent of this productivity slowdown, is not easily observed in the data, so it is not possible to know whether this is an important effect. Greenwood and Yorukoglu [I9971 also obtain slower growth during the process of adjustment to new technologies because of costs of adoption and learning. In contrast to that paper, technological change is endogenous here, and the slower growth is due to the fact that the economy invests in improving skill-complementary technologies at the expense of technologies used by unskilled labor. Finally, it is instructive to do some back-of-the-envelope calculations to see whether the model can generate plausible effects. I take the relative supply shock to be the increase in the ratio of college graduates to high school graduates from 1971 to 1979, since 1971 was the starting year for the large change in the skill composition of the labor force. This gives the relative supply shock, A log (HIL) = log 6, as 0.4 (Table VIII in Katz and Murphy 119921). 1 take the long-run response to this increase in supply to be the proportional change in the college premium from 1971 to 1987, which is reported as 0.024 by Katz and Murphy [1992]. I compare this number with the long-run response implied by the model, q log 6 (= log o,, - log a,). I take the "short-run" response to be the change in the skill premium from 1971 to 1979, which is -0.10 [Katz and Murphy 19921. This number cannot be directly compared with the immediate effect of a one-time shock given in Proposition 3 because in reality the supply shock took place over a number of years, so technology must have adjusted during this period. Therefore, I compare it with (log a,, + log 0,,)12 - log a,, which is the simple average of the change immediately after the shock and the long-run response.


For a range of parameter choices, the model implies numbers very close to the data. For example, when P = 0.35 and p = 0.75, the model yields a short-run elasticity of substitution between college and noncollege workers in the right range and q = 0.06. This implies a short-term fall in the college premium of 11 percent, comparable to the one in the data, and a subsequent large increase, taking it to about 2.5 percent above its initial value. This is quite close to the actual behavior of the college premium. Similar results are obtained when P = 0.4 and p = 0.73, or when P = 0.45 and p = 0.7. These parameter choices can be given some justification in terms of more micro estimates (see Acemoglu [1997]), but are inherently arbitrary. So these results should be interpreted as purely illustrative. In particular, small changes in p change the quantitative implications by a large amount. Also, further increases in HIL in the 1980s make these calculations difficult to interpret. 111. Directed technical change and residual wage inequality Equating skilled workers to those with a college degree, I suggested that a model incorporating the directed technical change can match the evolution of the U.S. college premium. Another important aspect of the changes in the structure of wages is increased residual wage inequality. Using March Current Population Surveys, Juhn, Murphy, and Pierce [I9931 and Katz and Murphy [I9921 find that residual (within group) wage inequality began increasing during the 1970s while the college premium fell. Bernard and Jensen [I9971 find the same pattern in the census data. (But DiNardo, Fortin, and Lemieux [1996] do not find it using May Current Population Surveys.) To date, there has been no unified explanation for the simultaneous increase in residual inequality and the decline in the college premium during the 1970s.I4 In this section I suggest a simple extension of the model which accounts for this pattern. Suppose that skills are two-dimensional: education and skills unobserved to the econometrician. For lack of a better term, I call the latter ability. A fraction ph of college graduates have high ability, and the remainder have low ability. This fraction is pI < ph among low education workers. For example, ability (unobserved skills) could be related to college education, but not perfectly, so that some of the college graduates do not acquire the necessary skills, while some other workers do in spite of not having attended college. Therefore, abilitylunobserved skills are not innate, but acquired partly through education. There are H college graduates and L low education workers. Suppose also that the aggregate production function of the economy is

which basically combines the equivalent equations to (2) and (4), and also imposes that all firms use the same technology, which is true in

INNOVATION & GROWTH

equilibrium. The important assumption we make is that A,,, and A,, use skillcomplementary machines, qh(j), while A, and A,, use the q,( j ) machines. For example,

where xh,(j) is the quantity of skill-complementary machine j used in hl. This formulation implies that both high ability college graduates and high ability high school graduates use similar technologies (see Bartel and Sicherman [1997] for some evidence that advanced technologies are complementary to abilitylunobserved skills). An analysis similar to the one used previously implies that in BGP

where v = (1 (1 - (3)p) (see the Appendix for details). The proportion of high ability workers increases the relative abundance of technologies complementary to ability. This has exactly the same intuition as the results in Section 11. Now consider an exogenous increase in HIL over a number of periods. Because y, > '12 > pl,the proportion of high ability workers in the labor force increases, inducing a rise in QhlQl.The college premium behaves as in the previous section: first, it declines for a while in response to the increased supply of H workers. Then, as Q,,lQ, increases, the college premium also starts increasing, because there is a larger fraction of high ability workers among the college graduates. In contrast to the college premium, which falls first, however, residual wage inequality starts increasing immediately after the shock. To see this, consider the two measures of residual wage inequality in this model, oh= whhlw, and o' = wh,lw,,, which are the ratios of the wages of high to low ability workers within their education groups. Arguments similar to those developed before imply that -

oh=

(

[kr(e) e

-9

and m i=

,

where 0 and v are as defined above (see the Appendix). Notice that the increase in the supply of college graduates equally affects the numerator and the denominator of the measures of residual wage inequality, ohand a', so there is no contraction in residual inequality in response to the increase in HIL. But these measures are proportional to Qh/Q,, so the increase in Qh/QI


following the change in relative supplies leads to an immediate increase in residual wage inequality. Therefore, if technologies are complementary to unobserved skills, the approach developed in this paper predicts that in response to increases in the relative supplies of educated workers as in the 1970s, the college premium declines first and then increases, whereas residual wage inequality starts increasing immediately.

IV. Endogenous supply of skills Section I1 treated the relative supply of skills as exogenous. The increase in the supply of college graduates during the late 1960s and 1970s was argued to be largely exogenous rather than a simple response to anticipated higher returns in the future. Nevertheless, education choices are to some degree forward-looking and respond to returns. It is therefore important to endogenize the supply of skills and verify that the main results are robust. This analysis also provides new results regarding the joint behavior of skills and technology. Suppose now that a continuum v of unskilled agents are born every period, and each faces a flow rate of death equal to v, so that population is constant at 1 (as in Blanchard [1985]). Each agent chooses upon birth whether to acquire education to become a skilled worker. For agent x it takes K, periods to become skilled, and during this time, he earns no labor income. The distribution of K, is given by the function T(K) which is the only source of heterogeneity in this economy, due to credit market imperfections or differences in innate ability. The rest of the setup is unchanged. To simplify the exposition, I assume that T ( K ) has no mass points. I now define a BGP as a situation in which HIL and the skill premium remains constant. In BGP there is a single-crossing property: if an individual with cost of education K , chooses schooling, another with K,r. < K, must also acquire skills. Therefore, there exists a cutoff level of talent, K,such that all K, > K do not get education. Although HIL is in general a complicated function of past education decisions, when v is small, along BGP it takes the simple form,

The agent with talent K needs to be indifferent between acquiring skills and not. When he does not acquire any skills, his return at time t is

exp [-(r

+ V)(T

-

t)]w,(.r)dz = w,

exp [-(r

+v

-

g)z]d.r =

Wl

r+v-g

>

INNOVATION & GROWTH

where r + v is the effective discount rate and I have used the fact that along the BGP wages grow at the rate g = ( h - l)z*$(z*). If in contrast K decides to acquire education, he receives nothing for a segment of time of length K, and receives W, from then on. Therefore, the return to agent K from acquiring education, R ~ K ) can , be written as

In BGP, for K to be indifferent, we need R ~ K =) Rne at all times, so o E w,/w( = exp[(r + v - g)K]. Inverting this equation and substituting into (17), we obtain the relative supply of skills as a function of the skill premium (when v is small): (18)

H

--

L

F(ln ol(r + v - g)) 1-r(lnol(r+v-g))

A BGP equilibrium with endogenous skill formation is given by the intersection of the relative supply (18) with relative demand for skills given by (15). Ignoring the impact of HIL on g, which is likely to be small, equation (18) defines an upward sloping relative supply relation. When q > 0, (15) also defines an upward sloping relative demand curve, and multiple BGP equilibria, as drawn in Figure 11, are possible. Intuitively, when q > 0, a higher HIL increases o , encouraging workers with high K to obtain education and increasing HIL further. Skill Premium o

Relative Supply---Equation (18)

Figure II Balanced growth path equilibria with endogenous skills.


Government policy (e.g., the grant programs or the Vietnam era draft laws) can be thought of as reducing the cost of education and shifting the relative supply curve in Figure I1 to the right (or shifting the function T ( K ) to the left). When q > 0, the return to education w would also rise, thus raising HIL further. Therefore, the prediction of the model in this case is that subsidies to education lead to an increased tendency to acquire education, and also to a larger education premium due to the directed technology effect. Interestingly, when q > 0, education subsidies may harm those agents who do not take advantage of the increased incentive to attend college, which is different from the predictions of standard theory where even those who do not take advantage of education subsidies benefit. Also notice that a small exogenous increase in the demand for skills-an increase in y in equation (2)-increases the skill premium immediately, encouraging more skill acquisition. This induces the directed technology effect and increases the demand for skills further. If the supply of skills is sufficiently responsive to the skill premium, the exogenous increase in the demand for skills causes a decline in the skill premium before increasing it above its initial value. A formal analysis of transitory dynamics is more complicated. To simplify the discussion, suppose that there is a unique BGP and the supply of skills is not too responsive to the skill premium (i.e., T f ( K )is sufficiently small or the relative supply curve in Figure I1 is sufficiently steep). Then, it can be shown that in the neighborhood of the BGP, an increase in HIL, due to a decline in the cost of education or other reasons, first reduces the skill premium. Then, HIL and Q,,/Q, increase together, creating both skill-biased technical change and a larger supply of skills. In the case where q > 0, the economy ends up with higher skill premium, more skill-complementary technologies, and more skilled workers (see the Appendix). The process of adjustment is likely to take a long time because technology adjusts slowly (especially in the case where @(.)is steeply decreasing). Therefore, the skill premium will rise over time, and earlier generations will be less willing to invest in skills as the returns are far in the future. This pattern of slowly increasing HIL and a gradual shift toward more skill-complementarity technologies is similar to the experience of the United States economy over the past century.

V. The impact of trade on technology Increased trade with the LDCs where skilled labor is scarce is often suggested as a potential cause of increased wage inequality and contrasted with the explanations based on technology. Since technology has been treated as exogenous in the wage inequality literature, there has been little effort to uncover the links between these two explanations. This section shows that the direction of technical change is influenced by trade, modifying or

INNOVATION & GROWTH

qualifying many of the conclusions reached in the previous literature regarding the impact of trade on inequality. Suppose that the North, where the ratio of skilled to unskilled workers is equal to H"ILN, begins trading with an economy, the South, which has a skill ratio HSIL" < HNILN.There is no endogenous skill accumulation in either economy. What happens to wage inequality in the North? I will answer this question under three different scenarios: (a) no directed technical change; (b) directed technical change and new technologies sold to firms in the South on the same terms as firms in the North; (c) directed technical change and no property rights enforcement in the South. The first scenario is for a benchmark, and the truth presumably lies somewhere between (b) and (c), so that there is some sale of technology to the firms in the South, but the enforcement of intellectual property rights is less than perfect. Note that, in this model, factor price equalization is guaranteed without further restrictions because each sector employs only one of the nontraded factors (see Ventura [I9971 for a similar structure).

A. No technical change Suppose that Q, and Q, are given exogenously. Denote the steady state (BGP) skill premium in the North before trade opening by o N ,and the BGP skill premium after trade opening by ow.Also define A log o = log owlog o N ,H W= H N + HS, LW= L N + LS and H WILW= ~ H ~ Iwhere L ~ 8, < 1 by the fact that the North is more skill-intensive than the South (i.e., log 8 < 0). Equation ( 5 ) from Section I1 implies that (19)

A log o,,

= -8 log

6 > 0,

where the subscript NTC denotes "no technical change" and 8 was defined above. Since the South is less skill-intensive, trade with the South increases the relative price of skills in the North, which is the standard effect of trade.

B. Endogenous technical change and full property rights Suppose that A, and A, are endogenous as in Section 11, and assume that (i) before trade opening, there were no sales of technology to the firms in the South (and no foreign direct investment in the South by firms in the North); and (ii) after trade opening, firms in the South and the North are symmetric and property rights of R&D producers in the North are fully enforced in the South. Trade opening is then equivalent to a decline in the relative supply of skills from HNILNto HWILW.We can now use equation (15) from Section I1 to obtain the change in BGP skill premium after trade opening: (20)

A log o,, = q log 6,


where the subscript PR indicates that in this case there is endogenous technical change and property rights of R&D firms are enforced in the South. If q > 0, contrary to conventional wisdom, trade opening may actually reduce the skill premium for exactly the same reasons that a higher supply of skilled workers increased it in Section I1 (though as in Proposition 3, trade opening would first increase inequality and then reduce it). More generally, the directed technology effect implies that when intellectual property rights are fully enforced, it is unlikely that international trade increases the skill-premium by a large amount.

C. No intellectualpvoperty rights in the South A simple way of modeling the lack of intellectual property rights is to suppose that imitators produce and sell the latest machines invented by R&D firms in the North to firms in the South, so that Northern R&D firms do not receive any revenue from firms in the South. To simplify the analysis, suppose that imitators can produce a machine of quality q at marginal cost ql(1 - P), so that firms in the South use the same technology as the firms in the North. This specification implies that the market sizes for different machines are unchanged after trade opening. However, there is still an impact on the direction of technical change because the relative price of skill-intensive goods changes. Trade opening first depresses the price of labor-intensive goods (i.e., reduces p). However, in the BGP, (10) has to hold in order to equate the return to R&D in skill-complementary and labor-complementary machines, because R&D firms can only sell technologies to firms in the North. This implies that

so relative prices have to adjust back to their original level to restore equilibrium, and this requires an adjustment in the relative technology of skilled workers away from its original level. In particular, in the new BGP, QJQ,

= ~'I('-P)(HN/LN)PP~~'P)~-~

The relative wage is now a"'= y " " - p ) ( ~ N ~ ~ N )and % - ' the , change in the skill premium after trade opening is (21)

A log

= -log

6 > 0,

where the subscript NPR indicates that there is endogenous technical change but no enforcement of intellectual property rights in the South. The assumption of no intellectual property rights in the South has removed the market size effect completely (the relative market size is still H N I P ) , but the price effect on the incentives to innovate is present. As noted in

INNOVATION & GROWTH

Section 11, the price effect magnifies the negative effect of the increase in HIL on the skill premium, which explains the large impact of trade on wage inequality.15 Also, interestingly, trade opening in this case may also increase the skill premium in LDCs, because firms in LDCs use the same technology, and trade opening has induced skill-biased technical change in the North. This contrasts with the prediction of a model with exogenous technology. and in fact if In summary, we have A log a,,, > A log o,, > A log opR 77 > 0, A log opR< 0. That is, if property rights are fully enforced in the South, the decline in the relative supply of skills should not lead to a large increase in the skill premium. In contrast, if intellectual property rights are not enforced in the South, simple calculations that ignore the induced change in the direction of technical progress may be seriously underestimating the impact of international trade on inequality.

VI. Concluding comments The wages of college graduates and of other skilled workers relative to unskilled labor increased dramatically in the United States over the past fifteen years. To many economists and commentators, this is a direct consequence of the complementarity between skill and new technologies. It is not clear, however, why new technologies should complement skills. History is full of examples of new technologies designed to save on skilled labor. More generally, inventions and technology adoption are the outcome of a process of choice; as a society, we could have chosen to develop or attempted to develop many different technologies. It is therefore, necessary to analyze the direction of technical change as well as its magnitude. In its simplest form, this means to pose the question: "why do new technologies complement skills?" This paper suggested that the direction of technical change is determined by the size of the market for different inventions. When there are more skilled workers, the market for technologies that complement skills is larger, hence more of them will be invented, and new technologies will be complementary to skills. I formalized this observation and discussed its implications. I showed that an exogenous increase in the ratio of skilled workers or a reduction in the cost of acquiring skills could increase wage inequality. The likely path is first a decline, and then a large increase in the skill premium. These observations fit the U S . facts where the large increase in the ratio of college graduates during the late 1960s and 1970s first depressed the college premium and then increased it to higher levels than before. The most important area for future work is to develop a test of directed technical change, and its impact on the structure of wages. The testable implication of the model is that after an increase in the supply of college graduates, R&D directed at technologies complementary to college graduates should increase. Although it is difficult in general to determine which


technologies are complementary to skilled workers, most economists believe that computers are more complementary to skilled and educated workers than to the unskilled. For example, Autor, Katz, and Krueger [I9981 report that in 1993 only 34.6 percent of high school graduates use computers in contrast to 70.2 percent of college graduates. Moreover, Krueger [I9931 shows that controlling for education, workers using a computer obtain a wage premium which suggests that they are more skilled. From the R&D expenditure data reported by the NSF, we see that in 1960 company-funded R&D for office computing was 3 percent of the total company-funded R&D expenditure. This ratio has increased to 13 percent by 1987,16 suggesting that during this period of rapid increase in the supply of skills, there has been significantly more R&D directed to one of the technologies most complementary to skills. If other technologies and R&D expenditure can also be classified as complementary to college graduates, the hypothesis of this paper can be tested. A second area for future research is the application of these ideas to the male-female wage differentials. Since the 1970s, the labor force participation of women has increased substantially, and their wages relative to those of male workers have also increased. Part of this change is likely to have been due to reduced discrimination. However, to the extent that male workers use different technologies than female workers, the approach in this paper suggests a new explanation based on directed technical change. The degree to which women use different technologies than men within a plant or sector is probably limited. Nevertheless, women tend to work in different sectors and occupations, and these jobs use different technologies than traditionally male jobs (e.g., desk jobs versus construction). It is therefore conceivable that the greater participation of women may have affected the direction of technical change, and via this channel, reduced male-female wage differentials. This hypothesis can be investigated more carefully by studying the relative growth of industries that employ more women, and the relative rate of technical change in these industries.

Appendix Proof of Proposition 1 Equation (13) uniquely defines Q,,/Q,for z , = 2,. Then, using (lo), (12), and (13) and imposing z* = z, = z, gives equation (14), which uniquely defines z* because the left-hand side of (14) is strictly increasing in z* and the right-hand side is constant. This establishes that the BGP exists and is uniquely defined. Now substituting for A J A , and for p, (5) implies

Finally, substituting for Qh/Q,using (13) gives (15) in the BGP.

INNOVATION & GROWTH

Transition dynamics and proof of Proposition 2 Equation (10) immediately implies that z,(j) = z, out of BGP as well as along it. So we only have to determine the time path of z,, z,, Q,, and Q,,. Equation (9) holds at all times, so differentiating it with respect to time and using (8), we obtain

for s = I, h. I normalize B = Pl(1 P)"-P"Pin this Appendix to simplify the notation. Combining this with (8) and using (9), we obtain -

Finally, noting that Q,IQ, = (h

-

l)@(z,)z,and defining Q = Q,,lQ,, we also have

Equations (22) and (23) completely describe the dynamics of the system. T o analyze local dynamics and stability in the neighborhood of the BGP, I linearize these equations. Then, around the BGP, z, = z, = z*, Q = Q*, and ignoring constants, we have

ih = o(z*)(z,

-

z*)/(E&z*)/z*) + v,(z*,Q*)(Q

-

Q*),

i, = o(z*)(z, - z*)l(~&z*)lz*)- v,(z*,Q*)(Q - Q*)

and Q = o(z*)Q*(z, z,), where o(z*) = @'(z*)z* + @(z*) > 0. v, and v2 are analogously defined, and are both positive. The reason why deviations of Q from Q* affect z, and z, differently is that when Q > Q*, p, is above its BGP value, and p, is below its BGP value. This linearization enables us to reduce the three variable system to two variables: Q and 5 = z, - z,. Specifically, -

where v(z*,Q*) = vl(z*,Q*)+ v2(z*,Q*)> 0. This linear system has one negative and one positive eigenvalue, and thus a unique saddle path converging to the BGP equilibrium. The rate of convergence to the BGP is

Thus, when o(z*) = @'(z*)z*+ @(z*)is lower, or when o(.) is more steeply decreasing, convergence is slower. In fact, in the extreme case of Q(z) = 1 (where o(z*) is at its highest), all our BGP results would be unchanged, but ignoring nonnegativity


constraints on consumption, there would be n o transitory dynamics. That is, when Q < Q*, we would have z,= 0 and z, + for an infinitesimally short while. There would be once again transitory dynamics, however, if nonnegativity constraints on consumption are imposed. Next, I establish that if E&Z) is nonincreasing, the system is also globally saddle path stable. Since paths cannot cross and there are no other stationary points of the system, all paths that d o not cycle must go to infinity. Therefore, we only have to establish that there are no cycles. Suppose that Q < Q*. Note that in this case p , > ~ p , ~~Then ~ . consider case (A), where z,> z,. Then using (22) and the Therefore, z,will remain larger than z,, fact that E&Z) is nonincreasing, i,lz,> i,/z,,. and Q < 0. Thus, there cannot be any cycles, and all paths go to infinity when z,> z,. Now consider case (B), where z, > z,and i,lz,< i,lz,. Now Q > 0, and also as Q increases p , falls, and p, increases. Therefore, it will always be the case that iJz,< i,lz,. Hence, in this case too, cycles are not possible. Now consider case (C), where z, > z,and i,lz,> i,lz,. If as t + m, z, > z,,and i,lz,> i,,lz,,then we converge to z, = z,= z* and Q = Q*, and we know there is a unique saddle path locally and paths cannot cross. Therefore, we must be on that path. Instead if z, = z,at some point where Q # Q*,then once again cycles can be ruled out. We must have either that z, > z,and Q > Q* which puts us in case (A), and cycles are not possible, and all paths go to infinity. Or, it could be the case that z, > z,and Q > Q*, which, by the argument analogous to case (A), again rules out cycles. Thus, there must be a unique saddle path from all points Q < Q*. The proof for the case of Q > Q* is analogous.

Proof of Proposition 3 Take QJQ,as given. Then, given optimal monopoly pricing and profit maximization by firms, we have

Now substituting for p,, and p, and rearranging,

Substituting into

(3, we obtain

where 0 = (1 p)/(l (1 p)p) and v = (1 - (1 - p)p)-l as defined in the A log w = -0 log S. Once text. Therefore, at given technology (i.e., given Q,/Q,), technology adjusts to its new BGP level, we have the result of Proposition 1. Thus, A log 0 = q log 6. -

-

-

INNOVATION & GROWTH

Details of the model of Section ZZZ The demands for sector h machines now come from firms employing high ability college graduates and high ability high school graduates, and vice versa for sector 1 machines. These demand curves have the same elasticity as in the text. Thus, the optimal pricing policy is the same. Therefore, the free-entry condition for sector h machines, analogous to (lo), can be written as

and similarly for z,, where phh is the price of the intermediate good produced by high ability college graduates in terms of the final good, ph, is for high ability high school graduates, etc. (recall that B P . (1 - p)"-P)'Pin this Appendix). Then, using competitive pricing and the definition of A,,,

where v = (1 - (1 - P)p)-l and phi, p,, and p , are similarly defined. Substituting these into (24) and simplifying, we obtain (16) in the text. Finally, consider residual wage inequality among college graduates:

Substituting for A,,,, and A , gives the expression in the text. o' is derived similarly.

Transitory dynamics with endogenous skills I focus on the case of interest, which has q > 0. Linearizing around a BGP, Q still only depends on 5. Thus, ignoring constants, Q = a,,r, where a,, > 0. In contrast, 5 = a,,5 + a12Q a,,(HIL), where all coefficients are positive. This is because z, depends on V, which is an increasing function of Q, and decreasing in N , . Finally, around the BGP, we have that H = -vH + T(1og wl[r + v - g ] ) , and similarly for L. Therefore, the rate of change of HIL is a decreasing function of HIL and an increasing function of the relative wage o, which is itself decreasing in HIL and increasing in QJQ,. Thus, in the neighborhood of the BGP the linearized differential equation is (HIL) = a,,Q - a,,(HIL), where once again the coefficients are positive. Note that a,, is the response of the supply of skills to the skill premium, so it is smaller when T'(K) is lower; that is, when education choices are not very responsive to wages. Therefore, around the BGP, this system has two state variables and one control variable. Thus, for well-behaved transition dynamics, the linearized differential equation system needs to have two negative ( x , , ~ , )and one positive eigenvalues (x,). Standard arguments establish that x,x,x, = a,,(a,,u,, - a,,a,,). So when a,, is sufficiently small-so that education choices are not too responsive-ither all roots are positive, or two of them are negative. Also, x,x, + x,x, + x2(a3,+ a,,a,,) < 0, which implies that all roots cannot be positive. So long as education is not too responsive to the skill premium, the system is saddle path stable around the BGP. Therefore, -


when HIL and QJQ, are below their BGP value, we have z, > z,, and the economy converges to BGP by accumulating skills and more skill-complementary technologies.

Notes

* I have benefited from many insightful conversations with Jaume Ventura during the gestation of this project and from many of his comments on earlier versions of this paper. I also thank two anonymous referees, Joshua Angrist, Olivier Blanchard, Ricardo Caballero, Francesco Caselli, Gilles Durante, Oded Galor, Lawrence Katz, Michael Kremer, Kevin M. Murphy, Dani Rodrik, Fabrizio Zilibotti, and various seminar participants for useful comments and suggestions. Financial support from the National Science Foundation Grant SBR-9602116 is gratefully 1 For example, Bound and Johnson [1992], Berman, Bound, and Griliches [1994], Caselli [1997], Galor and Tsiddon [1997], and Krusell, Ohanian, Rios-Rull, and Violante [1997]. See Griliches [1956], Bartel and Lichtenberg [1987], and Goldin and Katz [I9981 for micro estimates of technology-skill complementarity, and Krueger [I9931 on the impact of computers on the structure of wages. 2 Economic motives do not play a direct role in all inventions. "Macroinventions," to use Mokyr's [I9901 term, are likely to be exogenous and stem from advances in basic science. For the thesis in this paper, it is sufficient that economic motives influence the direction in which these macroinventions are developed. 3 In this section, for some parameter values, skilled workers may have lower wages than the unskilled, i.e., w 5 1. One may want to impose y > ( H I L ) ' ~ ' l to ~ Pavoid 'P this, or alternatively, one could assume that skilled workers can use the machines designed for the unskilled and be more productive at this than the unskilled. When the supply of skills is endogenized in Section IV, the skill premium is always positive, so this parameter restriction is not necessary. 4 See Freeman [1986]. Practically, all estimates of the aggregate elasticity of substitution between high and low education workers are between o = 1 and 2. These estimates control for time trends in the demand for skills or use cross-sectional data. Thus, in terms of the model here, they correspond to the constant technology elasticity. So 110 = 1 pp < 1, and p > 0. Since a large part of the substitution between skilled and unskilled workers is within industries, p should not be interpreted as the elasticity of substitution between different goods. 5 Equivalently, the cost of R&D effort to improve vintage q,(j) is Bhq,(j). The assumption that R&D inputs are in terms of final output serves to highlight that changes in skill premium are not driven by changes in the level of R&D activity. If R&D uses more skilled labor, then the skill premium will increase in periods of high R&D activity, similar to the "skill-biased technology adoption" effect emphasized in Nelson and Phelps [1966], Galor and Tsiddon [1997], and Greenwood and Yorukoglu [1997], but this does not change the main results of the paper. 6 There is free entry by small R&D firms which ignore their impact on the invention probability of other firms working to improve the same machine. If there had been one large firm doing R&D on each machine, the left-hand side of (9) would have been [@'(z,(j))z,(j) + @(z,(j))]VJj). The choice between these two formulations does not change the results. Also, (9) ignores the constraint that total expenditure on R&D should not exceed current output. Assuming that @ is sufficiently decreasing would ensure that this constraint never binds. Alternatively, -

INNOVATION & GROWTH

7

8

9

10

11

12

13

14

this constraint does not apply if the economy can borrow from abroad at the interest rate r. T o see this, note that p is decreasing in HIL with elasticity P(l - p)l(l - (1 - P)p) which is less than P when p > 0. Although it is plausible for the market size effect to dominate in the case of skilled and unskilled workers, the price effect may dominate in other situations. For example, Hayami and Ruttan [I9701 discuss the different paths of agricultural development in the United States and Japan. The scarcity of land in Japan relative to the United States appears to have induced a faster rate of innovation and adoption of fertilizers, increasing output per acre. As in Aghion and Howitt [I9921 and Grossman and Helpman [1991], the growth rate increases with total population. This is not important for the focus of this paper. All the results of interest continue to hold if we impose z,+ z, = 7, which would remove the scale effect. Alternatively, we can impose that for z 2 2, zQ(z) = Q, < 00, and the scale effect would disappear once the population reaches a critical threshold. Further, an increase in HIL leaving total population unchanged may increase or decrease the BGP growth rate. The restriction z, + z, = 5 also removes the effect of HIL on the growth rate. The long-run relative demand curve is more elastic than the short-run demand curve even when p < 0, because from (1 3), an increase HIL reduces Q,,lQ,, but in this case, as (5) shows, the skill premium is decreasing in Ql,/Q,. So even when p < 0, an increase in HIL first reduces and then increases the skill premium. However, when p c 0, the long-run relative demand curve can never slope up. HIL has two effects on technology: first, it determines the quantities of machines purchased at a given Q,lQ, and second, it changes Q,/Q,. The second effect is the important one. T o see this, suppose that there is d o R&D, but A , is still determined by purchases of machines from a monopolist. In this case, the skill premium is again a decreasing function of HIL with the smaller elasticity, p)l(l - (1 - P)p), which is also the short-run elasticity in Proposition 3. -(I The increase in the supply of skills during the 1970s may have been anticipated. This does not change the qualitative conclusions reached in Proposition 3. The reason is that it is not profitable to invent skill-complementary technologies much before workers who will use them are in the market, because other firms are likely to improve on these technologies before the original inventor has had access to the larger market. It can be argued, however, that federal aid increased because the government forecast the increased need for college graduates. Even if this were the case, which is unlikely, the large part of the increase in the supply of college graduates due to the cohort size effect is still predetermined and "exogenous." The model does not predict a fall in unskilled wages, which has been a feature of the changes in wage structure during the 1980s. If there is depreciation of existing technologies, for example, because some of the old technologies are not compatible with new ones, the model also predicts that during adjustment to an increase in HIL unskilled wages may fall. See Acemoglu [I9961 for an alternative model for the decline in unskilled wages. Galor and Tsiddon [I9971 argue that ability is more valuable in periods of rapid technological change, which offers another explanation for the increase in residual inequality during the 1970s. Caselli [I9971 suggests, but does not develop, a related story where due to on-the-job-training, high ability workers benefit from rapid technological change first. Both stories can explain why residual inequality might have grown faster than the college premium during the 1970s, but without further modifications, not why college premium fell and residual inequality increased.

D I R E C T E D T E C H N I C A L C H A N G E & WAGE I N E Q U A L I T Y

15 This argument is related to Wood's [1994] suggestion that trade with the South may have reduced "defensive" unskilled-labor-saving innovations. However, it is not clear what mechanism Wood has in mind since a decline in unskilled wages should normally lead to the introduction of skill-replacing or unskilledlabor-complementary technologies. 16 These data come from various issues of Research and Development in Industry Detailed Statistical Tables published by the NSF. I am grateful to Sam Kortum for providing me with these data.

References Acemoglu, Daron, "Changes in Unemployment and Wage Inequality: An Alternative Theory and Some Evidence," CEPR Discussion Paper No. 1459, July 1996. -----, "Why Do New Technologies Complement Skills? Directed Technical Change and Wage Inequality," CEPR Discussion Paper No. 1707, September 1997. Ahmad, Syed, "On The Theory of Induced Invention," Economic Journal, LXXVI, (1966), 344-357. Aghion, Philippe, and Peter Howitt, "A Model of Growth through Creative Destruction," Econometrics, LX (1992), 323-351. Autor, David, Alan Krueger, and Lawrence Katz, "Computing Inequality: Have Computers Changed the Labor Market?" Quarterly Journal of Economics, CXIII (1998), 1169-1213. Barro, Robert, and Xavier Sala-i-Martin, Economic Growth (New York: McGraw Hill, 1995). Bartel, Ann, and Frank Lichtenberg, "The Comparative Advantage of Educated Workers in Implementing New Technologies," Review of Economics and Statistics, LXIX (1987), 1-1 1. Bartel, Ann, and Nachum Sicherman, "Technological Change and Wages: An Inter-Industry Analysis," NBER Working Paper No 5941, 1997. Baskir, Lawrence M., and William Strauss, Chance and Circumstances: the Draft, the War and the Vietnam Generation (New York: Alfred Knopf, 1978). Berman, Eli, John Bound, and Zvi Griliches, "Changes in the Demand for Skilled Labor within U.S. Manufacturing Industries: Evidence from the Annual Survey of Manufacturing," Quarterly Journal of Economics, CIX (1994), 367-398. Bernard, Andrew, and Bradford Jensen, "Understanding Rising and Falling Wage Inequality: Evidence from U.S. States," Yale University, mimeo, December 1997. Blanchard, Olivier, "Debt, Deficits and Finite Horizons," Journal of Political Economy, XCIII (1985), 223-247. Bound, John, and George Johnson, "Changes in the Structure of Wages in the 1980s: An Evaluation of Alternative Explanations," American Economic Review, LXXXII (1992), 371-391. Bureau of the Census, Statistical Abstract of the United States, 1971 (Washington, DC: 1971). -, Statistical Abstract of the United States, 1982-83 (Washington, DC: 1983). Caselli, Francesco, "Technological Revolutions," University of Chicago, mimeo, June 1997. David, Paul, Technical Choice, Innovation and Economic Growth: Essays on American and British Experience in the Nineteenth Century (London: Cambridge University Press, 1975).

INNOVATION & G R O W T H DiNardo, John, Nicole Fortin, and Thomas Lemieux, "Labor Market Institutions and the Distribution of Wages: 1973-1992," Econometrica, LXIV (1996), 10011044. Freeman, Richard, The Overeducated American (New York: Academic Press, 1976). ----, "Demand For Education," Chapter 6 in Orley Ashenfelter and Richard Layard, editors, Handbook of Labor Economics, Vol I (Amsterdam: North-Holland, 1986), pp. 357-386. Galor, Oded, and Daniel Tsiddon, "Technological Progress, Mobility and Economic Growth," American Economic Review, LXXXVII (1997), 363-382. Goldin, Claudia, and Lawrence Katz, "The Decline of Noncompeting Groups: Changes in the Premium to Education, 1890 to 1940," NBER Working Paper No. 5202, 1995. Goldin, Claudia, and Lawrence F. Katz, "The Origins of Technology-Skill Complementarity," Quarterly Journal of Economics, CXIII (1998), 693-732. Greenwood, Jeremy, and Mehmet Yorukoglu, "1974" Carnegie-Rochester Conference Series on Public Policy, XLVI (1997), 49-95. Griliches, Zvi, "Capital-Skill Complementarity," Review of Economics and Statistics, LI (1956), 465-468. Grossman, Gene, and Elhanan Helpman, "Quality Ladders in the Theory of Growth," Review of Economic Studies, LVIII (1991), 43-61. Habakkuk, H. J., American and British Technology in the Nineteenth Century: Search for Labor Saving Inventions, (Cambridge: Cambridge University Press, 1962). Hayami, Yujiro, and Vernon Ruttan, "Factor Prices and Technical Change in Agricultural Development: The U.S. and Japan, 1880-1960," Journal of Political Economy, LXXII (1970), 1115-1 141. John, Chinhoi, Kevin M. Murphy, Brook Pierce, "Wage Inequality and the Rise in Return to Skills," Journal of Political Economy, CI (1993), 410-442. Katz Lawrence, and Kevin Murphy, "Changes in Relative Wages: Supply and Demand Factors," Quarterly Journal of Economics, CVII (1992), 35-78. Kennedy, Charles, "Induced Bias in Innovation and the Theory of Distribution," Economic Journal, LXXIV (1964), 541-547. Kiley, Michael, "The Supply of Skilled Labor and Skill-Biased Technological Progress," Board of Governors of the Federal Reserve System, mimeo, March 1997. Krueger, Alan, "How Computers Have Changed the Wage Structure: Evidence from Microdata, 1984-1989," Quarterly Journal of Economics, CVIII (1993), 33-60. Krugman, Paul, "And Now for Something Completely Different: An Alternative Theory of Trade, Education and Wages," Massachusetts Institute of Technology mimeo, March 1997. Krusell, Per, Lee Ohanian, Victor Rios-Rull, and Giovanni Violante, "Capital Skill Complementary and Inequality," University of Rochester, mimeo, 1997. McPherson, Michael, and Morton Schapiro, Keeping College Affordable: Government and Educational Opportunity, (Washington, DC: Brookings Institution, 1991). Mokyr, Joel, The Levers of Riches: Technological Creativity and Economic Progress (New York: Oxford University Press, 1990). Nelson, Richard, and Edmund Phelps, "Investment in Humans, Technological Diffusion, and Economic Growth," American Economic Review Papers and Proceedings, LVI (1966), 69-75.

DIRECTED TECHNICAL CHANGE & W A G E INEQUALITY

Romer, Paul, "Endogenous Technological Change," Journal of Political Economy, XCVIII (1990), S71-S102. Samuelson, Paul, The Foundations of'Economic Analysis (Cambridge, MA: Harvard University Press, 1947). ---, "A Theory of Induced Innovations along Kennedy-Weisacker Lines," Review of Economics and Statistics, XLVII ( 1 965), 444-464. Schmookler, Jacob, Invention and Economic Growth (Cambridge, MA: Harvard University Press, 1966). Ventura, Jaume, "Growth and Interdependence," Quarterly Journal of Economics, CXII (1997), 57-84. Walde, Klaus, "Relative Quality of Education, Induced Technological Change and Wages," Universitat Dortmund Discussion Paper, February 1997. Williamson, Jeffrey, Coping with City Growth during the British Industrial Revolution (Cambridge: Cambridge University Press, 1990). Wood, Adrian, North-South Trade, Employment and Inequality: Changing Fortunes in a Skill Driven World (Oxford: Clarendon Press, 1994).

A NEW VIEW O F TECHNOLOGICAL CHANGE' Anthony B. Atkinson and Joseph E. Stiglitz Source: Economic Journal, 79:315 (1969), 573-78.

