Advances in Input-Output Analysis: Technology, Planning, and Development

ADVANCES IN INPUT-OUTPUT ANALYSIS

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ADVANCES IN INPUT-OUTPUT ANALYSIS Technology, Planning, and Development

Edited by

WILLIAM PETERSON

New York Oxford OXFORD UNIVERSITY PRESS 1991

Oxford University Press Oxford New York Toronto Delhi Bombay Calcutta Madras Karachi Pctaling Jaya Singapore Hong Kong Tokyo Nairobi Dar es Salaam Cape Town Melbourne Auckland and Associated Companies in Berlin Ibadan

Copyrighl (c) 1991 by Oxford University Press, Inc. Published by Oxford University Press, Inc., 200 Madison Avenue, New York, New York 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Advances in input output analysis : technology, planning, and development / edited by William Peterson. p. cm. Selected papers from the Eighth International Conference on InputOutput Techniques held in August 1986 in Sapporo. Japan. Includes index. ISBN 0-19-506236-1 1. Input -output analysis —Congresses. I. Peterson, William. II. Internationa] Conference on Input-Output Techniques (8th : 1986: Sapporo-shi, Japan) HB142.A28 1991 658.5'03- dc20 90-40536

1 3579 864 2

Printed in the United States of America on acid-free paper

Preface The chapters in this volume have been selected by the Program Committee from among papers presented at the Eighth International Conference on Input-Output Techniques, held in August 1986 in Sapporo, Japan. Although the task of choosing a small number of presentations from the large number of submissions was not an easy one, the choice was designed to reflect both the wide geographical spread of inputoutput techniques as a tool for economic analysis and planning and the range of economic issues to which they have recently been applied. Thus the volume includes applications to both market and socialist economies, to economies at very different levels of development, and to problems of social policy as well as to problems that are more conventionally economic in nature. The choice also reflects one of the major features of input-output analysis as a branch of economics—the positive interaction between the development of the underlying theoretical framework and the systematic collection and organization of the statistical data needed to ensure that the theory can be applied to the problems for which it was designed. Some of the chapters here represent that fusion of theory and data that is essential for progress in applied economics. Others either put forward new methods of analysis, and hence suggest areas where further improvements in our statistical knowledge are likely to be valuable, or describe the continuing efforts of national statistical offices to refine the data sources that underly our knowledge. The Conference was made possible by the generous financial and organizational help of the sponsors, the United Nations Industrial Development Organization (UNIDO), and the host, the University of Hokkaido. I would like, on behalf of all those who attended the Conference, to thank them both for their efforts. 1 would also like to thank the staff of Oxford University Press for their help with this volume. The Conference coincided with an important milestone in the brief history of input-output analysis, the fiftieth anniversary of the publication in August 1936 of Wassily Leontief s first paper on the topic in the Review of Economic Statistics. In addition the organizers succeeded in ensuring that the Conference coincided with an equally important occasion, Professor Leontief s eightieth birthday. All those present will retain warm memories of the party that was held in honor of this event and marked the close of the Conference. The papers included in this volume show how much has been achieved by those working in the tradition Professor Leontief founded, and the authors join in hoping that he will accept the dedication of this volume as a very belated birthday present. Cambridge, England July 1990

W. P.

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Contents Contributors, ix 1. Introduction, 3 WILLIAM PETERSON

I THEORETICAL DEVELOPMENTS IN INPUT-OUTPUT ANALYSIS 2. On the Mathematical Transformation of Input-Output Matrices over Time or Space, 17 A. GHOSH 3. The Absolute and Relative Joint Stability of Input-Output Production and Allocation Coefficients, 25 CHIA-YON CHEN AND ADAM ROSE

II THE COMPILATION OF INPUT -OUTPUT TABLES 4. Considerations on Revising Input-Output Concepts in the System of National Accounts and the European System of Integrated Economic Accounts, 39 CARSTEN STAHMER

5. The Simultaneous Compilation of Current Price and Deflated Input-Output Tables, 53 S. DE BOER AND G. BROESTERHUIZEN

III INPUT-OUTPUT AND THE ANALYSIS OF TECHNICAL PROGRESS 6. Technical Progress in an Input- Output Framework with Special Reference to Japan's High-Technology Industries, 69 SHUNTARO SHISHIDO, KIYO HARADA, AND YUJI MATSUMURA

7. Explaining Cost Differences Between Germany, Japan, and the United States, 108 SHINICHIRO NAKAMURA

8. Price Behavior with Vintage Capital, 121 P. N. MATHUR

9. Input-Output, Technical Change, and Long Waves, 137 E. FONTELA AND A. PULIDO

10. Private-Led Technical Change in Prewar Japanese Agriculture, 149 SHIN NAGATA

viii

Contents

IV INPUT-OUTPUT AND THE ANALYSIS OF SOCIALIST ECONOMIES 11. The SYRENA (SYnthesis of REgional and NAtional Models) Model Complex, 161 A. G. GRANBERG, V. E. SELIVERSTOV, V. I. SUSLOV, AND A. G. RUBINSHTEIN

12. A Planning Scheme Combining Input-Output Techniques with a Consumer Demand Analysis: A Concept and Preliminary Estimates for Poland, 173 LEON PODKAMINER, BOHDAN WYZNIKIEWICZ, AND LESZEK ZIENKOWSKI

13. Some Macroeconomic Features of the Hungarian Economy Since 1970, 187 !,. HAI.PERN AND G. MOLNAR

V INPUT-OUTPUT AND DEVELOPING COUNTRIES 14. Key Sectors, Comparative Advantage, and Internationa! Shifts in Employment: A Case Study for Indonesia, South Korea, Mexico, and Pakistan and Their Trade Relations with the European Community, 199 JACOB KOL

15. Import Substitution and Changes in Structural Interdependence: A Decomposition Analysis, 211 D. P. Pal VI THE ANALYSIS OF SOCIAL AND ENVIRONMENTAL PROBLEMS 16. A Long-Term Projection of the Industrial and Environmental Aspects of the Hokkaido Economy: 1985-2005, 223 FUMIMASA HAMADA

17. An Application of Input-Output Techniques to Labor Force Allocation in the Health and Medical and the Social Welfare Service Sectors, 236 YOSIIIKO KIDO

Index, 244

Contributors

S. DE BOER

YOSHIKO KIDO

Central Bureau of Statistics Voorburg, The Netherlands

Social Development Research Institute Tokyo, Japan

G. BROESTERHUIZEN

Central Bureau of Statistics Voorburg, The Netherlands CHIA-YON CHEN

Department of Mining and Petroleum Engineering National Cheng Kung University Tainan, Taiwan E. FONTELA

Department of Economics University of Geneva Geneva, Switzerland A. GHOSH Department of Economics Jadavpur University Calcutta, India

JACOB KOL Department of Economics Erasmus University Rotterdam, The Netherlands P. N. MATHUR

Department of Economics University College of Wales Aberystwyth, Wales YUJI MATSUMURA

Department of Economics University of Tsukuba Tsukuba, Japan G. MOLNAR

Institute of Economics Budapest, Hungary

A. G. GRANBERG

U.S.S.R. Academy of Sciences Novosibirsk, Soviet Union L. HALPERN

Institute of Economics Budapest, Hungary FUMIMASA HAMADA

Department of Economics Keio University Tokyo, Japan KIYO HARADA

Foundation for Advancement of International Sciences Tokyo, Japan

SHIN NAGATA

Department of Economics University of Hokkaido Sapporo, Hokkaido, Japan SHINICHIRO NAKAMURA

Department of Economics Waseda University Tokyo, Japan o. p. PAL Department of Economics University of Kalyani Kalyani, India

ADVANCES IN INPUT-OUTPUT ANALYSIS

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1 Introduction WILLIAM PETERSON

The papers presented as chapters in this volume have been selected by the Program Committee from among those presented at the Eighth International Conference on Input-Output Techniques, held in August 1986 in Sapporo, Japan. The Conference was made possible by the United Nations Industrial Development Organization (UNIDO), which gave financial and organizational help, and the University of Hokkaido, which hosted the event. On behalf of all those who attended the Conference I would like to thank both for their efforts. It is clear from the wide range of papers presented at the Conference and from the worldwide home bases of the participants that input-output analysis has become an essential tool of applied economics. Yet it would be misleading in this introduction to ignore the fact that, particularly in the developed market economies, the combination of the evolution of macroeconomic theory since the early 1970s and the methodological insistence that models must be based on analysis of the optimizing behavior of rational agents threatens to distance input-output analysis from "mainstream" economics. Since I believe that both of these fields would lose from such a development, it seems appropriate here both to discuss factors that have contributed to it and to suggest how input-output economics can learn from, and also contribute to, the more general development of empirical economics. The field in which the danger of divorce between the input-output tradition and mainstream economics is most acute and most clearly visible is one that has occupied a number of researchers in input-output analysis for many years: the integration of a disaggregated input-output-based model of production and employment with a macroeconomic model explaining the evolution of final demand. These integrated models have been seen as the appropriate tool for detailed business forecasting, for the investigation of economic policy in the medium and long term, and for the analysis of changes in industrial structure brought about by exogenous supply shocks such as natural resource discoveries. Improvements in computing facilities and data availability have allowed the technical problems involved in constructing such models to be largely overcome, and the models are now in use on a regular basis in several developed countries (see, for example, Barker and Peterson [1987] for the United Kingdom, or Almon, Buckler, Horwitz, and Reimbold [1974] for the United States). Yet, as suggested here, two important components of these models are at

4

Introduction

variance with the newly established orthodoxies of economic theory. First, the recent theoretical revolution in macroeconomics, and in particular the move away from a traditional Keynesian framework in which the level of activity is determined by effective demand (itself a function of a relatively small number of "flow" variables and policy instruments), has enlarged enormously the range and complexity of the behavioral relationships that must be modeled. In particular it is clear that both "forward-looking" variables (such as asset prices and exchange rates) and "stockflow" identities (such as the links between current sectoral budget deficits and financial accumulation) must be analyzed if such models are to generate plausible long-run forecasts of macroeconomic developments and (conditional on these macroeconomic forecasts) of the structural evolution of industry. The difficulty is, of course, that such an analysis is essentially part of the research program of macroeconomics rather than of input-output analysis. In addition, a substantial and influential school of macroeconomists (of which Lucas and Sargent [1979] are representative) believes that, in future, macroeconomic models will become both much smaller and more heavily based on purely theoretical reasoning. Such an evolution, which has already started in the United States (Kydland and Prescott, 1982), clearly will make it harder to integrate the industrial detail provided by inputoutput analysis. Second, and perhaps partly for ideological reasons (since the phenomenon is more noticeable among English-speaking economists), there has been renewed emphasis on the importance of reconciling empirical observation with the fundamental assumption made by economists in the free-market (as opposed to the socialist) tradition, that of rational optimizing behavior. This assumption fits ill with the key assumption of conventional input-output analysis—that producing firms will be prepared to supply whatever is demanded at a price that reflects average production costs (which include an allowance for "normal" profits). The perfectly elastic supply curve which this type of behavior implies can be reconciled with profit maximization only if the economy being modeled satisfies the conditions of the nonsubstitution theorem (Koopmans, 1951), in particular constant returns to scale and a single primary factor of production. If this is not the case, then not only does it become necessary to model the behavior of individual firms (which will of course depend on the competitive structure of their markets), but it also becomes impossible to argue that the industry, rather than the decision-making enterprise, is the appropriate unit for analysis. However, assuming that the behavior of individual optimizing agents can be modeled by assuming a single representative firm (whose output is aggregate gross domestic product) is as least as unsatisfactory as building models that lack foundations based on the postulate of rational maximization. Thus if the task of reconstructing economics on this methodologically purist basis is to proceed, it will at some stage have to attack the problem of modeling market relationships between producers. Here input-output analysis clearly has a large contribution to make, since it provides the statistical framework within which the interactions between enterprises through the supply of intermediate goods can be studied. Indeed the efforts made to date to model economic behavior in terms of the actions of enterprises (for example the work of Eliasson [1985] on the Swedish economy) have relied heavily on input-output data for their implementation. A second field in which the significance attached by input-output analysis to

Introduction

5

industrial interdependence and diversity carries an important lesson for conventional economics is that concerned with the interrelation of macroeconomics and industrial organization. It is obvious that the highly aggregate models favored by the "new classical macroeconomics" can only be a starting point for analysis, and that the perfect-competition assumption that these models embody is in many respects extremely misleading. A number of recent papers (for example, Hall [1986] and Bils [1987]) have employed disaggregated industry data to argue that important macroeconomic phenomena, such as the cyclical behavior of profit margins, cannot easily be rationalized in terms of a perfectly competitive model. The input-output tradition, with its stress on modeling technology in terms of the production relationship seen by the individual producer (that between gross output and all distinguishable inputs) rather than in terms of a net output measure constructed after the event by statisticians, is clearly relevant to such research. The fact that, despite these problems of consonance with economic theory, input-output analysis is now a well-established branch of economics means that research has moved away from trying to refine the theoretical structure of inputoutput models toward extending the range of applications and improving their realism and accuracy. Thus only two chapters with primarily theoretical contents are included in this volume, and both of these are directed explicitly at practical problems. The first, by A. Ghosh (Chapter 2), addresses an issue that has long been a concern of those engaged in the design of planning or forecasting models based on an inputoutput table. The inevitable delays in the collection and processing of production statistics mean that such models are typically based on an input-output table that is already several years out of data. Further, such obsolete information must also be used to forecast over a horizon that in some applications will extend well into the next century. Thus the need for simple techniques that can be used to extrapolate inputoutput coefficients is a long-standing one. The most common solution to this problem, the RAS technique (Bacharach, 1970), which assumes the original and extrapolated matrices to be biproportional to each other, has the advantage of computational simplicity and minimal data requirements. Professor Ghosh examines the conditions under which an alternative solution, based on the use of similarity transforms, is useful. Clearly the condition that two input-output systems should be similar is a stringent one. For example, it is easy to see that if one system is more productive in the sense of requiring less intermediate input per unit of output for any commodity, then (because the maximal eigenvalue of the more productive system is higher) similarity is ruled out. This means that the second approach is more likely to be useful in interregional comparisons or comparisons between countries at a similar level of development than in comparisons over time. However, if the basic model is extended to allow for linear error components in the technology matrices, an empirical measure of similarity based on the goodness of fit of a regression of intermediate demand on gross output can be derived. It is important to stress that the purpose of such a regression is not the indirect computation of the input-output coefficients, since it is well known (Arrow and Hoffenberg, 1959) that such coefficients cannot be estimated reliably from highly collinear time series. The fact that individual coefficients cannot be estimated, however, does not rule out computation of the similarity indices suggested here, just as multicollinearity in a statistical problem does not rule out the computation of a subset of regression functions.