The recent literature on technological progress has almost entirely been based on the assumption that its effect can be represented as shifting the production function outwards-as illustrated in Fig. 1. Technical advance is assumed to raise output per head for all possible techniques. The advocates of this approach seem, however, to have forgotten the origins of the neoclassical production function: as the number of production processes increases (in an activity analysis model), the production possibilities can be more and more closely approximated by a smooth, differentiable curve. But the different points on the curve still represent different processes of production, and associated with each of these processes there will be certain technical knowledge specific to that technique. Indeed, both supporters and critics of the neoclassical theory seem to have missed one of the most important points of the activity analysis (Mrs. Robinson's blueprint) approach: that if one brings about a technological improvement in one of the blue-prints this may have little or no effect on the other blue-prints. If the effect of technological advance is to improve one technique of production but not other techniques

k

Output per man

Capital per man

Figure 1

A N E W VIEW OF TECHNOLOGICAL C H A N G E

t

Capital p e r man

Figure 2

of producing the same product, then the resulting change in the production function is represented by an outward movement at one point and not a general shift-see Fig. 2. This figure shows the extreme case where technical progress is completely "localised" to one technique: there are no spillover improvements in other techniques. It reality we should expect that a given technical advance would give rise to some spillovers and that several techniques would be affected. However, we would reach the traditional position only if there were spillovers to every technique. This means that a technical advance would have to be such as to raise productivity on, say, every type of textile loom from the fully automated to the crudest hand loom.2 In this note we shall examine some of the implications of the "localisation" of technical progress and contrast this view with the traditional assumption that technical progress leads to a general shift in the production function.

For the most part, increases in technical knowledge involve either experience in production ("learning by doing") or research activity. These factors have both received considerable attention in the literature, but where technical progress is localised there are several important implications which have not yet been brought out. We consider first the case of learning by doing. If the knowledge acquired through learning is localised, then the shift in the production function will be located at the point where the firm (or economy) is now operating. This in turn means that when a firm is deciding which technique to use it must take account of the effect of its current choice of technique on future production possibilities. Consider the case of a firm for which learning is effectively internalised and which is choosing between two techniques, one more capital-intensive than the other. If it adopts the more labour-intensive technique, then this means that the productivity of this technique will be increasing through learning, while that of the capital-intensive technique will be unchanged. It cannot, therefore, base its choice of technique solely on current factor prices, but must take account of the value of the increase in

INNOVATION & GROWTH

knowledge associated with each technique-in other words, it cannot behave completely myopically. The cost-minimising condition is

where C, is the marginal cost on the ith technique; pi is the value of the gain in knowledge from producing one more unit using the ith technique. If the firm places a sufficiently high value on increases in knowledge about the second technique, then it may use this, even though it has a higher cost at current factor prices. (Such an argument could be used to justify, for example, the adoption of atomic power plants: even though the cost per kilowatt hour is higher, the knowledge gained in their construction offsets the additional cost.) Suppose that the firm expects wages to rise and that at some point in time it will switch from the labour-intensive technique (1) to the more capital-intensive technique (2) (and will never switch back). When should it make the switch? At the point of switching, p, will be zeroknowledge about the first technique has no value, since it will never be used again. On the other hand, p, will in general be positive, so that the firm will switch when the marginal cost on the capital-intensive technique is higher than that on the labour-intensive technique. This would not, of course, happen where technical progress was not localised.' In the above discussion it was assumed that the benefits from learning by doing were internal to the firm. As Arrow has pointed out,4 where the benefits are external, there is a case for government intervention to raise investment or output to the socially optimal level. But where technical progress is localised, the Government should be concerned not merely with the level of investment or output, but must make sure that firms are directed towards the "right" technique on long-run considerations. This is particularly relevant to underdeveloped countries trying to encourage infant industries: where technical progress is localized, the Government should be concerned with subsidising infant techniques rather than infant industries. In this case a tariff may not merely be inefficient but may be totally ineffective: the Government will want, for example, to encourage an "intermediate7' manufacturing technique, but neither traditional nor highly automated methods of producing the same product. Turning to the case where technical progress is the result of research and innovational activity, there has been a considerable literature on the optimal amount to spend on adding to technical knowledge. But where technical progress is localised to one technique, there is a second important question that we must answer-which technique should we improve? Research activity can be directed towards the improvement of any process, but once it has been carried out, the resulting knowledge is specific to one particular process. In terms of the recent growth-theory literature, technical knowledge has the same characteristics as "putty-clay" capital. This means that

A NEW VIEW OF TECHNOLOGICAL CHANGE

when the firm is choosing which technique to develop it must take account of future as well as present factor prices. A firm will not necessarily allocate research expenditure to the technique in current use when it expects that rising wages will lead it to develop and use a more capital-intensive technique in the future. Again, the firm cannot behave myopically.

The concept of localised technical progress also throws light on the question as to whether underdeveloped countries should devote resources to developing new techniques of production. It is sometimes argued that the problem of the allocation of resources to research is not relevant for a present-day underdeveloped country, since it will benefit from technical progress in the advanced countries, and any independent research would simply be a duplication of effort. But if, as we have suggested, technical knowledge is highly specific to particular production processes this will not be the case. Where technical progress is "localised," technical progress in the advanced countries, whether from research or learning by doing, will leave relatively unaffected the less-capital-intensive techniques that the underdeveloped country would choose in the light of its factor endowment. Indeed, in some industries the effect of localisation has been so strong that the advanced techniques dominate the less capitalintensive ones, requiring both less labour and less capital.' Where technical progress is localised to one technique, and there are positive rates of labour and capital augmentation, it is clear how this can happen-see Fig. 3. It is also clear from Fig. 3 that localised technical progress is likely to lead to reductions in the short-run elasticity of substitution.

-

Labour

Figure 3

INNOVATION & GROWTH

The dominance of these advanced capital-intensive techniques has led to a widespread feeling that under developed countries should adopt these rather than more labour-intensive processes. But this takes no account of the possibility of undertaking research: even though techniques with a lower capital-labour ratio may at present be inefficient, it could pay to devote resources to improving them. This is relevant to the recent debate on "intermediate technology," in which it has been argued that underdeveloped countries should use techniques which require capital of the order of £100 per man rather than £1,000 per man. We are suggesting that even where these techniques do not exist, it may pay these countries to develop them. Whether or not it will in fact do so depends on the extent to which the technique is dominated by the advanced technique, on the resources required to improve it, on the time horizon of the planners and so on.

Our approach may be contrasted with some recent versions of the theory of induced innovation, in which there is an innovation possibility schedule: the firm is assumed to be faced with the choice between different degrees of factor-augmenting technical progress. In this case present decisions will affect future production possibilities, just as where technical progress is localised, but at least two unreasonable assumptions are employed: (a) In the Drandakis-Phelps6 and Samuelson7 models the choice of the kind of factor-augmenting technical progress is made on the basis of current factor prices only.* (b) More fundamentally, the firm's choice is restricted to purely factor-augmenting technical p r o g r e ~ s .Would ~ it really want to raise productivity on handcarts as well as forklift trucks?'' The view of technical progress presented in this note contrasts sharply with the dominant mathematical theories of growth, which are essentially ahistorical in character. Where technical progress is localised, history is very important. Suppose, for example, that an economy is in long-run equilibrium using a relatively labour-intensive technique when suddenly a plague wipes out a large proportion of the labour force, so that wages rise and a more capita-intensive technique is adopted. Technical progress is now localised to this technique, and it is possible that the economy will continue to use it rather than return to the more labour-intensive one. In this case the history of the economy is qualitatively and quantitatively different from what it would have been had there been no plague. For instance, the capital-output ratio in the new long-run equilibrium may be larger than in the old; if there is more "learning by doing" associated with more capitalintensive techniques the rate of technological change may be increased. But if history is important, so then is planning present activities with a view to their long-run consequences. In this note we have discussed some of the implications for the firm and for a planned developing country.

A N E W VIEW OF TECHNOLOGICAL CHANGE

Notes 1 The authors are very grateful to G. de Menil, P. A. Diamond, R. S. Eckaus, F. H. Hahn, M. Piore, M. Rothschild, K. Shell and J. H. Williamson for their helpful comments on an earlier draft. Stiglitz's research was supported in part by the United States-United Kingdom Educational Commission and the National Science Foundation. 2 Indeed, the usual assumption of Harrod neutrality assumes that the percentage reduction of labour requirements per unit of output be the same for all techniques. 3 Whether technical change is localised or not, if there is learning by doing, the firm will always produce at a level where marginal revenue is less than short-run marginal cost; equilibrium will require marginal revenue to equal shortrun marginal cost minus the present discounted value of the marginal reduction in future costs from the learning. 4 K. Arrow, "The Economic Implications of Learning by Doing," Review of Economic Studies, Vol. 29, June 1962, pp. 155-73. 5 For examples of dominance, see A. K. Sen, The Choice of Techniques (Oxford: Basil Blackwell, 1962), and R. S. Eckaus, "The Factor Proportions Problem in Underdeveloped Areas," American Economic Review, Supplement, Vol. L, May 1960, pp. 642-8. 6 E. M. Drandakis and E. S. Phelps, "A Model of Induced Invention, Growth, and Distribution," ECONOMIC JOURNAL, December 1966, pp. 823-40. 7 P. A. Samuelson, "A Theory of Induced Innovation on Kennedy-von Weizsacker Lines," Review of Economics and Statistics, 1965. 8 The early literature on induced innovation made much more sense from this point of view. See, e.g., W. Fellner," Two Propositions in the Theory of Induced Innovation," ECONOMIC JOURNAL, June 1961, pp. 305-8. W. Nordhaus, "The Optimal Rate and Direction of Technical Change," Essays on the Theory oj'Optima1 Economic Growth, K . Shell, ed. (Cambridge: M.I.T. Press, 1967), has made some progress in eliminating this unrealistic assumption. 9 If there is only one technique available at any point of time the whole question of localization is, of course, irrelevant. See G. Kennedy, "Induced Bias in Innovation and the Theory of Distribution," ECONOMIC JOURNAL, September 1964, pp. 541-7. 10 The recent article by Drandakis and Phelps (op. cit.) illustrates some of the other difficulties which this approach runs into. As they recognize, there is no reason to restrict the innovation possibility schedule to the positive orthant; if, however, there is negative augmentation of one factor the "new" isoquant will intersect the "old" one. They then worry whether the new isoquant is really the envelope of the two, or whether one must tell some story about forgetting techniques. The whole difficulty arises because they assume that technical progress applies to aN processes.

THE ORIGINS O F ENDOGENOUS GROWTH Paul M. Romer Source: Journal oJ'Economic Perspectives, 8:l (1994), 3-22.

The phrase "endogenous growth" embraces a diverse body of theoretical and empirical work that emerged in the 1980s. This work distinguishes itself from neoclassical growth by emphasizing that economic growth is an endogenous outcome of an economic system, not the result of forces that impinge from outside. For this reason, the theoretical work does not invoke exogenous technological change to explain why income per capita has increased by an order of magnitude since the industrial revolution. The empirical work does not settle for measuring a growth accounting residual that grows at different rates in different countries. It tries instead to uncover the private and public sector choices that cause the rate of growth of the residual to vary across countries. As in neoclassical growth theory, the focus in endogenous growth is on the behavior of the economy as a whole. As a result, this work is complementary to, but different from, the study of research and development or productivity at the level of the industry or firm. This paper recounts two versions that are told of the origins of work on endogenous growth. The first concerns what has been called the convergence controversy. The second concerns the struggle to construct a viable alternative to perfect competition in aggregate-level theory. These accounts are not surveys. They are descriptions of the scholarly equivalent to creation myths, simple stories that economists tell themselves and each other to give meaning and structure to their current research efforts. Understanding the differences between these two stories matters because they teach different lessons about the relative importance of theoretical work and empirical work in economic analysis and they suggest different directions for future work on growth.

THE ORIGINS OF ENDOGENOUS GROWTH

Version #I: The convergence controversy The question that has attracted the most attention in recent work on growth is whether per capita income in different countries is converging. A crucial stimulus to work on this question was the creation of new data sets with information on income per capita for many countries and long periods of time (Maddison, 1982; Heston and Summers, 1991). In his analysis of the Maddison data, William Baumol (1986) found that poorer countries like Japan and Italy substantially closed the per capita income gap with richer countries like the United States and Canada in the years from 1870 to 1979. Two objections to his analysis soon became apparent. First, in the Maddison data set, convergence takes place only in the years since World War 11. Between 1870 and 1950, income per capita tended to diverge (Abramovitz, 1986). Second, the Maddison data set included only those economies that had successfully industrialized by the end of the sample period. This induces a sample selection bias that apparently accounts for most of the evidence in favor of convergence (De Long, 1988). As a result, attention then shifted to the broad sample of countries in the Heston-Summers data set. As Figure 1 shows, convergence clearly fails in this broad sample of countries. Income per capita in 1960 is plotted on the horizontal axis. The average annual rate of growth of income per capita from 1960 to 1985 is plotted on the vertical axis.' On average, poor countries in this sample grow no faster than the rich countries. Figure 1 poses one of the central questions in development. Why is it that the poor countries as a group are not catching up with the rich countries in the same way that, for example, the low income states in the United States have been catching up with the high income states? Both Robert Lucas (1988) and I (Romer, 1986) cited the failure of cross-country convergence to motivate models of growth that drop the two central assumptions of the neoclassical model: that technological change is exogenous and that the same technological opportunities are available in all countries of the world. To see why Figure 1 poses a problem for the conventional analysis, consider a very simple version of the neoclassical model. Let output take the simple Cobb-Douglas form Y = A(~)K'-PLP.In this expression, Y denotes net national product, K denotes the stock of capital, L denotes the stock of labor, and A denotes the level of technology. The notation indicating that A is a function of time signals the standard assumption in neoclassical or exogenous growth models: the technology improves for reasons that are outside the model. Assume that a constant fraction of net output, s, is saved by consumers each year. Because the model assumes a closed economy, s is also the ratio of net investment to net national product. Because we are working with net (rather than gross) national product and investment, s Y is the rate of growth of the capital stock. Let y = YIL denote output per worker and let k = KIL denote capital per worker. Let n denote the rate of

INNOVATION & GROWTH

Unlled

states I

0.0

0.2 0.4 0.6 0.8 1.O 1.2 Income per capita relative to United States in 1960

Figure I Testing for convergence.

growth of the labor force. Finally, let a """ over a variable denote its exponential rate of growth. Then the behavior of the economy can be summarized by the following equation:

The first line in this equation follows by dividing total output by the stock of labor and then calculating rates of growth. This expression specifies the procedure from growth accounting for calculating the technology residual. Calculate the growth in output per worker, then subtract the rate of growth of the capital-labor ratio times the share of capital income in total income from the rate of growth of output per worker. The second line follows by substituting in an expression for the rate of growth of the stock of capital per worker, as a function of the savings rate s, the growth rate of the labor force n, the level of the technology A ( t ) , and the level of output per worker, y. Outside of the steady state, the second line of the equation shows how variation in the investment rate and in the level of output per worker should translate into variation in the rate of growth. The key parameter is the exponent p on labor in the Cobb-Douglas expression for output. Under the neoclassical assumption that the economy is characterized by perfect competition, p is equal to the share of total income that is paid as compensation to labor, a number that can be calculated directly from the national income accounts. In the sample as a whole, a reasonable benchmark for P


is 0.6. (In industrialized economies, it tends to be somewhat larger.) This means that in the second line of the equation, the exponent (-P)/(l - P) on the level of output per worker y should be on the order of about -1.5. We can now perform the following calculation. Pick a country like the Philippines that had output per worker in 1960 that was equal to about 10 percent of output per worker in the United States. Because 0.1-' is equal to about 30, the equation suggests that the United States would have required a savings rate that is about 30 times larger than the savings rate in the Philippines for these two countries to have grown at the same rate. If we use 213 instead of .6 as the estimate of P, the required savings rate in the United States would be 100 times larger than the savings rate in the Philippines. The evidence shows that these predicted saving rates for the United States are orders of magnitude too large. A key assumption in this calculation is that the level of the technology A ( t ) is the same in the Philippines and the United States. (The possibility that A(t) might differ is considered below.) If they have the same technology, the only way to explain why workers in the Philippines were only 10 percent as productive as workers in the United States is to assume that they work with about 0.1'/"-~'or between 0.3 percent and 0.1 percent as much capital per worker. Because the marginal product of capital depends on the capital stock raised to the power -P, the marginal product of an additional unit of capital is O.l-P/"-B'times larger in the Philippines than it is in the United States, so a correspondingly higher rate of investment is needed in the United States to get the same effect on output. Figure 2 plots the level of per capita income against the ratio of gross investment to gross domestic product for the Heston-Summers sample of countries. The correlation in this figure at least has the correct sign to explain why poor countries on average are not growing faster than the rich countries-that is, a higher level of income is associated with a higher investment rate. But if p is between 0.6 and 0.7, the variation in investment between rich and poor countries is at least an order of magnitude too small to explain why the rich and poor countries seem to grow at about the same rate. In concrete terms, the share of investment in the United States is not 30 or 100 times the share in the Philippines. At most, it is twice as large. Of course, the data in Figures 1 and 2 are not exactly what the theory calls for, but the differences are not likely to help resolve the problem here. For example, the display equation depends on the net investment rate instead of the gross investment rate. Because we do not have reliable data on depreciation for this sample of countries, it is not possible to construct a net investment ratio. A reasonable conjecture, however, is that depreciation accounts for a larger share of GDP in rich countries than it does in poor countries, so the difference between the net investment rate in rich and poor countries will be even smaller than the difference between the gross investment rates illustrated in the figure. The display equation also


0.0

0.2 0.4 0.6 0.8 1.O 1.2 Income per capita relative to United States in 1960

Figure 2 Per capita income and investment.

calls for output per worker rather than output per capita, but for a backof-the-envelope calculation, variation in income per capita should be close enough to variation in output per worker to show that a simple version of the neoclassical model will have trouble fitting the facts. The way to reconcile the data with the theory is to reduce P so that labor is relatively less important in production and diminishing returns to capital accumulation set in more slowly. The theoretical challenge in constructing a formal model with a smaller value for P lies in justifying why labor is paid more than its marginal product and capital is paid less. To explain these divergences between private and social returns, I proposed a model in which A was determined locally by knowledge spillovers (Romer, 1987a). I followed Arrow's (1962) treatment of knowledge spillovers from capital investment and assumed that each unit of capital investment not only increases the stock of physical capital but also increases the level of the technology for all firms in the economy through knowledge spillovers. I also assumed that an increase in the total supply of labor causes negative spillover effects because it reduces the incentives for firms to discover and implement labor-saving innovations that also have positive spillover effects on production throughout the economy. This leads to a functional relationship between the technology in a country and the other variables that can be written as A(K, L). Then output for firm j can be written as Y, = A(K, L)q-*L,*,where variables with subscripts are ones that firm j can control, and variables without subscripts represent economy-wide totals. Because the effect that a change in a firm's choice of K or L has on A is an external effect that any individual firm can ignore, the exponent a measures the private effect of an increase in employment on

THE ORIGINS OF ENDOGENOUS G R O W T H

output. A 1 percent increase in the labor used by a firm leads to an a percent increase in its output. As a result, a will be equal to the fraction of output that is paid as compensation to labor. Suppose, purely for simplicity, that the expression linking the stock of A to K and L takes the form A(K, L ) = KYL-Yfor some y greater than zero. Then the reduced form expression for aggregate output as a function of K and L would be Y = K ' - ~ L P where p is equal to a - y. This exponent P represents the aggregate effect of an increase in employment. It captures both the private effect a and the external effect -y. In the calculation leading up to the equation displayed above, it is this aggregate or social effect that matters. According to this model, P can now be smaller than labor's share in national income. Using a simple cross-country regression based on an equation like the display equation, I found that the effect of the investment rate on growth was positive and the effect of initial income on growth was negative. Many other investigators have found this kind of negative coefficient on initial income in a growth regression. This result has received special attention, particularly in light of the failure of overall convergence exhibited in Figure 1. It suggests that convergence or regression to the mean would have taken place if all other variables had been held constant. After imposing the constraint implied by the equation, I estimated the value of p to be in the vicinity of 0.25 (Romer, 1987a, Table 4). With this value, it would only take a doubling of the investment rate-rather than a 30- or 100-fold increase-to offset the negative effect that a ten-fold increase in the level of output per worker would have on the rate of growth. These figures are roughly consistent with the numbers for the United States and the Philippines. For the sample as a whole, the small negative effect on growth implied by higher levels of output per worker are offset by higher investment rates in richer countries. Robert Barro and Xavier Sala i Martin (1992) subsequently showed that the conclusions about the size of what I am calling P (they use different notation) were the same whether one looked across countries or between states in the United States. They find that a value for P on the order of 0.2 is required to reconcile the convergence dynamics of the states with the equation presented above. Convergence takes place, but at a very slow rate. They also observe that this slow rate of convergence would be even harder to explain if one introduced capital mobility into the model. As a possible explanation of the slow rate of convergence, Barro and Sala i Martin (1992) propose an alternative to the neoclassical model that is somewhat less radical than the spillover model that I proposed. As in the endogenous growth models, they suggest that the level of the technology A(t) can be different in different states or countries and try to model its dynamics. They take the initial distribution of differences in A(t) as given by history and suggest that knowledge about A diffuses slowly from high A to low A regions. This would mean that across the states, there is

INNOVATION & GROWTH

underlying variation in A ( t ) that causes variation in both k and y. As a result, differences in output per worker do not necessarily signal large differences in the marginal product of capital. In fact, free mobility of capital can be allowed in this model and the rate of return on capital can be equalized between the different regions. Because the flow of knowledge from the technology leader makes the technology grow faster in the follower country, income per capita will grow faster in the follower as diffusion closes what has been called a technology gap.2 The speed of convergence will be determined primarily by the rate of diffusion of knowledge, so the convergence dynamics tell us nothing about the exponents on capital and labor. The assumption that the level of technology can be different in different regions is particularly attractive in the context of an analysis of the state data, because it removes the prediction of the closed-economy, identicaltechnology neoclassical model that the marginal productivity of capital can be many times larger in poorer regions than in rich regions.' According to the data reported by Barro and Sala i Martin (1992), in 1880, income per capita in states such as North Carolina, South Carolina, Virginia, and Georgia was about one-third of income per capita in industrial states such as New York, Massachusetts, and Rhode Island. If P is equal to 0.6, - P) is equal to -1.5 and (113)-' is equal to about 5. This means that the marginal product of capital should have been about five times higher in the South than it was in New England. It is difficult to imagine barriers to flows of capital between the states that could have kept these differences from rapidly being arbitraged away. In particular, it would be difficult to understand why any capital investment at all took place in New England after 1880. But if there were important differences in the technology in use in the two regions, the South may not have offered higher returns to capital investment. In a third approach to the analysis of cross country data, Greg Mankiw, David Romer, and David Weil (1992) took the most conservative path, showing that it is possible to justify a low value for P even in a pure version of the closed economy, neoclassical model which assumes that the level of technology is the same in each country in the world. The only change they make is to extend the usual two-factor neoclassical model by allowing for human capital H as well as physical capital K. They use the fraction of the working age population that attends secondary school as a measure of the rate of investment in human capital that is analogous to the share of physical capital investment in total GDP. They conclude from their cross-country growth regressions that Y = A(t)K"3H'13L113 is a reasonable specification for aggregate output. In this model, the exponent P on the fixed factor of production L has been reduced from 0.6 to 0.33. This lower value of is consistent with the data on income shares because total wage payments consist of payments to both human capital and unskilled labor. If K and H vary together across countries, this


specification implies that it takes about a three-fold increase in investment (an increase by the factor 0.1-0.5to be precise) to offset a 10-fold increase in output per worker in a comparison across nations. Once one takes account of variation in investment in schooling as well as in investment in physical capital, a factor of three is roughly consistent with the variation in total investment rates observed in the Summer-Heston sample of countries. Although Mankiw, Romer and Weil do not examine the state data, it is clear what their style of explanation would suggest. They would assume that the same technology was available in the North and the South. Suppose that Northern states had levels of both human capital and physical capital that were higher than those in the Southern states in the same ratio. A value of p equal to 113, together with the fact that output per capita was about one-third as large in the South in 1880, would imply that rate of return on physical capital and the wage for human capital were both about (113)-O5 (or about 1.7) times higher in the Southern states than they were in the New England states. Compared to the factor of 5 implied by the model without human capital, these parameters would imply much smaller incentives to shift all capital investment to the South. (They would imply, however, that human capital would tend to migrate from the North to the South.) The implication from this work is that if you are committed to the neoclassical mode, the kind of data exhibited in Figures 1 and 2 cannot be used to make you recant. They do not compel you to give up the convenience of a model in which markets are perfect. They cannot force you to address the complicated issues that arise in the economic analysis of the production and diffusion of technology, knowledge, and information. An evahation of the convergence controversy

The version of the development of endogenous growth theory outlined above skips lots of detail and smooths over many complications that made this seem like a real controversy at the time. In retrospect, what is striking is how little disagreement there is about the basic facts. Everyone agrees that a conventional neoclassical model with an exponent of about one-third on capital and about two-thirds on labor cannot fit the cross-country or crossstate data. Everyone agrees that the marginal product of investment cannot be orders of magnitudes smaller in rich countries than in poor countries. The differences between the different researchers concern the inferences about models that we should draw from these facts. As is usually the case in macroeconomics, many different inferences are consistent with the same regression statistics. This history has many elements in common with other stories about the development of economics. The story starts with the emergence of new data. These present anomalies that lead to new theoretical models, some of which differ markedly from previous, well-accepted models. Then a more

INNOVATION & GROWTH

conservative interpretation emerges that accommodates the new evidence and preserves much of the structure of the old body of theory. In the end, we have refined the set of alternatives somewhat, but seem to be left in about the same position where we started, with too many theories that are consistent with the same small number of facts. But economists who accept this interpretation come to the conclusion that we do not have enough data only because they restrict attention to the kind of statistical evidence illustrated in Figures 1 and 2. They fail to take account of all the other kinds of evidence that are available. My original work on growth (Romer, 1983; 1986) was motivated primarily by the observation that in the broad sweep of history, classical economists like Malthus and Ricardo came to conclusions that were completely wrong about prospects for growth. Over time, growth rates have been increasing, not de~reasing.~ Lucas (1988) emphasized the fact that international patterns of migration and wage differentials are very difficult to reconcile with a neoclassical model. If the same technology were available in all countries, human capital would not move from places where it is scarce to places where it is abundant and the same worker would not earn a higher wage after moving from the Philippines to the United States. The main message of this paper is that the convergence controversy captures only part of what endogenous growth has been all about. It may encompass a large fraction of the recently published papers, but it nevertheless represents a digression from the main story behind endogenous growth theory. The story told about the convergence controversy also tends to reinforce a message that I think is seriously misleading-that data are the only scarce resource in economic analysis.

Version #2: The passing of perfect competition The second version of the origins of endogenous growth starts from the observation that we had enough evidence to reject all the available growth models throughout the 1950s, 1960s, and 1970s. What we lacked were good aggregate-level models. This version of the origins of endogenous growth is therefore concerned with the painfully slow progress we have made in constructing formal economic models at the aggregate level. It suggests that progress in economics does not come merely from the mechanical application of hypothesis tests to data sets. There is a creative act associated with the construction of new models that is also crucial to the process. The evidence about growth that economists have long taken for granted and that poses a challenge for growth theorists can be distilled to five basic facts. Fact # I : There are manyjirms in a market economy. The fact is so obvious that we often do not bother to state it, but it clearly will not do to have a


model in which there are overwhelming forces that tend to concentrate all output in the hands of a single, economy-wide monopolist. Fact #2: Discoveries differ from other inputs in the sense that many people can use them at the same time. The idea behind the transistor, the principles behind internal combustion, the organizational structure of a modern corporation, the concepts of double entry bookkeeping-all these pieces of information and many more like them have the property that it is technologically possible for everybody and every firm to make use of them at the same time. In the language of public finance, ordinary goods are rival goods, but information is nonrival. Fact #3: It is possible to replicate physical activities. Replication implies that the aggregate production function representing a competitive market should be characterized by homogeneity of degree one in all of its conventional (that is, rival) inputs. If we represent output in the form Y = AF(K, H, L), then doubling all three of K, H, and L should allow a doubling of output. There is no need to double the nonrival inputs represented by A because the existing pieces of information can be used in both instances of the productive activity at the same time. (The assumption that the market is competitive means that the existing activity already operates at the minimum efficient scale, so there are no economies of scale from building a single plant that is twice as large as the existing one.) If farming were the relevant activity instead of manufacturing, we would clearly need to include land as an input in production, and in the economy as a whole, it is not possible to double the stock of land. This does not change the fundamental implication of the replication argument. If aggregate output is homogeneous of degree 1 in the rival inputs and firms are price takers, Euler's theorem implies that the compensation paid to the rival inputs must exactly equal the value of output produced. This fact is part of what makes the neoclassical model so simple and makes growth accounting work. The only problem is that this leaves nothing to compensate any inputs that were used to produce the discoveries that lead to increases in A . Fact #4: Technological advance comes from things that people do. NO economist, so far as I know, has ever been willing to make a serious defense of the proposition that technological change is literally a function of elapsed calendar time. Being explicit about the issues here is important nevertheless, because it can help untangle a link that is sometimes made between exogeneity and randomness. If I am prospecting for gold or looking for a change in the DNA of a bacterium that will let it eat the oil from an oil spill, success for me will be dominated by chance. Discovery will seem to be an exogenous event in the sense that forces outside of my control seem to determine whether I succeed. But the aggregate rate of discovery is endogenous. When more people start prospecting for gold or experimenting with bacteria, more valuable discoveries will be found. This will be true even if discoveries are accidental side effects of some other activity (finding gold as a side effect of

INNOVATION & GROWTH

ditch-digging) or if market incentives play no role in encouraging the activity (as when discoveries about basic molecular biology were induced by government research grants). The aggregate rate of discovery is still determined by things that people do. Fact #5: Many individuals andJirms have market power and earn monopoly rents on discoveries. Even though the information from discoveries is nonrival (as noted in fact 2), economically important discoveries usually do not meet the other criterion for a public good; they typically are partially excludable, or excludable for at least some period of time. Because people and firms have some control over the information produced by most discoveries, it cannot be treated as a pure public good. This information is not like a short-wave radio broadcast that everyone can access without the permission of the sender. But if a firm can control access to a discovery, it can charge a price that is higher than zero. It therefore earns monopoly profits because information has no opportunity cost. The neoclassical model that was developed and applied by Robert Solow (1956, 1967) and others constituted a giant first step forward in the process of constructing a formal model of growth. The discussion of the convergence controversy, framed as it was almost entirely in terms of the neoclassical model, illustrates the model's power and durability. Like any model, the neoclassical model is a compromise between what we would like from a model and what is feasible given the state of our modeling skills. The neoclassical model captured facts 1, 2, and 3, but postponed consideration of facts 4 and 5. From a theoretical point of view, a key advantage of the model is its treatment of technology as a pure public good. This makes it possible to accommodate fact 2-that knowledge is a nonrival good-in a model that retains the simplicity of perfect competition. The public good assumption also implies that knowledge is nonexcludable, and this is clearly inconsistent with the evidence summarized in fact 5-that individuals and firms earn profits from their discoveries. This assumption was useful, nevertheless, as part of an interim modeling strategy that was adopted until models with nonrivalry and excludability could be formulated. Endogenous growth models try to take the next step and accommodate fact 4. Work in this direction started in the 1960s. For example, Karl Shell (1966) made the point about replication noted above, showing that it left no resources to pay for increases in A . He proposed a model in which A is financed from tax revenue collected by the government. Recent endogenous growth models have tended to follow Arrow (1962) and emphasize the private sector activities that contribute to technological advance rather than public sector funding for research. A subset of these models has tried to incorporate both fact 4 (that technological advance comes from things people do) and fact 5 (the existence of monopoly rents). These are sometimes referred to as neo-Schumpeterian models because of Schumpeter's

T H E O R I G I N S OF E N D O G E N O U S G R O W T H

emphasis of the importance of temporary monopoly power as a motivating force in the innovative p r o c e ~ s .In~ addition, there are two other distinct kinds of endogenous growth models. Spillover models have already been mentioned. Linear models will be described below.6 With the benefit of hindsight, it is obvious that growth theorists would eventually have to do what economists working at the industry and firm level have done: abandon the assumption of price-taking competition. Otherwise, there is no hope of capturing fact 5. Even at the time, the point received at least some attention. In his 1956 paper, Solow remarked in a footnote on the desirability of extending the model to allow for monopolistic competition. One of his students, William Nordhaus (1969), subsequently outlined a growth model that did have patents, monopoly power, and many firms. For technical reasons, this model still invoked exogenous technological change, so it is not strictly speaking a model of endogenous growthbut it could have been extended to become one. Because a general formal treatment of monopolistic competition was not available at the time, little progress in this direction took place for the next 20 years. Even though it is obvious in retrospect that endogenous growth theory would have to introduce imperfect competition, this was not the direction that the first models of the 1980s pursued. Both my model (1986) and Robert Lucas's model (1988) included fact 4 without taking the final step and including step 5. In both of these models, the technology is endogenously provided as a side effect of private investment decisions. From the point of view of the users of technology, it is still treated as a pure public good, just as it is in the neoclassical model. As a result, firms can be treated as price takers and an equilibrium with many firms can exist. This technique for introducing a form of aggregate increasing returns into a model with many firms was first proposed by Alfred Marshall (1890). To overturn the pessimistic predictions of Malthus and Ricardo, he wanted to introduce some form of aggregate increasing returns. To derive his downward sloping supply curve from an industry with many firms, Marshall introduced the new notion of increasing returns that were external to any individual firm. External effects therefore entered into economics to preserve the analytical machinery of supply and demand curves and price taking in the presence of increasing returns. The analysis of other kinds of external effects-smoke, bees, and so on--came later.' As noted in the previous discussion of spillover models, Arrow (1962) constructed a model along these lines. In a simplified form, output for firm j in his model can be written as Y, = A(K)F(K,, L,), where as before, K without a subscript denotes the aggregate stock of capital. For technical reasons, Arrow, like Nordhaus, did not emphasize the fact that his model could lead to sustained, endogenous growth. For the parameter values that he studies, if the size of the population is held constant, growth eventually comes to a halt.

INNOVATION & GROWTH

Lucas's model has a very similar underlying structure. There, it is investments in human capital rather than physical capital that have spillover effects that increase the level of the technology. It is as if output for firm j takes the form Y, = A(H)F(K,, H,). Both of these models accommodated facts 1-4 but not fact 5.8 In my first paper on growth (Romer, 1986), I assumed in effect that aggregate output could be written as Y = A(R)F(R,, K,, L,) where R, stands for the stock of results from expenditure on research and development by firm j.9 I assumed that it is spillovers from private research efforts that lead to improvements in the public stock of knowledge A. This seemed appealing because it recognized that firms did research and development on purpose and that the relevant spillovers or incomplete property rights were associated with the results from research and development. (In the microeconomic analysis of research and development at the industry level, Zvi Griliches (1979) used this same kind of formulation.) But to make this model fit within the framework of price-taking with no monopoly power, I assumed that the function F was homogeneous of degree one in all of its inputs, including R. This, unfortunately, violates fact 2, that research is a nonrival good and fact 3, that only rival goods need to be replicated to double output. If I had admitted that R, was nonrival, the replication argument would have implied that the firm faced increasing returns in the inputs R,, K,, and L, that it controlled, because output would double merely by replicating K, and Li. My sleight of hand in treating R, as a rival good and making F homogeneous of degree 1 in all three of K, L , and R may seem like a trifling matter in an area of theory that depends on so many other short cuts. After all, if one is going to do violence to the complexity of economic activity by assuming that there is an aggregate production function, how much more harm can it do to be sloppy about the difference between rival and nonrival goods? Unfortunately, quite a bit. The distinctions between rival and nonrival inputs, and the distinction between excludable and nonexcludable goods, are of absolutely fundamental importance in modeling and in policy formulation. For years, the economic analysis of science and technology policy consisted of little more than a syllogism. The major premise was that the government should provide public goods and the private sector should provide private goods. The minor premise was that basic research is a public good and applied research is a private good. Once you think carefully about nonrivalry and excludability, it is clear that the major premise is misleading because it understates the possible role for collective action. Governments can usefully provide goods that are nonrival but are not true public goods, because they are potentially excludable. The minor premise is simply wrong. Applied research is not an ordinary private good. Discussion in policy circles is now taking place using new terms--critical technologies, generic


research, and pre-competitive research-that are only vaguely defined but that take the discussion outside of the simple dichotomy between public goods and private goods. This is probably useful, but it would lend needed structure to this discussion if participants paid more attention to the distinction between the two different aspects of publicness (nonrivalry and nonexcludability) and looked more formally at the different kinds of policy challenges that nonrivalry and nonexcludability present. The linear model branch of endogenous growth theory pursued even more aggressively the strategy I used.1° If 1 could treat the part of knowledge that firms control as an ordinary input in production-that is, as an input that is rival and hence is not associated with increasing returns-why bother to allow for any nonrival inputs at all? In effect, these models assumed that output could be written as Y = F(R, K, H) for a homogeneous of degree 1 production function F. These models assumed that research R, physical capital K, and human capital H were like ordinary inputs. If there are no nonrival goods, there are no increasing returns. It is then a relatively simple matter to build a perfectly competitive model of growth. To simplify still further, these models often aggregate R, K, and H into a single broad measure of capital. Suppose we call it X. Then we can write F ( X ) as a linear function: Y = F ( X ) = ax, hence the name linear models. If we assume that a constant fraction of output Y is saved and used to produce more X, the model generates persistent, endogenous growth. Relative to the neoclassical model, these models capture fact 4--that technological change comes from investments that people make-at the cost of abandoning fact 2, that technology or knowledge is a nonrival good. Proponents of the linear model and the neoclassical model have sometimes been drawn into pointless arguments about which model is worse. Proponents of the linear growth models point out that the neoclassical model fails to capture fact 4. Proponents of the neoclassical model observe that the linear model cannot capture fact 2. This dispute is partly an outgrowth of the convergence controversy. Both sides specify that output takes the form Y = K ' - ~ and L ~ then argue about whether P is bigger than zero (as the proponents of the neoclassical model claim) or close to zero (as some versions of the linear growth model suggest). This is not a very useful debate. There are circumstances in which each model can be a useful expositional device for highlighting different aspects of the growth process, but presumably the agenda for the profession ought to be to capture both facts 2 and 4 and pick up fact 5 to boot. Neo-Schumpeterian growth Two steps were required for the neo-Schumpeterian models of growth to emerge. The first was that after struggling for years to preserve perfect competition, or at least price-taking in the presence of external effects, growth


theorists had to decide to let go. It helped that economists working on industrial organization had given them something else to hang onto. By the late 1970s, there were aggregate models with many firms (fact l), each of which could have market power (fact 5). The most convenient such model was developed by Avinash Dixit and Joseph Stiglitz (1977). William Ethier (1982) subsequently showed how their model of preferences over many goods could be interpreted as a production function that depended on a large number of inputs in production. Once people who were interested in growth recognized that this approach offered the alternative to a competitive market structure, there was only one technical detail that remained to be resolved, the detail that had kept both Nordhaus and Arrow from producing models of endogenous growth. All models of growth need at least one equation which describes the evolution of something like A(t)." This equation usually takes the form

where A with a dot denotes the time derivative of A . Models that produce steady state growth fill in the blank with a constant and set the exponent $ equal to 1. For example, if we set 41 equal to 1 and insert a constant g in the blank, we have the driving equation behind the neoclassical model with exogenous technological change. Mathematically, this kind of formulation is not robust. If $ turns out to be even slightly greater than 1, the equation implies that the stock of technology will go to infinity in finite time. When we use this same kind of model to study population growth, this lack of robustness does not raise any particular difficulties. We understand that functional forms are always approximations, and that a linear differential equation leading to exponential growth is a particularly convenient approximation. But Nordhaus and Arrow both worked at a time when there was real concern about the knife-edge character of the assumptions about $ . I 2 If it was less than one, growth eventually stopped. If it was even slightly greater than one, everything blows up. As a result, economists stayed well away from the edge and assumed that @ had to be strictly less than 1. In a model like Nordhaus's, growth can be kept going only by adding a second kind of knowledge A, that grows exogenously. (Formally, bringing in exogenous technological change amounts to bringing in a new equation in which the exponent corresponding to has already been set to 1, and it only takes one equation with this property to keep things going.) I devoted a great deal of attention to this robustness problem in my analysis of the spillover models. I modified other functional forms elsewhere in the model to construct robust models of endogenous growth in which the level of output and its rate of growth stayed finite for all time for a range of values of 41 that were strictly bigger than 1 (Romer, 1983;

THE ORIGINS O F ENDOGENOUS G R O W T H

1986). For values slightly less than 1, growth eventually stopped but could persist, nevertheless, for a very long time. The mathematical analysis in this more complicated robust model was much harder than the analysis that is possible when @ is equal to 1. The difference between the two models is the difference between studying the phase plane of a nonlinear differential equation system and solving a simple linear differential equation. Once it is clear that we could build a complicated model that is robust, there is every reason to work with the simple special case whenever possible. By the late 1980s, economists like Kenneth Judd (1985) and Gene Grossman and Elhanan Helpman (1989) were working out models of growth with monopolistic competition. Like Nordhaus and Arrow, they stayed well away from the case where @ was equal to 1. Judd invoked exogenous technological change to keep his economy growing. Grossman and Helpman were investigating the connection between trade and growth, and settled for an analysis of transitional dynamics of the model as it converged to a steady state level of income where growth stopped. In each model, monopoly profits motivate discovery. I took what I had learned about generating sustained growth from my analysis of spillover models and applied it to the monopolistic competition model. I constructed two very simple models of sustained growth that accommodated all five of the facts cited above. One of these did not invoke any spillover effects at all (Romer, 1987b). The other combined both monopoly power and spillovers-that is, incomplete intellectual property rights (Romer, 1990). In each of these models I set the analog of @ equal to 1. I knew that by repeating my analysis of the spillover model, it would be possible to construct more complicated robust models with the same qualitative implications. Research on endogenous growth models in which monopoly profits motivate innovation has progressed rapidly since then and has uncovered a number of unexpected connections between market size, international trade, and growth, as the article by Grossman and Helpman in this symposium explains.

Conclusions The economics profession is undergoing a substantial change in how we think about international trade, development, economic growth and economic geography." In each of these areas, we have gone through a progression that starts with models based on perfect competition, moves to price-taking with external increasing returns, and finishes with explicit models of imperfect competition. It is likely that this pattern will repeat itself in other areas like the theory of macroeconomic fluctuations. The effects of this general trend may be far-reaching. Ultimately, it may force economists to reconsider some of the most basic propositions in

INNOVATION & GROWTH

economics. For example, I am convinced that both markets and free trade are good, but the traditional answer that we give to students to explain why they are good, the one based on perfect competition and Pareto optimality, is becoming untenable. Something more interesting and more complicated is going on here.14 In each of the areas where our understanding has changed, evidence that challenged the models of perfect competition and supported the models with imperfect competition had been apparent all along. Everyone knew that there was lots of intra-industry trade between developed nations and little trade between the North and the South. Everyone knew that some developing countries grew spectacularly while others languished. Everyone knew that people do the things that lead to technological change. Everyone knew that the number of locally available goods was limited by the extent of the market in the city where someone lives and works. In evaluating different models of growth, I have found that Lucas's (1988) observation, that people with human capital migrate from places where it is scarce to place where it is abundant, is as powerful a piece of evidence as all the cross-country growth regressions combined. But this kind of fact, like the fact about intra-industry trade or the fact that people make discoveries, does not come with an attached t-statistic. As a result, these kinds of facts tend to be neglected in discussions that focus too narrowly on testing and rejecting models. Economists often complain that we d o not have enough data to differentiate between the available theories, but what constitutes relevant data is itself endogenous. If we set our standards for what constitutes relevant evidence too high and pose our tests too narrowly, we will indeed end up with too little data. We can thereby enshrine the economic orthodoxy and make it invulnerable to challenge.15 If we do not have any models that can fit the data, the temptation will be to set very high standards for admissible evidence, because we would prefer not to reject the only models that we have. When I look back on my work on growth, my greatest satisfaction comes from having rejected the first round of external effects models that I tried. I am glad that I was able to learn something about robustness and nonrivalry from struggling with these models, but was still able to let go when a better alternative became apparent. My greatest regret is the shift I made while working on these external effects models, a shift that took me away from the emphasis on research and knowledge that characterized my 1986 paper and toward the emphasis on physical capital that characterized the empirical work in the paper cited in the discussion of convergence (1987a). This paper contributed to the convergence controversy and to an emphasis on the exponents on capital and labor in aggregate production. I am now critical of this work, and I accept part of the blame. Looking back, I suspect that I made this shift toward capital and away from knowledge partly in an

THE ORIGINS OF ENDOGENOUS G R O W T H

attempt to conform to the norms of what constituted convincing empirical work in macroeconomics. No international agency publishes data series on the local production of knowledge and inward flows of knowledge. If you want to run regressions, investment in physical capital is a variable that you can use, so use it I did. I wish I had stuck to my guns about the importance of evidence like that contained in facts 1 through 5. If macroeconomists look only at the cross-country regressions deployed in the convergence controversy, it will be easy to be satisfied with neoclassical models in which market incentives and government policies have no effect on discovery, diffusion, and technological advance. But if we make use of all of the available evidence, economists can move beyond these models and begin once again to make progress toward a complete understanding of the determinants of long-run economic success. Ultimately, this will put us in position to offer policy-makers something more insightful than the standard neoclassical prescription-more saving and more schooling. We will be able to rejoin the ongoing policy debates about tax subsidies for private research, antitrust exemptions for research joint ventures, the activities of multinational firms, the effects of government procurement, the feedback between trade policy and innovation, the scope of protection for intellectual property rights, the links between private firms and universities, the mechanisms for selecting the research areas that receive public support, and the costs and benefits of an explicit government-led technology policy. We will be able to address the most important policy questions about growth: In a developing country like the Philippines, what are the best institutional arrangements for gaining access to the knowledge that already exists in the rest of the world? In a country like the United States, what are the best institutional arrangements for encouraging the production and use of new knowledge?

Acknowledgements I have beneJitted from comments by Jeffrey Frankel, Alan Krueger, David Romer, Carl Shapiro, and Timothy Taylor on early drafts of this paper. This work was supported by N S F Grant #SES 9023469 and by the Canadian Institute for Advanced Research.

Notes 1 The data here are taken from version IV of the Penn World Table. The income measure is RGDP2. See Summers and Heston (1988) for details. 2 Nelson and Phelps (1966) give a theoretical model that allows for diffusion of the

technology between countries. Fagerberg (1987) interprets cross-country growth regressions in the context of a technology gap model instead of a neoclassical model or a spillover model. For further discussion of diffusion, see also Barro and Sala i Martin (forthcoming 1994) and Jovanovic and Lach (1993).

INNOVATION & GROWTH 3 See King and Rebelo (1993) for a fuller discussion of both the price and quantity implications of the neoclassical model. 4 See Kremer (1993) for a stimulating look at this question from a very long-run point of view. 5 Of course, Stigler's law applies in this case: The person that any result is named after was not the first person to derive or state the result. It just helps to have a label so that you can keep track of the players without a scorecard.6 Richard Nelson and Sidney Winter (1982) developed an alternative evolutionary model of growth. Their verbal, descriptive style of theory, which they label appreciative theory, was flexible enough to accommodate facts 1-5. This style of work can be thought of as a complement to formal theory, not a substitute for it. It leaves open the problem of constructing a formal theory that could accommodate these facts. 7 For an explicit treatment showing that Marshallian external increasing returns is ultimately an untenable way to model any process involving learning or knowledge, see Dasgupta and Stiglitz (1988). 8 Lucas actually makes A depend on per capita H rather than total H. The difference between these two formulations is not relevant for the discussion here, but is important for some of the other implications of the model. 9 For consistency with the rest of the discussion, I distinguish here between R and K. In the paper, I actually dropped physical capital from consideration so that I have only one state variable to deal with. This leads to a potential confusion because I also used the symbol K for knowledge instead of R. 10 One of the early linear models was Uzawa (1965). Important recent papers in this line of work include Becker, Murphy, and Tamura (1990), Jones and Manuelli (1990), and Rebelo (1991). 11 Sometimes other variables like H or K are used in place of A , but the basic issues are the same. 12 See Stiglitz (1990) for a discussion of how people working on growth at the time perceived this problem. 13 Paul Krugman has made influential contributions in all of these areas. See Krugman (1990, 1991, 1993) for a discussion of the changes in these fields. 14 Romer (forthcoming) offers a demonstration that, for example, the costs of trade restrictions in a developing country can be far greater in the context of a model with imperfect competition than they are in a model with perfect competition. 15 In their discussion of real business cycle theories and the kind of evidence used to test them, Greg Mankiw (1989) and Robert Solow (1988) have both made a similar point about explicit statistical versus broader kinds of evidence.

References Abramovitz, Moses, "Catching Up, Forging Ahead, and Falling Behind," Journal of Economic History, June 1986, 46:2, 385-406. Arrow, Kenneth J., "The Economic Implications of Learning by Doing," Review of Economic Studies, June 1962, 29, 155-73. Barro, Robert J., and Xavier Sala i Martin, "Convergence," Journal of Political Economy, April 1992, 100:2, 223-51. Barro, Robert J., and Xavier Sala i Martin, "Chapter 8: Diffusion of Technology." In Barro, R. J., and X. Sala-i-Martin, eds., Economic Growth. New York: McGraw Hill, forthcoming 1994.

THE O R I G I N S OF ENDOGENOUS G R O W T H Baumol, William J., "Productivity Growth, Convergence, and Welfare: What the Long-run Data Show," American Economtc Review, December 1986, 76:5, 107285. Becket, G., K Murphy, and R. Tamura, "Economic Growth, Human Capital, and Population Growth," Journal of Political Economy, October 1990, 98:s Part 2, S12-S137. Dasgupta, P., and J. Stiglitz, "Learning-by-Doing, Market Structure, and Industrial and Trade Policies," Oxford Economic Papers, June 1988, 40:2, 246-68. De Long, J. Bradford, "Productivity Growth, Convergence and Welfare: Comment,"

American Economic Review, December 1988, 7 8 5 , 1138-54. Dixit, A., and J. Stiglitz, "Monopolistic Competition and Optimum Product Diversity," American Economic Review, June 1977, 67:3, 297-308. Ethier, W. J., "National and International Returns to Scale in the Modern Theory of International Trade," American Economic Review, June 1982, 72:3, 389-405. Fagerberg, Jan, "A Technology Gap Approach to Why Growth Rates Differ," Research Policy, 1987, 16, 87-99. Griliches, Zvi, "Issues in Assessing the Contribution of Research and Development to Productivity Growth," Bell Journal of Economics, Spring 1979, 10, 92116. Grossman, Gene, and Elhanan Helpman, "Product Development and International Trade," Journal of Political Economy, December 1989, 97:6, 1261-83. Heston, Alan, and Robert Summers, "The Penn World Trade (Mark 5): An Expanded Set of International Comparisons, 1950-1988," Quarterly Journal of Economics, May 1991, 106, 327-68. Jones, Lawrence, and Rodolfo Manuelli, "A Convex Model of Equilibrium Growth: Theory and Policy Implications," Journal of Political Economy, October 1990, 98:5 Part 1, 1008-38. Jovanovic, Boyan, and Saul Lach, "Diffusion Lags and Aggregate Fluctuations," mimeo, New York University, August 1993. Judd, K. L., "On the Performance of Patents," Econometrics, May 1985, 53:3, 567-85. King, Robert G., and Sergio Rebelo, "Transitional Dynamics and Economic Growth in the Neoclassical Model," American Economic Review, September 1993, 83:4, 908-31. Kremer, Michael, "Population Growth and Technological Change: One Million B. C. to 1990," Quarterly Journal of Economics, August 1993, 108:3, 681-716. Krugman, Paul, Rethinking International Trade. Cambridge: MIT Press, 1990. Krugman, Paul, Geography and Trade. Cambridge: MIT Press, 1991. Krugman, Paul, "Towards a Counter-Counter Revolution in Development Theory." Proceedings of the Annual World Bank Conference on Development 1992, Supplement, Washington, D.C., World Bank Economic Review, 1993, 15-38. Lucas, Robert E., Jr., "On the Mechanics of Economic Development," Journal of Monetary Economics, July 1988, 22: 1, 3-42. Maddison, A., Phases of Capitalist Development. Oxford: Oxford University Press, 1982. Mankiw, N. Gregory, "Real Business Cycles: A New Keynesian Perspective," Journal of Economic Perspectives, Summer 1989, 3:3, 79-90.

INNOVATION & G R O W T H Mankiw, N. Gregory, David Romer, and David N. Weil, "A Contribution to the Empirics of Economic Growth," Quarterly Journal of Economics, May 1992, 107, 407-37. Marshall, Alfred, Principles of Economics. London: Macmillan, 1890. Nelson, Richard R., and Edmund S. Phelps, "Investment in Humans, Technological Diffusion, and Economic Growth," American Economic Review, May 1966, 56, 69-75. Nelson, Richard R., and Sidney G. Winter, An Evolutionary Theory of Economic Change. Cambridge: The Belnap Press of Harvard University Press, 1982. Nordhaus, William D., "An Economic Theory of Technological Change," American Economic Review, May 1969, 59:2, 18-28. Rebelo, Sergio, "Long Run Policy Analysis and Long Run Growth." Journal of Political Economy, June 1991, 99:3, 500-21. Romer, Paul M., "Dynamic Competitive Equilibria with Externalities, Increasing Returns and Unbounded Growth," Ph.D. dissertation, University of Chicago, 1983. Romer, Paul M., "Increasing Returns and Long-Run Growth," Journal of Political Economy, October 1986, 945, 1002-37. Romer, Paul M., "Crazy Explanations for the Productivity Slowdown," In Fischer, S., ed., NBER Macroeconomics Annual. Cambridge: MIT Press, 1987a, 163-202. Romer, Paul M., "Growth Based on Increasing Returns Due to Specialization," American Economic Review, May 1987b, 77:2, 56-62. Romer, Paul M., "Endogenous Technological Change," Journal of Political Economy, 1990, 98, S71-102. Romer, Paul M., "Two Strategies for Economic Development: Using Ideas and Producing Ideas," Proceedings of the Annual World Bank Conference on Development 1992, Supplement, Washington, D.C., World Bank Economic Review, 1993. Romer, Paul M., "New Goods, Old Theory and the Welfare Costs of Trade Restrictions," Journal of' Development Economics, forthcoming February 1994, 43: 1. Shell, Karl, "Toward a Theory of Inventive Activity and Capital Accumulation," American Economic Review, May 1966, 56, 62-68. Solow, Robert, "A Contribution to the Theory of Economic Growth," Quarterly Journal of Economics, February 1956, 70, 65-94. Solow, Robert, "Technical Change and the Aggregate Production Function," Review of Economics and Statistics, August 1957, 39, 3 12-20. Solow, Robert, "Growth Theory and After," American Economic Review, June 1988, 78:3, 307-17. Stiglitz, Joseph, "Comments: Some Retrospective Views on Growth Theory." In Diamond, Peter, ed., Growth, Productivity, and Unemployment. Cambridge: MIT Press, 1990, 50-68. Summers, Robert, and Alan Heston, "A New Set of International Comparisons of Real Product and Price Levels Estimates for 130 Countries, 1950-1985," Review of Income and Wealth, March 1988, 34:1, 1-25. Uzawa, Hirofumi, "Optimum Technical Change in an Aggregative Model of Economic Growth," International Economic Review, January 1965, 6, 18-31.

A M O D E L O F GROWTH THROUGH CREATIVE DESTRUCTION Philippe Aghion and Peter Howitt' Source: Econornetricu, 60:2 (1992), 323-51

A model of endogenous growth is developed in which vertical innovations, generated by a competitive research sector, constitute the underlying source of growth. Equilibrium is determined by a forward-looking difference equation, according to which the amount of research in any period depends upon the expected amount of research next period. One source of this intertemporal relationship is creative destruction. That is, the prospect of more future research discourages current research by threatening to destroy the rents created by current research. The paper analyzes the positive and normative properties of stationary equilibria, in which research employment is constant and GNP follows a random walk with drift, although under some circumstances cyclical equilibria also exist. Both the average growth rate and the variance of the growth rate are increasing functions of the size of innovations, the size of the skilled labor force, and the productivity of research as measured by a parameter indicating the effect of research on the Poisson arrival rate of innovations; and decreasing functions of the rate of time preference of the representative individual. Under laissez faire the economy's growth rate may be more or less than optimal because, in addition to the appropriability and intertemporal spillover effects of other endogenous growth models, which tend to make growth slower than optimal, the model also has effects that work in the opposite direction. In particular, the fact that private research firms do not internalize the destruction of rents generated by their innovations introduces a business-stealing effect similar to that found in the partialequilibrium patent race literature. When we endogenize the size of innovations we find that business stealing also makes innovations too small.

INNOVATION & GROWTH

1. Introduction The main contribution of the literature on endogenous growth pioneered by Romer (1986) and Lucas (1988) has been to endogenize the underlying source of sustained growth in per-capita income, namely the accumulation of knowledge. There are many channels through which societies accumulate knowledge, including formal education, on-the-job training, basic scientific research, learning by doing, process innovations, and product innovations. This paper examines a channel that has received little attention in the endogenous growth literature, namely that of industrial innovations which improve the quality of products. This channel introduces into endogenous growth theory the factor of obsolescence; better products render previous ones obsolete. Obsolescence exemplifies an important general characteristic of the growth process, namely that progress creates losses as well as gains. It also embodies Schumpeter's idea of creative destruction (1942, p. 83, his emphasis): The fundamental impulse that sets and keeps the capitalist engine in motion comes from the new consumers' goods, the new methods of production or transportation, the new markets, . . . . [This process] incessantly revolutionizes the economic structure from within, incessantly destroying the old one, incessantly creating a new one. This process of Creative Destruction is the essential fact about capitalism. The present paper constructs a simple model of growth through creative destruction, by modelling the innovation process as in the patent-race literature surveyed by Tirole (1988, Ch. 10) and Reinganum (1989). The expected growth rate of the economy depends upon the economy-wide amount of research. The paper shows that equilibrium in such an economy is determined by a forward-looking difference equation, according to which the amount of research in any period depends upon the expected amount of research next period, similar to the difference equation that defines equilibrium in the two-period overlapping-generations model of money (Azariadis (1981), Grandmont (1985)). More specifically, the model assumes, following Schumpeter, that individual innovations are sufficiently important to affect the entire economy. A period is the time between two successive innovations. The length of each period is random, because of the stochastic nature of the innovation process, but the relationship between the amount of research in two successive periods can be modelled as deterministic. The amount of research this period depends negatively upon the expected amount next period, through two effects.

A MODEL O F G R O W T H T H R O U G H CREATIVE D E S T R U C T I O N

The first effect is that of creative destruction. The payoff from research this period is the prospect of monopoly rents next period. Those rents will last only until the next innovation occurs, at which time the knowledge underlying the rents will be rendered obsolete. Thus the expected present value of the rents depends negatively upon the Poisson arrival rate of the next innovation. The expectation of more research next period will increase that arrival rate, and hence will discourage research this period. The second effect is a general equilibrium effect working through the wage of skilled labor, which can be used either in research or in manufacturing. In order to be consistent with the conditions for labor-market equilibrium, the expectation of more research next period must correspond to an expectation of higher demand for skilled labor in research next period, which implies the expectation of a higher real wage of skilled labor. Higher wages next period will reduce the monopoly rents that can be gained by exclusive knowledge of how to produce the best products. Thus the expectation of more research next period will discourage research this period by reducing the flow of rents expected to accrue to a successful innovator. This functional relationship between research in two successive periods has a unique fixed point, which defines a stationary equilibrium. The stationary equilibrium exhibits balanced growth, in the sense that the allocation of skilled labor between research and manufacturing remains unchanged with each innovation; the log of GNP follows a random walk with drift. This is not always, however, the only equilibrium in the model. As in the overlapping-generations literature the functional relationship can also be satisfied by cyclical trajectories. One noteworthy implication of the negative dependency of current research upon future research is the possible existence of what we call a "no-growth trap," a cyclical equilibrium in which the level of research oscillates deterministically between two levels each period, and in which the lower of these two levels is zero. An economy in such an equilibrium would stop growing in finite time, because with no research there would be no innovation, and hence the period with no research would never come to an end. The (rational) expectation that the next innovation would be followed by a very high level of research would discourage anyone from undertaking that innovation. Another implication is that the average growth rate of the economy is not necessarily increased by an increase in the productivity of research. In particular, a parameter change that makes research more productive in some states of the world can discourage research in other states, by increasing the threat of obsolescence faced by the product of research in those other states, to such an extent that the average growth rate is reduced. From a normative point of view, the average growth rate in stationary equilibrium may be more or less than socially optimal because of the presence of conflicting distortionary effects. Specifically, although the model

INNOVATION & GROWTH

includes the appropriability and intertemporal spillover effects which generate a less than optimal growth rate in Romer's (1990) model, it also has effects that work in the opposite direction. In particular, there is a "business-stealing" effect of the sort familiar from the patent-race literature (Tirole (1988, p. 399)). That is, researchers do not internalize the destruction of existing rents created by their innovations. When the size of innovations is taken as given, the business stealing effect can lead to too much growth. In addition, we find that when the size of innovations is endogenized, the business stealing effect tends to make innovations too small. Other papers in the endogenous growth literature that model vertical product innovations include Segerstrom, Anant, and Dinopoulos (1990), who assume that the time between successive innovations is deterministic. They have a richer intersectoral structure than the present paper, and address a different set of questions. Stokey (1988) models vertical product innovations and obsolescence in a perfectly competitive model where innovations are the unintentional by-product of learning by doing. The cost-reducing innovations of Shleifer (1986) can also be interpreted as vertical product innovations. His model does not endogenize growth, however, except in a limited dichotomous sense; that is, the long-run average growth rate is fixed by the exogenously specified rate of invention, except in the singular case where no inventions are ever implemented and the economy stops growing. Corriveau (1988) has a discrete-time analysis of endogenous growth based on cost-reducing innovations as in Shleifer, in which the possibility of simultaneous discoveries creates a different kind of "business-stealing" effect. In his model the payoff to current research is independent of future research because rents to innovations are assumed to accrue only in the same period as the research from which they resulted. Grossman and Helpman (1991) construct a model of vertical product innovation that explicitly integrates the analysis of Segerstrom, Anant, and Dinopoulos (1990) with that of the present paper. Judd (1985) and Romer (1990) model growth based on horizontal product innovations, using the Dixit-Stiglitz (1977) model of product variety. These models involve no obsolescence; new products are no better than existing ones. They also involve no uncertainty. King and Rebelo (1988) introduce uncertainty into an endogenous growth model by assuming a random rate of return to the accumulation of human capital under conditions of perfect competition. Within the patent-race literature the paper closest to the present is that of Reinganum (1985), which also emphasizes the affinity to creative destruction. The present paper adds to Reinganum's model the general equilibrium effects of future research on the rents created by current research, and of the level of manufacturing employment on the cost of research. The paper also

A MODEL OF G R O W T H T H R O U G H CREATIVE DESTRUCTION

generalizes the Reinganum model by allowing the stream of innovations to continue forever, and by explicitly analyzing the effect of the future level of research on the prospective reward to current r e ~ e a r c h . ~ Section 2 below presents the basic model of the paper. This basic model assumes for simplicity that each innovation creates an economy-wide monopoly in the production of intermediate goods. Section 3 derives the functional relationship between research in two successive periods that defines equilibrium. It then analyzes the determinants of the average growth rate and the variability of the growth rate in stationary equilibrium. One of those determinants is the degree of market power possessed by an intermediate-good monopolist, which is parameterized in the model. Section 4 characterizes the welfare properties of stationary equilibria in the basic model, under the assumption of a fixed size of innovations. Section 5 introduces the possibility of nondrastic innovations. Section 6 generalizes the model by allowing research firms to choose the size of innovations as well as their arrival rate. Section 7 deals with a strategic monopsony effect that has been ignored until this point in the argument, by which an intermediate firm can extend the expected lifetime of its monopoly by hiring more than the short-run profit-maximizing amount of skilled labor, at the cost of a higher real wage. Section 8 relaxes the assumption of a single economywide monopoly in the production of intermediate goods. Section 9 contains brief concluding remarks.

2. The basic model 2.A. Assumptions

There are three classes of tradeable objects: labor, a consumption good, and an intermediate good. There is a continuum of infinitely-lived individuals, with identical intertemporally additive preferences defined over lifetime consumption, and the constant rate of time preference r > 0. The marginal utility of consumption is assumed constant; thus r is also the rate of interest. There is no disutility from supplying labor. There are three categories of labor: unskilled labor, which can be used only in producing the consumption good; skilled labor, which can be used either in research or in the intermediate sector; and specialized labor, which can be used only in research. Each individual is endowed with a one-unit flow of labor. Let M, N, and R denote respectively the mass of unskilled, skilled, and specialized individuals. The consumption good is produced using the fixed quantity M of unskilled labor, and the intermediate good, subject to constant returns. Since M is fixed, the production function can be written as

INNOVATION & GROWTH

where F' > 0, F" < 0, y is the flow output of consumption good, x the flow of intermediate input, and A a parameter indicating the productivity of the intermediate input. The intermediate good is produced using skilled labor alone, according to the linear technology

where L is the flow of skilled labor used in the intermediate sector. Research produces a random sequence of innovations. The Poisson arrival rate of innovations in the economy at any instant is h$(n, R), where n is the flow of skilled labor used in research, h a constant parameter, and $ a constant-returns, concave production function. Both h and $ are given by the technology of research. There is no memory in this technology, since the arrival rate depends only upon the current flow of input to research, not upon past research. Assume that skilled labor is an essential factor in research: $(O, R) = 0. Then an economy that allocates no skilled labor to research will not grow, because it will experience no innovations. (The "linear" case where $(n, R) = n, that is, where R = 0, will be used frequently.) Time is continuous, and indexed by z 2 0. The subscript t = 0, 1 . . . denotes the interval starting with the tth innovation (or with z = 0 in the case of t = 0) and ending just before the z + 1st. The length of each interval is random. All prices and quantities are assumed to remain constant within each interval. If n, is applied to research in interval t, the length of the interval will be exponentially distributed with parameter h$(n,, R). Each innovation consists of the invention of a new intermediate good, whose use as input allows more efficient methods to be used in producing the consumption good. Real-world examples include such "input" innovations3 as the steam engine, the airplane, and the computer, whose use made possible new methods of production in mining, transportation, and banking, with economy-wide effects. An innovation need not, however, be as revolutionary as these examples, but might consist instead of a new generation of intermediate good, similar to the old one. Specifically, use of the new intermediate good increases the productivity parameter A in (2.1) by the factor y > 1. There are no lags in the diffusion of te~hnology.~ The most modern intermediate good is always produced, so that:

where A, is the initial value given by history. (Of course, it is always possible to produce the consumption good using an old technology, with a correspondingly old intermediate good.)


A successful innovator obtains a patent which it can use to monopolize the intermediate sector. (Section 8 relaxes this assumption by allowing for a finite number of monopolistic competitors.) The patent is assumed to last forever. However, the monopoly lasts only until the next innovation, at which time the intermediate good is replaced by the next vintage. All markets are perfectly competitive except that for intermediate goods.

2.B. The intermediate monopolist's decision problem For ease of presentation the analysis starts by assuming that innovations are always drastic; that the intermediate monopolist is unconstrained by potential competition from the previous patent. This assumption will be relaxed in Section 5 below. The intermediate monopolist's objective is to maximize the expected present value of profits over the current interval. When the interval ends so do the profits. The only uncertainty concerns the length of the interval. Except in Section 7 below, the monopolist is assumed to take as given the amount of research at each time, and hence also takes as given the length of the interval. Let x, be the flow of the intermediate good produced by the monopolist during interval t. By (2.2), x, also equals employment of skilled labor in manufacturing. The inverse demand curve facing a monopolist charging the price p, (relative to the numeraire consumption good) is the marginal product

Thus the monopolist chooses x, to maximize [A,F'(x,) - w,]x,, taking as given A, and the wage w, of skilled labor. Define the "productivity-adjusted wage" as w, = w,lA,, and the "marginalrevenue function" as 8 ( x ) = F'(x) + xFM(x).Assume that marginal revenue is downward-sloping and satisfies Inada-type conditions. 1: 3 ( x ) < 0for all s > 0,lim,,, ASSUMPTION

8 ( x )=

00,

lirn,,,

G ( x ) = 0.

Then for any positive w, the monopolist's choice of output x, is given by the first-order condition

where f is the function 8 - ' . The flow of monopoly profits is

INNOVATION & GROWTH

where E(o) = - ( l ( c ~ ) ) ~ F " ( T ( o Note ) ) . that T and E are each strictly positivevalued and strictly decreasing for all positive or. An example satisfying Assumption 1 is the Cobb-Douglas example, in which the consumption-good technology is F(x) = x a , 0 < a < 1, which yields

2. C. Research

There are no contemporaneous spillovers in research; that is, a firm employing the amounts z, s of the two factors in research will experience innovations with a Poisson arrival rate of h@(z,s), independently of the inputs of other firms. The objective of a firm in choosing z and s at each date is to maximize the flow of expected profits from research:

where F+,, is the value of the t + 1st innovation, and w: is the wage rate of specialized labor. Because @ has constant returns, and because the total flow of specialized labor must equal R in equilibrium, it follows from the Kuhn-Tucker conditions for maximizing (2.9) that (2.10)

w, 2 cpf(n,)hK+,, n, 2 0 , with at least one equality,

where cp(n,) = $(n,, R ) , and n, is the economy-wide flow of skilled labor used in research during interval t. Note that (2.1 1)

cp(0) = 0 , and

cp'(n) > 0 , cpl'(n) 5 0

for all n 2 0.

As we shall see, all research is conducted by outside research firms rather than by the incumbent monopolist. Because of constant returns to scale the number of research firms is indeterminate. The value Vf+, to an outside research firm is the expected present value of the flow of monopoly profits nt+lgenerated by the t + 1st innovation over an interval whose length is exponentially distributed with parameter hcp(n,+,):


The reason why the monopolist chooses to do no research is that the value to the monopolist of making the next innovation would be I/,+,which is strictly less than the value I/,+, to an outside firm. This is an example of the Arrow effect, or replacement effect (see Tirole (1988, p. 392)). The efficiency effect, or rent-dissipation effect, according to which an outside firm might receive a smaller payoff from an innovation than would the present incumbent, because of having to compete with the present incumbent, is absent in the case of drastic innovations because the flow of profit x,,, in (2.12) is independent of whether the firm earning those profits has access to the previous ~ a t e n t . ~ There is an important intertemporal spillover in this model. An innovation raises productivity forever. It allows each subsequent innovation to raise A, by the same multiple y, and with the same probability hq(n,), but from a starting value that is higher by the multiple y than it would otherwise have been. The producer of an innovation captures (some of) the rents from that productivity gain, but only during one interval. After that the rents are captured by other innovators, building upon the basis of the present innovation, but without compensating the present i n n ~ v a t o rThis .~ intertemporal spillover plays a role in the welfare analysis of Section 4 below. The model also embodies Schumpeter's idea of "creative destruction." Each innovation is an act of creation aimed at capturing monopoly rents. But it also destroys the monopoly rents that motivated the previous creation. Creative destruction accounts for the term hq(n,+,) in the denominator of I/,+, in (2.12). More research reduces the expected tenure of the current monopolist, and hence reduces the expected present value of its flow of rents.

v,

2 . 0 . Capital markets The structure of capital markets can be specified in many different ways. One is to suppose that there is a frictionless Walrasian credit market in which future expected consumption can be discounted at the constant rate r. Another is to suppose that there is no credit market. According to the latter specification all nonresearch workers consume their wage income at each instant, the owners of the monopoly intermediate firm consume their flow of profits at each instant, and research workers receive no pay unless their firms innovate, at which time they are paid in shares of the next intermediate firm. According to either specification, all research firms could be assumed to be owned by their workers, and (2.9) would represent the expected flow of surplus to be divided among them. The crucial assumption that utility is linear in consumption makes these different specifications all equivalent, by removing any motive to use capital markets for risk-sharing.

INNOVATION & GROWTH

3. Perfect foresight dynamics and balanced growth 3. A. Equilibvium At any point in time there is only one decision for society to make; namely, how to allocate the fixed flow N of skilled labor between manufacturing and research. Combining (2.5),(2.7), (2.10), (2.12) and the equilibrium condition N = nr + x, yields

(3.1)

wv

- nr) > Y ~ ( W N - nt+,)), n, 2 0 , with at least one equality. Wnr) r + Wnr+J

Condition (3.1) determines research employment at t as a function of research employment at t + 1:

where y ~ :[0, N) + R+is a strictly decreasing function wherever it is positivevalued. The functional relationship y~ between research employment in two successive periods is illustrated in Figure 1, where c(nr) is the "marginal marginalcost,beneAt

Figure I The effect of future research on current research: n , = ~ ( n , and ) n, = ~ ( n , ) The . pair (0, n" constitutes a no-growth trap.

A MODEL O F G R O W T H T H R O U G H CREATIVE D E S T R U C T I O N

cost of research" and b(n,+,)the "marginal benefit of research," defined by

By (2.11) and Assumption 1, c is strictly increasing, b is strictly decreasing, and c(n,) + 00 as n, + N. It follows that in the case illustrated in Figure 1, where c(0) < b(O), ~ ( n , , , )is well defined on [0, N ) , and is positive and decreasing if and only if7 n,, < A. In the case where c(0) 5 b(0), ~ ( n , , , )is identically zero. In economic terms, there are two reasons for the negative dependency of current research on future research, corresponding to the two places in which n,,, enters the expression for the marginal benefit of research, b(n,+,).That is, a foreseen increase in research next period discourages research this period (a) by raising future wages and hence reducing the flow of profits R ( 6 ( N - n,,,)) to be captured from the next innovation, and (b) by raising the rate of creative destruction hq(n,+,)next period and hence shortening the expected lifetime of the monopoly to be enjoyed by the next innovator. A perfect foresight equilibrium (PFE) is defined as a sequence {n,}$ satisfying (3.2) for all t 2 0. In Figure 1 the sequence {no, n,, n,, . . . } constructed from the counterclockwise spiral starting at no constitutes a PFE. A stationary equilibrium corresponds to a PFE with n,, constant. It is defined as the solution to ri = tq(A). There exists a unique stationary equilibrium. As Figure 1 shows, if c(0) < b(0) then ri is positive, and is defined by

Q(N - A ) - yR(Q(N - A ) )

h'(4

-

r

+ hq(ri)

In this case growth is positive because innovations arrive at the Poisson rate hq(ri) > 0. If c(0) 2 b(0) then A = 0 and there is no growth, because the Poisson arrival rate of innovations is hq(0) = 0. Henceforth, assume that c(0) < b(0) and ri > 0. Other equilibria may also exist. A two-cycle is a pair (no,n l ) such that no = ~ ( n land ) n1 = W(n0).It defines a PFE of period two. If both no and n' are positive, the PFE is a "real" two-cycle. If either no or n1 is zero, it is a "no-growth trap." In a real two-cycle, the prospect of high research in odd intervals discourages research in even intervals, and the prospect of low research in even intervals stimulates research in odd intervals.' A no-growth

INNOVATION & GROWTH

trap is the extreme case in which the prospect of high research in odd intervals shuts down research completely in even intervals. Although the no-growth trap defines an infinite sequence {n,),", the oscillation will cease after one innovation. From then on no growth will occur because no innovations will occur. It is clear from Figure 1 that a no-growth trap exists ie(o)= 0 and r is small enough. A real two-cycle will exist if a if lim,,, no-growth trap exists and9 cr(A) + bf(A) > 0. Consider the Cobb-Douglas example: F(x) = xa, with a linear research technology cp(n) n. From (2.8), the equation (3.3) defining a positive A is

-

and the condition for A to be positive is

Since 5(w) = 0, a no-growth trap exists when r is small. Sinceiobf(A)lc'(ri) -+ 0 uniformly in r as a -+ 0, a real two-cycle exists when a and r are small enough. 3.B. Research in stationary equilibrium

The rest of the paper focuses on stationary equilibria. Comparative-statics analysis of (3.3) shows the following proposition. PROPOSITION 1: The amount of research employment ft in a stationary equilibrium increases with: (a) a decrease in the rate of interest r; ( b ) an increase in the size y of each innovation; (c) an increase in the total endowment N of skilled labor; or ( d ) an increase in the arrival parameter h. This proposition is intuitive: (a) A decrease in the rate of interest increases the marginal benefit to research, by raising the present value of monopoly profits. (b) An increase in the size of each innovation also increases the marginal benefit to research, by raising the size of next interval's monopoly profits relative to this interval's productivity. (c) An increase in the endowment of skilled labor both increases the marginal benefit and reduces the marginal cost of research, by reducing the wage of skilled labor. (d) An increase in the arrival parameter decreases both the marginal cost and the marginal benefit of research, because on the one


hand it results in more "effective" units of research for any given level of employment, but on the other hand it also increases the rate of creative destruction during the next interval. The former effect dominates. The above discussion of result (d) suggests an interesting implication of creative destruction that could arise if the arrival parameter h were permitted to vary from one interval to the next. Suppose, for example, that with each successful innovation a new value of h was drawn from the finite set {h,, . . . , A,) according to a fixed transition matrix B. Transition into a high-h state could represent a fundamental breakthrough leading to a Schumpeterian wave of innovations, whereas transition to a low-h state could represent the exhaustion of a line of research. Then a stationary equilibrium would involve not one level of research employment but one for each state. Now consider the effects of a ceteris paribus increase in 1,. This parameter change might raise research employment in state 2, but it would tend to reduce research employment in other states, by increasing the rationally expected rate of creative destruction during the next interval. Furthermore, even though the parameter change represents an unambiguous improvement in the productivity of the research technology, it might reduce the average level of research employment in stationary equilibrium. Indeed, Appendix 1 works out a numerical example in which, in the limit, as h, becomes infinite, average research employment falls to zero. The linear Cobb-Douglas example of (3.4) and (3.5) above yields an additional comparative-statics result by parameterizing the degree of market power enjoyed by an intermediate monopolist. Specifically, l - a is the Lerner (1934) measure of monopoly power (price minus marginal cost divided by price), (1 - a)-' is the elasticity of demand faced by an intermediate monopolist, and 1 - a is the fraction of equilibrium revenue in the intermediate sector accruing to the monopolist, n,/(n, + w,x,). Thus, by all measures, the degree of market power is measured inversely by the parameter a . According to (3.4), an increase in the degree of market power (decrease in a ) increases the stationary-equilibrium amount of research A whenever fi is positive. According to (3.9, given fixed values of the parameters y, h, r, and N, the stationary-equilibrium amount of research will be positive if and only if there is at least some minimal degree of market power; that is, if and only if a is less than the critical value

If the degree of market power falls short of this minimal value, then the flow of monopoly profits from the next innovation would not be enough to induce positive research aimed at capturing those rents even if they could be retained forever, with no creative destruction in the next interval.