6

Introduction

The second theoretical chapter, by Chia-yon Chen and Adam Rose (Chapter 3), explores a problem that has arisen in the use of input-output methods in planning, especially under conditions of physical shortage. Input-output systems are usually treated as demand driven in the sense that the composition and level of final output are determined elsewhere in the model; the activity levels in the various production sectors are adjusted to ensure that supply is adequate to meet demand. In such a framework the nonsubstitution theorem provides a justification for the key assumption that production coefficients are invariant with respect to changes in the scale of output. Under certain circumstances, however, it may be appropriate to assume instead that the allocation of output across consuming sectors is stable, possibly because of bureaucratic inertia in the planning process, and to look at the behavior of a supply-oriented system in which output levels are determined jointly by the accepted allocation rules and the availability of a small number of "key" inputs in short supply. The obvious difficulty with this approach is that it may imply a violation of the technological constraints represented by the conventional production coefficients. The aim of Chapter 3 is to analyze the practical importance of this difficulty by relating the changes in the two types of coefficients to each other, thus establishing the extent of technological substitution necessary for a system trying to cope with (possibly short-term) physical shortages by simple allocation rules. In their empirical application, Professors Chen and Rose consider the effects on the Taiwanese economy of a 50 percent cut in the availability of aluminum, under the assumption of proportional supply rationing, and show that the implied changes in technology for the majority of industries (except for metal products, which is relatively aluminum intensive) are comparatively small. The two chapters on the statistical compilation of input-output tables that follow (Chapters 4 and 5) both show the importance of integrating the analysis of productive relationships into the framework of national accounts. Such an approach is clearly essential if input-output data are to be used as the basis for efforts at disaggregated modeling of the national economy, either for forecasting and policy analysis or for planning purposes. However, such integration also makes it possible to focus on tracing the source of errors in national accounts and making needed improvements in reporting procedures. The development of international conventions for the compilation of inputoutput tables and national accounts statistics has provided applied economists with a huge amount of data on which to base the estimation of key relationships and the testing of alternative hypotheses. It has also offered politicians the scope for comparisons that often are regrettably misleading and chauvinistic. Carsten Stahmer in Chapter 4 addresses problems that have arisen in revising two of the most important of these statistical conventions, the U.N. System of National Accounts (the SNA) and the European System of Accounts (the ESA). Both of these are based on a tabular presentation of the various transactions in the economy that draws directly on the concepts of input-output analysis. One important proposal put forward by Professor Stahmer concerns the appropriate statistical unit for which input-output tables should be constructed. Historically such tables have been based on the concept of the establishment, with establishments producing similar principal products being classified to the same industry. Although this approach seems to fit with the idea that input-output tables

Introduction

1

express the fundamental technological relationships of the economy, it is at variance both with the increasing importance to the economy of conglomerate firms and with the tendency, already discussed, of economists to analyze the behavior of the economy in terms of the choices of the agents who actually make decisions. Both of these factors would suggest that input-output tables should move toward employing the enterprise as the fundamental statistical unit, and this is the course of action recommended in Chapter 4. Clearly such a move would be likely to increase the importance of joint production in the input-output representation of the economy, but this is a problem already built into the commodity-industry distinction employed by the existing SNA. Chapter 5, by S. de Boer and G. Broesterhuizen, describes the process of constructing input-output tables in the Netherlands, where the integration of inputoutput concepts and national accounts is well established. The major advance set out here is the simultaneous use of a wide range of sources to produce consistent measures of both the volume and value of transactions and the prices at which these are carried out. In theory these three measures are related by the equation value = volume x price, but it is well known that real-world data derived from a wide range of inconsistent sources require substantial modification before this equation is satisfied. Elimination of this type of discrepancy at the stage of data collection is an essential step if economists are to ensure that their empirical findings are robust to the choice of alternative data sources. Without such a step it is hard to see how they can achieve any progress toward a body of generally accepted propositions in economics. Five of the chapters in this volume apply concepts and techniques drawn from input-output analysis to the problems of measuring technical change across countries or through time, and of evaluating the impact of such change on the economy. This is an application where what I have argued to be the central feature of input-output analysis—the use of a statistical framework sufficiently flexible to represent both the individual production process and the national aggregate—is peculiarly valuble. Given sufficiently detailed data, observed differences in input-output coefficients can be identified in principle with the effects of particular innovations; at the same time, as was first shown by Domar (1961), macroeconomic measures of differences in total factor productivity can also be interpreted as weighted averages of all the individual coefficient changes. These weights sum to more than 1, reflecting the fact that productivity improvement in industries producing intermediate or capital goods has a favorable impact on all "downstream" activities (Peterson, 1978). In Chapter 6, Shuntaro Shishido, Kiyo Harada, and Yuji Matsumura apply this methodology to the analysis of high-technology industry in Japan. In doing so they are fortunate to be able to use the extremely detailed input-output tables, distinguishing over 500 intermediate inputs, that have been published by the Government of Japan. At the level of disaggregation they studied, a conventional examination of interindustry differences in the productivity of primary inputs would be difficult to interpret, since each producing sector will rely heavily on intermediate rather than primary inputs. As new industries develop and grow, their reliance on outside sources for components and specialized services changes, and although national accounts statisticians attempt to allow for such structural changes in constructing measures of net output, they may not always do so adequately. The work in Chapter 6 shows that during the 1970s most observed changes in input-output coefficients can be accounted for by two factors: differing rates of total factor productivity growth in the individual sectors of the economy and the response

8

Introduction

of firms to price changes that arise largely as a result of such differential technical change. As is well known, these factors can be identified with the S and R components, respectively, of the RAS method for updating input-output coefficients. By using expert opinion on the probable evolution of factor productivity in individual sectors of the economy, it becomes possible to forecast the technological structure of the Japanese economy in the year 2000 and the implication of these changes for employment and international trade. In Chapter 7, Shinichiro Nakamura applies a similar methodology to the comparison of productivity levels and changes in the United States, Japan, and West Germany. As one might expect, the need to ensure cross-country data comparability means that the high level of disaggregation used in the previous chapter must be sacrificed. The aim of Chapter 7 is an important one—to establish how far the comparative cost differences that are largely responsible for determining the direction of international trade reflect differences in productivity and how far they reflect differences in the rewards paid to primary factors. Clearly, comparisons of this kind cannot be based on prevailing exchange rates, and purchasing power parity indices are used instead. Professor Nakamura's findings show that, for both Japan and Germany, the industries with comparatively low unit costs were those for which total factor productivity was relatively high, while the United States was competitive in those industries in which input prices were low. Another finding is that Japan still possesses some characteristics of a "dual" economy, since Japanese industry falls clearly into "high-productivity" and "low-productivity" sectors. The value of the conceptual framework provided by the input-output model of technology, with its focus on aggregate productivity measures as summarizing the combination of a number of distinct production processes, is also shown in the chapter by P. N. Mathur (Chapter 8). In a pioneering study, Carter (1953) showed how the evolution of technology in the U.S. cotton industry could be modeled as resulting from the gradual introduction of new plant. This initial insight into the role played by different vintages of equipment has become an essential building block in many models of productivity growth. Unfortunately, only in very rare cases are economists in a position to apply this model of innovation and its effects directly. Since it is exceptional for production techniques to evolve in such a way that at any particular time only one type of capital good is purchased by all producers, even complete information on the composition of plant in terms of vintages would not be sufficient to characterize the range of attainable input coefficients. In addition, the information about utilization that is needed can only be provided on the basis of returns by individual firms, and hence is usually inaccessible to economists because of confidentiality rules. In these circumstances the investigator is thrown back on indirect tests of the hypothesis that technical change is embodied in particular vintages of equipment. The procedure followed by Professor Mathur is to assess the rate of technical change through time by evaluating how the profitability of individual sectors would have changed if the observed changes in input prices had occurred without any alteration in the input-output coefficients for the industry in question. If technical change were occurring in a competitive industry we would expect that the computed profits accruing to a particular technology would decline as new and more efficient plants came into operation. Indeed, this pattern characterized approximately half of the U.S. industries included in Professor Mathur's study.

Introduction

9

Although these figures are illuminating, it is important not to claim too much for the method of analysis. In the first place, since what is observed is the average inputoutput coefficient rather than that relating to a specific piece of equipment, the method cannot distinguish between decreases in the average coefficient that are directly related to the introduction of new plant and decreases that occur as firms gain experience and improve the efficiency with which existing plant is utilized. Second, although the study finds that there is some correlation between industries with low rates of technical obsolescence (in the sense that old technology remains profitable over a long period) and high concentration ratios, the correlation may arise because it is easier to maintain stable oligopolies and limit entry in "mature" industries where the technology is well known and innovations are rare. Chapter 9, by E. Fontela and A. Pulido, adopts a Schumpeterian approach to the study of technical change and its role in determining the "long waves" of economic growth. The fact that input-output analysis offers a methodology for looking both at individual innovations and at their influence on economic aggregates means that it can in principle be used to quantify such an approach. However, there are substantial problems in applying such concepts in practice, as Fontela and Pulido point out. In particular the dissemination of new technology is surprisingly slow, even when this technology offers substantial cost advantages, and this means that distinguishing changes in coefficients that arise because of innovations from those that reflect changes in product mix or, regrettably, in statistical conventions is extremely difficult. Furthermore, in countries where input-output data are collected within a national accounts framework, the conventional input-output matrix is only one component of the system of accounts, and innovations may show up in the consumption or investment converters as well as in the input coefficients. Nonetheless, the productivity indices for individual French industries quoted in Chapter 9 do provide some support for Schumpeterian theories of the long wave, which predict that the bunching of innovations will lead deviations of productivity growth from trend to be strongly correlated across industries. The final chapter in this section, that by Shin Nagata (Chapter 10), represents an application to a historical problem, the prewar development of Japanese agriculture, which is of considerable relevance to developing countries today. Professor Nagata applies mixed estimation techniques, exploiting both cross-section and time-series data, to the problem of estimating a production function. An important feature of his analysis is the significance attached to intermediate inputs, both purchased inputs such as chemical fertilizers and "productivity-increasing activities" undertaken by individual farmers, in explaining the evolution of agricultural productivity during this period. Traditionally, one major application of input-output analysis has been to the construction of disaggregated models of individual national economies. In the countries of the Socialist bloc, and in those developing countries where the government has committed itself to a major role in the organization of production either directly through public ownership of key enterprises or indirectly through administrative controls, such models are seen as an essential part of the planning process, and their behavioral (as opposed to technical) content is often limited. In contrast, economists constructing such models for developed market economies have seen them as more detailed versions of conventional macroeconomic models, with which they have many behavioral relationships in common. Such models are usually

10

Introduction

designed for forecasting and policy analysis exercises as well as for studying the evolution of industrial structure. Although a number of such models were discussed in papers presented at the Conference, for a variety of reasons it has not proved possible to include any of the papers concerned in this volume. Nor is there any example of what has become known as the "computable general equilibrium" approach to economic modeling (as surveyed, for example, by Waelbroeck [1987]), although such models draw heavily on the concepts and data sources associated with input-output analysis. Instead the three chapters in Part IV of this book illustrate some of the uses made of input output techniques in socialist countries. A. G. Granberg and his collaborators report on SYRENA in Chapter 11. SYRENA is an extremely ambitious complex of planning models for the Soviet Union that incorporates both regional and national components. Here also the list of prospective model developments, such as the construction of linked macroeconomic and financial models, shows the flexibility of the inputoutput framework as a basis for more general modeling exercises. Leon Podkaminer, Bohdan Wyznikiewicz, and Leszek Zienkowski in Chapter 12 show how a relatively simple extension of the basic input-output model to incorporate a consumer-demand system in which the composition of consumption is sensitive to relative prices can be employed to analyze some of the critical problems of economic management that have faced Polish planners during the past decade. Their methodology makes possible the assessment of the extent of disequilibrium in consumer markets by comparing "market-clearing" prices for the postulated structure of consumer preferences with the prices that were actually observed. One important contribution of such a study is that it explicitly incorporates both intermarket spillovers in consumption and the "general equilibrium" implications for production and employment of attempts to equilibrate supply and demand. It is thus likely to provide a more accurate assessment of the shortages facing the economy, albeit on a rather aggregated basis, than casual observation of queues and waiting lists. In particular the authors' finding that in 1977 food prices were not disproportionately low is at variance with the assumptions that have lain behind subsequent policy choices. Realistically the authors do not see either a drastic price reform, involving the universal adoption of market-clearing prices, or the adjustment of supply to meet demand at the current administratively set prices as being a feasible or sensible response to the problem. Instead they conduct an exploratory analysis, based on a linear programming model of the Polish economy, to find solutions that are, if not optimal in the conventional sense, at least superior to the actual outcome. Although the model they employ is a static one, by treating fixed capital formation as exogenously given and by regarding the current balance of trade (equivalent to the change in Poland's net foreign assets) as an objective variable the authors can ensure that such an improvement is not achieved at the expense of future consumption levels. The most important of their results is not the quantitative improvement in consumption attainable by moving to a different set of relative prices, but the qualitative finding that their recommendation of a relative fall in food prices is diametrically opposed to the course that policy has actually followed. The final chapter in this section, by L. Halpern and G. Molnar (Chapter 13), again focuses on the problems raised for socialist planners by the discrepancy between administratively imposed and economically appropriate prices. In their application, to the Hungarian economy during the 1970s, the dual prices (costs of production)

Introduction

11

emerging from a closed input-output model are compared with observed prices to assess the extent of overvaluation or undervaluation affecting particular sectors of the economy. Such deviations are extremely significant, both because under the New Economic Mechanism that operated in Hungary after 1968 there were tendencies for overvaluation to be associated with overproduction, and because they may have serious adverse implications for the planners' ability to attain their desired income distribution. The chapter can thus be seen as a "supply-oriented" version of that by Professor Podkaminer and his collaborators. Setting prices incorrectly has adverse effects not because it distorts consumer choice (which is not modeled in their paper) but because it encourages excessive investment and expansion in the sectors concerned. The major contribution that input-output concepts and data have made to the analysis of economic development was reflected both in the large number of Conference participants from developing countries and in the generous sponsorship provided by UNIDO. Out of a large number of papers in this area we selected two that focus in particular on the use of input-output techniques as tools for the analysis of trade patterns and comparative advantage. Jacob Kol (Chapter 14) considers the probable effects on employment in the European Community and a group of (relatively industrialized) developing countries of a balanced increase in trade in manufactures. In this example there is no analogy of the Leontief paradox (Leontief, 1954), since the developing countries concerned are found to export labor-intensive goods as well as to use processes that are much more labor intensive than those employed by the corresponding industries in the EC. A trade expansion would therefore lead to substantial employment gains in the developing countries at the cost of a small employment decline in the EC as production shifted to the output of nonlabor-intensive exports. One important limitation of this result is worth noting: It neglects any macroeconomic effects that might result from the trade expansion by assuming the structure and level of domestic final demand in both countries to be unaffected by the expansion. There is thus an implicit assumption that EC governments would compensate for the fall in labor income associated with lower employment by cutting taxes, while developing country governments would be required to raise taxes in order to avoid higher labor incomes leading to higher consumption. Professor Kol also considers the extent of intersectoral linkages in the four developing countries under study and confirms earlier findings that forward linkages are relatively important for primary products, backward linkages for manufacturing. D. P. Pal in Chapter 15 uses input-output data for India to decompose import substitution into two components: direct import substitution—the change in the import ratio for industry i that would occur if 1 unit of this industry's output were supplied by domestic production rather than imports, with the output of all other industries remaining constant—and indirect import substitution—the additional effects that arise because the expansion of industry i affects other industries in the economy and hence feeds back to the originating industry. This decomposition is in a sense the quantity analogue of the distinction in the international trade literature between nominal and effective protection rates. Professor Pal's estimates show that the Indian economy has displayed increasing import substitution over time, with only the nonferrous metal sector showing evidence of a significant indirect substitution effect. The final two chapters in this volume apply input-output techniques to

12

Introduction

environmental and social, rather than purely economic, problems. Here the major contribution input-output methodology can make is the incorporation of technical and scientific information in a fashion that is explicit and easily understood by specialists working in the areas concerned. In addition, insofar as the output of pollutants or the demand for skilled labor of various types responds to economic developments, it is plausible to argue that changes in economic structure, defined in terms of variables such as the industrial composition of output, are likely to be more important determinants than macroeconomic growth. Fumimasa Hamada (Chapter 16) considers the environmental problems likely to arise over the next twenty years as a result of economic development of the island of Hokkaido (the northern island of Japan, of which Sapporo, the location of the Conference, is the capital). Although Hokkaido is currently relatively underpopulated and underindustrialized compared with the rest of Japan, it is expected to grow rapidly over the period of Professor Hamada's study, with an especially large expansion of residential construction. Professor Hamada links a small Keynesian macroeconomic model for Hokkaido (which treats economic developments in the rest of Japan as exogenous) with an input-output model to determine industrial structure and with additional technical relationships to determine local demand for fuel, power, and water and the output of four major pollutants. The rapid expansion of employment and manufacturing industry implies that technical progress in pollution control is needed if environmental standards are not to decline severely. In Chapter 17 Yoshiko Kido addresses a problem of great importance in Japan and other developed countries—the growing proportion of elderly and inactive members of the population. This has major implications for the allocation of the labor force between health care and industrial activities. Professor Kido uses input-output techniques to analyze the linkages between industrial and "social service" sectors. In practice these linkages are effectively one-way (so that the relevant block of the Leontief inverse is triangular), since social services supply almost all their output directly to households. Although the expansion of demand for social services has been rapid, technical progress (particularly in health care) has in the recent past slowed the increase in numbers employed. It is hard to know whether this will continue in the future: Although much high-technology medicine, particularly the widely publicized forms of it, are extremely labor intensive, other developments, such as the discovery of effective drugs for mental illness, have had labor-saving effects. REFERENCES Almon, C., M. B. Buckler, L. M. Horwitz, and T. C. Reimbold. 1974. 1985: Interindustry Forecasts of the American Economy. Lexington, Mass.: Heath. Arrow, K. J., and M. Hoffenberg. 1959. A Time Series Analysis of Interindustry Demands. Amsterdam: North-Holland. Bacharach, M. O. L. 1970. Biproportional Matrices and Input- Output Change. Cambridge: Cambridge University Press. Barker, T. S., and A. W. A. Peterson. 1987. The Cambridge Multisectoral Dynamic Model of the British Economy. Cambridge: Cambridge University Press. Bils, M. 1987. "The cyclical behaviour of marginal cost and price." American Economic Review 77: 838-855. Carter, A. P. [A. P. Grosse]. 1953. "The technological structure of the cotton textile industry." In W. W. Leontief et al., Studies in the Structure of the American Economy. New York: Oxford University Press.

Introduction

13

Domar, E. D. 1961. "On the measurement of technical change." Economic Journal 71: 709-729. Eliasson, G. 1985. The Firm and Financial Markets in the Swedish Micro-to-Macro Model. Stockholm: Almqvist & Wiksell. Hall, R. E. 1986. "Market structure and macroeconomic performance." Brookings Papers on Economic Activity 2: 285-322. Koopmans, T. C. 1951. Activity Analysis of Production and Allocation. New York: Wiley. Kydland, F. E., and E. S. Prescott. 1982. "Time to build and aggregate fluctuations." Econometrica 50: 1345-1370. Leontief, W. W. 1936. "Quantitative input and output relations in the economic system of the United States." Review of Economic Statistics 18: 105-125. Leontief, W. W. 1954. "Domestic production and foreign trade: The American capital position reconsidered." In R.E. Caves and H. G. Johnson (Eds.), Readings in International Economics. London: George Allen and Unwin. Lucas, R. E., and T. J. Sargent. 1979. "After Keynesian macroeconomics." In R. E. Lucas and T. J. Sargent (Eds.), Rational Expectations and Econometric Practice. London: George Allen and Unwin. Peterson, A. W. A. 1978. "Total factor productivity: A disaggregated analysis." In K. D. Patterson and K. E. Schott (Eds.), The Measurement of Capital. London: Macmillan. Waelbroeck, J. 1987. "Some pitfalls in applied general equilibrium modelling." In T. F. Bewley (Ed.), Advances in Econometrics—Fifth World Congress. Vol. 2. Cambridge: Cambridge University Press.

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I THEORETICAL DEVELOPMENTS IN INPUT-OUTPUT ANALYSIS

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2 On the Mathematical Transformation of Input-Output Matrices over Time or Space A. GHOSH

THE TRANSFORMATION RULE One feature of input-output matrices is that if they are of the same order and have the same classification it may be possible to find a transformation between any two of them. If such a transformation can be related to the output vectors concerned by a scalar or a diagonal matrix, then the resulting transformation of the matrices can easily be computed and can be expressed in canonical form, and the implicit technological transformation that lies behind this transformation can be brought out clearly. The object of this chapter is to demonstrate some useful properties of inputoutput matrices of the same order, conceptualized as forming a group. A group is defined as a set of elements, and a method of combining them, satisfying the following conditions. Let (At), the typical input-output matrix,1 be a member of the group. 1. Then if (Ai) and (Aj) are members of the group, the product ( A ) ( A j ) and (Aj)(Ai) are also members of the group, that is, the product sets also satisfy the usual conditions on the coefficient matrix. 2. [(A l -A ] yiA3]= [ A . i ( A j - A k ) ] 3. There is an element I such that I-Ai = Ai-I and for every (At) we have

(ACAr*) = 1.

A subgroup is any subset of elements made up of the members of a group that itself satisfies the definition of a group. A right or left co-set of a subgroup g or a group G is the set of elements of G obtained by multiplying each of the elements of g in turn (using right or left multiplication, respectively) by some element of G not in g. Using the above properties we can conceptually formulate that the elements (A() are members of the group G. Under the conventional restrictions on the input-output coefficients, the existence of the Leontief inverse has been proved by various authors. The associative law also follows from the property of matrix multiplication itself.

18

Theoretical Developments in Input-Output Analysis

The commutative property (1) states that (At • Aj) and (Aj • At) are both members of the group. Here we assume that the group G contains not only A( and Aj but also their products, A^Aj and At- Ah which are not necessarily equal. Intuitively we conjecture that this will be true under certain conditions and will follow from the invariance property of the Leontief matrix under nonsingular transformations, in the case where such transformations lead to the formation of another matrix of the Leontief type. The group G thus contains not only At and Aj but also their products. Let us assume that G contains a subgroup g that is a co-set of G, and that (AJ, ( A 2 ) , . . . , (Ak) belong to G and T t , T 2 , . . . , T k belong to g such that Ti(Ai)= A k and so on, that is, that the co-set group contains matrices Tf that transform Ai to Ak, where Ai ,Ak belong to G but not to g. We may thus associate a co-set of transformation matrices Ti that, when premultiplied into Ai, results in Ak, one of the members of G not in g. It is thus possible at least conceptually to move from any matrix Ai to Aj using a suitable member from the co-set group. The physical significance of this, assuming the existence of co-set g, is that at least theoretically we may move from any (7 — Ai) to (I — Aj), provided the corresponding member from the co-set g is estimated. In this paper we demonstrate that a sequence of output vectors, and the corresponding row vectors of transaction flows, can be used to find a set of regression equations giving estimates of the coefficients a ij . These regression matrices, designated R, can be used to estimate the corresponding transformation matrix T using a similarity transformation. (See the appendix for a list of symbols used in this chapter.) Obviously, if we conceive of continuous groups then any output vector X and its neighborhood vector X + dX will give rise to a T + dT in g, which will give a very close approximation to T, and in the limiting case the T will produce the exact A matrix with which we started. But as X and X + dX move away from each other, the estimation of / — Aj from I — (Ai + dAi) will become more and more approximate. In theory, therefore, the input-output space is conceived of as an affine space, permitting movement from any point denoted by I — Aj to any other point I — Ak by estimating the relationship of the corresponding regression coefficients from the row vectors whose sums result in Xj and Xk, and which give rise to the regression systems Aj Xj and Ak Xj, where Aj and Ak have been estimated from historically given sets of transaction flows and their totals. We may now proceed to a demonstration of the properties of such transformations and their possible uses.

PROPERTIES OF TRANSFORMATIONS Let us assume that in two countries P and Q there are two input-output systems, relating to the same years, expressed as

y = Ax

for P

and

n = BO for Q

where A and B are the input -output coefficient matrices and x and 6 are the outputs, y and n being the total intermediate outputs. Let us assume (2) that there is a transformation matrix T such that

x = TO

and

y = T/i

In other words, let us assume that over a historical series of x for P, 0 for Q, y for P,

Mathematical Transformation of Input-Output Matrices

19

and ju for Q a unique transformation exists that satisfies the above conditions. Also, we have already assumed that y = Ax, fj, = B9. Then

by our earlier relation Then A and B are similar matrices, with the same eigenvectors and eigenvalues and identical traces. Assuming that a unique transformation exists such that the matrix Tcan be obtained, we can use T to obtain the matrix B from the matrix A. Since the matrix A and the matrix B are matrices of constants, of the same order and with inverses, there is a transformation T such that AT = TB. Suppose we regress the set \n as functions of the set x over the historical period for which the date has been generated, the regression being constrained to pass through the origin. Let the regression coefficient set R so obtained be

But for any specific year we also have the relation

by virtue of our input-output relation

Or or Thus the regression coefficient matrix suitably transformed gives the A matrix or and as before

We have, therefore,

Thus the regression, on the assumption that the data were generated by the inputoutput model, gives a coefficient matrix which, after using the transformation T, gives us back the B matrix. If we can estimate R, and if we know A, then the transformation T is exactly determined. Several comments regarding our assumptions are now in order. What do these assumptions imply? Assumption (1) states that

This is simply a statement of the input-output model, without the final demand

20

Theoretical Developments in Input -Output Analysis

vector, so that y and /i are intermediate outputs and it is assumed that total intermediate output can be derived by the familiar input-output equations. But assumption (2) implies that the intermediate output vector fj, in Q can be regressed on the set of outputs x of P, and x the total output of P can be regressed on the set of outputs 0 of Q, both sets of outputs being considered over a period of time. What is the justification for this assumption, in the case where assumption (1) is accepted? A characterization of the transformation matrix T can be obtained as follows. Consider the following three-sector input-output matrix, where y is intermediate demand and x is total output, and the aij's are fixed constants with respect to a base period

Let us assume that this model is used to generate a time series xc1(t), xc2(t), xc3(t) for given y,(z), y2(t), y3(t) for n years. Let us now assume that this time series so generated consists of n values of xct(t) and yt(t). If we use these series of x-(f) and y i (t) to form a linear regression system for each equation of the form y, = £a,.Xy with the condition that the equation passes through the origin, then the regression expression of each (say the first one) equation will be of the following form

In a similar way we can also find « 2i , «,; by using the other sets of regression equations. From the series of generated values so obtained we can again form the variance-covariancc matrix consisting of, say, £(X)2 and Exjoc', when xi, xj denote generated values and the generated values will satisfy

Comparing the two systems—the original input-output equations and the regression using the generated values—it is obvious that the terms involving x are identical since the series themselves have been generated by using the theoretical model. Therefore, for any nontrivial solution (e.g., a; / 0), the two systems are identical and the input-output matrix A and the matrix fitted from the generated series (i.e., a) are identical. Let us consider two such input-output systems, one for country (P) and the other for country (Q), behaving exactly as an input-output model. Then we can consider the values of x(P) and y(P), and also of 0(Q) and n(Q), as giving rise to

Mathematical Transformation of Input-Output Matrices

21

Let us also assume that there is a unique transformation T so that

If there is such a unique transformation T we can then move from A(P) to B(Q\ as has been demonstrated earlier, by using the similarity transformation, for example If, therefore, there are two economies whose behavior is exactly described by the input-output rules, and if the total outputs and total intermediate outputs have an exact functional relation that transforms the total output and total intermediate output of one country to those of the other country, then we can pass from one of the input-output matrices to the other by obtaining the similarity transformation using a regression. We may now consider the fact that in the most plausible case both the inputoutput rules and the transformation obtained from the regression are subject to errors. Therefore, we have three sets of errors entering the relationship. We may call them eA, EB, and ^T. We thus have in effect the relation We may write this or

Taking expectations, and assuming eA,eB, er are independent random errors with zero mean, we have or or

The corresponding forms for correlated errors can also be easily be computed. It is to be noted, however, that while the relation will hold on the average, the error components will disturb specific cases depending on their size. If, however, we assume that the error components are also linear functions of time, then we have, on the assumption that &A = EA(Q) + f$A(l) Separating this expression into two components, one involving t and the other involving e,-(0), we have

22

Theoretical Developments in Input-Output Analysis

Again taking expectations we will be left with the original relationship, along with a variance or covariance component for the product of the E;'S, as well as a linear component of the errors in e f (f). Depending on the size of /J this will introduce a larger divergence in the relationship for larger values of t. For short periods, however, the results of the earlier experiments will still hold. The preceding results thus follow from our assumption of the operation of two input-output models over historical periods. If we know one of them, we can find the other using regression methods. But it is generally known that input-output coefficient matrices are not strictly constant. They can be affected by both systematic and random change over time. If we ignore systematic change, then the random change in the A or B matrix over time will give rise to errors in the coefficients, with an expected value of the regression coefficients that will again be equal to A or B. Hence if we ignore the impact of technological change for reasonable periods, we can find a specific matrix with the help of the expected values, as estimated by the regression coefficients, and we can find a transformation matrix T that, as a first approximation, will help us to move from one of the matrices to the other. It is obvious that, using the same kind of arguments and assumptions, one can find a matrix B for the same country referring to the year (t + k) using the matrix A referring to the year t and the historical series of y and x for t and (t + k). It is often our experience that total output vectors and total intermediate demand vectors are obtainable for each sector over time but that the coefficient matrix is not. It is also known that generally the total output and total intermediate output have a stable ratio for the different sectors, so that the coefficients of the transformation appropriate to outputs and those of that appropriate to intermediate outputs are not likely to diverge very significantly. Using this method, therefore, one can derive an input-output matrix for one country from that of another, or for one period from that of another, provided the regression error is not very large. In other words, for this method to be of practical use the observed values, and the computed values from the regression, should have a high correlation. Large changes over time, either random or systematic, between periods or between countries over a single period are potential sources of inaccuracy. The economic interpretation of the mathematical relation just described follows from the fact that, although it is estimated at a point in time, an input-output matrix is assumed to reflect a structural relation that is relatively invariant over time. To the extent that input-output coefficients are invariant, the time series generated by the system will follow the same rule, so that the expected values estimated by regression methods and those estimated from the input-output relation should be reasonably correlated. These two influences—the stability of the structural relationships and the nature of the change over time between them—determine the new coefficient matrix. If the change is random in character, the regression attempts to give an average structural relation over time. The present method therefore seeks to adjust the original structural interdependence using the historical transformation matrix between t and t + k for the same country, or between A and B, two related countries. We now move to the relationship (set out in the following section) between the estimated B matrix and a capital matrix. The B matrix now refers to a later period and the A matrix to a base period. We have from the dynamic balance equation with a capital matrix K,

Mathematical Transformation of Input-Output Matrices

23

where Ax = xt+r — xt, the unit interval being r and K being the capital coefficient matrix being defined for this unit interval. or

But we have B = T A T - l = R - 1 A R . Therefore or and

as also In this way the incremental output is related to the capital coefficient matrix as well as the transformation matrix T and its counterpart, the regression coefficient matrix R. As before, let us consider the effect of error in T.

Then

RT Ms the error term in the historical transformation between A and B. Since Therefore

Using the same regression matrix R for year t + k, we are committing an error given by the terms associated with e in the capital coefficient matrix. This error may be evaluated by correcting for c. USES OF TRANSFORMATION What is the use of this approach for input-output analysis? First, it says that all input-output matrices of the same order and classification can be transformed, if

24

Theoretical Developments in Input Output Analysis

there exists a nonsingular T. The existence of the latter allows a unique growth of the components of the vectors x or Ax that transforms one into the other. The existence of T thus illustrates the existence of a unique transformation, and also the existence of a balanced rate of growth by which one vector may be transformed into the other. The results given here may be easily applied to matrices for different regions, where the regional outputs and final demands for a period are known but where an input-output table exists only for one region and not for the other. The nature of the transformation matrix T also shows that we may have a balanced growth rate from one matrix to the other if we choose a suitable eigenvector and eigenvalue that will help us pass from A to B. This result is due to the similarity of the A and B matrices.

APPENDIX Symbols used in this chapter: A B K T R B

Input-output coefficient matrix for country P or for base period t. Input -output coefficient matrix for country Q or for period t + r. Capital coefficient matrix related to the incremental production between t + r and t. Transformation matrix relating A and B. Corresponding regression coefficient matrix used to estimate the coefficients by means of historical series on total intermediate output x and y, respectively. Error matrix. NOTE

To simplify notation, we have used the convention that the symbols Ah Aj represent the Leontief matrices I — At, I — Aj, respectively.

3 The Absolute and Relative Joint Stability of Input-Output Production and Allocation Coefficients CHIA-YON CHEN and ADAM ROSE

An important variant of the standard input-output model has been developed by Ghosh (1958). In contrast to the fixed input requirements of the Leontief production function, Ghosh's allocation function approach calls for fixed output, or sales, distributions across sectors. Rather than a demand-driven model with fixed coefficients in relation to column sums, the new formulation is a supply-driven model with fixed coefficients in relation to row sums. Applications of the allocation model have been numerous. One set deals with the direct and indirect impacts of natural resource supply shortages (see Davis and Salkin 1984; Giarratani, 1976). Another set of applications pertains to the calculation of Hirschman's (1958) concept of forward linkages (see Buhner-Thomas, 1982; Jones, 1976). Yet another pertains to the formulation of multiregional input-output models (see Bon, 1984, 1988). The conceptual soundness of the allocation function approach in several contexts has been supported by Ghosh's (1958) characterization of the behavior of monopolies and planned economies as dominated by supply considerations. Empirical support for the use of the model emanates from studies that have shown allocation coefficients to be as stable over time as are production coefficients (see Augustinovics, 1970; Bon, 1986; Giarratani, 1981). This chapter addresses a remaining concern of the legitimacy of the allocation model—what we refer to as the joint stability of the production and allocation versions of the I-O model. This concern emanates from the fact that an I-O system cannot be operated with both production and allocation coefficients simultaneously fixed, except for the most trivial cases. Stated another way, when using the allocation model does the constancy of allocation functions implicitly result in production coefficient changes that are unreasonable? Will the results of a simulation of the impacts of, say, an oil embargo help yield a meaningful distribution of the burden of the ensuing oil shortage, but at the same time possibly call for oil input substitutions that are technologically or economically infeasible? The aforementioned empirical tests shed little light on this question because they provide no theoretical linkage

26

Theoretical Developments in Input-Output Analysis

between the two types of coefficients and examine cases of small changes in basic conditions, unlike the sizeable changes that arise when the allocation model is applied to resource crises or economic development. THE BASIC ALLOCATION MODEL The supply-driven I-O model is based on an equilibrium condition of interacting forces through allocation functions. The basic balance equation of this model can be represented as follows:

where sij is the allocation coefficient defined as

and Xi is total supply of sector i, Xj is domestic output of sector j, Fi is total final demand of sector i, Vj is total primary input in sector j, and x(j is the amount of output of sector / purchased by sector j. Rewriting equation (1) in abbreviated matrix form yields where / is an identity matrix. Equation (2) can be formally solved by post multiplying both sides by (/ — S)~ ', yielding the result Given a change in primary inputs, the direct and higher order impacts on domestic output can be determined by equation (3). Row sums of (/ — S)~1 are supply multipliers, representing the total output change in the entire economy given unit changes in primary inputs. Ghosh (1958) justified the allocation model as being appropriate to cases of central planning and monopoly. These situations can be characterized as cases of rationing, which can also encompass instances in inherently competitive economies where a resource disruption is dealt with by administering the remaining supply. Ghosh noted: In economies of rationing since every sector registers a high demand for the scarce factors the general tendency of the rationing authorities is not to change the relative shares of each sector in the short-run since such relative shares are determined by a delicate balancing of different sectors' claims and counter-claims. This tendency considered from the problem of projection makes the allocation coefficient more stable in the short-run than production coefficients.