INNOVATION & GROWTH

3.C. Balanced growth Real output (i.e. the flow of consumption goods) in the economy during interval t is (3.6)

y, = A,F(N

-

I?),

which implies

Thus the time path of the log of real output In y(z) will be a random step-function starting at In yo = In F(N - A) + In A,, with the size of each step equal to the constant In y > 0, and with the time between each step {A,, A,, . . . } a sequence of iid variables exponentially distributed with parameter hq(fi). This statement and (3.3) fully specify the stochastic process driving output, in terms of the parameters of the model. Not surprisingly, this stochastic process is nonstationary. Suppose observations were made at discrete points in time 1 unit apart. Then from (3.7),

where E(T) is ln y times the number of innovations between z and z From the above analysis

+

1.

is a sequence of iid variables distributed Poisson with parameter hq(fi). Thus (3.8) can be written as

where e(r) = E(T)- hq(I?) In y. Note that e(z) is iid., with (3.10)

E(e(z)) = 0, var e(z) = hq(I?)(ln y)'.

From (3.9) and (3.10), the discrete sequence of observations on the log of output follows a random walk with constant positive drift. It also follows that the economy's average growth rate (AGR) and the variance of the economy's growth rate (VCR) are given by (3.11)

AGR = hq(I?) In y,

VCR = hq(fi)(ln y)2.

A MODEL O F G R O W T H T H R O U G H CREATIVE DESTRUCTION

Combining (3.1 1) with Proposition 1 allows one to sign the impact of parameter changes on the average growth rate. Increases in the arrival parameter, the size of innovations, the size of skilled labor endowment, and (in the Cobb-Douglas example) the degree of market power all raise AGR. Increases in the rate of interest lower it. The parameter changes have the same qualitative effect on VGR as on AGR. The effects are intuitive and straightforward. The effect of market power, combined with the finding that a minimal degree of market power is needed before growth is even possible, underlines the importance of imperfect competition for the growth process. The example of Appendix 1 shows, however, that in a more general setting where the arrival parameter h can vary from state to state, it is not always true that an unambiguous improvement in the productivity of the research technology will increase the economy's average growth rate. Instead, an increase in the arrival parameter in one state can discourage research in other states by increasing the rationally expected rate of creative destruction to such an extent that the economy's average growth rate falls.

4. Welfare properties of the stationary equilibrium This section compares the laissez-faire average growth rate derived above with the AGR that would be chosen by a social planner whose objective was to maximize the expected present value of consumption y(z). Since every innovation raises y(z) by the same factor y, the optimal policy consists of a fixed level of research. Expected welfare is

where n ( t , z) equals the probability that there will be exactly t innovations up to time z. Given that the innovation process is Poisson with parameter hq(n),we have

From (4.1) and (4.2),

Equation (4.3) identifies U as the initial flow of output AOF(x)discounted at the rate r - hv(n)(y - 1). This "social discount rate" is less than the rate of interest r because the stream of output will be growing over time. More specifically, the social discount rate is the rate at which each risk-neutral


individual in the economy would capitalize a stream that was perpetually subject to increases by the factor ( y - 1 ) with a Poisson arrival rate of hq(n), and constant otherwise. The socially optimal level of research n* maximizes U. The first-order condition for an interior maximum is (4.4)

F'(N - n*) ( y - l)F(N - n*) r - hq(n*)(y - 1) ' hq'(n*)

(If no solution exists to (4.4) then n* = 0.) This level of research would produce an average growth rate of hq(n*)lnl. Accordingly laissez-faire produces an average growth rate more (less) than optimal if ri > ( n*.

5. Nondrastic innovations Until this point the analysis has assumed that innovations are drastic; that the intermediate monopolist is not constrained by potential competition from owners of previous patents. The present section shows that the analysis of stationary equilibria can be generalized to the case where innovations are nondrastic. Innovations are nondrastic if and only if the previous incumbent could make a positive profit when the current one was charging the price p, = A,F'(T(o,)) which yields an unconstrained maximum to the current incumbent's profit. If innovations are nondrastic, the current incumbent sets the maximum price that gives the previous incumbent nonpositive profits, and satisfies all the demand at that price, leaving none to the previous incumbent. The previous incumbent could make a positive profit if and only if a competitive producer of consumption goods could produce at an average cost of less than unity by combining unskilled labor with the previous incumbent's good, buying the latter at a price equal to its average cost of production w,; that is, if and only if the condition:

INNOVATION & GROWTH

were to hold with strict inequality, where w;M is the equilibrium wage of unskilled labor and C is the unit-cost function associated with the production function F. In equilibrium all the unskilled labor is combined with the current incumbent's intermediate good. Thus the unskilled wage must satisfy the competitive equilibrium condition:

It follows that innovations are nondrastic if and only if (5.1) holds with strict inequality when w? satisfies (5.2) together with p, = A,F'(,Y(w,)). It also follows that if innovations are nondrastic then p, and w r satisfy (5.2) and (5.1) with equality. In the Cobb-Douglas example, where the unconstrained optimal price for the current incumbent is w,la,innovations are nondrastic if and only if

in which case"

The rest of the analysis of this section will focus on stationary equilibria with positive growth in the linear Cobb-Douglas example. The analysis assumes that the monopolist chooses to do no research, as in the case of drastic innovations. This implicitly places a lower bound on the size of innovations, because it requires the efficiency effect to be smaller than the replacement effect. Appendix 2 shows that the condition

is sufficient for the monopolist to do no research. Note that this condition is satisfied when y is close to the value aaat which innovations become drastic. If there is positive research during interval t , then, as before,

In a stationary equilibrium with positive growth, (5.4) and (5.6) imply

A MODEL O F G R O W T H T H R O U G H CREATIVE DESTRUCTION

Equation (5.7) defines the stationary equilibrium level of research fi. It is the same as the equation (3.4) that applies in the drastic case, except that the markup y"* in (5.7) replaces the markup ad in (3.4). The comparativestatics results of Proposition 1 apply to the solution of (5.7). In addition, the stationary equilibrium level of research defined by (5.7) is increased by an increase in market power (a decrease in a ) as in the drastic case. Thus in the linear Cobb-Douglas example all the comparative statics results derived for the case of drastic innovations are valid also when innovations are nondrastic. Comparison of (5.7) and (4.5) shows that the same welfare effects analyzed in Section 4 operate in the case where innovations are nondrastic, again with the result that research and growth under laissez-faire may be more or less than optimal.I6 As is customary in the patent-race literature this analysis has ruled out the possibility that the current and previous incumbent might contract to share the higher monopoly profits that could be earned if the previous incumbent agreed never to compete. For example, the previous incumbent might sell its patent to the current one; in the extreme case where the previous incumbent always had no bargaining power in negotiation with the current one, competition from previous vintages of the intermediate good would never constrain the monopolist, and the above analysis of drastic innovations would apply no matter how small the innovations were.

6. Endogenous size of innovations This section generalizes the analysis of stationary equilibria by allowing research firms to choose not only the frequency but also the size of innovations. It shows that under laissez-faire, innovations will be too small if they are drastic. In the nondrastic case, the tendency to make innovations too small is at least partly mitigated by the incentive for innovators to move away from their competitive fringe, which they can do by increasing the size of innovations. Assume that the arrival rate of innovations to a firm employing the factor combination (z, s) and aiming for innovations of size y is h@(z, s)v(y), where vf(y) < 0; the bigger the innovation, the harder it is to discover. Assume v"(y) < 0; the marginal cost (in terms of lower arrival rate) of aiming for larger innovations increases with the size of innovations. Then the product yv(y) is a concave function of y. The analysis focuses again on stationary equilibria with positive growth. Consider first the case of drastic innovations. By the same logic as before, the payoff to the t + 1st innovator is

INNOVATION & GROWTH

where is the stationary-equilibrium value of y. If the t + 1st innovation has size y, not necessarily equal to y, then A,+, = yA, and V,+,= yV,. Therefore the expected flow of profits to the research firm in interval t is

v

The firm takes as given. Thus its profit-maximizing choice of y also maximizes the product v(y)y. Because this product is a concave function of y, therefore y is defined by the condition"

The first-order condition for profit maximization with respect to skilled labor, together with (6.1) produces an expression analogous to (3.3):

The comparative statics analysis of Section 3 carries through unchanged, since 9 is determined by (6.3) independently of all parameters that do not enter the function v, with the obvious exception that it is no longer permissible to investigate the effects of a change in y. As in Section 4, the expected present value of consumption equals

where the denominator is the social discount rate. Therefore, independently of the choice of n, the social planner will choose y so as to maximize the expression v(y)(y - 1). The socially optimal value y* is then defined by

By concavity of yv(y),18 7 < y*. Innovations are too small under laissezfaire. This result is another manifestation of the business-stealing effect. The social planner chooses y so as to maximize the arrival rate multiplied by the net size ( y - 1) of innovations, whereas the private research firm, which does not internalize the loss of the existing vintage of intermediate good, maximizes the arrival rate times the gross size y. The socially optimal level of research employment n* satisfies the condition

(6.7)

F f ( N - n*) - v(y*)(y* - 1)F(N - n*) r - hq(n*)v(y*)(y*- 1) ' hqf(n*)


Comparison between (6.4) and (6.7) reveals the same welfare effects as in the analysis of Section 4. In addition, the fact that 9 < y* in itself makes A < n*. This is because, as we have seen, v(T)(f- 1) < v(y*)(y* - I). So if the other four effects were absent, and both ri and n* were determined by (6.7), the effect on research employment would be the same as if the laissez-faire economy had a smaller arrival parameter h, which would reduce A below n*. The economy's average growth rate hq(A)v(p) In 7 is affected by the fact that innovations are too small under laissez-faire, although the direction of the overall effect is ambiguous. The direct effect on In 7 is to decrease AGR. The direct effect on the arrival rate hq(A)v(y) is to increase AGR. The indirect effect on the arrival rate working through ~ ( 6 is) to decrease AGR. In the nondrastic case, the above business-stealing effect whereby innovations are too small under laissez-faire is mitigated by an additional effect, namely that private innovators tend to increase the size of innovations in order to increase their profit margins. This margin is independent of the size y in the drastic case but it increases with y in the nondrastic case. (In the Cobb Douglas example the profit margin is a-I - 1 if the innovation is drastic and y'la - 1 if nondrastic.) The following example shows, however, that this additional "profit-margin" effect does not necessarily overturn our earlier result to the effect that innovations are too small.

EXAMPLE: Let q(n) = n, F(x) = xi/'. From (5.3) innovations are nondrastic if y < f i .From (5.4), the payoff to the ( t + 1)st innovator in a stationary equilibrium is

where x(&, y) = (2@2)-2. In (629, g is the size of innovation to be chosen by the innovator during interval t , whereas 7 and 8 denote stationaryequilibrium values which the innovator takes as given. As in the drastic case, w,, = yw,. Therefore 7 must solve the equation

7 = argmax iv,

v(y)(y* - W ( 4 Y)YW, r + hv( j)(N - x(Q, y))

Since axlay < 0, we have f < argmax v(y)(y2- l)x(h, y)y = 9. From the above analysis we know that argmax v(y)(y - 1) = y*.

INNOVATION & GROWTH

Therefore a sufficient condition for < y* is that (y2- l)x(Q, y)y = (y - l)g(y) with gf(y) < 0. The latter is true,19 with g(y) Y) (y + l)y/4h2y4.

7. Strategic monopsony effect In this section the intermediate firm is assumed to take into account its influence on the amount of current research and thereby on the probability of its replacement. In particular, by increasing its demand x, for skilled labor, the monopolist can raise the wage rate that must also be paid to skilled workers in research. The effect is to reduce the equilibrium amount of research n, and consequently to delay the arrival of the ( t + 1)st innovation. The monopolist will trade this gain off against the higher wages it must pay its own skilled labor. The analysis focuses on stationary equilibria with positive growth. The monopolist during interval t chooses x, to maximize the expected present value of profits:

subject to

where (*) follows from (2.10). The magnitudes x,, n,, V,IA,, and w,lA, are constant, at the equilibrium values 2, n, V , and 8. Therefore 2 solves

V

= max T

[F'(x) - hycpf(N - x) V ] x r + hq(N - x)

The first-order condition is

From the constraint (*),

From (7.2), (7.3), and the definition of 6,


It follows that the stationary-equilibrium level of research n is given by the analogue to (3.3):

where the function

it,

is defined as

Assume that the expression (N - n)cpU(n)is nondecreasing in n. Then the left-hand side of (7.5) is increasing in A. If the right-hand side is still decreasing, then the solution to (7.5) is unique. It is straightforward to verify that all the comparative statics results in Proposition 1 apply to this solution, and that in the Cobb-Douglas example the solution is an increasing function of the degree of market power. Welfare analysis of stationary equilibria is somewhat affected by the strategic monopsony effect, but the overall result remains, namely that the laissez-faire average growth rate may be more or less than optimal. Comparison of (7.5) with (4.4) reveals the same intertemporal-spillover, appropriability, business-stealing, and monopoly-distortion effects as before, although the monopoly-distortion effect will be quantitatively different because it,(n) ic(6(N - n ) ) . There is an additional effect, however, from the presence of the term

+

on the left-hand side of (7.5). This additional effect is the "monopsonydistortion" effect. In the linear case, where cp" is zero, the constraint (*) indicates that the intermediate firm's wage rate is independent of the amount of skilled labor it hires, so the monopsony-distortion effect induces it to hire more skilled workers in order to reduce the amount of current research, and hence the amount of creative destruction. The effect just cancels the business-stealing effect, as can be seen by multiplying both sides of (7.5) by ( y - 1)ly. Thus in the linear Cobb-Douglas example, research and growth are unambiguously less than optimal. In the general case where cp" < 0 the monopsony-distortion effect is ambiguous, because hiring more skilled labor increases the intermediate firm's wage rate at the same time that it reduces creative destruction. Because of these conflicting tendencies it is straightforward to construct examples in

INNOVATION & GROWTH

which the overall monopsony-distortion effect vanishes. More specifically, given any specification of the model it is possible to perturb the research function cp in such a way2' that h and n* remain unchanged and the solution ri to (7.5) becomes equal to fi. Since h can be more or less than n* it follows that ri can be more or less than n*. The rest of the paper ignores the strategic monopsony effect, by assuming that intermediate firms take as given the wage of skilled labor and the amount of research. This assumption is based on our belief that the effect is not important, because it derives from the simplifying assumption that there is only one intermediate firm in the economy. If there were many competing intermediate firms, as in the next section, each might plausibly regard itself as too small to affect the skilled wage or the amount of research.

8. Many intermediate goods This section relaxes the simplifying assumption of a single economy-wide monopoly in intermediate goods. Suppose instead that there are rn different intermediate sectors. Output of the consumption good is y, = C;,A,F(x,), where x,, denotes the flow of output of the ith intermediate good during interval t , and where F has all the properties assumed above. (This requires that each sector have its own specialized brand of unskilled labor.) Following Shleifer (1986), suppose that innovations arrive in different sectors in a deterministic ~ r d e r . ~Specifically, ' the innovating sector is always the one with the lowest productivity parameter A,. Each innovator becomes a local monopolist in that sector for a period of rn successive innovations, and is replaced by the last of those m innovations. Let A, denote the productivity parameter in the leading sector, where an innovation has arrived most recently. Assume that A, = y('-k)"nA,when i is the kth most advanced sector. Then y is again the size of each innovation relative to the previous vintage of good in the same sector. Let 2, denote the stationary-equilibrium employment of skilled labor in the kth most advanced sector. Then 2 , maximizes the flow of profits:

Therefore,

where 1 is defined as above and o is again the stationary-equilibrium productivity-adjusted wage, w,lA,. The productivity-adjusted flow of profits in the kth-leading sector is

A MODEL OF G R O W T H T H R O U G H CREATIVE D E S T R U C T I O N

The productivity-adjusted wage is the solution to the equilibrium condition

which can be written as

o = 6 ( N - n), where the function 6 satisfies Assumption 1 above. Let the technology of research be the same as before, with an arrival parameter equal to mh. The length of each interval is distributed exponentially with parameter mhq(n), and each local monopoly lasts for m intervals. Let T, denote the time of the tth innovation. Then the value of the tth innovation is

and the condition for a positive stationary-equilibrium level of research is the analogue to (3.3):

In the linear Cobb-Douglas example this condition is the analogue to (3.4):

Since the right-hand side of (8.1) is a decreasing function2* of n and the left-hand side an increasing function, the solution to (8.1), ff it exists, is unique. If no solution exists, then the equilibrium level of research is zero. All the comparative-statics results of Proposition 1 apply to the solution of (8.1), with the possible exception of (b), the effect of y, the size of

INNOVATION & GROWTH

innovations. In the linear Cobb-Douglas example, however, it can be shown that (b) remains true, provided that the social discount rate (the denominator of U below) is po~itive.~' In stationary equilibrium each innovation raises the entire cross-sectional profile of productivity parameters by the factor yl"". It therefore raises GNP by y"", and raises the log of GNP by the factor (llm) In y. Since the Poisson arrival rate of innovation is mhri, therefore the economy's average growth rate is Ari In y, exactly as before. The variance of the growth rate is Afi(ln ~ ) ~ / r aggregation n; across many sectors reduces variability through a law of large numbers. By the same logic as in Section 4, social welfare is measured by

A social planner would choose (x,, . . . , x,,, n) to maximize U subject to the constraint,

and n 2 0. The first-order conditions for an interior maximum are

where p is a Lagrange multiplier. Let fi(N - n) denote the value of p such that the solutions (x,, . . . , xm) to (8.4) solve (8.3). Then (8.5) can be expressed as:

(8.6)

P(N - n*)

mQ'(n*)

(y-llm)k-l

= ,=I

(y'In' - l)F(x;) r - mhq(n*)(y"" - 1)

In the linear Cobb-Douglas example,

Comparison of (8.6) with (8.1) reveals the same four effects as before. The monopoly-distortion effect is still present because fi(N - n) > Q(N - n).


The appropriability effect applies sector-by-sector, and is amplified by the fact that

if the social discount rate is positive. As before, research and growth under laissez-faire may be more or less than optimal; in the linear CobbDouglas example, A < n* if y is large,24 but ri > n* if a is small and y is not too large.25

9. Conclusion The paper has presented a model of economic growth based on Schumpeter's process of creative destruction. Growth results exclusively from technological progress, which in turn results from competition among research firms that generate innovations. Each innovation consists of a new intermediate good that can be used to produce final output more efficiently than before. Research firms are motivated by the prospect of monopoly rents that can be captured when a successful innovation is patented. But those rents in turn will be destroyed by the next innovation, which will render obsolete the existing intermediate good. It would be useful to generalize and extend the analysis in several directions, such as assuming that technology is ultimately bounded, thereby requiring the size of innovations eventually to fall. The model would gain richness and realism if capital were introduced, either physical or human capital embodying technical change, or R and D capital that affects the arrival rate of innovations. Allowing unemployment, by introducing search into the labor market, would facilitate study of the reciprocal interaction between technological change and the business cycle. All these extensions seem feasible because of the simplicity and transparency of the basic model.

Appendix 1 An example with a random arrival parameter Let h follow a two-state Markov process on the space {h,,h2}with all transition probabilities equal to 112. A stationary equilibrium is an equilibrium in which the productivity-adjusted wage rate depends only on the state of the world, not on time. Let A,V, be the value of making the tth innovation and moving into state j. Assume the linear case of q ( n ) = n. In any state i, the marginal expected return to research in interval t is h,A,+,(V,+ VJ2. This will equal the wage if positive research occurs in state i. If research occurs in all states, the V,'s must satisfy the analogue to (2.12):


Define n, = N - T ( h , y ( V ,+ V2)/2).Then the average level of research employment is

where q, is the asymptotic fraction of time spent in state i. It is easily verified that

To complete the example, take the Cobb-Douglas case ( F ( x )= xa), and suppose = 112 and r = N = h , = 1. Since I ( o ) = (ola2)"'"-" and E(w) = ((1 - a)la)wT (a),the formula for each V, can be rewritten as:

a = y-I

and

6,

When h , = 1, the solution to these equations is V , = V, = a 1 8 which implies n, = n, = fi = 113. As h , --t w, the solution approaches V , = 114, V, = 0, which implies n , = 0, n, = 1, and q, = n,l(n, + h , n , l h 2 )= 1; hence ii = 0. The economy's average growth rate equals j' In y, where f is the asymptotic frequency of innovations:

Thus when h , = 1, f ln y = (113) In 2 > 0; and as h ,

+ w, f

In y approaches 0.

Appendix 2 Derivation of condition (5.5) In the stationary equilibrium described in Section 5, the monopolist has no incentive to do research if

where V, =

(y"" - l ) w , ( N - f i ) r + hfi

is the value of the monopolist's current patent and


v5 =

[min (y2Ia, a - ' )- l]w,+,(N- ri) r + hri

would be the gross value of the next innovation to the current monopolist, for whom the innovation would be drastic if y2 > a-" if next period the level of research was the stationary-equilibrium value fi. In fact more than this level of research would be conducted if the monopolist were to innovate, because the monopolist could then charge a markup higher than y'Ia, so the value would actually be less than YK,. Substituting these expressions for V, and V f , into (A.l) and using the fact that w,,, = yw, produces 12

h[y min (y2'", a-I)- y - (y"* - l)](N - i ) r + hfi

Condition (5.5) follows immediately from (A.2) and (5.7).

Notes 1 The authors wish to acknowledge the helpful comments and criticisms of Roland Benabou, Olivier Blanchard, Patrick Bolton, Louis Corriveau, Mathias Dewatripont, Dick Eckaus, Zvi Griliches, Elhanan Helpman, Rebecca Henderson, Louis Phaneuf, William Scarth, Nancy Stokey, Patrick Rey, and the Co-Editor and referees of this journal. 2 That is, Reinganum's comparative-statics analysis follows the common practice of the patent-race literature in taking the reward to a successful innovation as given, whereas the following analysis shows that the effect of a parameter change on the time path of research involves feedback from future research to current research working through the two above-mentioned channels: creative destruction and the general equilibrium wage effect on profits, both of which flow through the reward to a successful innovation. 3 Scherer (1984) combines process- and input-oriented R and D into a measure of "used" R and D, which he distinguishes from pure product R and D. He estimates that during the period 1973-1978 in U.S. industry the social rate of return to "used" R and D lay between 71% and 104%,,whereas the return to pure product R and D was insignificant. 4 Gradual diffusion could be introduced by allowing the productivity parameter after each innovation to follow a predetermined but gradual path asymptotically approaching the limit A,, and then to jump to A, upon the next innovation and follow a gradual path approaching A,+,. This would produce a cycle in research within each interval, as the gradual rise in productivity would induce manufacturing firms to hire more and more workers out of research until the next innovation occurs. 5 If, instead of a constant-returns research technology, each firm had an identical research technology with rising marginal cost, then the monopolist might d o some research, but the Arrow effect would imply that the monopolist would d o less research than each outside research firm, as shown by Reinganum (1985, Proposition 2) in a similar context. 6 This is the spillover identified by Romer (1990, pp. S83-S85). 7 The critical value A is defined by c(0) = b(A), unless lim,,, bin) > c(O), in which case A = N.

INNOVATION & GROWTH

8 Shleifer (1986) also finds deterministic cycles in a model of multiple equilibria with innovations. The source of multiplicity in Shleifer's model is a contemporaneous strategic complementarity, whereby the incentive to innovate this period is stronger the more innovations are occurring elsewhere in the economy this period. N o such strategic complementarity exists in the present model, in which more research this period raises the marginal cost of research without affecting the marginal benefit. Because Shleifer assumes that imitation destroys the return from innovations after one period, his model does not exhibit the dependency of current research upon future research which underlies the cycles, as well as the other equilibria, in the present model. Deneckere and Judd (1986) also generate cycles in a model of innovations. Their cycles arise from local instability of a unique equilibrium rather than from multiple equilibria. Like Shleifer, they also d o not allow for any effect of future research upon current research. 9 Consider the second-iterate function y2(n). Geometrically, is defined by reversing the spiral illustrated in Figure 1; thus no = yr2(n,). Suppose a no-growth trap exists. Then 0 = yr2(n) < n for small but positive n (see Figure 1). Because c'(ri) + b'(ri) > 0, therefore the counterclockwise spiral in Figure I spirals out in the neighbourhood of ri, so that yr2(n) > n for n close to but less than ri. By the continuity of yr2 there must exist an no strictly between 0 and 6 such that yr2(n0)= no. Evidently nu, y ( n O )constitute a real two-cycle. 10 In this example

v2

b(n) =

yit(&(N - n ) ) and c(n) = 6 ( N - n)lh. r + hn

Therefore

b(n) =

-yf'(&(N

- n))&'(N - n ) - hb(n) r

+ hn

and

cf(n)= - S ( N

-

n)lh.

Because hb(ii) = hc(ri) = & ( N - A), therefore

b'(ri)/ct(ri)=

hyit'(&(N

-

ri)) + h&(N - 6)/&'(N - 6 ) r + hri

But Ef(&(N- 6 ) ) = -(N - 6 ) and &(N - ri) = a 2 ( N- $)a-I. Therefore

From this and (3.4),

(y(ly a ) ) ( Y+ A)

b'(6)/cr(6)= -

-t

0

uniformly in r as a

-t

0.

11 Two additional spillovers could easily be included. First, researchers could benefit from the flow of others' research, so that an individual firm's arrival rate would be a constant-returns function of its own and others' research. Second, there could be an exogenous Poisson arrival rate of imitations that


costlessly circumvent the patent laws and clone the existing intermediate good. Both would have the effect of lowering AGR. Also, as shown in Aghion and Howitt (1988), the inclusion of would introduce another source of cycles in the economy, since each imitation would make the intermediate industry perfectly competitive, which would raise manufacturing employment, until the next innovation arrives. 12 In the patent-race literature the business-stealing effect is usually derived in a symmetric model with no incumbent, in which all research firms enjoy some positive surplus because there is no free entry. An example is Mortensen (1982), who identifies the business-stealing effect with the comment: "Wasteful competition arises because none of the contestants takes account of the loss of the prospect that others suffer when the former's discovery ends the game" (p. 970). In the present paper the loss accrues not to the other research firms, whose value remains equal to zero, by free entry, even after an innovation by another firm, but to the incumbent monopolist who, because of the replacement effect, has chosen not to participate in the patent race. As Tirole (1988, p. 399) notes, there is another negative externality that would occur if the research technology had memory. Specifically, a firm might engage in research in order to reduce the probability that its rivals will win the race. This effect is absent from the present model, in which one firm's research has no effect on the others' probabilities of innovating. 13 From (4.5), as y rises to the upper limit 1 + rl;lN, n* approaches N while, from (3.4), ri is bounded below N. 14 If I l a > 1 + rlhN, then ri > 0 for all y, whereas if y 5 1 + a r l h N , then n* = 0. These inequalities are compatible with the condition derived below for innovations to be drastic, name1 that y 2 a-", as can be verified with the example: a = 112, y = &, rlhN = 2($ - 1). 15 In the Cobb-Douglas example, the unit-cost function is

16

17 18 19

20

It follows from this and (5.2) that if the incumbent charged the unconstrained profit-maximizing price a-'w,, the unskilled wage would be wy = (1 - a)a2a"l-aJ~,(w , l ~ , ) - " " l ~Putting ). this into (5.1) yields the condition y l a-". Treating (5.1) as an equality and solving it and (5.2) simultaneously for (wy, p,) yields p, = y""w,. - 1)hN Suppose y = fi and a = 112. T o get ri < n* let r approach from above; then n* approaches N whereas ri is bounded below N. T o get ri > n* let r = 2(& - 1)hN; then n* = 0 and ri > 0. In either case y = a", but the example is robust to a small decrease in y that would satisfy the necessary and sufficient condition (5.3) for innovations to be nondrastic without violating the sufficient condition (5.5) for the monopolist to do no research. Note that it is always possible to choose the function v so that the solution to (6.3) satisfies the condition for innovations to be drastic in the Cobb-Douglas example: y 2 a-*. Since v' < 0, (6.6) implies that v(y)y is locally decreasing at y*, so that y* exceeds the point 7 at which v(y)y is maximized. Because it compares y* with 7, this analysis would apply even if the research firm ignored the negative effect that its choice of y has o n the value of an innovation by reducing the equilibrium eve1 of x,,, and hence raising the rate of creative destruction next period. Just perturb cp in such a way that cp(ri), cp(n*), cp'(ri), and cpf(n*) remain unchanged, but cp"(fi) is made equal to -cp'(n^)ly(N - n^). This can be done without

(a

INNOVATION & G R O W T H altering the sign of cp' and cp" on [0, N). According to (3.3) and (4.4), A and n* will be unchanged. This perturbation makes the second factor on the left-hand side of (7.5) equal to unity when ii = ri, and makes %(A)= it(c%(N- ri)). Since ri solves (3.3) it will now also solve (7.5). 21 The alternative of allowing innovations to be randomly distributed across sectors is analyzed in an Appendix to an earlier version of this paper, available from the authors upon request. This Appendix assumes a continuum of sectors and a continual flow of innovations. Whoever innovates at date 7 is thereby allowed to enter a randomly chosen sector with the "leading technology" A(s), where A(s) grows continuously at the exponential rate o h . The possibility that the same sector might receive two innovations in rapid succession, before the leading technology has advanced by much, implies that in stationary equilibrium some positive (and endogenous) fraction of innovations will be nondrastic. The model yields all the comparative-statics results of Proposition 1 above, except possibly for result (b). 22 Note that

= 0. where it, > it, > . . . > itm> it,+, 23 It suffices to show that the right-hand side of (8.2) is increasing in y. The ratio of sums in this expression can be regarded as the expected value of the discrete random variable

under the truncated geometric distribution with parameter yl/m'a-') < 1. The effect on this ratio of a marginal increase in y is the sum of the effect on each z, and the effect of changing the parameter of the distribution. The former is positive. The latter would also be positive, by first-order stochastic dominance, if z, were decreasing in k, which it is if the social discount rate is positive. 24 From (8.7), as y"" rises to the upper limit 1 + rlmhN, n* approaches N while, from (8.2), A is bounded below N. 25 If l l a > 1 + rlhN then ri > 0 for all y, whereas if y"" I 1 + arlmhN, then n* = 0.

References AGHION,P., AND P. HOWITT(1988): "Growth and Cycles through Creative Destruction," Unpublished, University of Western Ontario. AZARIADIS, C. (1981): "Self-Fulfilling Prophecies," Journal oj'Economic Theory, 25, 380-396.

A MODEL OF G R O W T H T H R O U G H CREATIVE D E S T R U C T I O N

L. (1988): "Entrepreneurs, Growth, and Cycles," Unpublished, UniverCORRIVEAU, sity of Western Ontario. DENECKERE, R. J., AND K. L. JUDD(1986): "Cyclical and Chaotic Behavior in a Dynamic Equilibrium Model, with Implications for Fiscal Policy," Unpublished, Northwestern University. (1977): "Monopolistic Competition and Optimum ProDIXIT,A., AND J. STIGLITZ duct Diversity," American Economic Review, 67, 297-308. GRANDMONT, J.-M. (1985): "On Endogenous Competitive Business Cycles," Econornetrica, 53, 995- 1045. GROSSMAN, G. M., AND E. HELPMAN (1991): "Quality Ladders in the Theory of Growth," Review of Economic Studies, 58, 43-61. JUDD, K. L. (1985): "On the Performance of Patents," Econornetrica, 53, 567-585. KING,R. G., AND S. T. REBELO (1988): "Business Cycles with Endogenous Growth," Unpublished, University of Rochester. LERNER,A. P. (1934): "The Concept of Monopoly and the Measurement of Monopoly Power," Review of Economic Studies, 1, 157- 175. L u c ~ s R. , E. JR. (1988): "On the Mechanics of Economic Development," Journal of Monetary Economics, 22, 3-42. MORTENSEN, D. T. (1982): "Property Rights and Efficiency in Mating, Racing and Related Games," American Economic Review, 72, 968-979. J. (1985): "Innovation and Industry Evolution," Quarterly Journal of REINGANUM, Economics, 100, 81-99. -(1989): "The Timing of Innovation: Research, Development and Diffusion," in Handbook of Industrial Organization, Vol. I , ed. by R. Schmalensee and R. Willig. Amsterdam: North-Holland. ROMER,P. M. (1986): "Increasing Returns and Long-Run Growth," Journal of Political Economy, 94, 1002-1 037. (1990): "Endogenous Technological Change," Journal ofPolitica1 Economy, 98, ,371-S102. SCHERER, F. M. (1984): Innovation and Growth: Schumpeterian Perspectives. Cambridge, MA: MIT Press. SCHUMPETER, J. A. (1942): Capitalism, Socialism and Democracy. New York: Harper and Brothers. P. S., T. C. A. ANANT,AND E. DINOPOULOS (1990): "A Schumpeterian SEGERSTROM, Model of the Product Life Cycle," American Economic Review, 80, 1077-1091. SHLEIFER, A. (1986): "Implementation Cycles," Journal of Political Econonfy, 94, 1163-1 190. STOKEY, N. L. (1988): "Learning by Doing and the Introduction of New Goods," Journal of Polilical Economy, 96, 70 1-71 7. TIROLE,J. (1988): The Theory of Industrial Organization. Cambridge, M A : M.I.T. Press. -

12 GROWTH THEORY FROM A N EVOLUTIONARY PERSPECTIVE The differential productivity puzzle Richard R. Nelson and Sidney G. Winter* Source: American Economic Review, 65:2 (1975), 338-44.

This is a further progress report on our efforts to develop a theoretical structure capable of integrating what is known about processes of technical change at the level of the firm or the individual invention and what is known about technological advance as reflected in industry or economy-wide time series data on output and inputs (see Nelson and Winter, 1973 and forthcoming). Our endeavor is motivated by a belief that a theoretical structure that integrates these two kinds of knowledge would be useful in enabling better understanding of certain important phenomena that have proved difficult to comprehend within traditional models. Prominent among these phenomena, and the focus of this paper, are the vast disparities in various measures of productivity growth and technical change across different sectors. To cite illustrative numbers (from J. Kendrick's 1973 study), the yearly change in output per worker (1948-1966) was 5.6 percent in farming, 4.6 percent in mining, 2.9 percent in manufacturing. Within manufacturing, yearly productivity growth ranged from 6.0 percent in chemicals to 1.7 percent in leather products. The great intersectoral differences in growth experience clearly are a puzzle for growth theory. Nor is the puzzle strictly intellectual. While W. Baumol may have put the matter too emphatically, consideration of rapid productivity growth sectors and slow productivity growth sectors suggests strongly that many of the nation's problems relate to sectors where technological advance (using that term to serve as a proxy for productivity growth) has been slow. There have been a number of attempts by economists to explain crossindustry differences within the framework provided by traditional neoclassical theory. Kendrick's 1961 study, particularly the work of N. Terleckyj

G R O W T H THEORY FROM A N EVOLUTIONARY PERSPECTIVE

contained in that study, set the style for much of this work. Roughly speaking, the technique has been to regress a measure of productivity growth against various industry variables, particularly research and development (R&D) spending of various sorts. Recent studies have broken R&D spending in an industry into self-financed and government-financed and have tried to account for the effect of R&D expenditures by supplying industries. The research has shown that industries differ greatly in the magnitudes of different kinds of research and development that feed into them and that these differences are related to differences in the growth of productivity. (For a good survey, see Terleckyj.) The studies have been useful and provocative, but have not cut very deep. Clearly there are severe specification problems. The regression equations involve complex interactions in which factors influencing the demand side and the supply side of the technical change process are intertwined and confounded with other forces. There is a tangle of causations, from R&D to productivity growth, from productivity growth and lowered prices to growth of output, from growth of output in the presence of scale economies to productivity growth, from expansion of the industry to greater incentives for research and development, and so on. Even if it were granted that causation runs, at least in part, from research and development spending to enhanced productivity, what explains the great differences in (direct and indirect) R&D spending across industries? Among the range of possible explanations, two stand in stark contrast regarding their implications. One is that research and development activity is more powerful when directed toward the technologies of certain industries than toward the technologies of others; therefore, the disparities in rates of technical progress reflect some kind of innate differences in ability to advance efficiently the different kinds of technologies which R&D allocation decisions rationally reflect. A second explanation (not mutually exclusive) focuses on differences in institutional structure that influence the impact of research and development on productivity and the extent to which R&D spending is optimal. The proposition is that the effectiveness with which R&D output is screened and employed varies among industries. Moreover, industries also differ significantly in the extent to which patent rights and other protections internalize the returns to inventions that flow out of firm R&D spending, and in the extent to which government subsidization permits the undertaking of highvalued research and development projects where externalities are important. Needless to say, the differences in these explanations matter profoundly in terms of their policy implications. In order to probe the issues it would seem valuable to look beneath the industry time series data and analyze the more micro aspects of technical change in the different sectors: the sources of key inventions, their costs and who bore the costs, the motives of the organizations in the sector, the

INNOVATION & GROWTH

constraints under which they operate, how new technology is screened and spread, etc. Without arguing that it is impossible to enrich the basic neoclassical model so as to do this, for reasons discussed at length elsewhere (Nelson and Winter, forthcoming) we believe it more straightforward to work within a set of assumptions that in some ways narrow and in some ways broaden those contained within the more traditional model. We do not want to argue about whether our proposal really is a special case of traditional theory. Rather, the question we want considered is: Is this a fruitful way to theorize? Our theoretical focus is on the following three questions: What are the sources of productivity growth in firms? What is the nature of the technological advance process? How can we characterize the way in which new technology is screened and spread throughout an economic sector? Put simply, we propose that the dominant source of productivity growth in a firm is new technology, that the processes that generate technological advance tend to operate stochastically and locally, and that selection and spreading forces in a sector work out rather slowly over time. In combination, these commitments represent the starting points of a "technological mutation" theory of changes in the characteristics of firms, with a "selection environment" operating on the new technological mutations-in short, an "evolutionary theory." But we have a lot more in mind than merely a metaphor. Within an evolutionary theory, productivity growth is explained, in an accounting sense, in terms of, first, the generation of new technologies and, second, changes in the "weights" associated with the use of different existing technologies. We have been trying to model the stochastic processes that generate new technology in order to identify the factors that might explain why certain kinds of technical advances might be more likely than others. But the aspect of our work we want to sketch at more length here is the characterization of the selection environment for a new invention. Given a flow of new technologies, the selection environment determines how relative use of different technologies changes over time. The selection environment influences the productivity growth generated by any given invention, and it also influences strongly the kinds of R&D that firms in the industry will find profitable. Consider an invention-innovation that has been introduced to the economy-for example, the first model 707 aircraft produced by the Boeing Aircraft Company, a new seed variety tried by a farmer, a pioneering doctor trying a new anticancer drug, the first use of "open classrooms" in a school system. A necessary condition for survival of an innovation is that it be perceived as worthwhile by the organizations that directly determine whether it is used or not. If the innovation is to persist and expand in use, the firm or farm must find a new product or process profitable to produce or employ, the doctor must view the treatment as efficacious, the school system must be persuaded that the new classroom technique is good educational practice


and worth the cost. Sectors obviously differ greatly in terms of the nature of the organizations that ultimately must decide on worth and particularly the salient objectives that determine worth. However, the question of whether or not the organizations (firms) find the innovations worthwhile depends not only on the objectives of the firms. In almost all economic sectors the firms-for-profit private organizations, public agencies, individual professionals-are subject to monitoring mechanisms that partly determine whether an innovation scores well or poorly according to the objectives of the firms and that may impose more direct constraints on firm behavior. A key part of this monitoring mechanism involves the individuals or organizations who are the demanders or beneficiaries of the goods or services produced by the firms in the sectors. Thus, the profitability of 707 aircraft to Boeing depends on how the airlines react to these planes. The seed must produce corn that is profitable at prevailing prices. Patients must agree to the new treatment, etc. In some sectors there are additional constraints imposed on the individual firms by agencies assigned a legal responsibility to monitor or regulate the activity of the industry. Thus the Boeing 707, before it could be put into commercial use, had to pass Federal Aviation Agency tests. New pharmaceuticals are regulated, etc. Selection environments differ greatly in the structure of demanders and monitors, and in ways their reactions feed back to influence the desirability of a particular innovation to the firms in question. Industries differ not only in the objectives of the firms and demand and regulatory constraints facing them. They also differ in the relative importance of the mechanisms by which innovations, accepted by that environment, spread. There are, roughly speaking, two distinct kinds of mechanisms for the spread of an innovation. One of these is greater use of an innovation by the firm that first introduces it. If the firm produces a variety of products or undertakes a variety of activities, this may occur through substitution of the new activity for older ones. Or the firm may grow by investing new resources. In sectors which involve a number of administratively distinct organizational units on the supply side, there is a second innovationspreading mechanism that needs to be considered-imitation. Imitation of certain innovations may be deliberately spurred by the institutional machinery: thus the agricultural extension service encourages widespread adoption by farmers of new seed varieties. Or the institutional machinery may deter or block imitation, as the patent system blocks the adoption by one firm of patented innovations created by a competitor. Industries clearly differ greatly in the importance of these two mechanisms and how they work. We propose that a rigorous general model of the selection environment can be built from specification of these three elements: the definition of "worth" or profit that is operative for the firms in the sector, the manner in which consumer and regulatory preferences and rules influence what is

INNOVATION & GROWTH

profitable, and the investment and imitation processes that are involved. In the remainder of this paper we shall discuss some important qualitative differences in sectotal selection environments that become the focus of attention once one poses the theoretical problem in the way we have. Market sectors differ significantly among themselves. And many sectors involve important nonmarket components that have special characteristics. While we have not yet attempted modeling to capture the kind of differences in fine structure we shall be describing, this is high on our agenda of business. The perception that market competition in a sector operates like a selection environment was explicit in the writings of many of the great nineteenth and early twentieth century economic theorists. J. A. Schumpeter was well within the classical tradition. In a stylized Schumpeterian evolutionary system, there is both a carrot and a stick to motivate firms to introduce "better" production methods or products. Better here has an unambiguous meaning: lower cost of production or a product that consumers are willing to buy at a price above cost. In either case the criterion boils down to higher monetary profit. Successful innovation leads to both higher profit for the innovator and to profitable investment opportunities. Thus profitable firms grow. In so doing they cut away the market for the noninnovators and reduce their profitability which, in turn, will force these firms to contract. Both the visible profits of the innovators and the losses experienced by the laggers stimulate the latter to try to imitate. Both expansion of the innovator and imitation by competitors are essential aspects of the Schumpeterian process. In the standard descriptions of dynamic competition, expansion of the innovator is likely to be stressed. It is surprising, therefore, that the relationship between innovation and investment has not been subjected to more serious empirical investigation. While almost all theories of firm investment would lead one to expect a positive relationship between successful innovation and investment, this has not been tested in the major studies of investment behavior. The exceptions are studies where the author's basic hypothesis is oriented around the Schumpeterian interactions. D. Mueller does find that lagged R&D expenditure by a firm has a positive influence on its investment in new plant and equipment. E. Mansfield's studies (1968) also give support for a "Schumpeterian" view. Perhaps his most interesting results involve comparisons of firm growth rates, where he finds that innovating firms tend to grow more rapidly than the laggers. However, while the advantage of the innovators tends to persist for several periods, the advantage damps out with time, apparently because other firms have been able to come up with comparable or superior innovations. In contrast to the sparseness of studies of the relationship of investment to successful innovation, there have been a large number of studies which have focused on the spread of innovation by imitation in profit-oriented


sectors. It is not useful here to review the details of these studies, save to note that many of them have documented the role of profitability of an innovation in influencing the speed with which that innovation spreads. (For a good survey, see Mueller 1967.) In most of the cases studied, the innovations were inputs produced by a supplier and the early adopters were not in a position to block subsequent use by their competitors. In some instances this was not the case. For example, a glass producing company, Pilkington, holds the basic patents on the float glass process and presumably had an interest in limiting diffusion to other firms except where Pilkington was blocked from the market. It is interesting that the analysts of diffusion have not always been cognizant of these differences. It also is quite surprising that in no study of which we are aware has there been an attempt to study the expansion of the innovator and imitation of the innovator together. It would seem apparent that, in order for a market selection environment to work effectively, a rather fine balance is required between the two mechanisms. Preservation of competitive structure in the face of innovation is delicate. A. Phillips' description of competition in the industry that produces aircraft for commercial airlines reveals one extreme. The "expansion of the successful innovator" mechanism works powerfully here. This is a sector in which firms are able to expand capacity rapidly and where it is costly and time consuming to imitate another company's successful product. Further, demanders are quite sensitive to product quality and cost. In this institutional regime, a company that comes up with a superior product has a great advantage over its competitors, and because of the lags and cost of imitation, other firms may be forced out of business. And indeed, it appears that successful innovation has come close to destroying competitive structure in the civilian air frame industry. On the other hand, the efficacy of Schumpeterian competition requires that firms be able to achieve significant size and that imitation not be too easy. Consider the situation in agriculture where it is very difficult for a successful firm to expand significantly and rapidly because of the cost and complexity of purchasing particular pieces of adjacent land. This puts the full burden of the spread of profitable new technology on imitation mechanisms. But at the same time it limits the profitability to any individual farmer of innovating and thus reduces the incentives to search out new techniques and to take risks. Implicitly this has been recognized. An elaborate subsidized mechanism has developed to disseminate widely among farmers information regarding the best new techniques. While economists have concentrated their attention on market sectors, research on the selection environments of nonmarket sectors has been undertaken principally by anthropologists, sociologists, and political scientists. This in itself would lead to some significant differences in focus and analysis. But to a considerable extent the differences in analysis reflect real differences in the selection environments.

INNOVATION & GROWTH

A hallmark of nonmarket sectors is that the separation of interest between firms on the one hand and consumers and regulators on the other is not as sharply defined as in market sectors. The relationships between a public agency, like a school system and its clientele (students and parents), and sources of finance (mayor, council, and voters) simply do not have that armdistance quality that marks the relationships between the seller and potential buyer of a new car. The public agency is expected to work in the public interest of its own volition and, indeed, to play a key role in the articulation of that interest. This is so in many nominally "private" sector activities, like the provision of medical services by a doctor. The doctor is not supposed to make his decisions regarding the use of a new drug on the basis of whether this will profit him, but rather on his expectation of how this will benefit his patients. This is not to say that, in fact, interests of firms and consumers always are consonant. In most nonmarket sectors (as in market sectors where competition is lax), the firm has a good deal of discretionary power regarding what it is to provide, and the customer may have little direct power to reward or punish performance. In any case, the motivations of the firms in the sector are not assumed to be monetary profit. Analysis of the operative values of the firms, therefore, should be a centerpiece of studies of nonmarket selection. This makes analysis difficult. As in the theory of consumer behavior, as contrasted with the theory of the firm, tastes matter; these may be hard to analyze, and they may not be stable. Thus in the J. Coleman, E. Katz, and H. Menzel study of the diffusion among physicians of a new pharmaceutical, the authors did not even attempt to specify in what ways the new pharmaceutical was superior medically to preexisting alternatives. K. Warner's study of the diffusion of cancer chemotherapy reveals doctors trying to assess the patient's best interest, but often having few objective criteria to go on. In sectors that involve significant regulatory or political controls or division of responsibility, there is an additional difficulty in analysis of the operational definition of worth. Many different parties may have to go along before an innovation can be operative. In L. Friedman's study of bail reform, the courts and the police both had to agree to the proposal, and legislative agreement was necessary where budget was involved. Thus collective decision processes are involved. The interaction of firms, and demanders and monitors, certainly is more subtle than in market sectors. Nonseparation of suppliers and demanders leaves little room for firms to compete among each other for consumer dollars. Because of this innovations must spread largely through imitation across the spectrum of noncompetitive firms producing the goods or service in question. At the same time there is no incentive for the innovating firm to deter imitation. Organizations that cannot expand into the terrain of others and know that others cannot encroach on their territory have little to gain from preventing

G R O W T H THEORY FROM AN EVOLUTIONARY PERSPECTIVE

others from adopting their successful innovations. Indeed, in most of the sectors under consideration here, there are formal arrangements for cooperation and the flow of information among the firms. Consider the quasi market for the provision of physician's services. Without strong constraints afforded by consumers or outside regulators, consumer welfare is guarded (perhaps not so securely) largely by professional standards of efficacy of treatment. To assess the efficacy of new treatments doctors consult with each other and apparently aim for professional consensus, guided by the judgments of certain key experts. L. Mohr's study of the spread of new practices and policies across local public health services reveals a similar "professionalism" at work. In such sectors, the screening and spreading of innovations depend in large part on these collective evaluation and information spreading mechanisms. We hope we have persuaded you that there is considerable variation among sectors in their "selection environments" and that these differences can affect both the speed and the extent of spread of any innovation. It might be conjectured that these differences would influence the level of productivity at any time but not its rate of growth. We think this is wrong for two reasons. First, even if one assumes that the rate of advance of "best practice" is not influenced by the selection environment, it is not apparent that sectors need be characterized by a constant ratio of average to best practice. In some nonmarket sectors it is hard to identify strong forces that will prevent that ratio from failing. Second, and probably more important, the selection environment feeds back powerfully on the incentives for R&D by the firms in the sector. In industries like aviation there may be overstimulation. In agriculture, support of R&D is dependent upon suppliers or public sources of finance. Analysis of the incentives for R&D support by the firms in nonmarket sectors would appear to require a detailed study of operative values and sources of finance, but we would conjecture that in many cases the incentives for R&D support are quite weak. Thus one of the most important reasons for study of selection environments is that such analysis is necessary before one can evaluate the adequacy of prevailing R&D institutions. Space limitations have forced us drastically to oversimplify and to curtail the discussion. We hope we have given at least a slight flavor of the kind of institutional richness that our proposed mode of theorizing aims to encompass. But the proof of the pudding will be in the eating.

Note

* Yale University and the University of Michigan, respectively. Support for the project from the National Science Foundation is gratefully acknowledged, as is the helpful criticism on this paper by Susan Ackerman, Richard Levin, and Sharon Oster, all of Yale University.

INNOVATION & GROWTH

References W. Baumol, "Macroeconomics of Unbalanced Growth: The Anatomy of Urban Crisis," Amer. Econ. Rev., June 1967, 57, 415-26. J. Coleman, E. Katz, and H. Menzel, "The Diffusion of an Innovation Among Physicians," Sociometry, Dec. 1957. L. Friedman, Innovation and Diffusion in Nonmarkets: Case Studies in Criminal Justice, Yale Univ., doctoral dissertation, 1973. H. Grabowski, and D. Mueller, "Managerial and Stockholder Welfare Models of Firm Expenditures," Rev. of Econ. and Statist., Feb. 1972. J. Kendrick, Postwar Productivity Trends in the United States, 1948-1969, Nat. Bur. of Econ. Res., Princeton 1973. -, Productivity Trends in the United States, Nat. Bur. of Econ. Res., Princeton 1961. E. Mansfield, Industrial Research and Technological Innovation, New York 1968. -, "Determinants of the Speed of Application of New Technology," in B. R. Williams, ed., Science and Technology in Economic Growth, New York 1973. L. Mohr, "Determinants of Innovation in Organizations," Amer. Pol. Sci. Rev., 1969. D. Mueller, "The Firm's Decision Process: An Econometric Investigation," Quart. J. of Econ., Feb. 1967. R. Nelson, and S. Winter, "Toward an Evolutionary Theory of Economic Capabilities," Amer. Econ. Rev. Proc., May 1973, 63, 440-49. "Neoclassical versus Evolutionary Theories of Economic Growth," and -, Econ. J., forthcoming. A. Phillips, Technology and Market Structure, Lexington 1973. N. Terleckyj, "The Effect of R and D on the Productivity Growth of Industries," draft, Oct. 1973. K. Warner, Diffusion of Leukemia Chemotherapy, Yale Univ., doctoral dissertation 1974.

G E N E R A L PURPOSE TECHNOLOGIES 'Engines of growth'? Timothy F'. Bresnahan and M. Trajtenberg Source: Journal of Econometrics, 65 (1995), 83-108.

Abstract Whole eras of technical progress and growth appear to be driven by a few 'General Purpose Technologies' (GPT's), such as the steam engine, the electric motor, and semiconductors. GPT's are characterized by pervasiveness, inherent potential for technical improvements, and 'innovational complementarities', giving rise to increasing returns-to-scale. However, a decentralized economy will have difficulty in fully exploiting the growth opportunities of GPT's: arms-length market transactions between the GPT and its users may result in 'too little, too late' innovation. Likewise, difficulties in forecasting the technological developments of the other side can lower the rate of technical advance of all sectors.

1. Introduction Economists have known for a long time that technical change is the single most important force driving the secular process of growth (Abramovitz, 1956; Solow, 1957). Yet, relatively little progress has been made in accounting for the 'residual' of aggregate production functions,' largely because economic theory tends to treat all forms of technical change in the same, diffuse manner. In fact, we can hardly distinguish in our models between a momentous invention such as the transistor and the development of yet another electronic gadget. By contrast, economic historians emphasize the role played by key technologies in the process of growth, such as the steam engine, the factory system, electricity, and semiconductors (Landes, 1969; Rosenberg, 1982). Anecdotal evidence aside, are there such things as 'technological prime

INNOVATION & GROWTH

movers'? Could it be that a handful of technologies had a dramatic impact on growth over extended periods of time? What is there in the nature of the steam engine, the electric motor, or the silicon wafer, that make them prime 'suspects' of having played such a role? In this paper we attempt to forge a link between the economic incentives for developing specific technologies and the process of growth. The central notion is that, at any point of time, there are a handful of 'general purpose technologies' (GPT's) characterized by the potential for pervasive use in a wide range of sectors and by their technological dynamism. As a GPT evolves and advances it spreads throughout the economy, bringing about and fostering generalized productivity gains. Most GPT's play the role of 'enabling technologies', opening up new opportunities rather than offering complete, final solutions. For example, the productivity gains associated with the introduction of electric motors in manufacturing were not limited to a reduction in energy costs. The new energy source fostered the more efficient design of factories, taking advantage of the newfound flexibility of electric power. Similarly, the users of microelectronics are among the most innovative industries of modern economies, and they benefit from the surging power of silicon by wrapping around the integrated circuits their own technical advances. This phenomenon involves what we call 'innovational complementarities' (IC), that is, the productivity of R&D in a downstream sector increases as a consequence of innovation in the GPT technology.* These complementarities magnify the effects of innovation in the GPT, and help propagate them throughout the economy. Like other increasing returns-to-scale phenomena, IC create both opportunities and problems for economic growth through technical advance. Development of GPT-using applications in a wide variety of sectors raises the return to new advances in the GPT. Advances in GPT technology lead to new opportunities for applications. Such positive feedbacks can reinforce rapid technical progress and economic growth. The problem is that these complementary innovative activities are widely dispersed throughout the economy, making it very difficult to coordinate and provide adequate innovation incentives to the GPT and application sectors. These difficulties are hardly surprising, considering that uncertainty and asymmetric information, which make coordination difficult, are essential features of the process of new knowledge creation (Arrow, 1962). Moreover, time gaps and sequentiality are an inherent feature of technological development, particularly in the context of GPT's (e.g., the transistor could not come before electricity, nor could interferon before DNA). Therefore, coordination in this context would require aligning the incentives of agents located far from each other along the time and the technology dimensions. Since GPT's are connected by definition to wide segments of the economy, coordination failures of this nature may have far reaching consequences for growth.

GENERAL PURPOSE TECHNOLOGIES

A great deal of theoretical work has been done in recent years on the role of increasing returns in endogenous growth, going back to Romer's (1986) contribution. However, many of these models regard the economy as 'flat', in that they do not allow for explicit interactions between different sectors.' The locus of technical change does not matter much in those models, and hence there is little room to discuss explicitly the industrial organization of inventing sectors. Closely related, technical change is often assumed to be all-pervasive, that is, to occur with similar intensity everywhere throughout the economy. Clearly, one could not build a theory of growth that depends upon the details of bilateral market relations, when those details could refer to any or all of the myriad markets that make up the economy. By contrast, we identify here a particular sector (the GPT prevalent in each 'era') that we regard as critical in fostering technical advance in a wide range of user industries, and presumably in 'driving' the growth of the whole economy. The price that we pay, though, for the sharp focus is that the analysis is partial equilibrium, and hence the implications for aggregate growth stem just from the supply side, and abstract from general equilibrium type of

feedback^.^ We organize the analysis in order to draw two sets of implications out of a simple model of decentralized technological progress. In Sections 2 and 3 we consider the implications of generality of purpose and innovational complementarities for the economy-wide incentive to innovate. These sections emphasize the vertical relations between the procedures in GPT and application sectors, and the dual appropriability problem that arises in that context. Section 4 turns to a set of dynamic issues: the role of bilateral inducement of technical progress over time, the difficulties of the GPT and AS sectors in forecasting each others' rate of progress, and the consequent 'too little, too late' decisions that slow the arrival of social gains from a GPT. Section 6 concludes with directions for further research. One of Zvi Griliches's earliest contributions was the study of hybrid corn, a technology that can surely be regarded as a GPT in the context of agriculture. Indeed, that is how Griliches himself (1957, p. 501) perceived it: 'Hybrid corn was the invention of a method of inventing, a method of breeding superior corn for specific localities.' Many of the themes of our analysis are also familiar from Griliche's work: the private incentive to adopt new technologies (Griliches, 1957), the return to innovations at the firm level (Griliches, 1958, 1984), and the causes and consequences of returns-to-scale (Griliches, 1971). This paper attempts to integrate these themes in the hope of illuminating some broader phenomena.

2. Incentives to innovate in the GPT and application sectors Several common themes emerge from surveying past and present GPT's.' A generic function (or 'general concept') such as 'continuous rotary motion'

INNOVATION & GROWTH

for the steam engine, or 'transistorized binary logic' for the integrated circuit, can be applied in many sectors. Yet advancing the performance of objects embodying these functions and making them economically viable pose great challenges. Thus, cheaper steam power called for mechanically better engines using improved materials, and a superior understanding of thermal efficiency. More advanced integrated circuits have their own complex logic, but also call for advances in photolithography and other manufacturing processes. Finally, making the general concept work in any specific situation requires further complementary innovation, and often a great deal of ingenuity. Who knew that continuous rotary motion could make sewing cheaper, or that carburetion in an automobile engine and addressing envelopes were binary logic activities? These observations about technology inform and drive the forthcoming analysis. Our model is of a stylized set of related industries with highly decentralized technical progress, centered around the GPT. To fix ideas, think of this sector as semiconductors. The level of technology in that sector, called z, appears to users in the application sectors as quality attributes. In semiconductors these are the speed, complexity, functionality, size, power consumption, reliability, etc. of integrated circuits. While almost all interesting real-world examples have multidimensional z , we formulate the model in terms of a scalar z . ~Finally, the economic return to improved technology in the GPT comes by selling a good embodying the technology at price w, in markets where the GPT firm(s) exercise some degree of monopoly power. The economic incentives for innovation in the GPT depend on the prevailing market structure and appropriability, as well as on the demand function in the applications sectors, which determines GPT revenue as a function of w and z . In this framework an applications sector (AS) is an actual or potential user of the GPT as an input; each AS engages in its own innovative activity, leading to a level of own technology T,. Fig. 1 shows some the AS's using semiconductors: early transistors were incorporated in hearing aids, shortly after in radios, computers, and then television sets. The development of the integrated circuit permitted applications in many entirely new products (e.g., CT scanners, camcorders). A particularly important subclass of integrated circuits is microprocessors, which permitted the creation of 'smart devices' (personal computers, laser printers, automobile engine control systems). In parallel to the appearance of new applications, the GPT fosters continued change in existing sectors such as military or civilian aircraft. More generally, adapting and adopting the GPT for different sectors is itself an innovative activity. For GPT's as pervasive as semiconductors, innovation in the different AS's can be very diverse. What is shared among applications sectors is the level of GPT technology and not necessarily any other economic feature.'


Uotation:

GPT:

AS. 2:

v:

:

General Purpose Technology Application Sector a "~uality"of the GPT Iarket price of the 6PT Marginal cost of GPT Technological level (or " p e r f o ~ c e wof) AS. Gross rents of the ith sector, i: GPT, AS. BDD costs of the ith sector, i: GPT, AS.

(T: vector of T,'s)

Figure 1 The framework of analysis.

We begin by modelling the incentives to innovate facing the GPT and AS'S. The key technical assumptions are generality of purpose and innovational complementaritie~.~ These translate, in a world of imperfect appropriability, into two distinct externalities: the 'vertical' externality between the GPT and each application sector, and the 'horizontal' on across application sectors. We then examine the welfare consequences of these externalities in the context of a simple one-step innovation game.

2.1. Modelling the application sectors Each application sector (indexed by a ) determines the level of its own technology, To2 0, and its demand for the GPT good, X". The objective function which the single AS acts as f i t maximizes is maxn"(w, z , T,) - C"(T,) = Va(w,z), r,

(1)

INNOVATION & GROWTH

no

where C(.) are invention costs and stands for the gross private returns to technical advance in the AS. We assume that if Y(w, z) < 0 the sector takes some opportunity action with value normalized to zero.9 The definitions of 0, and 0. z, T, and w imply that l l g > 0, It is standard in models of vertical integration to treat the downstream sector as a single entity, and hence to refer to n" as 'the' payoff to the AS, without distinguishing between buyers and sellers within the sector; see, for example, Hart (1988) and Bolton and Whinston (1993). In general, though we do not expect market arrangements within any given AS to result in optimal innovation incentives. Thus, we provide in Section 2.2 three moves examples of the economic underpinnings of n u ; in all of them together with social surplus in response to changes in z, w, or T,, but only in one of the examples is identical to social surplus. As usual in these types of models, we assume C", 0 and C", > 0. Most importantly, we assume the presence of 'innovational complementarities' (IC),

n",

n",

nu

nu

In words, the marginal value of enhancing the AS'S own technology rises with the quality of the GPT. The solution to (1) leads to the technology investment function of the AS, T, = R"(w, z).

(3)

It is immediate from the assumption of IC that Ru(.) is upward-sloping in

z: technological improvements in the GPT induce complementary innovation in the AS. Relying on Shephard's lemma, the demand of the AS for the GPT input is given by

and hence the expenditure on purchasing the GPT input is En = wXa(w, z, T,), which is obviously the revenue function of the GPT. Since the GPT sector will be assumed to exercise monopoly power, it is convenient to state some of the assumptions in terms of the 'inverse' marginal revenue function, M T = a ~ " i =a (~x u + WX:,.). We assume that demand is downward-sloping (X, < 0) and that X G > 0, X, > 0, that is, that superior technology is demand-enhancing. We also assume that X , 5 0, which implies that demand does not become steeper as it shifts up following a quality upgrade in the GPT. This ensures that a GPT monopolist cannot appropriate more than the incremental surplus thus, the GPT producer will understemming from an increase in z, provide z (as in Spence, 1975).

nf;


We make the following assumptions about the derivatives of MR (mirroring those about demand):

that is, z and T , are assumed to shift marginal revenue in the same direction as the shift in demand; these, together with the (conventional) assumption that MR,,< 0, ensure that the return to the GPT producer from investing in quality upgrades increases with T, (see Appendix 1). So far we have discussed the behavior of a single application sector, but the very concept of a GPT implies the existence of multiple AS's. For simplicity, assume that for all {z, w} the ranking of AS's according to the maximized value of their payoff, Vu(w,z), is the same. In that case the marginal AS is uniquely determined by the smallest positive VU(w,z). Let A(w, z) be the set of sectors that find it profitable to use the GPT; clearly, A(.) will include more sectors the larger z is, and fewer sectors the higher is w. Thus, holding prices fixed, higher z's induce higher level of T, in each active AS, and cause an expansion of the set of AS's by making it profitable for extramarginal sectors to adopt the GPT. 2.2. Examples of the economic underpinnings of U"

We provide here three alternative interpretations of nu(.),all having distinct buyers and sellers within each AS: sellers purchase the GPT good, combine it with their own technology, and sell their output to buyers. The examples differ in the assumptions regarding the industrial organization of the AS, and total surplus. and therefore in the relationship between Consider first the case where there is perfect, costless contracting between buyers and sellers in the AS, and hence assume that they are able to design the cost-minimizing industry structure (just as they would if they were to vertically integrate). That is, they sign contracts which just cover C0(T,) without affecting any allocational decision at the margin. Let the payoff to buyers be equal to the consumer surplus, CS(Pu, z, T,), where P, is the price of the AS good;" thus, quantity demanded equals -CS,(P,, z, T,). On the supply side, denote by y(z, T,) the unit cost function, and assume that one unit of the AS good uses one unit of the GPT input (as one microcomputer uses one microprocessor). Then,

nu

INNOVATION & GROWTH

nu

that is, maximizes consumers' surplus minus costs, including the costs of buying the GPT good. In other words, the AS acts in this case as fi it maximizes total surplus of the sector." Eq. (5) shows also that one of the likely sources of innovational complementarities (IC) is CS;, > 0. For example, final demanders of hearing aids are better off only if the quality of the transistor z is designed into the listening device via To. It is the quality of their improved hearing, which Notice also that relies on the two technologies, that drives the IC in Pa = y(z, To), and hence Xa(w, z , TJ = - CSp,,[y(z, T,), z, T,]. This may provide a rationale for the assumption that Xz, > 0, which we shall rely upon later on: the assumption holds if the IC arise indeed from CS,, > 0. The first-best contracts of the previous example may be difficult to negotiate or enforce. As a second example, suppose instead that price-taking buyers face a monopoly seller in the AS. Then, using the same notation,

nu.

na

Thus is in this case the part of the surplus that is captured by the monopoly seller, and not total surplus as in the first example.12 As a third and final example, suppose that the sellers in the AS are would be producer's surplus in the AS, which price takers; once again will be zero if the firms in the AS are all identical with flat marginal costs. and social welfare will be larger than in the Clearly, the gap between monopoly case. These examples make it clear that in a wide range of cases the payoff function governing the behavior of the AS is highly correlated with total sector surplus, though not necessarily identical to it. In any event, our analysis focuses on the efficiency of the productive sector of the economy, and abstracts from spillouts to the consumers of the AS'S.

na n"

2.3. Incentives for innovation in the GPT sector We assume that the GPT sector sells an undifferentiated product and that it exercises monopoly power in setting its price w.I3 Thus, the restricted profit function is ng(z, T, c) = max(w - c) I,

Xa(w, z , T,),

(6)

atA

where c is the constant marginal cost of producing the good embodying the GPT, T is the vector of technology levels of the AS'S, and A = A(w, z). The innovating behavior of the sector is characterized by (for z 2 0)


where CR(z)stands for the cost-of-innovating function, exhibiting C, > 0 and C,, > 0. The solution to (7) gives us the reaction function

which will be upward sloping in T (the proof is in Appendix 1): we have assumed that higher T,'s shift demand and marginal revenue up, hence the private return to investment in z increases with T,.

This is then the second half of a dual inducement mechanism: an improvement in the technology of any AS increases the incentives for the GPT to upgrade its technology, just as a higher z prompts the AS'S to invest in higher T,'s. The technology levels of the AS's and of the GPT, { T ,z), can be thus characterized as 'strategic complements' (Bulow et al., 1985). 2.4. Equilibrium in the market for the GPT and the social optimum

Assuming that the GPT and the AS'S engage in arms-length market transactions (and hence ruling out technological contracting or other forms of cooperative solutions), we can easily characterize the (Nash) equilibrium as follows (we rely here on Milgrom and Roberts, 1990): { T o ,z") is an equilibrium if Tz

=

Ru(zo), VLZ, and z0 = R ~ ( T " ) ,

where for some AS'S it may be that Tz = 0. The multiplicity of potential participant AS'S will tend to induce multiple equilibria. There is always a 'low' equilibrium (i.e., 10, 0 ) ) and, if the reaction functions are concave, at least one interior equilibrium. Different numbers of participating AS'S may support other interior equilibria as well. Moreover, one can always define constrained equilibria, one for each subset A C A , where A is the superset of all possible AS's. The plausibility of alternative equilibria is interesting in itself; however, here we are interested primarily in analyzing the efficiency of different vertical arrangements vis-a-vis the social optimum. Thus, for comparison purposes we choose the 'best' decentralized equilibrium, that is, the one exhibiting the largest A , denoted by A", which will be associated also with the largest z" and To. Now to the social optimum. First we impose marginal cost pricing ( w = c), which implies llR= 0. For any A C 2 the social planner's problem is

Denoted by {T*, z*} the arguments that fulfill (8); likewise,

INNOVATION & GROWTH

A* = argmax S(A). A

Proposition 1.14The social optimum entails higher technological levels than the decentralized equilibrium, i.e., z* > z", T,* > Tz, 'da, and A" A*.

The reason for the divergence between the social optimum and the decentralized Nash equilibrium lies in the complementarities between the two inventive activities and the positive feedbacks that are generated. Consider the following thought experiment: starting from the social optimum {z*, T * } and reasoning 'backwards', each player would want to innovate less: lowering z lowers each T , which, in turn, means less commercial opportunity for the GPT sector, and hence a lower z. Moreover, a lower z means lower nu's, resulting in reductions in the size of A(w, z ) as some AS's payoffs to utilizing the GPT become negative. This means that the market for the GPT shrinks, prompting a further cutback in z, and hence in the T, of those applications sectors that remain active. It is important to note that the assumption of monopoly pricing by the GPT is not the villain, as can be seen by considering alternative pricing mechanism. First, pick a pricing rule that gives the AS's the right incentives to innovate: the only such rule is w = c, which leads to no appropriability and thus no innovation in the GPT. Second, attempt to pick a pricing rule that gives the GPT the social rate of return to innovation. Clearly, a single w(.) would not suffice, only the perfectly price-discriminating GPT monopolist would earn the social return. But price discrimination would leave zero returns to technical advance in the AS's. A fully specified technology contract might solve the problem if it is binding (a big 'if'), but that just underlies the point made here: any arms-length market mechanism under innovational complementarities necessarily entails private returns that fall short of social returns for either upstream or downstream innovations, under all plausible pricing rules.

3. Two positive externalities The feedback mechanism leading to social rates of return greater than private returns reflects two fundamental externalities. The first is vertical, linking the payoffs of the inventors of the two complementary assets, and follows from innovational complementarities. The second is horizontal, linking the interests of players in different application sectors, and is an immediate consequence of generality of purpose. The vertical externality is closely related to the familiar problem of appropriability, except that here it runs both ways, and hence corresponds to a bilateral moral hazard problem (Holmstrom, 1982; Tirole, 1988). Firms in any AS and GPT sector have linked payoffs; the upstream firm would innovate only if there is a mechanism (involving w > c) that allows it to


appropriate some of the social returns. The trouble is that, for any w > c, the private incentive for downstream innovation is too low. Thus, any feasible pricing rule implies that neither side will have sufficient incentives to innovate. Recently, several scholars as well as industrial advocates have suggested broad-based changes in government policy to increase appropriability in sectors that would qualify as GPT's (primarily semiconductors). Typically, these policy initiatives concern intellectual property protection, limits on foreign competition, and the relaxation of antitrust standards for these sectors. Our analyses suggests that policy measures of this nature cannnot sensibly be evaluated in isolation. To be sure, such measures would improve the incentive to innovate in the GPT sector, but they might also lower the returns to complementary investments made by users of the GPT throughout the economy. The second externality stems from the generality of purpose of the GPT. From the vantage point of the GPT, the AS's represent commercial opportunity; thus, the more AS's there are and the larger their demands, the higher will be the level of investment in the GPT technology. From the point of view of the AS's, expansions in the set A , enhancements to T,, and increases in the willingness to pay for the GPT by any AS'S makes all other AS'S better off by raising z. Yet, in equilibrium, each AS finds itself with too few 'sister sectors', each innovating too little.15 The point is that z acts like a public good while RR is the fixed cost needed to produce that good. However, in contrast to the traditional analysis of public goods, attempts to cover such costs with transfer prices impose a tax that discourages innovation. The horizontal externality illuminates policy issues in the economics of technology connected with the role of large, predictable demanders. It is often claimed that the procurement policy of the U.S. Department of Defense (DOD) and NASA 'built' the microelectronics-based portion of the electronics industry in the U.S. during the fifties and sixties. Obviously, the presence of a large demander changes the conditions of supply, and this may benefit other demanders. However, NASA and the DOD also had a high willingness to pay for components embodying z well outside current technical capabilities, and were willing to shoulder much of the risk through procurement assurances. In so doing NASA and the DOD may have indeed set in motion (and sustained for a while) the virtuous cycle mediated by the horizontal externality. However, it is only a coincidence that the horizontal spillouts came from the demand activities of government agencies. In the same technology, large private demanders such as the Bell System and IBM contributed directly to the development of fundamental advances in microelectronics. Earlier GPT's displayed similar patterns, as for example in Rosenberg's (1982) description of the importance of improvements in the quality of

INNOVATION & GROWTH

materials for 19th century U.S. growth. Much of the private return to improvements in material sciences (and engineering) came from a few key private sectors, notably transportation. The need to build steel rails for the railroad and to contain steam in both railroads and steamships provided a type of demand parallel to that of the government body noted above. Focused on improvements in inputs that press the technical envelope, having high willingness to pay because of their own technological dynamism, such demanders provide substantial horizontal spillouts to the extent that the technical progress that they induce is generally useful. These examples seem to suggest that 'triggers' often take the form of exogenous forces that shift the rate of return to GPT technology. Thus in the 19th century, the importance of certain sectors (e.g., transportation), driven by the economic development of the country, may have been the key. In the post Wold War I1 era, the onset of the Cold War resulted in a government procurement policy which may have played a similar role. In each case, the positive feedback aspects of GPT and AS developments then took over, generating very large external effects, and unleashing a process of technical change and growth that played out for decades. 3.1. Externalities and technological contracting Clearly, the vertical and horizontal externalities offer strong motives for breaking away from the limitations of arms-length market transactions, by increasing the degree of cooperation and explicit contracting between AS's and the GPT and between the AS's themselves. To illustrate, consider the case where any two sectors can form a binding technology contract, be it the GPT sector and an AS or a pair of AS's. In the former case they will + in the latter, they will pick the two pick z and T, to maximize Ta7sto maximize the sum of the two AS's payoffs. The result of either contract will be that z and To will be larger for all application sectors. Payoffs will be larger for the GPT sector and for all AS's not party to the contract as well. Note, however, that the activity of forming binding technology contracts is subject to the same externality as the provision of technology itself. Just as every AS would like to see other AS's advancing their own technology, so too each sector would like to see others making technology-development contracts with the GPT. Clearly, lack of enforceability as well as imperfect technology forecasting limit the practical importance of contracting. Recent events in the computer and telecommunications markets show how these considerations work in the real world. For many years, coordination between GPT-related sectors and their AS's was made simpler by the presence of dominant firms such as IBM and AT&T. These firms took a leading role not only in the development of the GPT, but also in the encouragement of complementary innovations in specific directions. This ability

(nu ng);


to commit to specific technological trajectories and therefore to direct the overall innovation cluster was labelled 'credibility' by those AS who benefited from the tacit coordination, whereas those that did not saw it just as the exercise of plain market power. Over time, technological and regulatory forces have significantly reduced the leading role of these dominant firms. There is no longer a single actor who can direct technical progress, but instead there are a few innovators of both complementary and competing technologies that influence the gradient of advance in GPT-related industries. In parallel, a wide range of weaker mechanisms have emerged for coordinating and directing technical progress. 'Strategic alliances', participation in formal standards-setting processes, consortia, software 'missionaries', and the systematic manipulation of the trade press have all emerged as standard management tools in micro-electronics-based industries. These mechanisms permit both revelation of the likely direction of technical advance within particular technologies and the encouragement of complementary innovations. Yet they probably fall short of offering the means to internalize the bulk of the externalities discussed above.

4. The dynamics of general purpose technologies In previous sections we assumed a one-shot game, allowing us to discuss the two main externalities associated with GPT's. We turn now to dynamic aspects of the performance of GPT's, such as the role of informational flows between sectors and their implications for growth. A suitable framework to model the way by which the innovational efforts of the GPT and the AS's unfold and interact over time is the theory of dynamic oligopoly as developed by Maskin and Tirole (1987) (henceforth M&T), which centers around the concept of Markov Perfect Equilibrium (MPE).16 In what follows we sketch the model and (re)state the pertinent results from M&T in terms of GPT's and AS's. Denote by xU(z,, T,) the instantaneous profit function of the AS and by xK(z,, T,) that of the GPT (for simplicity we assume that w is fixed)." The GPT and the AS are assumed to move in alternate periods of fixed length z. In the present context, z has a natural interpretation, namely, it is the length of time it takes to develop the 'next generation' (either of the GPT or of the AS), given that the other side has already developed its current technology. Thus, the quality level of the GPT at time t - 1 is z,_, and it remains constant for the next two periods (i.e., for a length of time of 22). Given z,-,, the AS develops its technology up to level T,, over a period of length z. Similarly, after the realization of T, it takes the GPT z to develop its next generation, z,,,, which will be marketed in period t + 1. We refer throughout to a single AS facing the GPT, since the case with multiple AS's is far more complex and hard to analyze."