Ghosh went on to state that the relative instability of production functions may not be a serious problem because of the likelihood of substitution opportunities. However, this dismissal overlooks two important considerations. First, the allocation model is being used increasingly to analyze short-run responses to supply disruptions, and substitution possibilities bear a direct relationship to time. Second, until recently there was no indication that the production coefficient changes brought about by invoking fixed distribution patterns are anything but random, inefficient, or even beyond the range of substitution possibilities.1

Joint Stability of Production and Allocation Coefficients

27

THE BASIS OF THE JOINT STABILITY RELATIONSHIP As already mentioned, the substitution among inputs (i.e., changes in input coefficients) implicit in the solution of the allocation model may be unreasonable. This section presents the theoretical basis of the joint stability of allocation and production coefficients. First, given the possibility that a reduction of a primary factor results in an adjustment in direct requirement coefficients during application of the supply-driven model (see equation 3), we define the changes in conventional input requirement coeffcients as follows:

where a|$ is the new input coefficient, atj is the original input coefficient, x* is the new amount purchased by sector) as input from sector i, and Xf is the new output level in sector j. At the same time, the supply-driven I-O model carries over its fixed allocation coefficients from the original to the simulated situation:

and

Incorporating equations (5aj and (5b) into equation (4) and rewriting it yields

If we define

equation (6) can be written as follows:

Then, we may write the relationship between ay and a* as

28

Theoretical Developments in Input-Output Analysis

Equation (8) enables us to state as a theorem: The stability of production input combinations implicit in the solution of the supply-driven model depends on the ratio of relative changes in corresponding sectoral gross outputs. 2

In other words, as long as the impact based on the supply-driven model does not cause much difference among relative changes in sectoral gross outputs, production coefficients will exhibit stability. The theorem follows from the basic properties of the allocation model, which spreads the initial impact of changes in basic factors proportionally across all sectors. We note also the mathematical condition in equation (8) that exerts downward pressure on coefficient changes—percentage changes in production coefficients are related to relative, or weighted, values of sectoral outputs based on equal proportional allocations. For example, if gross output levels for two goods each equal 100, and then change to 125 and 120, the 25-percent difference in growth rates translates into only a 4.2-percent increase in the corresponding production coefficient.3 It is possible to make an a priori judgment about joint stability on the basis of the basic character of a given I-O model. The direct proportional increase or decrease in the distribution of a factor across all sectors helps move the solution toward equal proportional output changes. Any differences will be caused by indirect and induced supply-side effects. This enables us to state a corollary of our theorem: Joint stability will bear an inverse relationship to the size of the allocation model sectoral multipliers.

This is due to the fact that multipliers are a combination of direct effects (that involve the same proportional change across all sectors) and higher order impacts. The smaller the secondary impacts, the more dominant are the equal proportional impacts of the direct effects in the end result.4

ABSOLUTE VERSUS RELATIVE JOINT STABILITY There is some confusion over the definition and implications of the joint stability property, first elucidated by Chen and Rose (1986).5 Therefore, we offer a clarification, following Rose and Allison (1989). We define absolute joint stability as the requirement that both production and allocation coefficients remain constant after an application of either the production or allocation version of the inputoutput model.

As such, joint stability represents an ideal property. As pointed out earlier, it will hold only in the trivial cases where all percentage changes in sectoral supply stimuli/restrictions are equal or all percentage changes in sectoral final demand increases/decreases are equal. Though the joint stability property will typically not hold in an absolute sense, it is possible that coefficient changes will be rather small and within tolerable limits of accuracy in many contexts. Therefore, we define the more operational concept of "relative joint stability" as the degree to which production coefficients of an input-output model approximate their original value after an application of either the production or allocation version of the model.

Joint Stability oj Production and Allocation Coefficients s

29

Employing our previous notation, absolute joint stability can then be stated as where, in effect, expression (9) will hold only when ei = ej Relative joint stability can be defined as the extent to which Some confusion has arisen in the literature to the extent that expression (8) is referred to as the Chen-Rose joint stability condition. This may stem from the related use of the terms consistency and joint stability in our original paper (see Chen and Rose, 1986, pp. 1-2). The derivation of expression (8) does indicate that there is a consistent relationship between afij and aij via sij. But this holds by definition whether Aaij is large or small. Our contention is that the degree of instability is likely to be small in most instances and well within tolerable limits in comparison to other areas where approximation is used. Approximation methods have an honorable tradition in mathematics, economics, and regional science. Examples include entire fields such as calculus and statistical inference, as well as special techniques such as translog forms to approximate twice differentiable expenditure or cost functions, the estimation of consumer surplus using ordinary demand curves, and biproportional matrix methods for adjusting input-output coefficients. Of course the question of what constitutes a tolerable error must still be addressed. There is no definitive cutoff level for all models and applications. However, given established practices in the literature on non-survey I-O model construction, errors of a few percent are explicitly viewed as tolerable (see, e.g., the review by Jackson and West [1989]), and, given the established practice of applying a model calibrated for one time period to another at least a few years hence, small errors are implicitly condoned.6

AN ILLUSTRATION To examine the relative joint stability of allocation and direct requirement coefficients empirically, we applied the supply-driven I-O model to the case of an aluminum shortage in Taiwan.7 Aluminum is considered a strategic material in the economy of Taiwan because of its role as an input into the metals, machinery, transport equipment, and electrical supply industries and because of its limited number of substitutes. Moreover, Taiwan is completely dependent on imports for its bauxite, alumina, and scrap, and is able to supply only 50 percent of its processed aluminum (Chen, 1984). The supply shortage we simulated was on the order of 50 percent of Taiwan's 115.9-million-ton consumption of aluminum in 1979. This level was chosen because it represents a significant supply shock and thus has great potential to destabilize production coefficients. We also note that while an allocation system implies an equal proportional direct sharing of the shortage across sectors, there are other worthy policy approaches and models that are applicable.8 In this case study, the aluminum sector is treated as an exogenous sector and put into the primary input group so that we can evaluate the impact of aluminum supply restrictions. Consequently, equation (3) is changed to

TABLE 3.1 Comparison (in absolute % difference") of original and new input coefficients in major aluminum-using sectors Miscellaneous Metals

Metal Products

Machinery

Electrical Equipment

Transport Equipment

Construction

Sector

Original

New

Original

New

Original

New

Original

New

Original

New

Original

New

01 02 03 04 05 06

0.000000 0.000000 0.000091 0.000000 0.005937

0.000000 0.000000 0.000092* 0.000000 0.005950

0.000000 0.000000 0.000000 0.000000 0.003960

0.000000 0.000000 0.000000 0.000000 0.004052*

0.000000 0.000000 0.000002 0.000000 0.003207

0.000000 0.000000 0.000002 0.000000 0.003219

0.000001 0.000000 0.000000 0.000000 0.000667

0.000001 0.000000 0.000000 0.000000 0.000673

0.000000 0.000000 0.000253 0.000000 0.000232

0.000000 0.000000 0.000255 0.000000 0.000234

0.000370 0.000000 0.001528 0.000000 0.000000

0.000371 0.000000 0.001531 0.000000 0.000000

0.000062 0.110533 0.000000

0.000062 0.110773 0.000000

0.000098 0.000479 0.000017

0.000101* 0.000490* 0.000017

0.000240 0.000140 0.000005

0.000241 0.000141 0.000005

0.000624 0.000218 0.000015

0.000629 0.000220 0.000015

0.000000 0.000083 0.000000

0.000000 0.000084* 0.000000

0.000000 0.036893 0.000000

0.000000 0.036942 0.000000

0.000260

0.000261

0.002077

0.002126*

0.001223

0.001228

0.002864

0.002890

0.000907

0.000915

0.001192

0.001194

0.000244

0.000245

0.005252

0.005377*

0.004878

0.004899

0.008963

0.009046

0.008081

0.008153

0.060429

0.060541

0.001080

0.001082

0.007669

0.007845*

0.003056

0.003067

0.010477

0.010567

0.003489

0.003518

0.001757

0.001759

0.000248 0.000030

0.000248 0.000030

0.000802 0.000171

0.000820* 0.000175*

0.003101 0.000306

0.003114 0.000307

0.002853 0.000539

0.002879 0.000543

0.021426 0.000282

0.021612 0.000284

0.000638 0.000000

0.000639 0.000000

0.000538

0.000539

0.015960

0.016330*

0.000917

0.000921

0.003969

0.004004

0.002656

0.002678

0.000087

0.000087

0.000000

0.000000

0.000002

0.000002

0.000000

0.000000

0.000038

0.000039*

0.000002

0.000002

0.000000

0.000000

0.000538

0.000539

0.007485

0.007655*

0.004665

0.004680

0.039077

0.039403

0.010969

0.011056

0.021879

0.021898

Agriculture Livestock Forestry Fisheries Coal 7 products Crude oil and gas 07 Other minerals 08 Food manufacturing ig 09 Textile and apparel 10 Wood and wood products 11 Pulp, paper, and products 12 Rubber and products 13 Petrochemicals 14 Industrial chemicals 15 Chemical fertilizer 16 Plastics and products

17 Miscellaneous chemicals 18 Petroleum refining 19 Cement and products 20 Nonmetal mineral products 21 Iron and steel 22 Aluminum 23 Miscellaneous metals 24 Metallic products 25 Machinery 26 Electrical apparatus and equipment 27 Transport equipment 28 Miscellaneous manufactures 29 Construction 30 Electricity 31 Gas and city water 32 Transport and communications 33 Trade 34 Services Average absolute % difference1"

0.002511

0.002514

0.014476

0.014796*

0.002661

0.002668

0.006780

0.006832

0.008165

0.008225

0.010521

0.010524

0.008244

0.008263

0.005682

0.005814*

0.004754

0.004772

0.003301

0.003330

0.005709

0.005757

0.008051

0.008063

0.000071

0.000071

0.000117

0.000120*

0.000069

0.000069

0.000000

0.000000

0.000000

0.000000

0.128983

0.129171

0.002773 0.074054 0.001562

0.002894 0.002780 0.074198 0.241486 0.000784** 0.041026

0.269429 0.043342 0.010929

0.269429 0.042454* 0.010912

0.070464 0.101386 0.008532

0.071938* 0.101386 0.008697

0.021298 0.000503

0.021158 0.000500

0.002777 0.001415

0.000698 0.000268 0.011260

0.000698 0.000268 0.011291

0.000135 0.012067 0.041723 0.068107

0.010335 0.003900 0.041469 0.303338 0.002737** 0.008760

0.004693 0.010431 0.041824 0.092000 0.004423** 0.011117

0.054958 0.004735 0.092753 0.115933 0.005612** 0.001240

0.055056 0.116061 0.000622*

0.017386 0.033292 0.109015

0.017414 0.032662* 0.109015

0.021980 0.052535 0.005282

0.022125 0.051799* 0.005308

0.003432 0.024170 0.048272

0.003453 0.023822* 0.048496

0.000186 0.039082 0.003049

0.000186 0.038249* 0.003041

0.002817 0.001436

0.024461 0.001802

0.024340 0.001794

0.392184 0.000634

0.392184 0.000634

0.013412 0.282836

0.013407 0.282836

0.034819 0.000929

0.034561 0.000922

0.001258 0.001653 0.022259

0.001284* 0.001689* 0.022786*

0.001738 0.001431 0.013967

0.001740 0.001434 0.014027

0.003673 0.002161 0.008583

0.003696 0.002177 0.008663

0.002204 0.001717 0.009402

0.002217 0.001729 0.009486

0.000851 0.000852 0.003043

0.000850 0.000852 0.003048

0.000135

0.001536

0.001572*

0.000424

0.000426

0.001019

0.001029

0.000798

0.000805

0.000611

0.000612

0.012095 0.041848 0.068290

0.011921 0.035591 0.036667

0.012199* 0.036445* 0.037535*

0.013681 0.035600 0.045536

0.013736 0.035764 0.045731

0.011647 0.018505 0.048082

0.017752 0.018684 0.048529

0.011593 0.049793 0.050404

0.011693 0.050255 0.050855

0.032192 0.040676 0.033486

0.032241 0.040764 0.033548

0.74

0.26

0.29

0.002963* 0.003884 0.247017* 0.302268 0.021011** 0.005446

1.98

"**Greater than 10.0%; "between 1.0 and 10.0%; all others less than 1.0%. Does not include the aluminum sector coefficients or coefficients with 0.00000 values.

b

0.40

0.78

32

Theoretical Developments in Input-Output Analysis

where Xm is a direct aluminum allocation vector and X and S the new supply vector and allocation matrix, respectively, excluding the newly defined exogenous sector— aluminum. The elements amj of the vector xm are defined as follows:

where m indicates the aluminum sector. For the case of a 50-percent supply reduction in 1979, we utilize equation (3') to compute a new set of gross outputs.9 These new gross outputs and the constant allocation coefficients can be used to calculate a new set of intersectoral flows, x*-, and new production coefficients, a*. The results of our simulation for the major aluminum-using sectors are shown in Table 3.1. Of course the aluminum input coefficients (row 22) are reduced by nearly 50 percent, or the size of the shortage. The reason that the aluminum input coefficient reductions are less than 50 percent is because the new gross outputs for all sectors of the economy have been lowered. We note that the percentage change in other coefficients is less than 1 percent for all but a few cases in the six major aluminumusing sectors, except metal products. This sector is the most aluminum intensive of the group and requires greater substitution throughout to compensate for the lack of aluminum input. Even then the average absolute percent difference in coefficients in the metal products sector is less than 2 percent. The range of average absolute percent differences for other aluminum-intensive sectors is 0.26 to 0.78, and is lower still for the remaining sectors in the economy. Moreover, no single input coefficient change, except those associated with aluminum or metal products, in any of the remaining sectors exceeds 1.0 percent. In general, nearly all the coefficient changes are positive, the major exception being input coefficients for metal products. The negative changes for these coefficients are due to the significant decrease in production of metal products due to the aluminum shortage that cannot be overcome by supply-side adjustments. Coefficient increases indicate a substitution for aluminum or a rearrangement of relative input combinations due to the workings of the supply-driven model. For the two major substitutes for aluminum—plastic and copper—the production input coefficients of the former increase in each case, while the coefficients of the latter increase in five cases and are constant in one.10 Before imparting too much behavioral interpretation to the model, we should point out alternative explanations for the vast number of upward changes in input coefficients. They could signify meaningful substitutions. They could also represent productivity increases associated with making available aluminum go farther, thereby making all other inputs higher proportions of the new reduced cost of production. On the other hand, the changes could be attributable to absurd machinations of the supply model if they represent, for example, a substitution of transportation for aluminum. Finally, however, there is Gruver's (1989) convincing demonstration that, for small changes, the supply-side model is a reasonable linear approximation of the actual production function.11 We can, however, conclude that in our example the production coefficients are remarkably stable.12 Any curious coefficient changes are still within the range of substitution possibilities or are so small that they would not jeopardize any real-world

Joint Stability of Production and Allocation Coefficients

33

coping strategy. Admittedly, part of the stability is due to the small sectoral gross output decreases in reaction to the 50-percent embargo, and the fact that the direct and indirect shortfall is spread across thirty-four sectors.13 However, that is the beauty of the supply model—it indicates how a supply shock can be cushioned by maintaining stability in distribution patterns.14

CONCLUSION This chapter has provided a theoretical understanding and empirical test of the joint stability of production and allocation versions of the I-O model. An empirical example showed a remarkable stability for the case of a sizeable supply disruption. The evidence supports a conclusion that use of the supply-driven, or allocation, version of the I-O model will not necessarily violate the basic production conditions of its conventional counterpart.