INNOVATION & GROWTH

With no adjustment costs, each firm maximizes at time t,

where 6 = exp (-rz) is the discount factor and r is the interest rate. Define a dynamic reaction function for Markov strategies (i.e., dependent only on the payoff-relevant state) for the AS as T, = Ra(z,_,)and, similarly for the GPT, z, = Rg(Tl-,).The pair (Ra, R" form a MPE iff there exist valuation functions (V', W'), i = a, g, such that (for the AS)

Ru(z) maximizes [x"(z, T) + 6 Wa(T)].

and analogous conditions hold for the GPT's valuation functions. It is easy to show that the reaction functions will be upward-sloping in this case, since the cross-derivatives of the payoff functions, xlr, are positive (because of innovational complementarities).19 M&T prove that, for any discount factor 6, (i) there exists a unique linear MPE which is dynamically stable, and (ii) the equilibrium (steady state) values of the decision variables (z', T' in the present case) equal the static Cournot-Nash equilibrium when 6 = 0, and grow with 6. An equivalent way of phrasing (ii) is that the (dynamic) reaction functions coincide with their static (or 'Cournot') counterparts as 6 goes to zero.20 In order to verify that this proposition holds also for the case of positively sloped reaction functions, we run simulations of the MPE that results from various values of the discount factor over its whole range (i.e., 6 E [O, 11 ). As shown in Appendix 2, the long-term equilibrium values {z", T e }increase indeed with the discount factor, and that is true for any value of the other parameter in the ~ y s t e m . ~ ' The dependence of the long-run equilibrium upon the discount rate has interesting implications in our context. In order to explore them we first modify the model to include 'adjustment costs' since it is not quite plausible that R&D costs will be a function of the absolute level of z (or T ) that the firm wants to achieve. Rather, it is more likely that R&D costs depend upon the intended increments in technology, that is, that they are a function of Az, = (z, - z,J, and similarly for T. M&T elaborate on the MPE that obtains in the case of quadratic profit functions, when adjustment costs take the form (a/2)(z, - z,-,)~,resulting in the linear dynamic reaction functions22


The long-term equilibrium values are then easily computed as T' = z' = b,l(l - 6, - 6,). Since even this simple case does not have closed form solutions (except in the limiting case of a large a), we resort once again to simulations and find that the discount factor plays here the same role as without adjustment costs, that is, the equilibrium values {z', T ' } increase in 6 (see Appendix 2).23Thus, the monotonicity of { z ' , T'} with respect to the discount factor generalizes both for the case of strategic complements, and for the case with adjustment costs. In the current context the discount factor 6 can be interpreted as a measure of the difficulty in forecasting the technological developments of the other side: the smaller 6 is, the more difficult it is for the AS to anticipate the future quality of the GPT, and vice versa.24Technological forecasting, in turn, depends upon a variety of institutional arrangements that may facilitate or hinder the flow of credible technological information between the GPT and the AS's. Thus, the above results imply that the more 'cooperative' the GPT and the AS's are in terms of informational exchanges, the higher the ultimate equilibrium levels {z', T'} will be, and, since the reaction functions are positively sloped, the larger the values { z , , T,} will be at each step in the sequence leading towards the steady state (see Fig. 2). Larger values at each step may translate in turn into faster aggregate growth, provided that in the process the GPT diffuses throughout a large number of sectors in the economy. Recalling that 6 = exp ( - r ~ ) a, useful way of thinking of 6 in the present context is as follows: Suppose that z is the required overall development time of each 'new generation' of both the GPT and the AS. However, assume now that a proportion (1 - 0) of the development can be done before the other side has completed its development (which implies of course that a proportion 8 has to be done afterwards). Thus, the 'effective' length of a period is r* = 07, 0 E [8, 01, 0 > 0, 8 I 1; obviously, the smaller is 0, the larger 6 will be [since 6 = exp(-Oz*) = exp(-0zr)l. If the relationship between the GPT and the AS takes the form of armslength market transactions, with no intended exchange of technological information between them, then 8 = 8, hence 6 will be small and so will { z ' , T'}. On the other hand, if all technically relevant information flows freely between the two players, then 8 = 8, leading to faster innovation and higher levels of long-run equilibrium technologies. Thus the value of 0, reflecting institutional and organizational arrangements, may profoundly affect the present and future pace of innovation. Presumably, concerted action by the players involved as well as government policy may be able to alter 8 and thus influence the rate of GPT-related technical change in the economy.

INNOVATION & GROWTH

Figure 2 Dynamic reaction functions, drawn on the basis of the numerical results shown in Table A.l, Case 1 [e.g., z'(6 = 0.9) = T'(6 = 0.9) = 1391.

As an example, consider the case of Intel, Inc. vis-a-vis manufacturers of personal computers. The latter knew for quite a while that the next generation of Intel's microprocessors was the 586 (the 'Pentium'), that it was due in the spring of 1993, that it was expected to have at least twice the 486's performance (see Table l), etc. On that basis they presumably were able to do part of the R&D for their next generation of PCs which will incorporate the 586. However, some of the development process requires that they actually get their hands on the 586, and test it in various configurations. How much they can develop prior to the actual appearance of the 586 depends inter alia upon the degree of detail of the technological information that

G E N E R A L PURPOSE TECHNOLOGIES

Table I Successive generations of a GPT: Actual and expected. Intel's microprocessor dynasty Chip 808618088

Introduced 197811979

80286

1982

Speedier than the 808818086, the 80286 also enabled computers to run for larger programs; first appeared on the 1984 IBM PCIAT

80386

1985

First Intel 32-bit microprocessor, capable of processing data in 32-bit chunks; gave PC's power to do bigger jobs, like running networks

80386SX

1988

Lower-priced version of the 80386, aimed at killing off the 80286, which was also produced by Advanced Micro Devices

80486

1989

Intel's 'mainframe on a chip'; with 1.2 million transistors, it is one of the most complex chips ever made

486SX

1991

The chip aimed at bringing mainframe power to the masses; it will eventually make the 80386 obsolete

586

1992

Expected to have 2 million transistors and at least twice the 80486's performance; its mission: to compete with RISC chips

686

199311994

Just entering the development phase, the 686 is likely to include sound and video-processing features for 'multimedia'

The chips that powered the first IBM PC's and PC clones; they crunch numbers in 16-bit chunks but have limitations in use of computer memory

From Business Week, April 29, 1991, p. 55

they manage t o obtain a n d the extent to which Intel is willing to make them privy of the development process.2526 O n the other hand, coordination attempts can involve substantial informational a n d reputational costs which can make technology forecasting quite difficult, as revealed for example in the old dispute between IBM and manufacturers of competing mainframe system and 'plug-compatible' peripherals2' o r in the current complaints of software developers against Micro~oft.~~ Clearly, the scope for coordination in the sense outlined above increases with the number a n d range of AS'S (and so does the loss in the case of a failure t o coordinate). F o r example, a n improvement in the ability of the PC industry to forecast technological advances in microprocessors may speed u p the use of microelectronics in cars, fostering larger improvements in cars themselves, stimulating the demand for chips a n d encouraging their further development, and so forth.19

INNOVATION & GROWTH

5. Concluding remarks This paper focuses on the interface between 'key' technologies and the industrial organization of the markets and firms that spring up around them. What makes them 'key' is their revealed dynamism and pervasiveness, which are endogenous to the system.30 The goal is to forge a link between the incentives to innovate in GPT-AS'S clusters and economic growth, which builds upon the industrial organization details of these markets. Our analysis shows that the unfolding of a GPT gives rise to increasing returns-to-scale, and that this plays an important role in determining the rate of technical advance in the cluster of associated sectors. On the other hand, this same phenomenon makes it difficult for a decentralized economy to fully exploit the growth opportunities offered by an evolving GPT. In particular, if the relationship between the GPT and its users is limited to arms-length market transactions there will be 'too little, too late' innovation in both the GPT and the application sectors. Likewise, difficulties in forecasting technological developments may lower the rate of technical advance of all sectors. Lastly, we have sketched a framework for the empirical analysis of GPT's as they interact with application sectors. In future work we intend to follow several tracks. First, we would like to conduct empirical studies of GPT's as they evolve over time, interacting with a wide range of using sectors. The starting point would be the dynamic reaction functions in (9) (allowing for a multiplicity of AS's), which can be easily turned into a system of simultaneous equations having as endogenous variables i l z and j b l ~ ,and as exogenous variables demand factors and the rate of advance of 'basic science' (i.e., advances that have a bearing on technical progress in the GPT, but that are not influenced themselves by the GPT). As empirical counterparts of zlz and TJT, one could use a wide variety of patents measures, as suggested in Trajtenberg et al. (1992). Another possibility would be to use hedonic-based price indices as proxies for i l z and IT,, but it is doubtful that one could obtain such indices for sufficiently many AS's. The key parameters of interest in such a system would be the slopes of the dynamic reaction functions, which determine the dynamic performance of the GPT-AS'S cluster, and hence impact the growth of the whole economy. Second, we would like to do micro-level studies, aimed at estimating 'technological value added': how much of the gains from innovation registered in markets for final products (i.e., the markets for the AS's) are 'due to' technological advances in the AS'S themselves, as opposed to stemming from innovations in the GPT incorporated in the AS's? In our notation the issue is estimating and comparing IT: versus n'$ We have collected extensive data on microcomputers, which may allow us to carry out this type of study.


Third, we aim t o carry out historical studies of GPT's and 'institutions' (in the broad sense): the intention would be t o examine the historical evolution of particular GPT's and of the institutions coupled with them, using our conceptual framework in trying to understand their joint dynamics. In particular, we would like to assess the extent t o which specific institutions facilitated o r hindered the GPT's in playing out their presumed roles as 'engines of growth'. A key hypothesis is that institutions display much more inertia than leading technologies. Thus, a s a GPT era comes t o a close and new GPT's emerge, a n economy may 'get stuck' with the wrong institutions, that is, those that enable the previous G P T to advance a n d carry the AS'S, but that may prove inadequate to d o as much for the new G P T .

Appendix 1: Proof of upward-sloping Rg(T) To show that R8(T)is upward-sloping, we perform the comparative statics exercise implied by maximizing Eq. (6) in the text, for a fixed A :

where

and

If the second-order conditions for a GPT profit maximum hold, our assumptions imply P, > 0, P2> 0, and hence R$ > 0. The intuition of this result is easy to see. High T , in any AS shifts the demand for the GPT good out. The expectation would be, with innovational complementarities, that this raises the private return to investing in z. This argument is not quite complete, however. Since the GPT sector earns its private return through monopoly power, we need a further set of conditions that z and T, shift marginal revenue in the same direction as the shift in demand - see numerator of p, and second term in Eq. (10). To complete the proof, consider what happens when an additional AS enters. In the case of fixed w, it is immediate that an additional AS increases optimal z. When w is free to vary, the result is implied by our assumptions: add the marginal sector to Eq. (6) with weight h and differentiate with respect to h. At h = 0, the impact on

INNOVATION & GROWTH

z is PIX:+ P2[X0 + ( W - c)X(l]> 0. For il> 0, the values of always positive. Thus, adding a sector always increases z.

PI and p2 change but are

Appendix 2: Simulations of MPE Case 1: No adjustment costs The profit functions are assumed to take the form:"

and similarly,

where d is a shift parameter common to both. Thus the reaction functions are

Solving for MPE renders the following two equation^:'^

Given 6 one can solve for b, in (13), and then, given 6, d, and the corresponding b,, one can solve for b, in (14). We solve for [b,, b,] out of this system for different values of the parameter 6 and compute the long-term equilibrium values,

As can be seen in (14), d impacts b, in a multiplicative fashion, but does not influence b,; hence {z', T'} are just multiples of d, and we can perform all simulations with a single value of d (we picked d = 100). The results are shown in Table A. 1.

Case 2: With adjustment costs The profit functions are the same as in (1 1) and (12), except that we subtract from for the AS and AP = (a/2)(z, - z,-J2 them the adjustment costs A" = (a/2)(Tr for the G P T sector. The corresponding reactions functions are


Table A. I Simulations of MPE. Case 1 : Without adjustment costs (d = 100)

Case 2: With adjustment costs (d = 100) ze(6, a ) = Te(6, a)

Using the software program 'Mathematica' we derived from (1 5) the three equations in the three unknowns [b,, b,, b,], solve for them for different sets of values of the parameters (6, d, a},and compute the long-term equilibrium

INNOVATION & GROWTH

As in the case without adjustment costs, d impacts b, in a multiplicative fashion but does not influence h , and b,; hence {z', T ' ) are multiples of d, and we can perform all simulations with a single value of d. Table A. 1 shows the results of the simulations for a = 1, 10, 100 and &(0.1, 0.9) in intervals of 0. I.

Acknowledgements Prepared for the Conference on R&D and Productivity in Honor of Zvi Griliches, Jerusalem, May 1991. We gratefully acknowledge the detailed comments and suggestions from Ariel Pakes. We also thank Zvi Griliches, Nathan Rosenberg, Edward Steinmueller, Scott Stern, Jean Tirole, and two referees for helpful comments on earlier drafts.

Notes 1 See, however, the series of papers in Parts I1 and IV of Griliches (1988). 2 In defining innovational complementarities and understanding their role, we were strongly influenced by Rosenberg's insightful 1979 essay, 'Technological Interdependence in the American Economy', reproduced in Rosenberg (1982). The formal analysis is close in spirit to that of Milgrom et al. (1991). 3 For a notable exception see Grossman and Helpman (1991), particularly their models of the product cycle. 4 Murphy et al. (1989) show that partial equilibrium implications are robust to general equilibrium considerations in a model with aggregate logic much like ours, but different microfoundations. 5 We do not attempt any serious review of the relevant technological facts here. Section 2 of Bresnahan and Trajtenberg (1992) has more detail. See also Mokyr (1990) and David (1990). 6 Think of it as the density with which transistors can be packed on a chip, the fundamental level of semiconductor technology which permits advances along most of the quality axes. 7 Not all historically important GPTs have this industrial organization. Many developments in early steam engine technology, for example, took place inside using industries such as mining and transportation. Our modelling strategy is to associate each technology with a separate economic agent, so as to illuminate the incentive to innovate for each. We then revisit the question of how these agents might be organized, by firms, contracts and markets. 8 We omit here two additional forces that are thought to play a similar role: Technological interrelatedess and diffusion in conjunction with learning-bydoing. The first means that there is 'learning by inventing'. The invention of particular subtechnology in the context of a GPT lowers the cost of inventing the next one, which, in turn, contributes to span other subtechnologies further down the line. The second is more conventional: As the number of downstream sectors using the GPT increases, the costs of producing the generalized input go down because of 'learning-by-doing', thus contributing to a self-sustained process of economy-wide growth. 9 If the GPT is critical for the very existence of the AS (e.g., semiconductors in microcomputers), then the value of the 'opportunity action' is identically zero; if the GPT is a noncritical enhancement (e.g., semiconductors in motor vehicle


engine control), the opportunity action would be the use of an alternative technology. 10 In our semiconductor example, the surplus could result from using personal computers based on microprocessors of quality z, and embodying computer architectures and other components of quality T. 11 Note that this formulation takes T, as given and assumes that CU(T,)is financed according to the terms of the contract struck between buyers and sellers. 12 Notice that in this case the demand for the GPT input is Y ( w , z, T,) = X"[y(z, To)/ ( 1 + ~ f ) z,, To],where is the elasticity of demand for the AS goods. 13 We abstract from the internal organization of the GPT 'sector', and treat it as a monopoly; however, the analysis below holds for pricing rules other than monopoly pricing. 14 The proof closely follows Cooper and John (1988) and Milgrom and Shannon (1992), and hence we omit it. We note only that it relies on Ru(z) and Rg(T) being upward-sloping and on the assumption that XZ, 5 0 (made in Section 2. I), which 5 C,,,nq(.),. implies 15 Note that this issue arises above and beyond the multiple equilibrium problem, since we have assumed that the 'best' Nash equilibrium is the one that holds. 16 A more thorough treatment, incorporating uncertainty explicitly, would follow Pakes and McGuire (1992); however, that is well beyond the scope of this paper. 17 We assume that these instantaneous profit functions have the same derivative properties as their static analogs of previous sections, but we further assume that nl(.),i = a , g, are bounded from above. 18 We conjecture that the qualitative results will be the same if instead there are a few large AS that act in tandem vis-a-vis the GPT or if the GPT acts as a Stackelberg leader vis-a-vis many small AS'S; however, further work needs to be done to prove that this is so, in particular one would have to deal appropriately with the problem of multiple equilibria. 19 See the proof of Lemma 1 in M&T (pp. 950 951): the negative slope of the reaction function stems directly from the assumption that n,, < 0. Thus. the converse holds for K , , > 0 (which is the equivalent of our K,, > 0). 20 M&T prove the proposition for the special case of quadratic profit functions; Dana and Montrucchio (1986) generalized the proof for any concave payoff function: see also Dana and Montrucchio (1987). 21 The other parameter is d, the constant in the quadratic profit function, which enters multiplicatively in the equations for I' and T', and hence does not affect the relationship between them and 6. 22 To recall, since M&T assume that the cross-derivatives of the profit function are negative, b, is in their case negative. Keep in mind that {b,, b,, b,) are unknowns, that are obtained by solving the system for the MPE. Here resides the main practical difficulty of the model, since the system of equations that needs to be solved (by simulations) in order to obtain {b,, b,, b,} can be very complex. 23 We also find that {z', T'} increase with the shift parameter of the profit function and decrease with a, but these are hardly surprising results. The simulations were run assuming symmetry between the GPT and the AS, which is in this case rather implausible (if only because there are no natural units to define z and T); that is, however, a mere technicality: the truly limiting assumption is the functional form of the profit and adjustment costs functions. 24 This is of course a shortcut to the explicit modelling of technological uncertainty, which would involve a game of incomplete information.

v

n:(.)

INNOVATION & GROWTH

25 It is interesting to note that, dramatically altering its conduct in this respect, Intel has been providing some of its users (such as Compaq) with details of the 586 as it was being developed. 26 The reverse condition is perhaps less obvious but not less important: to continue with the same example, Intel has been developing parts and circuits for personal computers (other than microprocessors) because '. . . through them Intel gains insight into trends: Knowing what needs to go on a board this year helps it determine what should go into microprocessors next year' (Business Week, April 29, 1991, p. 55). This is true to various degrees as one goes down the 'technological tree': thus, software developers need to actually have the new operating systems in order to develop software for them; in order to write new operating systems one needs to get one's hands on the (new) personal computers that will use them, and so forth. 27 The latter accused IBM of attempting to delay their innovation efforts through concealment of information about interface standards and uncooperative behavior in establishing market-wide standards (e.g., ASCII vs. EBCDIC) (see Brock, 1975; Fisher et a/., 1983). 28 They claim that Microsoft is less than candid about the features of forthcoming operating systems, thereby delaying efforts to produce complementary applications. In these examples, struggles for market power may have lead to anti-coordination incentives, an idea familiar from the standards literature (see David and Greenstein, 1990). Farrell and Saloner (1986) offer a theory in which there is a social gain to coordinating but rent seeking behavior leads to imperfect outcomes. 29 This has the flavor of the 'big push' in economic development (see Hirshman, 1960). 30 Surely there are more primitive features that attest to the potential of some technologies to become GPT's, but so far we have not been able to find a convincing characterization of such features. 31 We assume that d is large enough (relative to T and z ) so that within the relevant range dn"/dT > 0 and dnRlaz> 0. For convenience we omit here the subindex a in the T's. 32 Comparing this case (with xr,> 0 and hence a positive b,) to the one examined by M&T, one can see that our Eq. (13) is identical to their Eq. 20, but our Eq. (14) differs from their Eq. 21. 33 Jean Tirole informed us in a personal communication that the FOC as shown in Eq. 30 of their published paper (Maskin and Tirole, 1987) is missing terms, and he kindly made available to me an unpublished corrigendum with the correct equation, which is the one shown here, adapted to our case.

References Abramovitz, M., 1956, Resource and output trends in the United States since 1870, American Economic Review Papers and Proceedings 46, 5-23. Arrow, K. J., 1962, Economic welfare and the allocation of resources for inventions, in: R. Nelson. ed., The rate and direction of inventive activity (Princeton University Press, Princeton, NJ) 609-625. Bolton, P. and M. D. Whinston, 1993, Incomplete contracts, vertical integration, and supply constraints, Review of Economic Studies 60, 121-148. Bresnahan, T. and M. Trajtenberg, 1992, General purpose technologies: Engines of growth?, NBER working paper no. 4148.


Brock, Gerald W., 1975, US.computer industry: A study in market power (Ballinger, Cambridge, MA). Bulow, J., J. Geanakoplos, and P. Klemperer, 1985, Multimarket oligopoly: Strategic substitutes and complements, Journal of Political Economy 93, 488-51 1. Cooper, R. and A. John, 1988, Coordination failures in Keynesian models, Quarterly Journal of Economics 103, 441-463. Dana, R. A. and L. Montrucchio, 1986, Dynamic complexity in duopoly games, Journal of Economic Theory 40, 40-56. Dana, R. A. and L. Montrucchio, 1987, On rational dynamic strategies in infinite horizon models where agents discount the future, Journal of Economic Behavior and Organization 8, 497-51 1. David, P. A., 1990, The dynamo and the computer: An historical perspective on the modern productivity paradox, American Economic Review Papers and Proceedings, 355-361. David, Paul A. and Shane Greenstein, 1990, The economics of compatibility standards: An introduction to recent research, Economics of Innovation and New Technology 1, 3-41. Farrell, Joseph and Garth Saloner, 1986, Installed base and compatibility: Innovation, product preannouncements, and predation, American Economic Review 76, 940-955. Fisher, F. M., J. E. Greenwood, and J. J. McGowan, 1983, Folded, spindled, and mutilated: Economic analysis of U.S. vs. IBM (MIT Press, Cambridge, MA). Griliches, Z., 1957, Hybrid corn: An exploration in the economics of technological change, Econometrica 25, 501-522. Griliches, Z., 1958, Research costs and social returns: Hybrid corn and related innovations, Journal of Political Economy 66, 419-431. Griliches, Z., ed., 1984, R&D, patents, and productivity (University of Chicago Press, Chicago, IL). Griliches, Z., 1988, Technology, education, and productivity (Basil Blackwell, New York, NY). Griliches, Z. and V. Ringstad, 1971, Economies of scale and the form of the production function (North-Holland, Amsterdam). Grossman, G. M. and E. Helpman, 1991, Innovation and growth in the global economy (MIT Press, Cambridge, MA). Hart, O., 1988, Incomplete contracts and the theory of the firm, Journal of Law, Economics and Organization 4, 11 9 139. Hirshman, A. O., 1960, The strategy of economic development (Yale University Press, New Haven, CT). Holmstrom, B., 1982, Moral hazard in teams, Bell Journal of Economics 13, 324340. Landes, D., 1969, The unbound Prometheus (Cambridge University Press, Cambridge). Maskin, E. and J. Tirole, 1987, A theory of dynamic oligopoly, 111: Cournot competition, European Economic Review 31, 947-968. Milgrom, P. and J. Roberts, 1990, Rationalizability, learning and equilibrium in games with strategic complementarities, Econometrica 58, 1255-1277. Milgrom, P., Y. Qian, and J. Roberts, 1991, Complementarities, Momentum, and the evolution of modern manufacturing, American Economic Review, 84-88.

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Mokyr, J., 1990, The lever of riches (Oxford University Press, New York, NY). Murphy, K. M., A. Shleifer, and R. W. Vishny, 1989, Industrialization and the big push, Journal of Political Economy 97, 1003-1026. Pakes, A. and P. McGuire, 1992, Computation of Markov perfect Nash equilibrium: Numerical implications of a dynamic differentiated product model, NBER technical discussion paper. Romer, P., 1986, Increasing returns and long-run growth, Journal of Political Economy 94, 1002- 1037. Rosenberg, N., 1982, Inside the black box: Technology and economics (Cambridge University Press, Cambridge). Spence, M., 1975, Monopoly, quality and regulation, Bell Journal of Economics 6, 417-429. Solow, R., 1957, Technical change and the aggregate production function, Review of Economics and Statistics 39, 312-320. Tirole, J., 1988, The theory of industrial organization (MIT Press, Cambridge, MA). Trajtenberg, M., R. Henderson, and A. Jaffe, 1992, Ivory tower versus corporate lab: An empirical study of basic research and appropriability, NBER working paper no. 4146.

14

W H A T REQUIRES EXPLANATION? Richard G. Lipsey, Cliff Bekar and Kenneth Carlaw Source: E. Helpman (ed.), General Purpose Technologies and Economic Growth, Cambridge, M A : MIT Press, 1998, pp. 15-54.

To get at a working definition of a general purpose technology, we first summarize the state of the theoretical literature. We next look at illustrative historical examples, and using current theories in conjunction with the historical record, we identify a set of technological characteristics that define a GPT. Finally, we check our concept against additional examples and raise the question of its usefulness. In the course of our discussion, we enumerate what seems to us to be the most relevant of the rich set of facts and empirical generalizations that have been established by students of technological change. We hope these will play the same role that Kaldor intended for his stylized facts in macro growth theory, forcing theories out of the infinite number of spaces derivable from pure conjecture and into a finite number of empirically relevant spaces. It would be utopian to expect a theory to explain all of the awkward facts, but it is desirable that the theories we take seriously do not blatantly conflict with any of them. (This is by no means a weak requirement.) In the first two sections we consider theories that attempt to capture stylized versions of GPTs in rigorous formulations. We then consider theories that are appreciative in Nelson's (1995) sense of the term. These theories are able to include more of the observed empirical richness of GPTs than can formal theories, but at the cost of being unable to model them matematically.

1 Formal theories Bresnahan and Trajtenberg

In their seminal article on the theory of GPTs, Bresnahan and Trajtenberg (BT) (1992) argue that technologies have a treelike structure, with a few prime movers located at the top and all other technologies radiating out

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from them. They define GPTs as having three key characteristics: pervasiveness, technological dynamism, and innovational complementarities. Pervasiveness means that a GPT is used in many downstream sectors because it provides a genetic function, such as rotary motion. Technological dynamism results from its potential to support continuous innovational efforts and learning, which allows for large increases in the efficiency in the GPT over time. Innovational complementarities exist because ". . . productivity of R&D in the downstream sectors increases as a consequence of innovation in the GPT, and vice versa." The consequences of improving the GPT are reduced costs in the downstream application sector, the development of improved downstream products, and the adoption of the GPT in a growing range of downstream uses. The decision to improve the GPT induces more innovational effort in the final applications sectors, which in turn induces more innovation in the GPT. This vertical complementarity causes a nonconvexity in the implicit production function for R&D, which creates a coordination problem between the GPT sector and the application sectors. The nonconvexity is viewed as reflecting a number of real world phenomenon that surround innovation, including information asymmetries, sequencing of innovations, technological uncertainty and coordination problems. The single immortal GPT is owned by a monopolist who optimally chooses how fast to improve its general productivity. The GPT's users choose how fast to improve their specific application. The authors define a continuum of partial equilibria running from the myopic, noncooperative equilibrium, with a low rate of innovation, to a perfectly coordinated equilibrium. In the latter, all complementary relations are recognized and the rate of innovation is socially optimal. Helpman and Trajtenberg In the papers reprinted in chapters 3 and 4 of this volume, Helpman and Trajtenberg (HT) extend BT's paper by modeling a version of the "technology tree" using an explicit general equilibrium framework, by tracking the effects of a new GPT on macro aggregates, and by explicitly modeling the new GPT's diffusion to capture the horizontal externalities that BT discuss. At any one time there is only one GPT in use, and it is employed only by the sector producing final goods. An R&D sector invents supporting components that are used alongside the GPT, and a third sector produces them. The GPT's productivity depends on the number of these supporting components, which are specific to one GPT. They are modeled in a refinement of the production function found in Grossman and Helpman (1991), who based it on the Dixit-Stiglitz utility function which was developed to model monopolistic competition. This function has the property that as new supporting components are developed, total output increases while

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productivity per component falls, imposing a finite limit to the GPTs development. It also implies a vertical complementarity between the GPT and its supporting components, and a horizontal substitutability among the supporting components themselves. Each GPT arrives exogenously. It is immediately recognized as a GPT, and resources are diverted from final production to R&D, which develops the new GPT's supporting component. (If R&D is still going on to develop components for the old GPT, this activity stops immediately, and these resources also move to developing components for the new GPT.) The diversion of labor out of component production, where it produces monopolistically competitive rents, into R&D, where it produces no rents, causes what HT call an "output slowdown." In their model this is a fall in measured output. (It is not clear what happens to total factor productivity, since the assumptions needed for its precise calculation are violated by the existence of a monopolistically competitive sector.) A second possible cause of their output slowdown is a mismeasurement of the full value of the new R&D that makes no immediate contribution to final goods production. Eventually enough components are developed for the productivity of the new GPT to exceed that of the old, and final goods producers switch from the old to the new GPT. In their second paper HT model the process of a new GPT diffusion. There are many sectors that may potentially adopt the GPT, and each sector has a different productivity in using it. Each sector develops components for the GPT in sequence by diverting resources from production to R&D, starting with the one that has most to gain. (The free-rider problem is ruled out by assumption in both models.) Once it has made its initial component, each sector waits until the next to last phase of the economy's R&D is completed; then all sectors rejoin the R&D process to complete the final phase. Thus the transitional pattern from one GPT to another is determined by the sequencing of the R&D, not the diffusion of the GPT. Aghion and Howitt

Aghion and Howitt (this volume, chapter 5) provide their response to two empirically relevant issues in HT (1994), which is reproduced here as chapter 3. The first issue concerns the timing of slowdowns that occur immediately after the emergence of the new GPT. Aghion and Howitt argue that this is inconsistent with David's (1991) observations that it may take several decades for a major new technology to have a significant impact on macroeconomic activity. They interpret this to mean that there should be an initial period in which the macro data are unaffected by the arrival of a new GPT. Aghion and Howitt argue that measurement error and complementarities are two of the three reasons why we should expect to see this period of "no

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action". The third is social learning. To model this third reason, they adapt most of HT's framework. The new feature is that each sector must develop a specific intermediate good before anyone in that sector can profitably make components for the GPT. After the GPT arrives "serendipitously," firms must first develop sector-specific "templates" using fixed endowments of specialized labor that has no other use. During this phase no resources are moved and nothing changes in measured aggregates. A model of epidemic diffusion generates the desired social learning dynamics. Initially every sector's specialized labor engages in R&D to acquire its template. Success occurs with an initial low probability that increases as more and more sectors acquire templates. When each sector has its own template, resources are moved out of production into R&D to create components for the GPT. When a sufficient number of components have been created, the economy switches over to using the new GPT in production. Aghion and Howitt also address HT's explanation of the fall in measured output, arguing that the maximum size of the slowdown, based solely on a reallocation of labor to the R&D sector, could not be enough to account for observed slowdowns. Instead, the adjustment and coordination problems associated with the introduction of a new GPT, and its accompanying higher rates of innovation, might increase the rate of job turn over and accelerate the rate of obsolescence. They deal with the unemployment that would result from increased job turnover using a revised version of their main model described above. They deal formally with the obsolescence problem using a revised version of the model presented in Howitt's measurement paper (this volume, chapter 9). In this model there is a range of parametric values for which the increase in the rate of obsolescence, caused by a higher rate of technological change, can lead to a slowdown in measured output. Dudley

Dudley (forthcoming) follows Innis (1951, 1972) and Dudley (1995) in treating information and communication technologies (ICTs) as the fundamental technology from which all others flow (although he does not use the term GPT). His ICTs have three basic characteristics: to store, to transmit, and to reproduce information. Each ICT is better at some of these functions than others, and R&D increases that strength relative to the others as time goes by. Eventually the existing ICT fulfills its least efficient function too inefficiently to be tolerated. Research switches to the development of a new ICT as an endogenous response. Until the new ICT is well enough developed to be widely adapted, measured productivity growth will be slow (since all R&D is devoted to the sector producing the new ICT, which has a small weight in overall output). This whole process gives rise to an endogenous cycle of ICTs, each better at one of its three functions than the other two.


Each cycle is associated with a transitional slowdown. Dudley uses this shift from one type of ICT to another to explain broad historical trends and cycles over 1,000 years.

2 Appreciative theories Although none of the authors considered in this section use the term GPT, they employ concepts that are similar enough to be of interest to those seeking to understand the phenomenon of pervasive technologies. Freemun, Perez, und Soete

Several authors have used the concept of a technoeconomic paradigm (TEP), which is much broader than a GPT, since it covers the entire economic system that surrounds any set of pervasive technologies actually in use (e.g., see Freeman, Clark, and Soete 1982; Freeman and Perez 1988; Freeman and Soete 1987). A TEP is a systemic relationship among products, processes, the organizations, and the institutions that coordinate economic activity. A typical paradigm is based on a few key technologies and commodities that are mutually reinforcing, a few key materials whose costs are falling over time, a typical way of organizing economic activity, a typical supporting structure, a typical pattern of industrial concentration, and a typical pattern of geographical location. Although all the elements of a TEP are assumed to be systematically related, the driving force for change comes from what we would call a new GPT, some innovation that fundamentally alters the relationships among various technologies and between technology and the other elements of the TEP. The concept of a TEP has been used for two major purposes. The first is to argue that changes in important technologies induce structural changes across the whole economy. The second is to develop a theory of the long cycle in which the prevailing technology eventually runs out of scope for improvement, causing severely diminishing returns to further R&D and investment. This crisis in the old TEP provides the endogenous incentive for the development of new technologies that form the core of a new TEP. Mokyr

Mokyr (1990) considers two types of invention. "Micro inventions" are incremental in nature, largely improving existing technologies and responding to economic incentives, and "macro inventions" are defined as "inventions in which a radical new idea, without clear precedent, emerges more or less ab nihilo." They ". . . do not seem to obey obvious laws, do not necessarily to respond to incentives, and defy most attempts to relate them to exogenous economic variables" (p. 13).

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Mokyr's macro inventions serve two purposes that are relevant to a discussion of GPTs. First, without macro inventions the growth process would eventually come to a halt. Second, because they possess widespread complementarities, they provide a fertile ground for many supporting micro inventions. Lipsey and Bekar

Lipsey and Bekar (1995) study what they call "enabling technologies," which are defined mainly by their extensive range of use and their complementarities. Enabling technologies are roughly similar to GPTs, although the authors point to fewer classes and fewer cases within each class than we now accept as GPTs. Using historical and current evidence, they argue two main points. First, the introduction of such technologies have in the past caused major changes in the entire structure of the economy, as well as in its economic performance, changes that they call deep structural adjustments, or DSAs. Second, over the last two decades the industrialized economies have been going through such a period, this time caused by the current revolutions in two enabling technologies, made-to-order materials and computer-based ICTs. They also argue that the introduction of a new enabling technology is neither necessary nor sufficient for DSAs. It is not necessary because some less pervasive technologies have caused such economywide repercussions. It is not sufficient because some enabling technologies have not been associated with such wide-ranging repercussions.

3 GPTs in history If the concept of a GPT is to be useful, then GPTs must be identifiable. Our procedure is first to choose a set of important technologies according to their observed economic effects. We search through history to find examples in which a widely, used new technology caused changes that pervaded the entire economy, Lipsey and Bekar's DSAs. As a second step we look for common technological characteristics which we use to define a GPT.' The introduction of a major new technology whose effects reverberate through the entire economy, sometimes affecting the political, economic and social structures, is a relatively rare event. To get clear and dramatic examples of technologies which we want to include in our set of GPTs, we have ranged as far back in economic history as the neolithic agricultural revolution. Although the documentation of our earlier examples is less detailed than those from more modern times, we have selected only cases where the broad outlines of what happened are clearly established by historical and/or archaeological research. While the effects of many of the GPTs we examine may seem extreme to some readers, every one of those

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that we mention is supported by strong empirical evidence that is not easily appreciated until one looks at the historical record in some detail. Of course many of the GPTs only contributed to the outcomes that we mention, as opposed to being their sole cause. After choosing our examples, we found that they all fell within four main activities that are covered in the rest of section 2.3. Although we have not tried to be exhaustive, we believe we have identified most of the historical cases where new, pervasive technologies caused profound DSAs. Below we briefly allude to most of these, although space has caused us to delete our discussion of iron, steel, and several major transport technologies.

3.1 Information and communication technologies ( K T ) Providing, analyzing, and using information is essential to all coordinated economic activities. Writing

Before the invention of symbols to represent the spoken word, records were mostly held in human memory and communicated orally. (One important exception was the symbols for recording quantities that were the precursors of writing.) Writing was invented independently in several places, allowing information to be communicated accurately over time and distance, and leading to a major increase in the complexity of economic activities. Its invention in Sumer around 3,500 BC was accompanied by the development of sophisticated systems of taxation and public spending-systems that were quite impossible when most records were held in memory. The new public savings were largely used to finance the building of irrigation works, whose technology evolved rapidly. In Sume the area under cultivation increased, and agricultural surpluses rose. The populations of the largest settlements, which had been measured in the hundreds for millennia, increased over two centuries into the tens of thousands. A division of labor appeared among the priesthood whose members raised the taxes and supervised the first irrigation systems. Temples, larger and more complex than anything seen before, made their appearance. In short, there was a radical transformation of the societies of the TigrisEuphrates valley. The changes in the two or three centuries following the widespread use of writing probably exceeded the changes over the two or three millennia preceding it. While it is unlikely that all of these changes could be attributed directly to writing, the evidence does suggest that most of them would have been difficult, and some of them impossible, to accomplish in a society without written records (Dudley 1991, ch. 1; Schmandt and Besserat 1992).