NOTES 1. Giarratani (1980) has argued that the allocation model is not as theoretically sound as the production model because the latter is grounded on a behavioral assumption stemming from a branch of production theory whereas the former "rests on behavior about which we have little knowledge" (p. 188). However, Giarratani (1981) has found the allocation model to be as accurate as the conventional model in projections of the U.S. economy. Even stronger criticisms of the conceptual soundness of the allocation model have been offered by Oosterhaven (1981, 1988). Recent work by Gruver (1989) rebuts one of Oosterhaven's major charges concerning the economic sense of production input coefficient changes stemming from applications of the corresponding allocation version of an I-O model. 2. Note that the results of equation (8) are symmetric with respect to explaining changes in allocation coefficients as well. Note also that equation (8) is not the definition of joint stability, but rather a relationship on which it depends. 3. Since writing the first draft of this chapter in the summer of 1985, we have discovered two alternative derivations of equation (8) by Miller and Blair (1985) and Deman (1986). However, in the case of the former there was no discussion of the joint stability issue, and in the case of the latter there was only passing mention, followed by added confusion in Deman (1988). The reader is referred to Miller (1989) for a discussion of the restrictiveness of Deman's stability relationship based on biproportional matrix properties. We are also especially grateful to Miller for prodding us to clarify some of our original concepts. 4. Small multipliers are attributable to a lack of interdependence or a lack of self-sufficiency of an economy. Moreover, in regional economies, coefficient stability may be less crucial when intraregional trade coefficients are used. These coefficients represent purchases and sales between firms in the region and thus are typically smaller than full technical requirements. As Davis and Salkin (1984) pointed out, a significant increase in one of these coefficients may readiiy be made up by imports. Note also that the smaller the variance of the allocation multipliers, the more stable we expect production coefficients to be. However, it is more difficult to tie this condition to the structure of the economy, as we did in the case of the multiplier size. A balanced economic structure is not, for example, a sufficient condition for a low variance. 5. The first version of this chapter was circulated as a paper in 1985 and presented at the University of Pittsburgh Modeling and Simulation Conference in 1986, in addition to the International Conference on Input-Output Techniques. Since that time there has been a strong renewed interest in the supply-side I-O model. A number of contributions to the literature have referred to the Chen-Rose joint stability property. Several of these references

34

Theoretical Developments in Input-Output Analysis

indicate some confusion over the property and its implications. This is due in part to our ambiguous use of some terminology and our lack of elaboration on joint stability. Here we seek to clarify the issue by adding precise definitions to two different forms of joint stability. We wish to thank Ronald Miller, Frank Giarratani, Jan Oosterhaven, Faye Duchin, and H. Craig Davis for their helpful comments on earlier drafts of the paper. We accept responsibility for any remaining errors and omissions. 6. See Gruver (1989) for a linear programming formulation of the supply-side model that constrains coefficient changes. 7. Another confusion has arisen over the purpose of our empirical analysis (see, e.g., Oosterhaven, 1988). This analysis is not intended as a policy simulation of the impact of an aluminum restriction, but as a straightforward test of the joint stability property. To be useful, a simulation of a supply restriction for real-world policymaking would require explicit consideration of substitution behavior and economy-wide optimizing strategies, as well as the several other considerations noted by Oosterhaven (1988). For an example of a modified supply-driven model incorporating elasticities of substitution and also transformed to a linear programming format, the reader is referred to Chen (1984, 1986). The most rudimentary form of the allocation model is used here in order to focus on the inherent properties of the model and avoid biasing the results by complicating factors. 8. One alternative is an optimization strategy based on a linear programming model with and without input substitution (see Chen 1984, 1986). Another approach, following Stone (1961), involves the conventional I-O production model partitioned into unconstrained and constrained components. The formulation for the latter partition simply reverses the roles of gross output and final demand, that is, the gross output of the constrained sector is fixed and its final demand is unknown. The solution proceeds simply with fixed production coefficients and straightforward matrix multiplication. Thus it does not allow for any input substitution and is likely to exaggerate the impact of a shortage (see also Miller and Blair, 1985). 9. A thirty-four-sector Taiwan I-O table, developed by the government of the Republic of China (1981) was used in the simulations. A detailed description of the table and simulations are contained in Chen (1984). 10. Copper is included in the miscellaneous metals industry, and the aggregation may be responsible for this counterintuitive result. 11. Note that it is possible to include explicit substitution possibilities into the model if ownprice (and cross-price) elasticities of demand for aluminum (and between aluminum and its substitutes) can be calculated. A simulation including explicit substitutions such as these in an I -O-allocation-model framework resulted in a total gross output reduction due to a 50percent shortage of 17.5 billion Taiwan dollars, as opposed to the 18.8-billion Taiwan dollar reduction of the simple allocation model. Changes in input coefficients were remarkably similar to those depicted in Table 3.1 as well (see Chen, 1986). 12. Our results are supported by more recent work (see Allison, 1989; Rose and Allison, 1989) in which the relative joint stability of both technical and regional input coefficients in various Washington State I-O tables was tested. The results for a 50-percent aluminum restriction, as well as equally severe restrictions on other sectors, were very similar to those presented here. For example, in the case of the aluminum supply restriction in the 51-sector 1972 table, the vast majority of individual coefficient changes were less than 1.0 percent and no coefficient change outside the aluminum input row exceeded 4.0 percent. 13. Even with the modest aluminum input intensities of the Taiwan economy, the standard demand-driven I-O model would have reduced gross output in all aluminum-using sectors by 50 percent as well as by subsequent multiplier effects! Total gross output in the economy in our supply-driven model simulation was reduced by only 0.6 percent. 14. One shortcoming of the basic allocation version of the I-O model is that the final demands of the solution may be untenable, that is, may depart too much from society's needs. In cases where only a portion of the sectors are supply constrained, a partitioned supply-

Joint Stability of Production and Allocation Coefficients

35

driven model analogous to Stone's partitioned demand-driven model, discussed previously, can partially alleviate this concern. This formulation, developed by Davis and Salkin (1984), involves the use of allocation coefficients throughout while allowing the final demands for unconstrained sectors to be fixed (see Cronin [1984] for a classification and test of hybrid models, and Mizrahi [1989] for a theoretical and empirical examination of them). Our conclusions apply to such modified versions of the allocation model as well.

REFERENCES Allison, T. 1989. "The stability of input structures in a supply-driven input-output model: A regional analysis." M.S. thesis, Department of Mineral Resource Economics, West Virginia University, Morgantown. Augustinovics, M. 1970. "Methods of international and intertemporal comparison of structure." In A. P. Carter and A. Brody (Eds.), Contribution to Input-Output Analysis. Amsterdam: North-Holland. Bon, R. 1984. "Comparative stability analysis of multiregional input-output models." Quarterly Journal of Economics 99: 791-815. Bon, R. 1986. "Comparative stability analysis of demand-side and supply-side input-output models." International Journal of Forecasting 2: 231-235. Bon, R. 1988. "Supply-side regional input-output models." Journal of Regional Science 28: 41 50. Buhner-Thomas, V. 1982. Input-Output Analysis in Developing Countries. New York: Wiley. Chen, C. Y. 1984. "The potential impact of optimal adjustment associated with an aluminum supply restriction." Ph.D. diss., Department of Mineral Resource Economics, West Virginia University, Morgantown. Chen, C. Y. 1986. "The optimal adjustment of mineral supply disruptions." Journal of Policy Modeling 8: 199-221. Chen, C. Y., and A. Rose. 1986. "The joint stability of input -output production and allocation coefficients." Modeling and Simulation 17: 251-255. Cronin, F. J. 1984. "Analytical assumptions and causal ordering in interindustry modeling." Southern Economic Journal 50: 521-529. Davis, H. C., and E. L. Salkin. 1984. "Alternative approaches to the estimation of economic impacts resulting from supply constraints." Annals of Regional Science 18: 25-34. Deman, S. 1986. "Notes and comments: Production and allocation consistency of input-output coefficients." Mimeo, Department of Economics, University of Pittsburgh. Deman, S. 1988. "Stability of supply coefficients and consistency of supply-driven and demanddriven input-output models." Environment and Planning A 20: 811-816. Ghosh, A. 1958. "Input-output approach to an allocative system." Economica 25: 58-64. Giarratani, F. 1976. "Application of an interindustry supply model to energy issues." Environment and Planning A 8: 447-454. Giarratani, F. 1980. "The scientific basis for explanation in regional analysis." Papers of the Regional Science Association 45: 185-196. Giarratani, F. 1981. "A supply-constrained interindustry model: Forecasting performance and an evaluation." In W. Buhr and P. Friedrich (Eds.), Regional Development Under Stagnation. Baden-Baden: Nomos Verlagsgesellshaft. Gruver, G. 1989. "A comment on the plausibility of supply-driven input-output models." Journal of Regional Science 29: 441-450. Hirschman, A. O. 1958. The Strategy of Economic Development. New Haven, Conn.: Yale University Press. Jackson, R., and G. West. 1989. "Perspectives on probabilistic input-output analysis." in R. Miller, K. Polenske, and A. Rose (Eds.), Frontiers of Input-Output Analysis. New York: Oxford University Press.

36

Theoretical Developments in Input-Output

Analysis

Jones, L. P. 1976. "The measurement of Hirschmanian linkages." Quarterly Journal of Economics 90: 323-333. Miller, R. and P. Blair. 1985. Input -Output Analysis: Foundations and Extensions. Englewood Cliffs, N.J.: Prentice-Hall. Miller, R. E. 1989. "Stability of supply coefficients and consistency of supply-driven and demand-driven input-output models: A comment." Environment and Planning A 21: 11131120. Mizrahi, L. 1989. "A generalized input-output model: Combining demand- and supply-side systems." Ph.D. diss., Department of Urban Studies and Planning, Massachusetts Institute of Technology. Oosterhaven, J. 1981. Interregional Input-Output Analysis and Dutch Regional Policy Problems. Aldershot, England: Gower. Oosterhaven, J. 1988. "On the plausibility of the supply-driven input-output model." Journal of Regional Science 28: 203-217. Rose, A., and T. Allison. 1989. "On the plausibility of the supply-driven input-output model: Empirical evidence on joint stability." Journal of Regional Science 29: 451-458. Republic of China. 1981. Executive Yuan, Council for Economic Planning and Development, Taiwan Input-Output Tables. Taipei, Taiwan. Stone, J. R. N. 1961. Input-Output Models and National Accounts. Paris: Organization for Economic Cooperation and Development.

II THE COMPILATION OF INPUT-OUTPUT TABLES

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4 Considerations on Revising Input-Output Concepts in the System of National Accounts and the European System of Integrated Economic Accounts CARSTEN STAHMER

Although an intensive debate on the revision of international systems of national accounts (NA) has been going on for several years, the role of input-output (I-O) in the system has only recently been addressed (see Chantraine and Newson, 1985; Kurabayashi, 1985). An important contribution in this respect has been a 1985 paper by Vu Viet (Statistical Office of the United Nations). Apart from describing the impact of the revision of the NA systems on I-O, Viet gave a distinct overview about the problems arising in I-O compilation. In addition, proposals for a revision of I-O concepts have been put forward both by Stahmer (1985a) and by van den Bos (1985). This chapter is restricted to the revision of input-output concepts in the framework of the System of National Accounts (SNA) of the United Nations and the European System of Integrated Economic Accounts (ESA) (see United Nations, 1968, 1973; EUROSTAT, 1979). It does not cover the revision of I-O in the Material Product System (MPS) (see United Nations, 1971). The first part of the chapter focuses on the requirements for future input-output concepts. This is followed by a comparison of these requirements with the existing concepts. Finally, the chapter outlines proposals for future input-output concepts that meet the requirements as far as possible. Since all conceptual questions cannot be treated in a short chapter, the focus here is on connecting I-O data with other NA subsystems. This integration depends on two crucial points: the statistical units chosen and the treatment of transactions. While in the SNA and the ESA the concept of transaction is uniform throughout all subsystems, problems arise due to the varying statistical unit. Therefore the choice of the statistical unit will be considered here in depth. A revision of the concept of transaction is only touched on, taking into account a suggestion of the Dutch Statistical Office (see van Bochove and van Tuinen, 1985). The question of an appropriate price concept will not be dealt with at all (Vu Viet, 1985).

40

The Compilation of Input-Output Tables

OBJECTIVES FOR A REVISION OF I-O CONCEPTS Having a clear idea from the beginning about what is to be achieved by a revision of I-O will greatly facilitate our discussion. Thus five objectives are delineated here: (1) integration, (2) harmonization, (3) statistical basis, (4) evaluation, and (5) continuity. Some of these are conflicting goals, however, and the international discussion will have to decide on priorities.

Integration One of the most important objectives of the revision of I-O concepts is the further integration of I-O data into the system of NA (see Drechsler, 1985; Lal, 1985; Young, 1985). At present I-O is regarded as a special subsystem of NA, describing production activities and commodity flows. Because the statistical unit used in I-O differs from that in other NA subsystems, however, there is only a loose connexion, and a comprehensive description of all transactions—from production to capital finance— is rendered difficult. Possibilities of unifying the statistical units are discussed here. Nevertheless, it should be mentioned that such a unification might reduce the information value of an individual subsystem. This has been pointed out by Stone (1962) as a "solution of Procrustes."

Harmonization Since the SNA as well as the ESA comprise I-O concepts, harmonization of both concepts should be considered an important goal. As will be shown in the following section, I-O concepts now differ substantially in the two systems. This is true particularly for the presentation of I-O data but also for the statistical units as well as the classifications. Harmonization could substantially improve the international comparability of I-O results.

Statistical Basis Strict application of SNA and ESA recommendations for I-O compilation has caused problems for many countries, since the statistical basis is inappropriate or even missing. Thus, as a third objective of revising I-O, the concepts should take into account the available data. This would be the case particularly if I-O compilation concentrates on observable facts and if the macro concepts of NA measures are aligned more closely to (micro) business accountancy concepts (see Lutzel, 1985; Ruggles and Ruggles, 1982; van Bochove and van Tuinen, 1985). Evaluation On the other hand, an adjustment of I-O concepts in this direction could involve difficulties for the evaluation of the results. For the analysis of production activities and commodity flows, data are needed relating to homogeneous commodity groups. In reality, however, such data are not readily available. To bridge this gap, different solutions are recommended in NA systems. While the I-O concept of the SNA is aligned more to the collectability of data, the ESA focuses on the requirements of the

Revising Input-Output Concepts in the SNA and ESA

41

user. As a further goal of revising I-O concepts, a compromise between both aspects should be envisaged.

Continuity In addition to these four objectives, a fifth, more restrictive point has to be taken into account. Many countries reject a fundamental change of the SNA and the ESA. Instead, continuity of concepts is preferred to facilitate the work of both the producer and the user. However, development and continuity of I-O concepts are not mutually exclusive goals. Proposals have been elaborated to maintain the existing concepts while developing them by additional and more detailed presentations (see Chantraine and Newson, 1985; Kurabayashi, 1985). But it has to be stressed that in this way both the clearness and the coherence of the NA system might be affected.

INPUT-OUTPUT CONCEPTS IN PRESENT NA SYSTEMS

The SNA The SNA has been developed in such a way that the definition of transaction is uniform throughout the whole system. On the other hand, the classification of transactions varies between subsystems, particularly with respect to the statistical unit. For instance, production activities are presented for an establishment basis in principle, whereas for other transactions (e.g., income, capital, and finance) the enterprise or an equivalent unit are chosen. In support of the unit of establishment, two main reasons have been put forward: (1) A statistical unit should be homogeneous in its activities as far as feasible and (2) for a statistical unit, data on outputs and inputs should be available. In the SNA, transactions on the origin and use of national product are connected by a comprehensive description of production activities and commodity flows. A basic feature is the indirect, two-stage presentation of the interrelationship between the producing and the consuming unit. First, the output of the producing unit is shown in a commodity breakdown (make matrix). In a second step, the output by commodity group is allocated to the users (use matrix). There are two main reasons for this presentation. On the one hand, basic statistics customarily allow a breakdown of a producer's inputs by commodity, but not a subdivision of inputs according to the supplying unit. Furthermore, since production analysis aims at showing intercommodity relationships on the basis of homogeneous units, the rowwise breakdown of inputs into commodity groups is advantageous. In a simplified form, Table 4.1 shows the presentation of production activities and commodity flows in the "complete system" of the SNA. Since the production and use of commodities are combined at a deeply disaggregated level, this presentation may be considered as I-O data (though not in the form of a traditional I-O table with a uniform classification of rows and columns). Table 4.1 indicates that the SNA presentation of I-O data is much more complex than in traditional I-O tables. The combination of a commodity with an activity classification restricts the comprehensibility of the SNA concept. This difficulty is reinforced by the fact that this presentation applies to market production only. In

TABLE 4.1 Input-output data in the System of National Accounts Activities

Commodities

Activities Market Nonmarket

Components of value added

E

Commodities

Market

Nonmarket

—

Intermediate consumption

Intermediate consumption

Purposes

Purposes

Final consumption expenditure of households

£

Activities Fixed Increase capital in in stocks formation

Exports

Outputs Outputs (market)

— Imports Total supply

Total uses

Total outputs —

Value added Total inputs

Source: United Nations, Table 2.1, rows/columns 5 to 21.

—

Value added Imports Total supply

Final consumption expenditure of government and private nonprofit institutions

Exports

Total uses

Revising Input-Output Concepts in the SNA and ESA

43

contrast, nonmarket production is subdivided by using the same classification for both the production and the use side. Furthermore, in the SNA, final consumption expenditure is supposed to be broken down by purpose, and gross fixed capital formation should be subdivided by activity. Apart from presenting production activities and commodity flows in a matrix form (e.g., Table 4.1), it is also possible to use the form of accounts. Data on commodities from Table 4.1 may be used to establish commodity accounts (for different commodity groups). Data on market and nonmarket activities in this table are the basis for production accounts. The columns of Table 4.1 give the left-hand side ("outgoings") and the rows give the right-hand side ("incomings") of the accounts. An aggregation of such accounts provides for standard accounts as required in Appendix 8.2 of the SNA. As has been mentioned, institutional units like enterprises or their equivalent are used as the statistical unit in the SNA to present transactions other than production. It would have been appropriate to the SNA basic concept if the transition from establishment data to enterprise data were shown in a combined classification. In particular, the transition from establishments to enterprise for value added (including its components) and gross fixed capital formation would be of interest. In the SNA these items are shown separately according to both an establishment and an enterprise classification, but not in the combined presentation of a transition table.1 The lack of transition from establishment data to enterprise data at a disaggregated level represents a missing link between production entries and transactions on income and capital finance. Instead, only the totals can be compared. "The SNA resembles two pillars, leaning against each other for support, but joined together only at the very top" (see van Bochove and van Tuinen, 1985, p. 28). For purposes of I-O analysis the SNA presentation of production in a combined classification of commodity groups and industries is not directly helpful. Instead, I-O tables with a uniform classification of rows and columns are required. Chapter 3 of the SNA provides information about procedures for obtaining I-O tables by transferring I-O data. Starting from tables in a combined classification, and accepting certain assumptions, one is able to establish I-O tables with a uniform classification of rows and columns. The uniform classification may be either a commodity or an industry classification. These I-O tables, however, are not included in the "complete system" (Table 2.1) of the SNA. Practical experience with the I-O concepts of the SNA has revealed different points, which may be advantages as well as weaknesses: 1. The presentation of production activities and commodity flows with use of disaggregated I-O data has to be considered an essential advantage in comparison with earlier versions of the SNA, showing production activities only at an aggregated level. Further integration of I-O data with the SNA system has been obstructed by both varying statistical units and missing linkages between the different SNA subsystems. 2. The combined presentation by commodity group and institutional-type unit has proved successful. By this means, in many countries the basic statistics could be exploited without the need for extensive recalculations. However, according to an inquiry by Franz (1985) on behalf of the Organization for Economic Cooperation and Development (OECD), the statistical unit underlying industries—the

44

The Compilation of Input- Output Tables

establishment—has caused problems. In many countries data on establishments exist for the manufacturing sector only. Moreover, the data normally refer only to assignable direct costs. Difficulties arise when overhead costs, for example of a multiunit enterprise, have to be allocated to various establishments. In some countries, therefore, ancillary units like a central administration office are considered separate establishments, serving the other establishments of the enterprise. Because of these statistical difficulties, to apply the establishment concept countries have more or less to use enterprise data. 3. The transformation procedures given in the SNA are appropriate to compile I-O tables with a uniform classification of rows and columns on the basis of data in a combined classification. But the assumptions proposed (commodity technology and industry technology) are often insufficient for obtaining plausible results, even if they are combined. Some countries therefore have developed modifications of the SNA transformation methods in recent years.

The ESA The national accounting system for EC member countries (ESA) was developed parallel to the SNA in the 1960s. Although work was not strongly coordinated, as it is in the present revision, most concepts and definitions match. As has been pointed out here, a reduction in the remaining differences could be envisaged as an objective for the present revision. A comparison of I-O presentation in the SNA with that in the ESA reveals equivalences as well as major differences. Both systems recommend a distinction between production and other transactions (e.g., income, capital finance). In both systems the compilation of production activities and commodity flows is to be based on I-O data, the presentation of other NA subsystems on institutional sectors (comprising enterprise-type units). Differences mainly result from the fact that the SNA focuses on the collectability of data whereas the ESA stresses the requirements of the user. Consequently, for the presentation of production in the ESA, commodity x commodity tables are used. In the SNA, this type of I-O table is not included in the "complete system" (Table 2.1) but is presented as additional tables. The presentation of I-O tables with a commodity classification of rows and columns implies statistical units that are homogeneous in respect to their output. In reality, however, such units of homogeneous production for the most part do not exist. Often the subdivision of an enterprise's activities into units of homogeneous production is possible only on the grounds of assumptions. If the allocation of overhead costs to individual establishments is difficult already, it is worse for units of homogeneous production. The treatment of by-products and adjacent products is an exception from this idea of homogeneity in the ESA. These are transferred in a second step. Units of homogeneous production are aggregated to form a branch, that is, the branch produces all goods and services specified in a product classification, and only that classification. Table 4.2 shows the presentation of I-O data in the ESA. Since the definition of branches is uniform for columns and rows—apart from the treatment of by-products—it is possible to connect the supply and the use of commodities directly. Thus the intermediate step of the SNA make matrix, which reclassifies the output of

TABLE 4.2 Input-output data in the European System of Accounts Branches Market Commodities

Nonmarket

Intermediate consumption

Components of Value added Actual output value added Transfers of by-products, etc. Distributed output Imports I Total resources Source: EUROSTAT, 1979, Tables T4, T6b, T7c, T13.

Purposes Final consumption of households

Purposes Collective consumption of general government and private nonprofit institutions

Branch of Ownership Fixed capital formation

E Change in stocks

Exports

Total uses

46

The Compilation of Input-Output Tables

establishments to respective commodity groups, is redundant. The following calculation explains the linkages: intermediate consumption of branch A + gross value added of branch A = actual output of branch A + transfers of ordinary by-products and adjacent products = distributed output of branch A + imports of similar products = total resources of commodity group A = total uses of commodity group A Both systems provide a breakdown of private final consumption expenditure by purpose and a subdivision of gross fixed capital formation by kind of economic activity of the owner (in the ESA by branch of ownership). These subdivisions are presented in additional tables in the ESA. They have been included in the I-O system to allow a comparison between Tables 4.1 and 4.2. As for the SNA, in addition to the presentation in tables, accounts are used to show transactions in the ESA. However, a complete system like Table 2.1 of the SNA, from which both tables and accounts may be derived, is missing. The structure of the system of accounts differs substantially between ESA and SNA. In the SNA, production accounting is quite separate from the income and finance part. Furthermore, the presentation of production is based exclusively on I-O data. The ESA recommends a presentation of production by accounts, in a breakdown of both branch and institutional sector. In this case, I-O data are only the basis for the presentation by branch. The level of breakdown differs in the ESA for branches (fortyfour or twenty-five) and institutional sectors (eight), thus preventing a combination of both. The following accounts are assigned according to the ESA: The goods and services account (CO) of the economy. This account can be derived from the I-O table, which is classified on a product basis. It contains information on total resources and uses of goods and services, without a breakdown by commodity groups or by branch. The production account (Cl) for branches and for institutional sectors. Production accounts show the output of goods and services, intermediate consumption, and value added for branches and institutional sectors. Output is not broken down by user, and intermediate consumption is not shown by commodity group. The generation of income account (C2) for branches for institutional sectors. This account divides value added into its components (consumption of fixed capital, production taxes, subsidies, compensation of employees and operating surplus). Since the generation of income account has to be established for institutional sectors as well, these data are the basis for the presentation of further distributive and financial transactions. This procedure links production with other NA subsystems— at least at an aggregate level. However, at a disaggregated level transitions from data for institutional sectors to branches (I-O tables and accounts) are missing. Table 4.3 shows the ESA concept of presenting production. The appropriate SNA concept is shown for comparison. From practical work with the ESA, experience has been gained that should be

TABLE 4.3 The presentation of production in the System of National Accounts (SNA) and the European System of Accounts (ESA) SNA Tables i [ I-O data in a combined classification by commodity group and activity

ESA Accounts

Tables

Commodity accounts for commodity groups

I-O tables in a uniform commodity classification of rows and columns

Accounts Goods and services account for the economy Productionaccouaccounts Production accounts for branches for institutional sectors

cf. Table 4.1

Production accounts for activities

Production ] i i ] [

I-O data in a uniform ] commodity or an >! industry classification of rows and columns

Generation of income accounts for branches

Generation of income accounts for instit. sectors

Production

Income/ap ' 't 1 fi e

!

cf. Table 4.2

1

Accounts on income transactions (institutional sectors) Accounts on capital finance (institutional sectors)

I / alo 'tfin1 fi ncomecap

i Distribution of income accounts (instit, sectors) financial

Capital and financial financial accounts (instit, sectors)

48

The Compilation of Input-Output Tables

taken into account for a revision. In particular, in respect to the presentation of production the following points have been observed: The ESA concept of I-O tables in a product subdivision has proved successful from the point of view of the user. Comparisons in time and space as well as particular sector studies and I-O analyses could be based directly on such I-O data, without the need for recalculations. A further support has been the I-O methodology issued by EUROSTAT (1976). A problem that remains is the treatment of byproducts and adjacent products: On the one hand, I-O models require a transfer of such products in proportion to the change in output. On the other hand, this procedure does not guarantee an equality of the transfer, that is, the value taken out of the producing branch and the value included with the distributing branch. The restriction of the ESA, that I-O tables are presented only in a product classification, has recently caused critical comments on both sides, from the producer and the user of NA figures. In particular the question of whether production should be presented on the basis of—mostly—fictitious data instead of transactions actually observed has been stressed. In the latter case, the presentation should preferably be based on data of institutions like enterprises and establishments instead of units of homogeneous production. Nevertheless, apart from a presentation of data for institutional sectors, data for commodity groups and branches are needed. Only a combination of both concepts would allow the full spectrum of NA analyses to be applied. Serious reservations concerning the I-O concept of the ESA have been expressed by the producers. In most cases, the recommended breakdown of activities into units of homogeneous production cannot be derived directly from basic statistics. Therefore recalculations of basic data using theoretical assumptions are necessary. But since the ESA offers no assistance in this respect, each country applies its own method of recalculating its basic data to meet the EUROSTAT requirement for an appropriate I-O table. PROPOSAL FOR FUTURE I-O CONCEPTS OF THE SNA AND ESA The practical experience gained in applying the SNA and the ESA may be used as a starting point for a revision of the respective I-O concepts. The five objectives previously mentioned may serve as a guide: 1. 2. 3. 4. 5.

Integration of I-O data with the NA system Harmonization between the I-O concept of SNA and ESA Improved connection of I-O aggregates to basic statistics User-oriented I-O concepts Continuity of I-O concepts

A proposed revision is elaborated here. This proposal centers on continuity and dispenses with a full harmonization between the I-O concept of SNA and ESA. It aims to increase the degree of integration of I-O data with the NA system, to improve the connection between I-O data and basic statistics, and to allow further analysis by providing additional data. These objectives are to be fulfilled by developing more precise definitions, additional tables, and a more detailed description of procedures.

Revising Input-Output Concepts in the SNA and ESA

49

The proposal is closely in line with considerations of Dutch colleagues (see van Bochove and van Tuinen, 1985). The proposal initiates more precise and extended I-O concepts of the SNA and ESA. Accordingly, in the SNA a combined classification of commodity groups and establishments is maintained for presenting production. In addition, the ESA description of production activities and commodity flows would continue to be based on an I-O table with a homogeneous product classification.

The SNA Maintaining the establishment as the statistical unit to present production requires clearing up some questions. A major problem is the treatment of certain central activities of a multiestablishment enterprise (like separate administration and research activities). The SNA recommends (see United Nations, 1968, paragraph 5.19) distribution of these costs of activities (overhead costs) among the individual separate establishments. This corresponds to the ESA regulation (see EUROSTAT, 1979, paragraph 267). However, in different countries this common international regulation is not practiced. Instead, central activities are regarded as a separate establishment serving other producing units. From the point of view of regional analysis this is an advantage. Central activities are regarded as a resident unit of the respective region, without the need for distributing them (proportionately) among other regions. But even the treatment of central activities as separate establishments does not solve the allocation problem. Rather, an output of this establishment has to be determined (possibly by adding up costs), and to be allocated subsequently among the producing units as intermediate consumption. Two points are important for the treatment of central activities. First, the allocation procedure must be understandable. Second, the users must be able to get separate information on observed data and more or less fictitious allocations. As has been stressed, in the SNA the connection between production and other NA subsystems is insufficient. If the SNA maintains industries for production and institutional sectors for other transactions, transition tables should be envisaged. For certain flows such tables could show the detailed transition from an establishment to an enterprise classification. Such a "classification converter" meets a basic idea of the SNA: Subsystems of the NA system may have a different outlay according to the needs, but in such cases links should be established going beyond the aggregate level. Considering Table 2.1 of the "complete system" of the SNA, transition tables should be established to serve as a junction between production and income transactions. Transition tables could be included for value added (and its components) and gross fixed capital formation (possibly in a breakdown by categories), showing these items in a combined classification of industries and institutional sectors. Since many countries already dispose of a register connecting establishments to the owning enterprises, the statistical obstacles seem surmountable. Additionally, the transformation methods from I-O data in a combined classification to I-O tables with uniform classification of rows and columns should be improved. In practice, the methods described in Chapter 3 of the present SNA (United Nations, 1968) have turned out to be insufficient. Applying one of the proposed assumptions rigorously may result in implausible figures. Instead, some possibility of influencing the transformation procedure is necessary. This would be allowed by the

50

The Compilation of Input-Output Tables

following two-stage transformation method: (1) A special transformation matrix is established by applying a technology assumption to each row (column) to be transferred. The row and column totals of this matrix show the initial data and the results after transformation, respectively. (2) The elements of a special transformation matrix could be adjusted selectively in such a way that the margin vector containing the data to be transformed remains unchanged (see Stahmer, 1985b).

The ESA The ESA concept for I-O tables with a uniform product classification has proved reasonable, and no extensive revision seems necessary. However, the future treatment of by-products and adjacent products has to be discussed. As has been pointed out above, the present treatment involves difficulties for I-O analysis. As a solution, the transformation of such products could be based on the idea of the SNA make matrix. Accordingly, the transition from actual output (i.e., before transferring) to distributed output (i.e., after transferring) should be shown in a matrix instead of just a row. This output matrix would give the actual outputs by branch as column totals and the distributed outputs by commodity group as row totals. Thus the transfer of byproducts and so on is carried out within a column vector of this matrix. Table 4.4 outlines this new structure of I-O tables. It can be shown that such output tables are a framework for I-O models allowing for a consistent coverage of by-products. In this context, the output table serves as a transformation matrix from the row to the column classification (and vice versa) in each step of the iterative procedure of I-O models. In the ESA, a connection between the I-O table—showing data classified by branch (commodity groups)—and the production as well as income accounts— classified by institutional sector—is possible only at the aggregate level. For a closer connection a more disaggregated presentation of the production activities of institutional sectors is needed. Such a disaggregated presentation, in combination with a breakdown of output and intermediate consumption by commodity group, would TABLE 4.4 Commodity-classified input-output in a revised European System of Accounts Branches Commodities

E

Intermediate consumption

Final uses

Total uses

Imports

Total resources

Value added

X

Actual output

Commodities

Outputs

I

Actual output

Distributed output

+

Revising Input-Output Concepts in the SNA and ESA

51

provide for the connection to the commodity flows given in I-O tables. In disaggregating institutional sectors, a further question relating to the legal form of business enterprises has to be considered. A decision should be made whether data for nonfinancial corporate and quasi-corporate enterprises (sector S10) are shown separately from data for sole proprietorships and so on (included with the sector households S80), or whether the sectoral disaggregation should start from the totals of the nonfinancial enterprises without taking into account their legal form. From the statistical point of view it should be easier nowadays for most EC member countries to establish tables in a disaggregated, combined classification of institutional sectors and commodity groups than it was at the time the present ESA was developed. Both the extension of statistics on enterprises and the increasing use of computerized facilities for combining different statistics are in support of this suggestion. The extension of production and generation of income accounts for institutional sectors could be carried out in three steps: (1) The accounts could be given in a finer institutional breakdown in accordance with an ESA proposal (see EUROSTAT, 1979, paragraph 124). (2) and (3) The sectoral output and intermediate consumption could be broken down by commodity group. In general, the present ESA does not discuss the problem of deriving NA data from basic statistics. Accordingly a compilation methodology to establish I-O tables in a product classification is missing. This could be included in a future I-O methodology (see EUROSTAT, 1976). In addition, if production accounts for disaggregated sectors were extended as mentioned previously, a transition procedure to obtain data for homogeneous units based on institutional data should be recommended. Since the production activities of enterprises are usually more heterogeneous than those of establishments, the SNA procedures developed for transforming establishment data need modification in any case. Applying the twostage procedure described has proved successful—at least for the Federal Republic of Germany—even in the case of enterprise data. An overview of all suggestions given in this section for completing the SNA and the ESA is given in Table 4.5.