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Printing

Economic, political, and social historians agree that the widespread use of printing contributed in important ways to the dramatic changes that occurred in Europe between 1500 and 1700. With manuscripts, the major cost of duplications was the variable cost of the scribe's time; with printing, the major cost was the fixed cost of typesetting, and the marginal cost of printing an extra copy was small. This new cost structure made mass communication feasible. At first, printing achieved a low-level equilibrium typical of new technologies with network externalities (Arthur 1988). Texts were printed in Latin for the few who could read. To escape this equilibrium, two changes were needed. First, a relatively large amount of printed material had to be published in the popular vernaculars. The printers and grammarians of Europe played a key role in developing and implementing standardized version of each vernacular over the century following the introduction of printing. Second, a significant proportion of the population had to be trained to read the vernaculars. Here the Protestant revolution was critical. Protestant thinkers insisted that their followers be able to read and interpret the scriptures for themselves. Mass communication helped the Protestant revolution, since its direct appeal to the people would have been impossible without the many low-cost printed pamphlets written in the vernacular. As these developments occurred and the costs of large-scale publication fell, learning exploded. Monopolies of knowledge were upset. The Netherlands were tolerant of both printing and the new knowledge that it represented. Thinkers, writers, and printers, exiled from other parts of Europe, moved there. The creation of the Dutch information network based on low-cost reproduction of the printed word greatly increased productive efficiency and tax revenues. Although many factors contributed to their eventual victory over Spain, and their rivalry with Britain as a world trading power, research indicates that a key part of their success was owed to their liberal attitude toward the technology of printing and the learning that it embodied (e.g., see Dudley 1991; Cipolla 1993; Cardwell 1972; Huff 1993). Current ICT revolution

The latest ICT revolution is being driven by the electronic computer in its many and varied forms. Our account of it is brief, since most of the dramatic changes are well known and are referred to elsewhere in this volume. (For one excellent succinct survey, see Greenwood 1997.) The revolution is changing product design, production, marketing, finance, and the organization of firms. It is also creating a wide range of new products

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incorporating hard coded chips, computers, andlor software. Computers are used to fly aeroplanes, drive trains, operate machines, run buildings systems, warn of unsafe driving practices, monitor health, to facilitate communication through the interned, e-mail, and desktop publishing. By managing information flows more effectively than did the old, hierarchally organized, mass of middle managers, computers are causing major reorganizations in the management of firms. Labor productivity is increasing rapidly in many of the affected industries, even if it has yet to show up strongly in the aggregate data. 3.2 Materials

Materials are required for all consumers' goods and for all process technologies. Few services are provided by unaided labor, and most complex service operations require elaborate process technologies that are embodied in physical capital. The very concepts of the stone age, the bronze age, the iron age, and the age of steel highlight the importance of materials and the structural transformations caused when one pervasive materials technology succeeds another.

Bronze Stone, clay (pottery), and wood were the universal materials before the age of metals. Bronze gave its name to an age lasting for about fifteen centuries, starting about 2,800 BC. The invention of bronze, the first material malleable enough to be worked but strong enough for most uses, facilitated a vast range of new technologies for both civilian and military uses. These led to many wide-ranging social and political changes. Prior to bronze, the main external threat to town dwellers was attack by uncoordinated bands of migrant barbarians. With bronze weapons, trained armies and multiple city empires appeared for the first time, since bronze weapons and interlocking bronze shields gave enormous scale advantages to large armies over smaller ones. Cities now became walled against the main external threat of attack by well-equipped and disciplined armies. Once the optimal size of the state grew to cover a wide geographic area, it became too expensive to coordinate transactions through centralized authority. As a result the command system (documented to have been a major allocator of resources in compact single-city theocracies) was largely replaced by markets. Growing markets facilitated new divisions of labor. A bronze age empire of 2,400 BC was demonstrably more complex in economic, technological, and social dimensions than a stone age town of 3,000 BC. The reason, at least in part, is the introduction of the workable metal for which the age is named (Dudley 1991; Drews 1992).

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Made-to-order materials

New materials became increasingly important after the growth of the chemical industry at the end of the last century. Initially a new material was invented in isolation and used to substitute for some existing material. Today, however, materials are invented specifically for the new products and processes that are being developed. New materials are seen as crucial to the continued expansion of many important growth sectors, including microelectronics, transportation, architecture, construction, energy systems, aerospace engineering, the automobile industry, and, to look further into the future, fusion reactors, ersatz human organs, and solar conversion cells. The technology of made-to-order materials is creating clusters of related innovations in often widely differentiated industries: Changes in materials innovation and application within the last half century. . . have occurred in a time span which was revolutionary rather than evolutionary. The materials revolution of our times is qualitative as well as quantitative. It breeds the attitude of purposeful creativity rather than modification of natural materials, and also a new approach-an innovative organization of science and technology. (Kranzberg and Smith 1988, p. 88)

3.3 Power delivery systems Virtually all productive activities require the application of power. It is useful in some cases to distinguish between the primary generator of the power and the system that delivers that power. For example, electricity was the first power system to separate the place of generation from the place of use by more than the distance allowed by such physical links as belts and shafts. This separation had important consequences. Our analysis is not, however, affected by the distinction, so we treat the power source and its delivery mechanisms as a single technology, which we call "power delivery systems." Waterwheel

During the medieval period the spreading use of the waterwheel led to the mechanization of European manufacturing. The power of animals and humans (often slaves) was largely displaced by the wheel, setting Europe on a trajectory of mechanization which eventually took its industry well beyond that of Islam and China. The waterwheel went through many improvements. Furthermore important ancillary inventions, particularly the cam, which turns rotary motion


into linear motion, expanded its range of activities to include sawing, hammering, grinding, pumping, beer brewing, tanning, paper-making, and cloth fulling. During the Middle Ages the use of water power spread to include the development of floating mills, large dams, and mills that harnessed tidal power. These were capital intensive and were financed by some of the earliest share issues. Also new property rights had to be developed to regulate the use of the river for power (Gimpel 1967: Gies and Gies 1994). Technological improvements continued through the nineteenth century when water wheels were challenged by steam and finally eliminated by electricity in the late nineteenth and early twentieth centuries. Steam

Commercial steam power started with Savery's atmospheric engine. Although technically inefficient and dangerous, it was quite widely used because it outperformed the available alternatives, all of which used animate power. In 1712 Newcomen invented a crude but effective and relatively safe atmospheric steam pump which was soon widely used in coal mines. Micro improvements alone almost doubled the efficiency of the Newcomen engine. James Watt transformed Newcomen's engine into one in which steam did the driving rather than atmospheric pressure. Although he greatly improved the efficiency of his new reciprocating engine over the years, he did not believe in high pressure. Only after his patent expired in 1800, did the development of the high pressure engine allow steam to expand into many new uses especially in transportation. High-pressure engines required strong materials, which caused many improvements in metallurgy. Taken as a whole, late nineteenth-century steam engines enjoyed many orders of magnitude increases in efficiency over their early eighteenth-century counterparts (Landes 1969; Von Tunzelman 1995). Steam gradually replaced water power as the main source of industrial energy throughout the first half of the nineteenth century. At first, steam worked within factories designed for water power. Later, however, new factories were designed to suit the steam engine. The economies of scale associated with steam power made large factories more efficient than smaller ones. Locational advantages altered drastically, since factories were no longer tied to fast-moving water. The total amount of power available to industry increased many fold over water-powered factories. As is typical of the competition between old and new technologies, systems based on water power fought back, and a series of technological advances improved their efficiency through the early part of the nineteenth century. Right up to the end of the century, water was used to power many factories, particularly in the textile industry.

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Steam allowed for the creation of new products, new production techniques, and, eventually, many new industries. Steam engines slowly replaced sails at sea and rapidly replaced long-distance horse transport on land. The railways transformed the patterns of industrial location that had resulted from road and water transport, opening up new areas for the growing of grain and significantly lowering the price of food. Electricity

The dynamo converts mechanical power into flows of electrons that have multiple uses. It is probably the most pervasive energy delivery innovation of all time. Electricity started with only a small number of applications. Slowly, as technical problems were solved, the number of uses expanded, transforming the techniques and locations of production and leading to a range of new products and industries. Electricity powers factories and lights cities. It has spawned a range of new consumer's durables. For example, an assortment of electrically driven household machines including washing machines, dishwashers, vacuum cleaners, irons, refrigerators, deep freezers, and electric stoves transformed household work and eliminated the battery of servants that was required to run middle-class households in 1900. Electricity has powered an ongoing communications revolution, starting with the telegraph which, for the first time in history, provided a publicly available system that allowed information to travel faster than human messengers. The new communications technologies made possible by electricity evolved through the telephone, the radio, and the TV. Electricity also powers the computer which is the basis of the current ICT revolution. Electricity is therefore complementary with the new computer-based GPT. The full development of electricity's potential required substantial structural alterations across the entire economy. One of the most important was a drastic alteration in the layout of factories. Water and steam, used a central drive shaft whose power was distributed throughout the factory via a set of pulleys and belts. Because of heavy friction loss in belt transmission, machines that used the most power were placed closest to the drive shaft, and factories were built with two stories to get more machines close to the shaft. At first, electric motors merely replaced steam or water as the power source for the central drive; they were installed in a design adapted to the old power sources. Later, a separate motor was attached to each machine (the unit drive), after an intermediate stage of group drives. It was then slowly realized that the factory could be built as a single story and the machines arranged in the order of the flow of production. Only when the restructuring was completed, was the full potential of electric power in factories realized (Schurr 1990; David 199I).

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Electricity altered scale economies. In some lines of production, particularly assembly, scale economies were increased; in others, however, small-scale production became more cost efficient because an electric motor could be attached to each machine tool. The result was a system of small decentralized parts producers supplying large centralized assembly plants-a method of production that is still used today. The 1890s were also a time of intense merger activity, which was sometimes the cause, and sometimes the effect, of electrification (Chandler 1990).

Internal combustion engine The development of the internal combustion engine overlapped the later stages of steam and the early stages of electricity. It began as a relatively inefficient atmospheric engine in which the explosion of coal gas pushed a cylinder upward and atmospheric pressure pushed it down on its power stroke. Soon, however, the explosion of gas was used for the power stroke, and by setting the cylinder on its side, a quiet, efficient, highly successful four-cycle engine was produced. A decade passed before the technical difficulties of using gasoline were overcome and the engine became mobile. Multiple uses quickly developed. The automobile was one of the first to use it. The engine's relatively low weightlhorse-power ratio also overcame one of the most important obstacles to powered flight by heavier-than-air craft. The gasoline powered internal combustion engine thus enabled two of the twentieth century's most important transportation GPTs. As the design and efficiency of the internal combustion engine improved, its range of use increased. Its weightlpower ratio fell far enough to allow its use in lawn mowers, power saws, small commercial aircraft; forklifts, and anywhere else that a lightweight, dependable, mobile power source was required (Cardwell 1995, pp. 338-49). 3.4 Tvanspovtation

All goods production requires that something, be it raw materials, semifinished, or final goods, be transferred over space. We confine ourselves to the railway and the motor vehicle, omitting several other transport technologies that were revolutionary in their time and had the type of effects in which we are interested, such as aircraft, the iron steam ship, the threemasted sailing ship, rowed galleys, the original use of sails, and the wheel.

Railways The railway was enabled by the steam engine, the first mobile, inanimate power delivery system for land uses. (Waterwheels were tied to rivers, while wind was unsuitable as a mobile source of power on land.) Over time the

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railway largely replaced canals, as well as the horse and wagon for long- and medium-distance travel. In its turn it was challenged by the motor vehicle, but this competition did not lead to its elimination, only to its restriction to a smaller market. Even today railways remain an efficient way of transporting goods with low valuelweight ratios over long distances and of transporting people over the kind of middle distances that account for much European travel. The railway, in conjunction with the iron steamship and the telegraph, opened up vast parts of the world to settlement and allowed the production of foodstuffs for distant markets. This group of technologies was also the foundation of a growing tourist industry. Telegraphic communications permitted faster speed and required more complex forms of organization, which later spread from railway companies to other industries (Billington 1996). Motor vehicle The motor vehicle is a multiple purpose technology that has profoundly affected the twentieth-century economy. The truck in all its forms is a commercial and military transport vehical (armored it became the armored military car and tank, with momentous repercussions). The automobile is used for transport to work and shopping, for recreation, sport, and countless other purposes. Among the many structural adjustments caused by the automobile were important changes in the way people lived. It reinforced the move to the suburbs initiated by suburban electrical railways. Along with the refrigerator it helped replace the dominiant small grocery store by the supermarket, which gave rise to the suburban shopping center. Commercial trucking challenged railways over long and intermediate hauls and eliminated the horse and wagon for short hauls. Next the U.S. interstate superhighway system contributed to the movement of manufacturing from locations in the inner city near the rail head to the suburbs alongside the new highways, furthering the decay of the U S . inner cities. The automobile industry was profoundly affected by the development, early in the twentieth century, of machine tools that could cut prehardened steel. Because the new machine tools allowed a high degree of accuracy in production, parts with identical engineering specifications became identical in practice. Interchangeable parts made many of Henry Ford's early process innovations possible. It was a short step to add the conveyor belt that typified mass production techniques in the public's mind, but that was only the last step in a series of technological innovations following from prehardened parts (Womack et al. 1990). These developments spelled the end of the artisan in many lines of North American production and produced the highly paid, but relatively unskilled, worker doing repetitive work on


dedicated machinery.' Numerous union practices, such as job demarcation, came in its wake. Many of the important changes taking place in manufacturing today, such as lean production and just-in-time systems, had their start in the automobile industry, which has been a constant innovator of new production techniques.

4 Technological interrelatedness Interrelations among technologies play an important part in determining the overall reaction to specific technological changes. We call the technology that specifies each physically distinct, stand-alone, capital good a "main technology ." First, we note that most main technologies have differentiated parts. For example, a commercial airliner is made up of a large number of subtechnologies including an engine to deliver power, a thrust technology to turn that power into movement, a body, an undercarriage, a navigation system, and an internal control system. Analysis of these subtechnologies shows them to be made up of other subtechnologies. An aircraft's navigation system is composed, for example, of compasses, gyroscopes, computers, sensing devices, radios, radar, and so on. Analysis of each shows them all in turn to be made up of other smaller subtechnologies. Notice that some of the subtechnologies, such as compasses and food warmers, can also be used on their own as main technologies. In contrast, other subtechnologies, such as the aircraft's rudder or windows, are useful only as a part of this specific main technology. This fractal-like nature of the aircraft's makeup is typical of virtually all capital goods. It is also typical of consumers' durables, such as automobiles and refrigerators, that deliver services for use in consumption. The interdependence of the subtechnologies is often Leontieff in nature; the main technology will not function if you remove one of its subtechnologies. For example, a standard gasoline engine will not run without its spark plug. Other subtechnologies increase the efficiency of the main technology without being essential. For example, the air filter is not necessary for the internal combustion engine, but the engine efficiency is much increased by it. Each generic type of subtechnology, such as a spark plug or a tire, usually comes in several differentiated versions that are close substitutes for each other. Second, we observe that main technologies are typically grouped into technology systems, which we define as a set of two or more main technologies that cooperate to produce some range of related goods or services. They cooperate within one firm, among firms within one industry, among firms in closely linked sets of industries, and even across industries that are seemingly unrelated from an engineering point of view (Rosenberg 1976, 1982). Technology systems overlap each other in the sense that a subset of the technologies that are used to produce product A is used, along with other

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technologies, to make product B, and so on. In some cases the technology may be used in the process technology that produces the good that embodies it, as when computers are used to manufacture computers. In other cases some main technologies assist the operations of others without being necessary. For example, much of the value of a computer depends on its cooperation with its peripherals, such as printers, modems and software. Notice that many of the separate main technologies in some technology systems may simultaneously compete with, as well as complement, each other. Trucks deliver freight to the railhead, making railways more useful and profitable, but they also compete with rail for long-distance haulage. Notice the effects of a technology system cannot be correctly measured by estimating the consequences of introducing each main technology in the absence of the others. Because of complementarities the effect of the whole is substantially larger than the sum of the effects of the parts. One excellent example is the technology system created by the development in the nineteenth century of the railroad, the iron steamship, the telegraph, and refrigeration. Individually each would have been important. Acting together, they globalized the markets for many agricultural commodities with many resulting DSAs. Third, technological interrelationships occur in the vertical relations among industries when the output of one is used as an input by another. Materials-producing industries, such as iron and steel, forest products, and aluminium, create inputs used in manufacturing. Fourth, some industries that produce different and unrelated outputs use similar process technologies-a phenomenon that Rosenberg (1976) calls "technological convergence." This facilitates discontinuous jumps in product technologies because each such product may not have to develop its own radically different process technology. For example, early in the twentieth century the new aircraft industry used process technologies that were already well developed by the bicycle and sewing machine industries. (For a formal treatment of this point, see Bresnahan and Gambaradella, chapter 10 this volume.) In summary, the economy's overall technology system is a set of interlocking embodied technologies. First, there is the fractal-like web of lowerlevel, subtechnologies that form any one main technology. Although some of the subcomponents in this engineering structure are necessary, others are important auxiliaries but not essential. Furthermore each general type of subcomponent often comes in various versions which compete with each other. Second, there is an external structure of interrelations across capital goods in one industry, as when several capital goods cooperate to produce a final product. Third, there are interrelationships across industries, as when the output of one industry is used as inputs in another. Fourth, there are process interrelationships when technologically distinct products are produced by technologically similar processes.


5 Defining a GPT Our view of definitions is nominalist not essentialist; definitions are not judged as being right or wrong but only as being helpful or unhelpful in delineating useful categories. We have now identified a group of GPTs by their impacts on the economy, However, if we want to develop theories that predict the effects of GPTs, including some that we have not yet identified and some that do not yet exist, we cannot define them by their effects. We thus search for a definition stated exclusively in terms of technological characteristics. Our definition must be wide enough to include all of those technologies we have identified above, and narrow enough to exclude other less important technologies, such as elastic bands and screw drivers. 5.1 What a GPT is not

We begin by discussing some defining characteristics that have been suggested by others but which we argue are neither necessary nor sufficient to identify the technologies on our list. Not defined by its demand churacteristics" Schmookler (1966) presents strong evidence that the amount of innovation in an industry, and its characteristic logistic curve of productivity development, are strongly influenced by demand. This is important evidence against those who argue that innovation is solely determined by technological possibilities. GPTs are no exception. A technology will not become a GPT unless it fills numerous demand niches; some will already be filled by existing technologies, some will already be perceived but only inadequately filled, and some will be created by the new GPT itself. Although this broad-based pattern of demand is a necessary condition for a new technology to evolve into a GPT, it is not part of its definition, which depends on its technological characteristics alone. Just as an adequate food intake is a necessary condition for an infant to grow into an adult but not a part of the definition of an adult, so a broad-based demand is a necessary condition for a new technology to evolve into a GPT, but not a characteristic that enters into its definition. This illustrates the general point that the conditions necessary for the development of the characteristics that define some object are not part of that object's definition. Not defined in terms of'a generic function Both Bresnahan and Trajtenberg (1995) and Helpman and Trajtenberg (chapter 3) make a defining characteristic of GPTs the provision of what they call a generic function which they illustrate by rotary motion. Webster's

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dictionary defines generic as "referring to a whole kind, class, or group." Thus the literal meaning of a generic technological function would be a function common to a class of technologies. For example, a generic function of all modes of transport is to move things about spatially, while a generic function of all toothpastes is to clean teeth. In this sense all technologies in some class must provide the generic functions that define the class. Taken in this sense, providing a generic function is not suficient to make a technology a GPT for at least two reasons. First, the generic function itself may be relatively unimportant, such as cleaning teeth. Second, both important and unimportant members of some given class of technologies will provide the generic functions that define their class. For example, rotary motion, a generic function whose provision Bresnahan and Trajtenberg use to identify the steam engine as a GPT, is produced by revolving axels or wheels that can be powered by many power delivery systems which we would not wish to include in our category of GPTs such as clockwork motors, the animate power of animals and humans, atmospheric pressure, elastic bands, and tidal forces. It is also worth noticing that a GPT is not typically characterized by a single generic function that it performs (therefore doing so cannot be necessary). Power delivery technologies, including the waterwheel and steam, provide power for all types of motion. One of the critical inventions in the long history of the waterwheel was the cam which turns the waterwheel's rotary motion into the linear motion to drive hammers, saws, presses, bellows, pumps, and many other important "nonrotary" activities. The principle of the cam acting in reverse also turns the linear motion of the pistons of steam and internal combustion engines into rotary motion where required, while the piston delivers linear motion directly in the many places where that is required. The dynamo does not deliver any sort of mechanical motion. Instead, it delivers electricity which is energy in the useful form of electron flows. Users then transform the electricity into the type of work that they require, including mechanical motion, lighting, heating, impulses for telegraphs, power for switches in the form of vacuum tubes and transistors, power for making aluminum, and so on, each of which may be separately construed as a generic function. It is possible, however, to reinterpret "genericness" to be a characteristic of a GPT. Consider a class of diverse technologies that use as an input the outputs of some single technology. That single technology many be described as generic to the class that uses it even though it may provide a variety of different functions such as turning a motor, heating an element, or operating a toggle switch. In this sense Bresnahan and Traijtenberg's GPT with a generic function means a technology with many and varied uses, characteristic which we also include in our definition developed below.


Not always exogenous nor always endogenous

Modern research has left little doubt that technological change is largely endogenous to microeconomic incentives. While technological change is also substantially influenced by pure scientific research, scientific agendas are often themselves strongly influenced by economic signals-as argued by Schmookler (1965) and Rosenberg (1982, 1994). Thus, both research and development are significantly endogenous, responding to the economic signal of profit expectations. Some historians and theorists have suggested as a matter of fact, or assumed as a matter of theoretical convenience, that new GPTs are exceptions to this rule (e.g., Mokyr 1990; Helpman and Trajtenberg, chapter 3 this volume). Others have argued that GPTs always occur as endogenous responses to economic incentives (e.g., Dudley 1995; Freeman et al. 1982). To proceed with this issue, we need to ask two questions: To what stage in the technology's evolution are we referring? And endogenous to what? To answer the first question, note that whatever the original source of some new technology, once its potential to create profits is appreciated, its further evolution becomes endogenous. Its R&D rapidly comes to be directed by profit-seeking decisions. So we must be referring to the early stages of a technology's evolution if we are to consider the possibility of it being exogenous to the economic system. Endogenous to the economic system. In some cases the initial development of a technology that evolves into a GPT is endogenous from the outset. Often it begins as a specialized response to the profit opportunities created by a localized "crisis" in some existing technology. For example, Newcomen's atmospheric engine, and Savery's before that, were endogenous responses to the need to pump water efficiently out of ever-deepening mines, a job that existing technologies could not do effectively. Exogenous to the economic system hut endogenous to science. A new technology is endogenous to pure science when its evolution is being driven primarily by non-profit-related motives associated with a scientific research program. The use of electricity as a power delivery system resulted from discoveries in a seventeenth-and eighteenth-century research program, which was largely driven by scientific curiosity as opposed to the pursuit of commercial gain.4 Furthermore the technology it replaced, the steam engine, had not reached any obvious limits to its possible i m p r ~ v e m e n t .Thus ~ electricity may best be regarded as exogenous to the economic system, at least until some time into the nineteenth century. Exogenous to the economic system but endogenous to the political-military system. A technology is endogenous to the political-military system if

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its evolution is being driven primarily by motives of military or political advantage. The electronic computer was initially developed to do complicated calculations associated with ballistics and code breaking. Although it was developed in universities, the research was funded by the military. It began as a single-purpose machine with very few economic applications. As it was slowly developed to handle different problems, more and more scope for economic uses became obvious and its evolution became increasingly driven by profit-seeking motives. Technologies of all sorts and sizes have various origins. The GPTs on our list include some technologies that developed as endogenous responses to economic signals and others whose development was exogenous to the economic system. To conform with the awkward facts, theories of GPTs should not make their early evolution either always exogenous or always endogenous to economic signals. A more difficult problem is to explain why GPTs are sometimes exogenous and at other times endogenous.

Not a radical new technology without clear antecedents Virtually all major technologies evolve along paths that include both small incremental improvements and occasional jumps. To distinguish these, investigators often define two categories. An innovation is incremental if it is an improvement to an existing technology and radical if it could not have evolved through incremental improvements in the technology that it challenges in some particular use (Freeman and Perez 1988). If we are only concerned with the consequences of technological change, this distinction is all that is needed. However, if we are interested in the origins of innovations, some confusions that exist in the literature require us to go further. To do so, we distinguish two separate evolutionary paths and two separate meanings of the term radical. The first path is the evolution of a series of technologies that are applied to a specijic use, such as the reproduction of the written word. All of the GPTs in our historical list are radical in this sense: They could not have evolved out of the technologies that they challenged and eventually displaced in some particular use. For example, bronze could not have evolved out of stone, nor electricity out of steam, nor the printing press out of quill and ink. The second path is the evolution of a spec& technology, such as the printing press. None of the technologies on our historical list, however, are radical in this sense: They did not appear more or less out of the blue. Instead, each had evolutionary paths stretching backward for centuries. For example, the replacement of carved wooden blocks by movable type was an incremental innovation in the technology of printing, which had a long evolutionary history stretching back to its early origins in China. However, from the point of view of technologies used for reproducing the written


word, printing was a radical innovation that replaced hand copying. Cases of technologies that are radical in the second sense appear to be much rarer and often are accidental discoveries. Three examples that can be argued as appearing out of the blue without clear parentage are X rays, penicillin, and radio astronomy. We must now ask if being radical in either sense is a necessary or a sufficient characteristic for a technology to be a GPT. Being radical in the first sense cannot be a sufficient condition. since many technologies that we would not want to call GPTs did not evolve out of the technologies they replaced: The nylon stocking did not evolve incrementally from the silk stocking, ball point pens did not evolve out of the fountain pen. We also argue that being radical in the first sense is not necessary. For example, the three-masted sailing vessel was a GPT that was not radical with respect to the nautical technologies that preceded it. The key to this innovation was the combination of the square rigged sail, which was used on the cog that the three-masted ship largely replaced along the Atlantic coast, and the lateen sail, which had been used in the Mediterranean for centuries. Yet the two in combination produced a radically new type of vessel that could make transoceanic trips in relative safety-a vessel that was subsequently improved by a series of smaller inventions covering such things as rigging, sails, and provisions. This can be seen as an evolutionary change in sailing technology, a recombination of existing subtechnologies. But its effects were as dramatic as if it had been a completely new technology. It transformed the map of European economic power and led to the first global expansion of European sea borne trade and colonization. It is easy to see that being radical in the second sense is neither necessary nor sufficient for a GPT, since none of our historical examples are of this out-of-the-blue variety, and some that are out of the blue are clearly not GPTs. A Confusion about Being Radical Those who debate whether economic growth is continuous or punctuated with occasional discontinuities do not usually distinguish between the two senses of radical. Those arguing for the absence of discontinuities often point out correctly that very few inventions are radical in the second sense of having no clear parentage. The apparent implication is that all innovations must be incremental. The strong suggestion is then that economic growth and technological change will all be continuous and devoid of discontinuities. Mokyr dissents from this conclusion. He does not, however, distinguish the two senses of radical but argues that what he calls macro inventions are radical in our second sense: They are "without clear precedent [emerging] more or less ab nihilo" (Mokyr 1990, p. 13). He concludes that there can be nonincremental, technological changes and discontinuities in the process of growth.

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We agree with Mokyr on the important issue that there can be nonincremental technological changes and big technological shocks to the economy. We argue, however, these are typically initiated by technologies that are radical only in the first sense of not evolving out of the technologies that they challenged. Thus we avoid having to maintain the dubious proposition that our GPTs (or Mokyr's macro inventions) are typically radical in the second sense of being without clear evolutionary histories and appearing more or less out of the blue. 5.2 What a GPT is

All of the technologies in our historical list share four characteristics. They enter as fairly crude technologies with a limited number of uses, but they evolve into much more complex technologies with dramatic increases in the range of their use across the economy and in the number of economic outputs that they produce. As mature technologies they are widely used for a number of different purposes, and they have many complementarities. In the following sections we elaborate on these observations in the following way: We assert that the four characteristics we have just listed are each necessary conditions for a technology to be a GPT. We then use empirical evidence to refute the assertion that any one of them is sufficient. We end by defining this bundle of four characteristics as necessary and sufficient for any technology to qualify as a GPT. Scope for improvement

The way in which agents learn about technologies, and the complexity of the economy's whole technology system, implies that any technology that ends up being widely used in many different applications must go through a process of evolution. Over time the technology is improved, its costs of operation in existing uses falls, its value is improved by the invention of technologies that support it, and its range of use widens while the variety of its uses increases. This is true of both the technologies of the products themselves, such as steel or the printing press, and of the processes by which they are made. Every one of the major technologies discussed in our historical section displays this evolutionary experience in which the processes of technological change and diffusion are intermingled in time, space, and function. Scope for improvement when a technology is first introduced is a necessary characteristic for a technology to become a GPT. Since this characteristic is shared by many technologies that we would not want to include as GPTs (e.g., ploughs, bicycles, and drill presses), it cannot be a sufficient condition.


Wide variety of uses

At a high enough level of abstraction, every technology, or class of technologies, produces only one output. For example, we can think of transport technologies as producing only transport, or power delivery systems as producing only energy. However, at a lower level of abstraction, technologies often produce more then one distinct output. For example, the dynamo provides mechanical power for a wide variety of productive activities including electric motors, lighting, heating, telegraphs, transistors, radios, televisions, computers, steel (mini-mills), and aluminium. Each of the technologies on our historical list are used in a wide variety of products and processes. Furthermore they are used as physical components in the makeups of main technologies and/or as main technologies within technology systems. Variety of uses is time dependant. A new GPT typically has a few very specific uses, but as it evolves, many applications are discovered. Thus a new technology of this type has implicit in it a major research program for improvements, adaptations, and modifications. So a necessary condition for a GPT is that at some stage of its development it comes to have a wide variety of uses. This cannot, however, be a sufficient condition, since there are a number of non-GPTs that also share this characteristic. For example, belts act as power delivery systems to, from, and within many machines; they also act as a transport system in assembly plants, in airports, and in loading and unloading transport vehicles. X rays are used in medical imagery, cancer treatment, security, archeology, saw milling, and mineralogy. However, both X rays and belts lack sufficient complementarities and range of use to be included within our definition of GPTs. Wide runge of use

By a technology's range of use we refer to the proportion of the productive activities in the economy using that technology. This range runs the gamut from one industry to the entire economy. For example, a posthole digger is used only in the manufacture of fences, a product not widely used in the economy. Electric lightbulbs and screw drivers are used more or less throughout the entire economy. Notice that having a wide range of use is not the same thing as having a wide variety of uses. For example, although it is widely used across the economy in many different settings, an electric lightbulb has only one use, to produce light. In contrast, lasers feed information to cash registers at store checkouts, provide precision cuts in surgical operations, read information from CDS, and print hard copies from computer outputs.

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Many of the GPTs that we have studied, such as electricity and computers, are, or have been, used across virtually all of the economy. Others, such as steam and automobiles, spread across most of the economy. As with number of uses, this is a characteristic that evolves over time. GPTs typically emerge as sector-specific technologies whose use spreads only slowly over the economy. For example, although steam power was initially only important in mining, by the end of its evolutionary trajectory its influence had spread across many sectors. Notice that having a wide range of use is relative to the part of the economy being studied. We define range of use with respect to the whole economy. Others who study, a sector, or an industry properly define range of use more narrowly. (For example, in chapter 7 of this volume Rosenberg looks at technologies that are GPTs in the chemical industry but might not be GPTs economywide.) So wide range of use is another necessary characteristic of GPTs, but it cannot be sufficient, since GPTs share this characteristic of widespread use with many other technologies, such as electric lightbulbs and screw drivers which produce a single economic output that is widely used across the economy. Strong technological complementarities with existing or potential new technologies

In standard microeconomic theory, complementarities refer to the response of quantities to a change in price. In contrast, when students of technological change speak of complementarities, they are often referring to the impact of a new technology. Furthermore technological interrelations are often referred to in the literature as complementarities, although the intended meaning is often "closely related" rather than complementarity in the theoretical sense. Game theory introduces the concept of "strategic" complementarities, where the actions of one agent affect the payoffs of another. In technological competition the most obvious example is when R&D done by A increases the expected value of the R&D done by B. This strategic complementarity covers some, but not all, of what we call complementarities. We reserve the term complementarity to deal with the response of the system to certain types of technological changes and distinguish two types of complementarities, which we call Hicksian and technological. Hicksian Complementarity The Hicksian concepts of complementarity and substitutability in production theory refer to the signs of the quantity responses to a change in some price. Net complementarity is defined for a constant level of output, while gross complementarity allows output to change in response to a change in one input price, and thus combines the output effect with the substitution effect.


An innovation that reduces the cost of an input, x, that is widely used as a service flow in many production processes will cause substitutions among inputs. It will also increase the demand for other inputs that prove to be gross complements to x. Where the demands for inputs other than x increase in response either to an actual fall in the price of x, or any other change in the production of x that cun he treated us if it were a fall in price, we call these Hicksian (gross) complementarities. In what follows we use that term complementarity in the gross rather than the net sense. Technologies that cooperate with each other, either as subtechnologies within one main technology, or as separate stand-alone parts of some technology system, are typically net substitutes and gross complements. If the price of one technology falls, and output is held constant, the use of that technology will increase at the expense of most others. In what we regard as the typical case, however, this substitution effect is small enough for the income effect to dominate, making the technologies gross complements. What we have just said refers to a set of cooperating generic technologies such as the parts of an internal combustion engine or a computer and its set of peripherals. As we have already noted, however, many of these generic technologies come in competing versions, such as brands of spark plugs or makes of printers. Each of these competing versions are both net and gross substitutes for each other, a fall in the price of one leading to a reduction in the use of the other competing brands.

Technological Complementarity Consider an innovation in one technology whose full benefit cannot be reaped until many of the other technologies that are linked to it are re-engineered, and the makeup of the capital goods that embody them are altered. We refer to these responses as "technological complementarities," defined as occurring whenever a technological change in one item of capital requires a redesign or reorganization of some of the other items that cooperate with it (in its internal makeup and/or in the main technology, and/or in the technology systems of which it is a part).6 The most important point about this type of complementarity is that the effects cannot be modeled as the consequences of changes in the prices of flows of factor services found in a simple production function. All of the action is taking place in the structure of capital and the consequent changes will typically take the form of new factors of production, new products, and new production functions. Our historical cases provide many illustrations of technological complementarities that cannot be modeled as if they were the consequences of price changes. For one example, the consequences of the introduction of electric power into factories could not be modeled as a response to a change in the price of power in a production function designed to reflect the technological requirements of steam. Even a zero price of steam power would not have led to the radical redesign of the plant which was the major source

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of efficiency gain under electricity (Schurr 1990; David 1991). This redesign depended on the introduction of the unit drive which attached an efficient power delivery system to each machine, something that was impossible under steam. For a second example, the massive set of adjustments in existing and new capital structures that Fordist mass production brought about could not be modeled as resulting from a fall in the price of noninterchangeable parts would have had an impact on the automobile industry which was both quantitively smaller and qualitatively different from the revolution in the organization of production that followed from interchangeable parts. We now note that having extensive Hicksian and technological complementarities is a necessary condition for a technology to be a GPT. Ceteris paribus, the more pervasive a technology, the more of both complementarities it is likely to have with other technologies. Because GPTs provide materials, power, transport, and ICT inputs that enter into virtually all production, and because they typically lie at the centre of large technology systems, they are vertically and horizontally linked to many other technologies. For this reason innovations in GPTs will typically induce major structural changes in many, sometimes even the great majority of, other technologies. But having these complementarities is not sufficient because many other technologies also have them. For example, the modern shipping container is a single-purpose technology that revolutionized cargo handling and had many complementarities, causing adjustments in size of ships, layout and location of ports, handling facilities, labor skills, the design of trucks and railcars, and international location of production. Necessary and sufficient conditionsfor a GPT

Virtually every new technology has some of the four necessary conditions for GPTs that we identified above. Early television had great scope for improvement but was limited in its variety of uses and complementarities; lightbulbs have a wide range of uses but for only one purpose, light; belts have a wide variety of uses but not a wide range of use throughout the economy; the innovation of shipping containers caused many technological complementarities as products and processes in the shipping and related industries were redesigned to accommodate them, but they have a limited variety of uses. It follows therefore that none of the conditions outlined above can be individually sufficient to identify a GPT. In order to identify GPTs by their technological characteristics, we look for technologies that have all of the four characteristics. Definition A GPT is a technology that initially has much scope for improvement and eventually comes to be widely used, to have many uses, and to have many Hicksian and technological complementarities.

W H A T REQUIRES E X P L A N A T I O N ?

6 Is the concept useful? Scales that measure scope for improvement, range of use, number of uses, and extent of complementarities would be densely inhabited with technologies throughtout. Thus there is no obvious break between those technologies that are just above the bottom end of any cutoff that we use to define a GPT and those that are just below it. Nonetheless, the concept of a GPT as a technology at the extreme end of all of the scales can be useful for building theories about technological change. After all, it is a common and helpful procedure to take a set of variables distributed over some scale, divide that scale into several intervals, and define a typical member of each interval. To check on the value of our definition, we apply it to a number of cases to see if there are technologies that are inappropriately excluded or included. 6.1 Further GPTs

In this section we mention technologies that our definition admits as GPTs.

Originally we did not have lasers on our list of potential GPTs. But, on close examination, they seem to satisfy our necessary and sufficient conditions. They began as a scientific curiosity with few, if any, obvious commercial applications. Today they are widely used in a growing number of disparate applications such as checking out goods at cash desks, playing CD recordings, printing hard copy, transmitting information over long distances, and substituting for a surgeon's knife. The range of applications may not yet be as wide as the other technologies on our list, but it is growing. If it continues to grow at its present rate, it will become one of the most important GPTs of the next century. Its cuts across several technology classes. Among other things it is a power delivery system, it is used as an ICT in many applications, and it is used as a cutting tool in many surgical and manufacturing operations. Internet In chapter 6 of this volume, Richard Harris deals with the Internet, a technology that is clearly a GPT by our definition: It is used widely and for many different purposes, it has many Hicksian and technological complementarities, and it has tremendous scope for improvement. Yet we have not listed it as a separate GPT because it is a subtechnology of what we call the modern computer-based information and communication GPT. This observation reenforces our general point about the fractal-like structure of

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technologies because a main GPT can give rise to derivative technologies that are GPTs in their own right. For some purposes, as in Harris's chapter, - it is useful to separate out these GPTs. For other purposes, as in our two chapters, it is useful to treat the entire system of technologies that derive from, and depend on, the electronic computer as a single GPT. Organizational technologies

At first we excluded organizational innovations, but when challenged, we found it impossible to maintain this exclusion. Our definition of a process technology as the specification of how to produce a given product, must cover more than just the machines that are employed, including as well the micro details of plant layout and other aspects of the organization of plants and firms. This raises the question of organizational GPTs, and we find at least three in the modern history of industrial nations.