TABLE 4.5 Proposals for completion of present System of National Accounts (SNA)/European System of Accounts (ESA) input-output concepts SNA

ESA

More precise definition of establishment (e.g., treatment of separate central ancillary units like administration, research)

Presentation of by-products and adjacent products in output table

Transformation tables from activities to institutional sectors (e.g., for value added and fixed capital formation)

Further institutional breakdown of production accounts; presentation of outputs and intermediate consumption in tables with a combined classification of commodity groups and institutional sectors

Improved procedures for transforming I-O data in combined classification to I-O tables in uniform classification

Description of transformation procedures from data in institutional classification to data in commodity classification

52

The Compilation of Input -Output Tables

NOTE 1. SNA (1968), Table 2.1, rows (columns) 29 to 32 and rows (columns) 56 to 70, respectively.

REFERENCES Chantraine, A., and B. Newson. August 1985. "Progress on the revision of the European System of Accounts." Paper presented at 19th Conference of the International Association for Research in Income and Wealth (IARIW), Noordwijkerhout, Netherlands. Drechsler, L. August 1985. "Statistical integration, necessity and conflict." Paper presented at 19th IARIW Conference, Noordwijkerhout, Netherlands. EUROSTAT. 1976. Community Input-Output Tables 1970-1975 Methodology. Special Series 1. Luxembourg: EUROSTAT. EUROSTAT. 1979. European System of Integrated Economic Accounts-ESA. 2nd ed. Luxembourg: EUROSTAT. Franz, A. August 1985. "National accounts sectoring and statistical units of reporting and classification." Paper presented at 19th IARIW Conference, Noordwijkerhout, Netherlands. Kurabayashi, Y. August 1985. "United Nations Statistical Office progress report on the review of the System of National Accounts." Paper presented at 19th IARIW Conference, Noordwijkerhout, Netherlands. Lal, K. May 1985. "Canadian input-output tables and their integration with other subsystems of the National Accounts." Paper presented at International Meeting on Problems of Compilation of Input-Output Tables, Baden, Austria. Lutzel, H. August 1985. "Market transactions in the national accounts." Paper presented at 19th IARIW Conference, Noordwijkerhout, Netherlands. Ruggles, N., and R. Ruggles. 1982. "Integrated economic accounts for the United States, 194780." Survey of Current Business 625: 1-53. Stahmer, C. May 1985a. "Integration of input-output with the international system of national accounts." Paper presented at Conference on Input-Output Compilation, Baden, Austria. Stahmer, C. 1985b. "Transformation matrices in input-output compilation." In A Smyshlyaev (Ed.), Input-Output Modeling. Proceedings of the Fifth International Institute for Applied Systems Analysis Task Force Meeting (Laxenburg, October 1984). Berlin: Springer-Verlag. Stone, R. 1962. "Multiple classification in social accounting." Bulletin of the International Statistical Institute 39, Part 3. United Nations. 1968. A System of National Accounts. Studies in Methods, Series F, No. 2, Rev. 3. New York. United Nations. 1971. Basic Principles of the System of Balances of the National Economy. Studies in Methods, Series F, No. 17, New York. United Nations. 1973. Input-Output Tables and Analysis. Studies in Methods, Series F, No. 14, Rev. 1. New York, van Bochove, C. A., and H. van Tuinen. August 1985. "Building block approach to flexibility of the SNA." Paper presented at 19th IARIW Conference, Noordwijkerhout, Netherlands, van den Bos, C. August 1985. "Integration of input-output tables and sector accounts: The possible solution." Paper presented at 19th IARIW Conference, Noordwijkerhout, Netherlands. Vu Viet, Q. August 1985. "Input-output standards in the SNA framework." Paper presented at 19th IARIW Conference, Noordwijkerhout, Netherlands. Young, P. C. May 1985. "The U.S. input-output experience, present status and future prospects." Paper presented at International Meeting on Problems of Compilation of Input-Output Tables, Baden, Austria.

5 The Simultaneous Compilation of Current Price and Deflated Input-Output Tables S. DE BOER and G. BROESTERHUIZEN

This chapter discusses a number of aspects of the procedure by which input-output tables are compiled in the Netherlands. These tables are compiled annually and are fully integrated in the System of National Accounts. A few years ago the method of compiling the input-output tables underwent a revision that, in our opinion, led to great improvement. The most significant improvement is that during the entire statistical process, from the processing and analysis of the basic data up to and including the balancing of the input-output tables, current-price data and deflated data are obtained simultaneously and in consistency with each other. We believe that this innovation may be of interest to other countries that currently compile inputoutput tables or wish to do so in the future, because many countries still—as the Netherlands used to do—first compile data in current prices and afterward calculate data in constant prices and changes in volume and prices, often on a higher level of aggregation. This means that an important opportunity for analysis of the interrelations between various kinds of data, and thus for better estimates, is used little or not at all. In cases where input-output tables are drawn up periodically, the comparability in time of the estimates is an important requirement. For an-extensive discussion on this matter the reader is referred to Al and Broesterhuizen (1985). Plausibility checks of observed changes between two periods can be carried out more easily and more meaningfully if the change in value is split into a volume change and a price change. In addition, with the informational aspect of economic statistics in mind, it is also important that there be complete consistency between deflated input-output tables and the tables with volume and price indices. This can be achieved by compiling both current-price data and deflated data simultaneously. Figure 5.1 shows part of the series of tables that then become available in the course of time. In the Netherlands, deflated data pertaining to a period t are always expressed in prices of the period t — 1. In this way the weighting schemes that are used to combine detailed indices to define changes at a higher aggregation level remain up to date. In this process the volume changes are combined using Laspeyres' formula and the price

54

The Compilation of Input-Output Tables

changes using Paasche's formula. The problems concerning the appropriate choice of index number formulae are not discussed in this chapter (the reader is referred to Central Bureau voor de Statistick, 1984, and Al, Balk, de Boer, and den Bakker, 1984). The Dutch input-output tables are currently still relatively limited in size. They consist of about 225 rows and 135 columns. The rows refer to industry groups, or to commodity groups that add up to industry groups. The columns refer to industry groups and final expenditure categories. The published tables—industry group x industry group tables—are derived from these tables by aggregation. In the last few years a number of developments in economic statistics have led, or will lead

Compilation of Current Price and Deflated Input-Output Tables

55

to, an improvement in the basic data available for the input-output table, or to better conditions for the processing and analysis of the basic data. Three aspects of this improvement are as follows: 1. The introduction of a standardized goods nomenclature for a large number of basic statistics, and in particular for price statistics 2. The start of annual statistics for the trade and service sectors 3. Automation of the processing and analysis of the basic material and the balancing of the input-output table These developments make it easier than it has been up to now to utilize volume and price data in the analysis and processing of the basic data. In the near future the Netherlands will probably switch over to compiling separate make and use matrices, in accordance with the recommendations of the SNA with respect to the compilation of input-output information. Therefore we have opted here to explain the procedure involving volume and price information with the aid of this widely known scheme of make and use matrices. The following sections contain a step-by-step discussion of the various stages within the statistical process. In this discussion we stress the simultaneous compilation of data in current prices and deflated data. The chapter concludes with a short look at the possibilities of applying the system we have described in various situations that differ with respect to the basic statistical material available.

THE STATISTICAL PROCESS IN THE NETHERLANDS General Remarks A number of phases can be distinguished in the compilation process of make and use matrices: 1. 2. 3. 4.

Data collection phase Adjustment phase Processing phase Balancing phase

For the sake of simplicity we here give the impression that these phases are passed through separately and consecutively. Actually the process is more an iterative one, in which the operations of a certain phase are followed by or carried out at the same time as operations in other phases. For example, during the balancing phase the basic material may still have to undergo some corrections, in which case the adjustment and processing phases will have to be repeated. In this section we shall look briefly at phases 1 and 2. Attention will be given to the available basic information that is used in the compilation of the make matrix and the use matrix. Phases 3 and 4 will be examined separately in the following sections. Available Basic Information The information used in compiling make and use matrices relates to a multitude of aspects of the economic process. There are data relating the production and input structure of industry groups, imports and exports of goods and services, household

56

The Compilation of Input-Output Tables

and government consumption, gross fixed capital formation, and stocks. These sources are not gone into here in detail; only the most important sources are outlined. The most important group of statistics involving the compilation of information by sector of industry is that covering annual production. These statistics are compiled or are currently in process of being developed for over 100 groups in manufacturing, 8 groups in construction, and more than 50 groups in the services sector, including a large number in trade. Among other things, these statistics give detailed information on sales (split into domestic sales and exports), purchases, and initial and final stocks of the goods manufactured and consumed. The data are usually specified by commodity, though on the user side in particular unspecified or only roughly specified transactions do occur. Where sales or purchases are specified by commodity, both values and volumes are given. In many cases, particularly for manufacturing, the results of the production statistics relate to a proportion of all the enterprises in the industry group concerned; results cover enterprises with at least ten employees. In the trade and services sector results usually relate to all enterprises; they are obtained by grossing up the results of the sample survey. For industry groups for which production statistics are lacking, many various, and often external, sources are used. In the case of agriculture, for example, there are ample functional statistics, that is, statistics relating to markets for certain goods (but not to producers). Often the only information for large parts of the services sector is the number of persons practicing a certain profession and the amount of wages and salaries. With respect to foreign trade, there are very detailed estimates of imported and exported goods and rougher estimates of imported and exported services. Data on consumption are based mainly on household budget surveys and figures for turnover in retail trade. Fixed capital formation is observed partly by means of direct surveys but mainly through indirect measurement in the context of the commodity-flow method of the input-output table. Finally, price statistics provide very detailed information on the prices of goods: imported goods, exported goods, goods produced domestically, and goods and services consumed by the public.

The Adjustment Phase Continuity In constructing the national accounts, great importance is attached not only to the accurate estimation of levels but also, to an even greater extent, to the accurate estimation of trends. Users of the national accounts and input-output tables require long time series of data, for example to estimate econometric models or to make comparisons over time. As has been explained elsewhere, the objectives of accurate levels and accurate changes cannot be achieved simultaneously (see for example, Algera, Mantelaers, and van Tuinen, 1982; Al and Broesterhuizen, 1985). Adjustment of the basic material should be carried out in such a way that the data for the year under review can be compared with those of the preceding year (in other words so that the change that can be calculated from the consecutive levels does in fact reflect the actual development of the variables in question). The specific problems involved in these categories of adjustment have already been described in detail in the references just given.

Compilation of Current Price and Deflated Input-Output Tables

57

Adjustment Because of Incomplete Data The basic statistics used are not always complete. We have already stated, for example, that production statistics for the manufacturing industry refer only to enterprises employing ten or more persons. These results therefore have to be grossed up to include enterprises employing fewer than ten people and self-employed persons. For this group of enterprises, production, consumption, and value added are estimated on the basis of the number of self-employed workers and the totals of wages and salaries paid, relative to figures relating to enterprises with more than ten employees. Another form of incompleteness may occur when the basic statistics are subject to systematic distortion. This could be the case for figures based entirely on tax returns from persons or enterprises. In these cases the basic data are grossed up by a certain percentage to take into account some degree of fraud. This involves an explicit grossing up of value added by nearly 1 percent of the gross domestic product (see also Broesterhuizen, 1984). Adjustment Because of Differences Between Company Accounts and the National Accounts The great majority of statistics used in compiling the national accounts are based on statements by enterprises. The information these enterprises supply to the Central Bureau is derived from their accounts. This means that inevitably there are differences between the information supplied and the information required in the context of the national accounts. Adjustments have to be made to translate figures for the financial year of the enterprise concerned into figures for the calendar year. The greatest differences, however, occur as a consequence of differences in valuation. In the framework of the national accounts, changes in stocks are valued in terms of actual prices. These changes cannot be expressed as the difference between the values of the initial and final stocks as stated by the enterprise if the enterprise does not assign the true value to stocks. The stated values of initial and final stocks then have to be corrected. These very laborious corrections are, if possible, carried out for each commodity by making use of volume data, where stated; the prices of the commodity; and knowledge of the valuation method applied in the industry group concerned.

THE PROCESSING AND ANALYSIS PHASE Once the adjustments described in the last section have been carried out, we have certain basic information that covers the entire field concerned; is comparable with that of the previous year; and, as far as definitions and registration are concerned, is in accordance with the guidelines of the national accounts. In the processing phase, an overview of receipts and expenditures is compiled for each industry group. To this end, specialists draw up estimates of volume and price changes in production, consumption, and value added. Plausibility checks are carried out on the results in each of these areas. In some cases, in particular in agriculture and the food industry and in some parts of the services sector, the available information consists only of these data on volumes and prices. The calculation of values, which is fairly laborious, can then be completed. In the majority of cases, however, and particularly in manufacturing, information

58

The Compilation of Input-Output Tables

currently available relates to production, consumption, and value added in current prices, while additional information is available on volumes and prices. Here an iterative process of analysis and adjustment of the data is used to arrive at estimates in current prices and in prices of the previous year. The procedure is roughly as follows: The most detailed basic data relating to values in current prices and volumes are used to determine the production or intermediate consumption of a large number of commodity (groups), in current prices and in prices of the previous year. If no volume data are available, price developments based on price statistics are used. Plausibility checks on the values of production and intermediate consumption thus obtained take place at the commodity (group) level, and also through comparisons of volume changes in production and intermediate consumption with each other and with other sources (viz., short-term statistics, employment data, etc.). If these volume changes turn out to be implausible, the derived data are subjected to further analysis. The sector specialist may conclude that a different deflator is required for a certain commodity group or that the original-value figures in current prices are incorrect. Adjustments are then made and new plausibility checks carried out at the level of total production and intermediate consumption. This process is repeated until definitive estimates are determined. It can be stated that the simultaneous compilation of data in current prices and in prices of the previous year results in an improvement in both sorts of data, compared with the results achieved by compilation of figures in current prices followed by deflation after the make and use matrices in current prices have been completed. This conclusion becomes even more obvious when we take into account the role played by price information in determining trade and transport margins on consumption goods and in allocating unspecified or incompletely specified items to commodity groups. Examples of these items are "other raw materials," "other costs," "other metalware," "wood products," and so on. Most of these used to be specified further on the basis of the allocation in the previous year, without specific price developments being taken into account. This can lead to serious distortions, as became very evident at the time of sharply increasing energy prices in the 1970s. For some time now a method of allocation that has been used in Denmark for a much longer period of time (see Thage, 1985) has been applied. In this method, the allocation is carried out on the basis of 1. 2. 3. 4.

The allocation of the corresponding item in the previous year Price changes of all the goods involved The value changes of the total item The assumption that all the components undergo the same volume change

The form of the make and use matrices does not strictly require consumption to be broken down into producers' values and the trade and transport margins. However, for the definitive balancing procedure (i.e., reconciling demand and supply for goods and services), such a breakdown is necessary. The data available to make this breakdown are limited, and it must therefore be carried out on the basis of assumptions. The method is completely identical to the allocation of the unclassified items described above. Particularly when sharp price fluctuations are involved, it seems more likely that the volume of trade and transport margins is proportional to the volume of consumption than that the nominal values of the margins are proportional to the nominal values of consumption. If the first assumption is taken as

Compilation of Current Price and Deflated Input-Output Tables

59

a starting point, then price changes for the trade margins will have to be incorporated separately. The allocation methods described above give only provisional results. Corrections can still be made during the balancing process. It should be clear that these methods entail an improvement with respect to the situation where the only allocation was carried out on the basis of the allocation of the previous year in current prices. In general, however, it is appropriate to give a word of warning about such allocation processes, which are, it should be stressed, necessary. As Thage (1985) has stated, the use of such classification routines in the make and use matrices may lead to a distortion in the direction of imposing greater constancy on the underlying economic structures. This conservatism, in the sense that the statistician will usually assume a gradual rather than an extreme structural change when faced with a lack of information, is justified because his objective must be the minimization of errors in his estimates. As he does not know in such cases the direction which the effects will take, he opts for an average.