Factory System The first industrial revolution's factory system meets our criteria. It was a response to particular innovations in capital goods. The automated textile machinery was first used in cottages, in a structure suitable for hand weaving. Gradually, production was shifted to factories in which water power fairly rapidly replaced human power to drive the machines. The factories required different organizations at all levels, including finance, and different amounts of human capital. Factories led to the decline of villages and the growth of industrial cities. The largest gains in productivity were postponed until, in the early nineteenth century, steam power replaced water power in many factories, leading to efficiencyincreasing redesigns of many of the automated machines. Starting in textiles, the factory system slowly spread to include virtually all of manufacturing by the end of the century. Mass Production This system largely eliminated craft production, which uses highly skilled workers and simple but flexible tools to make exactly what the consumer wants. Mass production uses narrowly skilled professionals to design products made by unskilled or semiskilled workers tending expensive single-purpose machines, which turn out standardized products in high volume.' It spread from the auto industry to cover most American manufacturing, making it the dominant method of organizing American (and Canadian) manufacturing in the mid-twentieth century. We do not say much more about it here because many of the main points have already been given in the section the automobile as a GPT. Flexible Manufacturing Unlike the factory system, lean production, flexible manufacturing, or Toyotiasm as it is variously called, was not driven by a major change in the technology of capital goods. Rather it was driven by 324


the need of Japanese automobile makers to produce competitively at a scale much less than was possible for U.S. firms. The principles of lean production spread from the shop floor to every phase of the firm's operations, from design, to marketing, to customer follow-up (Woomack 1990; Zuboff 1984). Working in flexible work groups rather than tending one dedicated machine required a different organization of the work force, different union practices, and different human capital. Different channels of feedback from production workers to supervisors developed. The justin-time inventory methods spread to assist industries across the whole economy and to alter the relations between assembly firms and their suppliers. The payoff was so large that Japanese automobile firms penetrated the North American and European markets in a very big way, and without the ensuing government intervention, one or more indigenous firms would probably have been eliminated. After a few very expensive false starts, North American firms have adopted the Japanese methods, first in automobile manufacture and slowly across a wide range of other products. European protectionism has kept the Japanese challenge more peripheral, and so European firms have not been forced into anything like the same amount of productivity-increasing changes as have occurred in North America. A Caveat These three organizational innovations clearly meet our criteria

for a GPT, and their effects were as large as many of the other more conventional GPTs that we have studied. However, when we expand our definition of GPTs to include organizational innovations, we are going beyond what many writers include in their concepts of technology and technological change. As we have repeatedly emphasized, classificatory systems are judged by efficiency and usefulness. In our view, there are enough similarities between innovations in capital goods and plant layouts to warrant creating another class of GPTs called organizational GPTs.

Some of the technologies that we have considered come close to being GPTs by virtue of sharing most of a GPT's characteristics.

Machines Most types of machinery have such a limited variety of uses that they do not come close to qualifying as GPTs. It was suggested to us, however, that machine tools should be regarded as a GPT. Early in the nineteenth century a distinct industry grew up to produce power-driven tools for use in manufacturing. Tools were typically developed for single purposes, and a few were then found capable of being adapted for multiple uses. For example, the turret lathe, which allowed a metal part to be subjected to a series of

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operations without being repositioned, was originally developed for the production of pistols. It was then progressively modified and adapted to produce key parts for sewing machines, watches, typewriters, locomotives, bicycles, and automobiles. Another important machine tool, the milling machine, was eventually used in the production of tools, cutlery, locks, arms, sewing machines, textiles machinery, printing presses, scientific instruments, and locomotives (Rosenberg 1976). Nonetheless, we role out machine tools because their range of use is restricted to manufactuing. From the point of view of the manufacturing industry a few key machine tools qualify as GPTs; from the point of view of the economy as a whole, they do not quite fulfill our criteria of widespread use. Single-purpose technologies

Another set of near-GPTs has major complementarities, and a wide range of use across the economy, but lacks the characteristic of having many different uses. As well as the modern examples we gave earlier, such as lightbulbs and shipping containers, in simpler societies many agricultural inventions also came into this class. From the time of the neolithic agricultural revolution until the nineteenth century, agriculture accounted for most of the national income in most countries. Any major innovation in agriculture therefore was widely used and had major impacts across most of the economy. The original domestication of plants, animal fertilizer, selective breeding and hybridization, the light plough, the heavy plough, crop rotation in the three-field system, and the modern green revolution have had tremendous and widespread impacts, although they are all single-purpose technologies. As society became more complex, however, the proportion of output accounted for by agriculture fell, diminishing the chances that any technological advance in agriculture would qualify as being widely used across most of the economy, and hence capable of exerting the type of economywide effects in which we are interested. 6.3 Uncertainties

Viewed in retrospect, the evolutionary path of a fully developed GPT has the appearance of inevitability. When the technology is in its infancy, however, an observer looking into the future cannot conceivably know if it will turn out to be a modest advance operating over a limited range, a GPT, or anything in between. For example, had the practical uses of electricity been developed 75 to 100 years earlier, Watt's low-pressure steam engine would not have developed into a GPT. Even when a technology has become established, it spreads in ways that are hard to predict (partly because emerging technological complementarities are hard to anticipate). Electricity, lasers,


and steam engines provide examples of GPTs with applications that could not have been foreseen early in their evolution (Rosenberg 1996). At this point one may wonder if the concept of a GPT is useful. If we cannot identify GPTs at their time of birth, and if their development trajectories are subject to such uncertainty, how can we theorize successfully about them? It is important to note, however, that uncertainty is present in virtually all technological developments. If uncertainty makes it impossible to theorize about GPTs, then we cannot theorize about any major technological change for the same reason. Since technological change is the main source of long-term economic growth, this would rule such growth out of the realm of economic analysis. Rather than take this defeatist attitude, it seems better to try to develop useful theories that can accommodate the inherent uncertainties. Theorizing trbout uncertainty

Since technological change is a path dependent, evolutionary process taking place under conditions of uncertainty, it may not be subject to the kind of testable theories as are other economic processes. Repeated experiments may not be possible, and all relevant variables (including tastes and technology) may be endogenous. Nonetheless, as with biological evolutionary processes, empirically relevant theories can be developed that uncover the system's laws of motion, even if those laws produce neither a unique stable equilibrium, nor a process that would necessarily repeat itself if it could be replayed. Rish m~alysis

Many do not agree with the above diagnosis and continue to apply maximizing theories to technological change in general and GPTs in particular. The theoretical papers in this volume all do so. If technological uncertainty can, for some predictive purposes, be treated as if it were merely a risky situation, then such theories will be useful. However, the existence of uncertainty is hard to deny and is accepted by virtually everyone who has studied technological change in detail. What can only be decided by experiment is how far the classical techniques of risk analysis can go in studying these situations. Limited predictability

Since our definition of a GPT is built on technological characteristics that are time dependent, the ability to identify a GPT must also be time dependent. Technological history is full of examples both of technologies that came to very little after their potential was widely acclaimed in the

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early stages of their development and of technologies that were thought to be of limited use but which developed into fully fledged GPTs over subsequent decades. We have, however, set down a definition in terms of technological characteristics and listed five categories of technologies that may aid in their identification. Do these give us any degree of predictability? Identification of Some Potential GPTs Some technologies can be identified early on as having the potential to develop all of the characteristics of a GPT. For example, if one is told that a technology will provide very low-cost power that can be delivered anywhere in the world, one can say that this technology, whatever its engineering characteristics, has the potential to become a GPT. Although no one can be sure how such technologies will in fact evolve, they should be watched closely. While electricity and nuclear power were both in this class early in their development, electricity clearly fits our definition of a GPT, while nuclear power does not (at least not yet). Impossible to Identify All Potential GPTs There will always be new technologies that look limited to all observers but that subsequently develop into GPTs because they evolve new applications and new functions that were unsuspected at the outset. So, although we may with reasonable confidence put some new technologies into the class of potential GPTs, we cannot with equal confidence assert that the remainder have no promise of developing into GPTs. IdentiJication of GPTs along the Way At some point before a GPT's full impact is felt, it will become clear that the technology is developing into GPT. For example, long before its full potential had been exploited (which is still in the future), it became apparent to many observers that electronic computers were on their way to becoming a pervasive GPT. It can be useful to identify a GPT even several decades after it has begun its evolution. This will help policy makers to understand the technological revolutions and the structural adjustments that typically accompany GPTs. Prediction of General but not Precise Path of Development Even though in some cases there is a good chance of classifying technologies that do and do not have the potential to evolve into GPTs, uncertainty cannot be avoided in predicting the path of development. For example, electricity was recognized as a technological marvel with many possible applications long before many of its current applications were known. The process of determining the specific uses is, of course, carried out by profit-maximizing firms seeking to exploit the new GPT. Even though it is difficult to enumerate all the specific uses and complementarities that will eventually be associated with a newly identified GPT, it is possible to predict some specific developments

W H A T REQIJIRES E X P L A N A T I O N ?

and that, qualitatively, the set will be large. Although the full potential of the computer, laser, satellite, and other related ICTs were not clear at the outset, some specific developments, such as networking, were predicted well in advance, and it has been clear for some time that we are living through a profound transformation associated with these GPTs. New GPT's Predicted? After all this analysis, can we identify future GPTs that are emerging on the current technological horizon? As we have suggested, a consideration of the characteristics of new technologies often allows us to identify potential GPTs. A consideration of their current evolutionary trajectory then allows us to assess whether or are not they are currently fulfilling their potential. Here are a few cases in point. Biotechnology is an obvious future GPT, although it is not yet widely used in producing economic value. Many diverse possible uses have already been established and more are being discovered at a rapid pace. Many of their practical applications, however, await further reductions in costs and an assessment of their side effects. What has happened so far makes us confident that biotechnology is an emerging GPT. Nuclear power is a different case. Low-cost, nonpolluting fusion would probably rate as an important GPT. Its effects would not be as pervasive as some other GPTs because it would likely displace the applications of existing hydroelectric generated power, at least in the first instance. Its main immediate advantage would be to free power production facilities from the constraint of being near fast-moving water or coal supplies. Thus it could affect the pattern of comparative advantage and the relative prices of many products. Low-cost fusion in micro generators would have a prodigious number of applications that would take fusion from being an important technology in electricity generation to being a GPT in its own right. Current uncertainties are such that we have no idea if low-cost, trouble-free nuclear power will be developed or if alternatives such as solar or geothermal power will dominate it. Superconductivity is another possibility. Its potential has been celebrated for decades, so far without major applications. N o one knows if the technical problems will be overcome to make it a major technological revolution. Since we can imagine several competing technologies that might make the transfer of power on a large scale unnecessary, such as small-scale solar power plants, we have no confidence in predictions that it will become a GPT within the next century. Nanotechnology, electronic machines smaller than human blood cells, is another possible GPT of the future with a large number of potentially valuable applications. These include allowing noninvasive surgical techniques, improved tolerances in material development, and drastically lowering the cost of producing integrated circuits. The potential for a new GPT is clear, while the evolutionary path is uncertain.

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7 Conclusion Economic historians have long argued whether technological change is always a process of continuous small incremental changes or is episodically punctuated by large qualitative changes. Growth economists have had similar arguments concerning aggregate growth rates. In this chapter we review historical evidence concerning the invention of pervasive technologies that are qualitatively different from anything previously experienced. They appear from time to time, sometimes causing deep structural adjustments. However, as we discuss in chapter 8, technological discontinuities need not cause discontinuities in observed aggregate growth rates. We have laid out the relevant set of technological characteristics that define GPTs, as well as detailing a set of awkward facts concerning their evolution. We hope that these facts go some way to setting the boundaries for further research. The definition we provide allows for the ex post identification of GPTs. It also allows ex ante identification of some technologies that, early in their development trajectories, have the potential to become GPTs, and others that are far enough along to be clearly developing into GPTs. An important challenge is to develop theories that incorporate more of the relevant characteristics of GPTs and are consistent with more of the facts that surround them.

Acknowledgements For comments and suggestions we are indebted to the members of the Canadian Institute for Advanced Research's Economic Growth and Policy Group to whom an earlier version of our chapters were presented and to Peter Howitt, Elhanan Helpman, Nathan Rosenberg, and an anonymous referee for comments on a later version. Although we have used many sources, our largest single debt for facts and insights is to Nathan Rosenberg.

Notes 1 We believe that this is what one does, but less explicitly, whenever one develops a theory about some new phenomenon. The phenomenon is observed, and we study it to see what seem to be its key characteristics. We then formalize a stylized vesion of these in a set of assumptions designed to capture the phenomenon (a process that Blaug 1980 calls adduction). If we define useful concepts we are able to develop a viable theory. 2 Ford did not invent the assembly line used, among other places, in the manufacture of firearms in the nineteenth century and in the production of Venetian galleys prior to the battle of Lepanto in 1574. But by insisting on standardized parts for his automobiles, he extended its use to mainline manufacturing. 3 This section was added only after more than one student of technology worried about our neglect of the demand side, for example, quoting ~ c h r n o o k k i (1972).


4 Dividing lines are seldom as clear-cut in reality as we would have them in theory. In this case, however, it seems fairly clear that the advances in knowledge about electricity were pretty well exogenous to the economic system right up until the early nineteenth century. When Volta developed his electric battery in 1799, the potential for valuable applications was immediately apparent. Many of the subsequent key discoveries by such scientists as Faraday and Maxwell, however, seem to have been primarily motivated by scientific curiosity. Just when the crossover from mainly exogenously to mainly endogenously driven occurred is debatable. It would seem to be somewhere in the first half of the nineteenth century, possibly around the middle of that period. 5 This seems to us to be an implication of von Tunzelman's detailed 1975 study of the steam engines, although he never says so in so many words. 6 Note that neither of the distinctions complementslsubstitutes and netlgross can be made in the case of technological complementarities. Let technology A change. Technology B is complementary with A if a change in its specifications is now required. The complementlsubstitute distinction turns on being able to sign the induced change in B, which we can do when the reaction is in the quantity of output but cannot do when the reaction is a redesign of the technology. The net1 gross distinction depends on being able to hold output constant, which we can do if process technologies are changing but cannot do when induced changes occur in product technologies. 7 The definitions come from Woomack, Jones, and Roos (1990).

References Arthur, B. 1988. Competing technologies: An overview. In G. Dosi, et al., eds., Technical Change and Economic Theory. London: Pinter. Billington D . 1996. The Innovators: The Engineers That Made America Modern. New York: Wiley. Blaug, M. 1980. The Methodology of E~~onomics. Cambridge; Cambridge University Press. Bresnahan, T. F., and M. Trajtenberg. 1992. General Purpose Technologies: "Engines of Growth"? NBER Working Paper 4148. Cardwell, D. S. L. 1972. Turning Points in Western Technology: A Study of Technology, Science and History. New York: Science History Publications. Chandler, A. 1990. Scale and Scopt,: The Dynamics of Industrial Capitalism. Cambridge, MA.: Belknap Press. Cipolla, C. 1993. Before the Industrial Revolution: European Society and Economy, 1000-1 700. New York: Routledge. David, P. 1975. Technical Choice, Innovation and Economic Growth. Cambridge: Cambridge University Press. David, P. 1991. Computer and dynamo: The modem productivity paradox in a not too distant mirror. In techno log,^ and Productivity: The Challenge for Economic Policy. Paris: OECD. Dosi, G., C. Freeman, R. Nelson, G. Silverberg, and L. Soete. 1988. Technical Change and Economic Theory. London: Pinter. Drews, R. 1992. End of the Bronze Age. Princeton: Princeton University Press. Dudley, L. 1991. The Word and the Sword: How Techniques of Information and Violence Have Shaped Our World. Cambridge, M A : Basil Blackwell.

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Dudley, L. (forthcoming). Communications and Economic Growth, European Economic Review. Forester, T., ed. 1988. The Materials Revolution. Cambridge: MIT Press. Freeman, C., J. Clark, and L. Soete. 1982. Unemployment and Technical Innovation: A Study of Long Waves in Economic Development. London: Pinter. Freeman, C., and C. Perez. 1988. Structural crisis of adjustment. In G. Dosi, et al. eds, Technological Change and Economic Theory. London: Pinter. Freeman, C., and L. Soete, eds. 1987. Technical Change and Full Employment. New York: Basil Blackwell. Gies, F., and J. Gies. 1994. Cathedral Forge and Water Wheel. New York: Harper Collins. Gimpel, J. 1967. The Medieval Machine: The Industrial Revolution of' the Middle Ages. New York: Holt, Rienehart and Winston. Greenwood, J. 1997. The Third Industrial Revolution: Technology, Productivity, and Income Inequality. Washington: AEI Press. Grossman, G., and E. Helpman. 1991. Innovation and Growth in the Global Economy. Cambridge: MIT Press. Huff, T. 1993. The Rise of Early Modern Science: Islam, China and the West. Cambridge: Cambridge University Press. Innis, H. A. 1951. The Bias of Communication. Toronto: University of Toronto Press. Innis, H. A. 1972. Empire and Communication. Toronto: University of Toronto Press. Kranzberg, M., and C. S. Smith. 1988. Materials in history and society. In T. Forester, ed., The Materials Revolution. Cambridge: MIT Press. Landau, R., T. Tylor, and G. Wright, eds. 1996. The Mosaic oJ'Economic Growth. Stanford: Stanford University Press. Landes, D. 1969. The Unbound Prometheus. Cambridge: Cambridge University Press. Lipsey, R. G., and C. Bekar. 1994. A structuralist view of technical change and economic growth. In Bell Canada Papers on Economic and Public Policy, vol. 3. Proceedings of the Bell Canada Conference at Queen's University, Kingston: John Deutsch Institute. Mokyr, J. 1990. The Lever of Riches: Technology Creativity and Economic Progress. Oxford: Oxford University Press. Nelson, R. 1995. The agenda for growth theory: A different point of view. IIASA Working Paper. Rosenberg, N. 1976. Perspectives on Technology. Cambridge: Cambridge University Press. Rosenberg, N. 1994. Exploring the Black Box: Technology, Economics, and History. Cambridge: Cambridge University Press. Rosenberg, N. 1982. Inside the Black Box; Technology and Economics. Cambridge: Cambridge University Press. Rosenberg, N. 1996. Uncertainty and technological change. In Landau, R., Taylor, L, and Wright, G., eds., The Mosaic of Economic Growth. Stanford, Stanford University Press. Schmandt-Besserat, D. 1992. Before Writing. Austin: University of Texas Press.


Schmookler, J. 1965. Catastrophe and utilitarianism in the development of basic science. In R . A. Tybout, ed., Econon?ic,s of Reseurch and Development. Columbus: Ohio State University Press. Schmookler, J. 1966. Invention and Economic Grobb~th.Cambridge: Harvard University Press. Schmookler, J. 1972. Patent, Invc'nfion, and Economic Change: Data und Selected Essays. Z. Griliches and L. Hurwicz, eds., Cambridge: Harvard University Press. Schurr, S., et ul. 1990. Electricity in the American Economy. New York: Greenwood Press. Von Tunzelmann, G. N. 1978. Steam Po~cerand British Industric~lizution to 1860. New York: Clarendon Press. Von Tunzelmann, G . N. 1995. Tec~hnologyund Industrial Progress: The Foundations of Economic Growth. Brookfield. VT: E. Elgar. Woomack, J. P., D. J. Jones, and D. Roos. 1990. The Machine that Chunged the World. New York: Rawson Associates. Zuboff, S. 1984. In the Age o f t h e Smur/ Machine: The Future qf Work and Power. New York: Basic Books.

T H E DYNAMO A N D T H E COMPUTER An historical perspective on the modern productivity paradox Paul A. David* Source: Americun Economic Review, 80:2 (1990), 355-61.

Many observers of recent trends in the industrialized economies of the West have been perplexed by the conjecture of rapid technological innovation with disappointingly slow gains in measured productivity. A generation of economists who were brought up to identify increases in total factor productivity indexes with "technical progress" has found it quite paradoxical for the growth accountants' residual measure of "the advance of knowledge" to have vanished at the very same time that a wave of major innovations was appearing-in microelectronics, in communications technologies based on lasers and fiber optics, in composite materials, and in biotechnology. Disappointments with "the computer revolution" and the newly dawned "information age" in this regard have been keenly felt. Indeed, the notion that there is something anomalous about the prevailing state of affairs has drawn much of its appeal from the apparent failure of the wave of innovations based on the microprocessor and the memory chip to elicit a surge of growth in productivity from the sectors of the U.S. economy that recently have been investing so heavily in electronic data processing equipment (see, for example, Stephen Roach, 1987, 1988; Martin Baily and Robert Gordon, 1988). This latter aspect of the so-called "productivity paradox" attained popular currency in the succinct formulation attributed to Robert Solow: "We see the computers everywhere but in the productivity statistics." If, however, we are prepared to approach the matter from the perspective afforded by the economic history of the large technical systems characteristic of network industries, and to keep in mind a time-scale appropriate

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for thinking about transitions from established technological regimes to their respective successor regimes, many features of the so-called productivity paradox will be found to be neither so unprecedented nor so puzzling as they might otherwise appear.

My aim here simply is to convince modern economic analysts (whether perplexed by the productivity slowdown, or not) of the immediate relevance of historical studies that trace the evolution of techno-economic regimes formed around general purpose engines.' The latter, typically, are key functional components embodied in hardware that can be applied as elements or modular units of the engineering designs developed for a wide variety of specific operations or processes. Accordingly, they are found ubiquitously distributed throughout such systems when the latter have attained their mature, fully elaborated state. James Watt's (separate condenser) steam engine design springs to mind readily as an example of an innovation that fulfilled this technological role in the first industrial revolution. My particular line of argument will be better served, however, by directing notice to the parallel between the modern computer and another general purpose engine, one that figured prominently in what sometimes is called the "second Industrial Revolutionn- -namely, the electric dynamo. (But, see also Herbert Simon, 1986.) Although the analogy between information technology and electrical technology would have many limitations if taken very literally, it proves illuminating nonetheless. Computer and dynamo each form the nodal elements of physically distributed (transmission) networks. Both occupy key positions in a web of strongly complementary technical relationships that give rise to "network externality effects" of various kinds, and so make issues of compatibility standardization important for business strategy and public policy (see my 1987 paper and my paper with Julie Bunn, 1988). In both instances, we can recognize the emergence of an extended trajectory of incremental technical improvements, the gradual and protracted process of diffusion into widespread use, and the confluence with other streams of technological innovation, all of which are interdependent features of the dynamic process through which a general purpose engine acquires a broad domain of specific applications (see Timothy Bresnahan and Manuel Trajtenberg, 1989). Moreover, each of the principal empirical phenomena that make up modern perceptions of a productivity paradox had its striking historical precedent in the conditions that obtained a little less than a century ago in the industrialized West, including the pronounced slowdown in industrial and aggregate productivity growth experienced during the 1890-1913 era by the two leading industrial countries, Britain and the United States (see my 1989


paper, pp. 12-15, for details). In 1900, contemporary observers well might have remarked that the electric dynamos were to be seen "everywhere but in the productivity statistics!"

At the turn of the century, farsighted engineers already had envisaged profound transformations that electrification would bring to factories, stores, and homes. But the materialization of such visions hardly was imminent. In 1899 in the United States, electric lighting was being used in a mere 3 percent of all residences (and in only 8 percent of urban dwelling units); the horsepower capacity of all (primary and secondary) electric motors installed in manufacturing establishments in the country represented less than 5 percent of factory mechanical drive. It would take another two decades, roughly speaking, for these aggregate measures of the extent of electrification to attain the 50 percent diffusion level (see my 1989 paper, Table 3, for estimates and sources). It may be remarked that, in 1900, an observer of the progress of the "Electrical Age" stood as far distant in time from the introduction of the carbon filament incandescent lamp by Edison, and Swann (1879), and of the Edison central generating station in New York and London (1881), as today we stand from comparable "breakthrough" events in the computer revolution: the introduction of the 1043 byte memory chip (1969) and the silicon microprocessor (1970) by Intel. Although the pace of the computer's diffusion in the business and public sectors of the industrialized societies during the past two decades has been faster than that recorded for the dynamo during its comparable early phase of adoption, it has been estimated that only 10 percent of the world's 50 million business enterprises today are using computers, and only 2 percent of the world's business information has been digitized (see Peter Lewis, 1989). The history of electrification after 1900 (see I. C. R. Byatt, 1979; Thomas Hughes, 1983; Ryoshin Minami, 1987) lends considerable plausibility to the "regime transition thesis" of Christopher Freeman and Carlotta Perez (1990). They suggest that productivity growth has been sluggish, and very well might remain so because the emergence and elaboration of a new technoeconomic regime based on computer and communications innovations (supplanting the mature, ossified Fordist regime of mass production) will, more than likely, be a protracted and historically contingent affair. Certainly, the transformation of industrial processes by the new electric power technology was a long-delayed and far from automatic business. It did not acquire real momentum in the United States until after 1914-17, when regulated regional utility rates for electricity were lowered substantially in relationship to the general price level (see my 1989 paper: Table 4, Figure 14), and central station generating capacity came to predominate

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over generating capacity in isoluted industrial plants. Furthermore, factory electrification did not reach full fruition in its technical development nor have an impact on productivity growth in manufacturing before the early 1920s. At that time only slightly more than half of factory mechanical drive capacity had been electrified. (On the significance for derived productivity growth of attaining 50 percent diffusion, see my 1989 paper, Appendix A.) This was four decades after the first central power station opened for business. The proximate source of the delay in the exploitation of the productivity improvement potential incipient in the dynamo revolution was, in large part, the slow pace of factory electrification. The latter, in turn, was attributable to the unprofitability of replacing still serviceable manufacturing plants embodying production technologies adapted to the old regime of mechanical power derived from water and steam. Thus, it was the American industries that were enjoying the most rapid expansion in the early twentieth century (tobacco, fabricated metals, transportation equipment, and electrical machinery itself) that afforded greatest immediate scope for the construction of new, electrified plants along the lines recommended by progressive industrial engineers (see Richard DuBoff, 1979, p. 142; and Minami, pp. 138-41). More widespread opportunities to embody best-practice manufacturing applications of electric power awaited the further physical depreciation of durable factory structures, the locational obsolescence of older-vintage industrial plants sited in urban core areas, and, ultimately, the development of a general fixed capital formation boom in the expansionary macroeconomic climate of the 1920s. The persistence of durable industrial facilities embodying older power generation and transmission equipment had further consequences that are worth noticing. During the phase of the U.S. factory electrification movement extending from the mid-1890s to the eve of the 1920s, the "group drive" system of power transmission remained in vogue (see Duboff, p. 144; Warren Devine, 1983, pp. 351, 354). With this system (in which electric motors turned separate shafting sections, so that each motor would drive related groups of machines), the retrofitting of steam- or water-powered plants typically entailed adding primary electric motors to the original stock of equipment. While factory owners rationally could ignore the sunk costs of the existing power transmission apparatus, and simply calculate whether the benefits in the form of reduced power requirements and improved machine speed control justified the marginal capital expenditures required to install the group drive system, productivity accountants would have to reckon that the original belt and shaft equipment (and the primary engines that powered them) remained in place as available capacity. The effect would be to raise the capital-output ratio in manufacturing, which militated against rapid gains in total factor productivity (TFP)-especially if the energy input savings and the quality improvements from better machine control were left out of the productivity calculation.

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This sort of overlaying of one technical system upon a preexisting stratum is not unusual during historical transitions from one technological paradigm to the next. Examples can be cited from the experience of the steam revolution (G. N. von Tunzelmann, 1978, pp. 142-43, 172-73). Indeed, the same phenomenon has been remarked upon recently in the case of the computer's application in numerous data processing and recording functions, where old paper-based procedures are being retained alongside the new, microelectronic-based methods-sometimes to the detriment of each system's performance (see, for example, Baily and Gordon, pp. 401-02). Finally, it would be a mistake to suppose that large potential gains from factory electrification were obtainable from the beginning of the century onward, just because there were farsighted electrical engineers who at the time were able to envisage many sources of cost savings that would result from exploiting the flexibility of a power transmission system based on electric wires, and the efficiency of replacing the system of shafting and belts with the so-called "unit drive7' system. In the latter arrangement, individual electric motors were used to run machines of all sizes (see Devine, pp. 362ff). The advantages of the unit drive for factory design turned out to extend well beyond the savings in inputs of fuel derived from eliminating the need to keep all the line shafts turning, and the greater energy efficiency achieved by reducing friction losses in transmission. Factory structures could be radically redesigned once the need for bracing (to support the heavy shafting and belt-housings for the transmission apparatus that typically was mounted overhead) had been dispensed with. This afforded 1) savings in fixed capital through lighter factory construction, and 2) further capital savings from the shift to building single-story factories, whereas formerly the aim of reducing power losses in turning very long line shafts had dictated the erection of more costly multistory structures. Single-story, linear factory layouts, in turn, permitted 3) closer attention to optimizing materials handling, and flexible reconfiguration of machine placement and handling equipment to accommodate subsequent changes in product and process designs within the new structures. Related to this, 4) the modularity of the unit drive system and the flexibility of wiring curtailed losses of production incurred during maintenance, rearrangement of production lines, and plant retrofitting; the entire power system no longer had to be shut down in order to make changes in one department or section of the mill. Although all this was clear enough in principle, the relevant point is that its implementation on a wide scale required working out the details in the context of many kinds of new industrial facilities, in many different locales, thereby building up a cadre of experienced factory architects and electrical engineers familiar with the new approach to manufacturing. The decentralized sort of learning process that this entailed was dependent upon the volume of demand for new industrial facilities at sites that favored reliance

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upon purchased electricity for power. It was, moreover, inherently uncertain and slow to gain momentum, owing in part to the structure of the industry responsible for supplying the capital that embodied the new, evolving technology. For, the business of constructing factories and shops remained extremely unconcentrated, and was characterized by a high rate of turnover of firms and skilled personnel. Difficulties in internalizing and appropriating the benefits of the technical knowledge acquired in such circumstances are likely to slow experience-based learning. A theoretical analysis of an interdependent dynamic process involving diffusion and incremental innovations based upon learning-by-doing (see my paper with Trond Olsen, 1986) demonstrates that where the capital goods embodying the new technology are competitively supplied, and there are significant knowledge spillovers among the firms in the supplying industry, the resulting pace of technology adoption will be slower than is socially optimal.

The preceding review of the sources of "diffusion lags" bears directly on the relationship between the timing of movements in industrial productivity, and the applications found for electric power within the industrial sector. A somewhat different class of considerations also holds part of the explanation for the sluggish growth of productivity in the United States prior to the 1920s. These have to do more with the deficiencies of the conventional productivity measures, which are especially problematic in treating the new kinds of products and process applications that tend to be found for an emergent general purpose technology during the initial phases of its development. Here, too, the story of the dynamo revolution holds noteworthy precedents for some of the problems frequently mentioned today in connection with the suspected impact of the computer (see, BailyGordon; and Gordon-Baily, 1989): 1) unmeasured quality changes associated with the introduction of novel commodities; and 2) the particular bias of the new technology toward expanding production of categories of goods and services that previously were not being recorded in the national income accounts. In the case of the dynamo, initial commercial applications during the 1890-1914 era were concentrated in the fields of lighting equipment and urban transit systems. Notice that qualitative characteristics such as brightness, ease of maintenance. and fire safety were especially important attributes of incandescent lighting for stores and factories, as well as for homes-the early electric lighting systems having been designed to be closely competitive with illuminating gas on a cost basis. Likewise, the contributions to the improvement in economic welfare in the form of faster trip speeds and shorter passenger waiting times afforded by electric streetcars, and later by subways (not to mention the greater residential amenities

INNOVATION & GROWTH

enjoyed by urban workers who were enabled to commute to the central business district from more salubrious residential neighborhoods), all remained largely uncaptured by the conventional indexes of real product and productivity. Measurement biases of this kind persisted in the later period of factory electrification, most notably in regard to some of the indirect benefits of implementing the "unit drive" system. One of these was the improvement in machine control achieved by eliminating the problem of belt slippage and installing variable speed d.c. motors. This yielded better quality, more standardized output without commensurately increased costs (see Devine, pp. 363ff). Factory designs adapted to the unit drive system also brought improvements in working conditions and safety. Lighter, cleaner workshops were made possible by the introduction of skylights, where formerly overhead transmission apparatus had been mounted; and also by the elimination of the myriad strands of rotating belting that previously swirled dust and grease through the factory atmosphere, and, where unenclosed within safety screening, threatened to maim or kill workers who became caught up in them. These more qualitative indirect benefits, however, came as part of a package containing other gains that, as has been seen, took the form of more readily quantifiable resource savings. Consequently, a significantly positive cross-section association can be found between the rise in the industry's TFP growth rate (adjusted for purchased energy inputs) during the 1920s, vis-a-vis the 1910s, and the proportionate increase of its installed secondary electric motor capacity between 1919 and 1929. Making use of this crosssection relationship, approximately half of the 5 percentage point acceleration recorded in the aggregate TFP growth rate of the U.S. manufacturing sector during 1919-29 (compared with 1909- 19) is accounted for statistically simply by the growth in manufacturing secondary electric motor capacity during that decade (see my 1989 paper, Table 5 , and pp. 26-27). But, even that did not exhaust the full productivity ramifications of the dynamo revolution in the industrial sector during the 1920s. An important source of measured productivity gains during this era has been found to be the capital-saving effects of the technological and organizational innovations that underlay the growth of continuous process manufacturing, and the spread of continuous shift-work, most notably in the petroleum products, paper, and chemical industries (see John Lorant, 1966, chs. 3, 4, 5). Although these developments did not involve the replacement of shafts by wires, they were bound up indirectly with the new technological regime build up around the dynamo. Advances in automatic process control engineering were dependent upon use of electrical instrumentation and electro-mechanical relays. More fundamentally, electrification was a key complementary element in the foregoing innovations because pulp- and paper-making, chemical production, and petroleum refining (like the

THE D Y N A M O A N D THE COMPUTER

primary metals, and the stone, clay and glass industries where there were similar movements towards electrical instrumentation for process control, and greater intensity in the utilization of fixed facilities) were the branches of manufacture that made particularly heavy use of electricity for process heat.

Closer study of some economic history of technology, and familiarity with the story of the dynamo revolution in particular, should help us avoid both the pitfall of undue sanguinity and the pitfall of unrealistic impatience into which current discussions of the productivity paradox seem to plunge all too frequently. Some closing words of caution are warranted, however, to guard against the dangers of embracing the historical analogy too literally. Computers are not dynamos. The nature of man-machine interactions and the technical problems of designing efficient interfaces for humans and computers are enormously more subtle and complex than those that arose in the implementation of electric lighting and power technology. Moreover, information as an economic commodity is not like electric current. It has special attributes (lack of superadditivity and negligible marginal costs of transfer) that make direct measurement of its production and allocation very difficult and reliance upon conventional market processes very problematic. Information is different, too, in that it can give rise to "overload," a special form of congestion effect arising from inhibitions on the exercise of the option of free disposal usually presumed to characterize standard economic commodities. Negligible costs of distribution are one cause of "overload"; information transmitters are encouraged to be indiscriminate in broadcasting their output. At the user end, free disposal may be an unjustified assumption in the economic analysis of information systems, because our cultural inheritance assigns high value to (previously scarce) information, predisposing us to try screening whatever becomes available. Yet, screening is costly; while it can contribute to a risk-averse information recipient's personal welfare, the growing duplicative allocation of human resources to coping with information overload may displace activities producing commodities that are better recorded by the national income accounts. In defense of the historical analogy drawn here, the information structures of firms (i.e., the type of data they collect and generate, the way they distribute and process it for interpretation) may be seen as direct counterparts of the physical layouts and materials flow patterns of production and transportation systems. In one sense they are, for they constitute a form of sunk costs, and the variable cost of utilizing such a structure does not rise significantly as they age. Unlike those conventional structures and equipment stocks, however, information structures per se do not automatically


undergo significant physical depreciation. Although they may become economically obsolete and be scrapped on that account, one cannot depend on the mere passage of time to create occasions to radically redesign a firm's information structures and operating modes. Consequently, there is likely to be a strong inertial component in the evolution of information-intensive production organizations. But, even these cautionary qualifications serve only to further reinforce one of the main thrusts of the dynamo analogy. They suggest the existence of special difficulties in the commercialization of novel (information) technologies that need to be overcome before the mass of information-users can benefit in their roles as producers, and do so in ways reflected by our traditional, market-oriented indicators of productivity.

Notes

*

Discussions with Paul Rhode were particularly helpful early in the research. I am grateful for comments from Steve Broadberry, Jonathan Cave, Nick Crafts, among the participants in the Economic History Summer Workshop held at Warwick University, July 10-28, 1989; from Timothy Taylor; and from Shane Greenstein, Avner Greif, Edward Steinmueller, and other participants in the Technology and Productivity Workshop at Stanford, October 1989. 1 This paper draws upon material developed in a longer work-my

1989 paper.

References Baily, Martin N. and Gordon, Robert J., "The Productivity Slowdown, Measurement Issues, and the Explosion of Computer Power," Brookings Papers on Economic Activity, 2: 1988, 347420. Bresnahan, Timothy F. and Trajtenberg, Manuel, "General Purpose Technologies and Aggregate Growth," Working Paper, Department of Economics, Stanford University, January 1989. Byatt, I. C. R., The British Electrical Industry 1875-1914; The Economic Returns to a New Technology, Oxford: Clarendon Press, 1979. David, Paul A,, "Computer and Dynamo: The Modern Productivity Paradox in a Not-Too-Distant Mirror," Center for Economic Policy Research, No. 172, Stanford University, July 1989. ----, "Some New Standards for the Economics of Standardization in the Information Age," in P. Dasgupta and P. L. Stoneman, eds., Economic Policy and Technological Performance, London: Cambridge University Press, 1987, ch. 7. ---- and Bunn, Julie A,, "The Economics of Gateway Technologies and the Evolution of Network Industries: Lessons from Electricity Supply History," Information Economics and Policy, Spring 1988, 4, 165-202. --- and Olsen, Trond E., "Equilibrium Dynamics of Diffusion when Incremental Technological Innovations are Foreseen," Ricerche Economiche, OctoberDecember, 1986, 40, 738-70. Devine, Warren, Jr., "From Shafts to Wires: Historical Perspective on Electrification," Journal of Economic History, June 1983, 43, 347-72.

THE D Y N A M O A N D T H E C O M P U T E R

DuBoff, Richard, Electrical Power it1 Amvrican Munujucturing 1889-1958, New York: Arno Press, 1979. Freeman, Christopher, and Perez, Carlotta, "The Diffusion of Technical Innovations and Changes of Techno-economic Paradigm," in F. Arcangeli et al., eds., The Diffusion of New Technologic~s,Vol. 3: Technology Diffusion and Economic Growth: International and Nutional Policy Perspectives, New York: Oxford University Press, forthcoming 1990. Gordon, Robert J. and Baily, Martin, N., "Measurement Issues and the Productivity Slowdown in Five Major Industrial Countries," OECD, Directorate of Science, Technology and Industry, Paris. June 1989. Hughes, Thomas P., Networks qf' Power: Electrfication in Western Society, 18801930, Johns Hopkins University Press, 1983. Lewis, Peter H., "The Executive Computer: Can There Be Too Much Power?," New York Times, December 31, 1989. p. 9. Lorant, John H., The Role of Cupital-Improving Innovations in American Manujacturing during the 1920's, New York: Arno Press, 1966. Minami, Ryoshin, Power Revohtron in the Industrialization of Japan: 1885-1940, Tokyo: Kinokuniya Co., 1987. Roach, Stephen S., "America's Technology Dilemma: A Profile of the Information Morgan Stanley, New York, September 22, Economy," Special Economic Stu+ 1987. -, "White Collar Productivity: A Glimmer of Hope?," Special Economic StudyMorgan Stanley, New York, September 16, 1988. Simon, Herbert A,, "The Steam Enginc and the Computer: What Makes Technology Revolutionary?," EDUCOM Bulletin, Spring 1986, 22, 2-5. von Tunzelmann, G. N., Steam Power und British Industrialization to 1860, Oxford: Clarendon Press, 1978.

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