THE BASIC SCHEME The basic scheme is formed by a use matrix and a make matrix (Figure 5.2). The contents of the use matrix are as follows: Columns: Relate to industry groups, including any subsidiary activities, and categories of final expenditure (export, final consumption, gross fixed capital formation, and changes in stock) Rows: Relate to Consumption of goods and services classified by standard commodity groups. Transactions are valued at purchasers' prices, including trade and transport margins and commodity taxes and subsidies Commodity taxes and subsidies paid to the government by each industry group, classified by type of tax Noncommodity taxes and subsidies paid to the government by each industry group, classified by type of tax Compensation paid to primary production factors for each industry group classified by category (wages and salaries, social insurance contributions paid by the employer, operating surplus) The column totals of the use matrix give the gross output for each industry group, valued at producers' prices, including the balance of product-linked taxes and subsidies and the totals for each category of final expenditure, respectively. The contexts of the make matrix are as follows: Columns: Contain the production classified by commodity group for each industry group, valued at the approximate basic value Rows: Give the produced trade and transport margins (this relates to subsidiary activities where industry groups outside trade are concerned) As a consequence of the fact that the inputs in the use matrix are valued at purchasers' prices including margins, the margins' row is empty there and the total of the row is therefore 0. In the make matrix the row for margins should also total 0. For this reason a balancing entry for margins is entered on the diagonal, and the margins are

FIGURE 5.2 sEE TEXT FOR DISCUSSION.

Compilation of Current Price and Deflated Input-Output Tables

61

allocated to the commodity groups to which they relate in the column "Trade and transport margins." The commodity taxes, levies, and subsidies entered as costs in the use matrix are included again in the make matrix, this time as a component of the value of production for industry groups. In the corresponding columns they are allocated to commodities, so that for each commodity group in the make matrix the row total is the total valued at purchasers' prices. For the sake of completeness the total of noncommodity taxes, levies, and subsidies and the components of value added are entered in a diagonal cell in the make matrix. Naturally there is a column with imports broken down by commodity group in addition to the domestic production of that commodity group. The column totals of the make matrix give the gross output of each industry group valued at producers' prices, total imports, and the totals for each category of primary costs. A characteristic of the scheme is that (after balancing) the corresponding totals for each commodity group and each industry group in the use matrix and the make matrix are equal. The choice of valuation for entries in the use and make matrices is made on the basis of the following considerations: Valuations should link up as closely as possible with the basic information. This consideration applies both to the money values of the flows and to the nature of the deflators to be used. As far as possible the basis of valuation within the use matrix and the make matrix should be the same. As many other desired valuations as possible should be capable of being derived as simply as possible from the chosen valuation. The precise dimensionality of the use and make matrices is not known at present. We expect that the standardized commodity groups will number about 1500, with about 200 industry groups. To simplify the necessary surveys, the number of final expenditure categories will remain limited. Detailed information on final expenditure (exports by group of countries, fixed capital formation by industry group, private consumption by trade channel, type of household, or income group) will probably be elaborated on in separate systems, which will naturally be related to the use matrix. A characteristic feature of the method of compiling input-output information described here is that for each period for which an input-output table is added to the existing series, transaction tables are compiled simultaneously with deflated values, volume indices, and deflators. This means that for each element of the make matrix and the use matrix five numbers play a part: the figures for t and t — 1 expressed in current prices; the figure for t in prices of t — 1, the volume index, and the deflator. Another way of putting this is that each time, five use matrices and five make matrices go to make up the system. Figure 5.3 gives an outline of this relationship. In principle, the information set out in this figure can be derived in a number of ways. It is necessary that data be present for three of the five pairs of tables. The "normal" situation is that A is known from the calculations of the preceding period and that B and C are derived from basic data that have been processed and checked in previous phases. Tables D and E are derived subsequently. In a situation with incomplete information, for example in the case of estimates for recent periods (in the Netherlands, the two most recent years

62

The Compilation of Input -Output Tables

FIGURE 5.3 See text for discussion. under review), the data are usually based on indicators for volume changes and deflators. In this case A, D, and E are entered and B and C are subsequently derived. The scheme can further be used for restoring continuity in the series of input-output tables following a general revision. Here the procedure is the other way around: C is the known quantity and it will usually be possible to retain previous values for E. If the revision also affects previously estimated volume indices, D should be adjusted accordingly. Revised versions of A and B can then be derived from C, D, and E. THE BALANCING PROCESS When all the stages of the statistical process described in the previous sections have been completed, the use matrix is completely filled, whereas in the make matrix only the columns referring to the production of industry groups and the imports of goods and services are filled. The trade and transport margins, commodity taxes, and subsidies for each industry group are then added to the make matrix. These data can be estimated with the aid of, for example, figures for the gross profit margins of commercial companies, turnover of transport companies, tax rates, and so on. The balancing of the use matrix and the make matrix is, in the first instance, related to the data as they are set out in Figure 5.2. For various reasons—the need for transformation to derive various types of input-output tables for example—it is necessary that the tables be balanced in each desired valuation. To this end each element in the use matrix has to be broken down into trade margin, transport margin, indirect taxes and subsidies, and approximate basic value. When the data on the margins and indirect taxes and so on have been entered in the make matrix, the structure to be balanced is complete (see Figures 5.2 and 5.3). Ex post, the totals of the use matrix and make matrix should be equal, both in current

Compilation of Current Price and Deflated Input-Output Tables

63

prices and in previous-year prices. Initially these equalities will be satisfied in only a very few cases. Various methods can be conceived of for eliminating the differences, the choice depending on factors specific to the country concerned (e.g., the availability of manpower and time) and on the nature of the basic statistical material. For a discussion of these methods, such as those used in Denmark and Norway, the reader is referred to Thage (1985) and to Furunes and R0geberg (1982). A number of characteristics of the balancing process to be applied in the Netherlands in the near future are given in the following. On the one hand the aim is the simultaneous compilation of estimates in current prices and prices of the previous year; on the other hand the aim is the balancing of commodity markets in two phases.

Simultaneous Balancing of Current Price and Deflated Data As in the preceding phases of the statistical process, the procedure in the balancing phase takes place as far as possible simultaneously for the data in current prices and the deflated data. Differences for a commodity group are eliminated by adjusting elements in either the use matrix or the make matrix. If a figure in current prices is adjusted, the consequences for the corresponding figure in prices of the previous year, in volume index, and in the deflator are examined. If a deflated figure is adjusted, a similar procedure takes place. This allows the possibility of checking the plausibility of an intended correction. Deflators that can be found in the various columns of the use matrix and the make matrix for a single commodity group constitute an important starting point for analysis of differences. These deflators were determined independently of each other in previous phases of the statistical process. Now they are compared and their consistency with each other is checked. Such checks can point to where corrections are needed. Some differences can only be eliminated by means of corrections on important aggregates: the gross output or the total input of goods and services of an industry group. As a consequence of such corrections, the value added as determined in the stages preceding the balancing stage must also undergo correction. In this respect, the simultaneous correction of data in current prices and deflated data makes analysis of the effect of such a correction on the change in operating surplus and on the volume change possible at the same time. It would often seem obvious to eliminate differences by making corrections in the consumption of households or in fixed capital formation. The method described here presents the possibility of directly analyzing the consequences of such corrections on the volume of final expenditure. If, according to statistical experts, intended corrections to value added or expenditure in either current prices or volumes turn out to lead to improbable results, alternative ways should be sought to eliminate the original discrepancy. It may be expected that balancing simultaneously in current prices and in constant prices will result in a different allocation of corrections than balancing only in current prices. This is due to the fact that simultaneous balancing allows the consequences of an intended correction to be seen more clearly. Balancing in Two Phases The first balancing phase consists of an analysis of the most important differences as far as size is concerned. This first phase may best be described as the search for

64

The Compilation of Input-Output Tables

inconsistencies in the figures collected and processed in the phases leading up to the balancing phase. Such inconsistencies may come about as a result of, for example, uncorrected errors in the observation of data, incomplete observations (e.g., of changes in stocks), the use of invalid assumptions in the allocation of unspecified items or in grossing up data for missing companies, and the use of unrepresentative deflators. Any or all of these errors can occur in previous phases of the process. In this first balancing phase, the elimination of differences takes place completely on the subjective grounds of human judgment. Both the use matrix and the make matrix are divided into blocks of interrelated commodity groups (e.g., metal products, foodstuffs, services). The idea behind this is that the consequences of corrections due to elimination of differences will be noticeable mainly within one such block. This first balancing phase continues until, in the opinion of statisticians, the remaining differences are so small that their elimination will have relatively insignificant consequences. For elimination of these remaining differences, which are likely to be numerous, a mechanical computer-based algorithm may be helpful. The fact that the matrices to be balanced are so large makes automation of part of the procedure in the balancing phase an absolute necessity. In the Netherlands we are currently experimenting with a method of eliminating differences in which each element of the make matrix and use matrix is assigned a confidence margin. When the balancing phase has been completed, the user has at his or her disposal a system of tables containing consistent and detailed information on the levels, volume changes, and price changes of goods and services transactions, in and between two periods. In addition this system includes detailed information on levels and trends in primary incomes and final expenditure in both nominal and real terms. All this is significant for various categories of users: policymakers, builders of macromodels and models of components of the economy (industry groups, final expenditure categories), market researchers, and others. Many users of national accounts data require long series of data on volume and price indices. This need can be met by means of a series of tables, as shown in Figure 5.1. Apart from this, users of input-output tables require information on the interindustrial relations of groups of economic agents and on the direct and indirect relations within the production structure of a certain country. To this end, they need input-output tables of the type industryxindustry and homogeneous activity x homogeneous activity. This information does not occur as such in the make matrix and the use matrix, since these are commodity x industry tables. The required input-output tables can, however, be derived from the use matrix and the make matrix by simple transformations. A description of these transformations falls outside the scope of this chapter; the reader is referred to the literature, for example United Nations (1968).

CONCLUSION Thus chapter describes how the quality of input-output information can be improved by making use of information relating to volume and price changes at each stage of the statistical process. This is explained with the aid of a system of make and use matrices such as the Netherlands is aiming to achieve in the near future. It should be mentioned, however, that the principle of applying price and volume data to the entire statistical process has already been in use for a number of years. The system presented here for the compilation and presentation of input-output

Compilation of Current Price and Deflated Input-Output Tables

65

data can be applied in a wide variety of statistical environments. Some relevant aspects of this environment are: The nature and specification of the available basic data The quantity and quality of the available manpower The time available In practice, statistical environments vary widely. On the one hand there are differences between different countries; on the other, there are differences in the completeness and detailed classification of data between recent and earlier years within countries. Depending on the availability of basic information, manpower, and computer capacity, the compilation of make and use matrices must to a greater or lesser extent always involve assumptions. These assumptions may relate, for example, to the allocation of unspecified items and to the relation between input and output. Making these assumptions always leads to loss of detail, since the tendency is to use averages. In each statistical environment statisticians have to determine how much loss of detail they consider acceptable. More assumptions are allowed with provisional data than with definitive data. The objective of the information to be obtained is also significant. If this objective is study of the input structure of industry groups or the composition of final expenditure, less reliance may be placed on the assumptions used than when the aim is estimates of the level, volume, or price changes of goods and services transactions in the context of the national accounts. Less loss of detail with use of assumptions can be expected if differences in price changes between various goods and services are taken into account. One condition for this is that there be sufficient relevant price information. The resulting disaggregation is, however, probably of a better quality than when disaggregation is carried out on the basis of nominal value data alone.

REFERENCES Al, P. G., B. M. Balk, S. de Boer, and G. P. den Bakker. 1984. "The use of chain indices for deflating the national accounts." Study prepared by the Dutch Central Bureau of Statistics under contract with EUROSTAT, Voorburg, Netherlands. Al, Pieter, and Guus Broesterhuizen. May 1985. "Comparability of input-output tables in time." Paper presented at International Meeting on Problems of Compilation of InputOutput Tables, Baden, Austria. Algera, S. B., P. A. H. M. Mantelaers, and H. K. van Tuinen. 1982. "Problems in the compilation of input-output tables in the Netherlands." In J. Skolka (Ed.), Compilation of Input-Output Tables. Berlin: Springer-Verlag. Broesterhuizen, Guus, 1984. "The unobserved economy and the National Accounts in the Netherlands: A sensitivity analysis." In W. Gaertner and A. Wenig (Eds.), The Economics of the Shadow Economy. Berlin: Springer-Verlag. Central Bureau voor de Statiskiek. 1984. "Input-outputtabellen 1981 in prijzen van 1980." In De Produktiestructuur van de Nederlandse Volkshuishouding. Vol. 12. Dutch Central Bureau of Statistics, Voorburg, Netherlands. Furunes, Nils Terje, and Svein Lusse R0geberg. 1982. "Compilation of input- output tables in Norway." In J. Skolka (Ed.), Compilation of Input-Output Tables. Berlin: Springer-Verlag. Thage, Bent. May 1985. "Balancing procedures in the detailed commodity flow system used as a basis for annual input-output tables in Denmark." Paper presented at International Meeting on Problems of Compilation of Input- Output Tables, Baden, Austria. United Nations. 1968. A System of National Accounts. Studies in methods series F, no. 2, Rev. 3. New York: United Nations.

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III INPUT-OUTPUT AND THE ANALYSIS OF TECHNICAL PROGRESS

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6 Technical Progress in an Input-Output Framework with Special Reference to Japan's High-Technology Industries SHUNTARO SHISHIDO, KIYO HARADA, and YUJI MATSUMURA

Rapid technical progress in Japan's manufacturing industries in recent years, especially after the oil price shock in 1973, has attracted much international concern among economists and policymakers. Although technical progress at the macroeconomic level has suffered from a deterioration since 1973, the manufacturing industries have experienced a remarkable annual increase in productivity, especially the high-technology industries such as robotics, microelectronics, fine chemicals, fine ceramics, and biotechnology. The rise in these new sectors, which have replaced the traditional ones such as steel, petrochemicals, ship building, and heavy electrical appliances, facilitated a rapid structural change during the 1970s that was characterized by a shift from capital-intensive and energy-using sectors to knowledge-intensive and energy-saving sectors. This chapter analyzes the mechanism behind this structural change in an inputoutput framework. It also analyzes factor productivity on a detailed sectoral basis with special reference to the high-technology industries. A new approach is presented in this context. It integrates factor productivity and relative price analysis with the input-output model by using the V-RAS method, a modified RAS method that includes primary factors (the V matrix) in a consistent framework. An empirical test of this approach over the period 1975 to 1980 provided fairly satisfactory results, and the approach was thus judged a reasonable basis for the analysis of a rapid change in industrial structures. Finally we present in this chapter alternative scenarios for the Japanese economy in the year 2000, with special reference to the high-technology industries, by using alternative technology assumptions. The international impacts of these scenarios are also discussed by combining the I-O model with a multicountry model. The technology studies and forecasts are based on detailed government I-O tables, comprising 544 x 409 matrices, which have recently been made available in terms of both current and constant prices (see Government of Japan, 1985).

70

Input-Output and the Analysis of Technical Progress

THE V-RAS METHOD: A MODIFIED APPROACH INTEGRATING TOTAL FACTOR PRODUCTIVITIES AND RELATIVE PRICES Since Stone's approach in 1963, a number of variants of the RAS method for analyzing and forecasting the input-output coefficient matrix have been attempted. In the context of the study of high-technology sectors showing rapid technical progress in Japan, we have developed a new approach that integrates traditional total factor productivity and related relative price analysis by expanding the traditional RAS method to cover both intermediate and primary input matrices. This method has the advantage of allowing analysis of technical changes in a consistent framework on the basis of an input-output matrix including real value added, that is, its component primary factors such as labor and capital. Our I-O coefficient matrix a*, therefore, is rectangular with dimension (n + m) x n, instead of the ordinary n x n, including m row vectors of primary input, which is specified, as below, in terms of constant prices of the base year.

where aij denotes an intermediate input coefficient and vmj a primary input coefficient, such as labor and capital costs; and r denotes total factor productivity (TFP), since both intermediate and primary input coefficients are expressed in constant prices of the base year. The basic idea for this definition of a£j lies in the fact that technical change can best be studied by analyzing both types of input factors simultaneously in a consistent framework. The use of a£,- has another advantage, since its summation over k gives the inverse of TFP, a most useful and comprehensive concept for measuring productivity (see Jorgenson and Griliches, 1967; Jorgenson, Kuroda, and Nishimizu, 1985). As shown in the following, the ordinary RAS method can be strengthened by this extension of the matrix of aij to the matrix a*, and by integrating the a*j with relative price analysis. This method may conveniently be termed V-RAS, since it includes the V matrix. Our model for technical change can be formulated in the following way.

Technical Progress in Japan's High-Technology Industries

71

where r = substitution parameter a = a* in base year s = efficiency parameter rf = r for intermediate input rs = r for primary input p = relative input price change over base year p = input price of intermediate input p = average input price p = p in base year \JL = import dependency ratio px = output price pm = import price pv = price of value added v = input coefficient of primary factor pf — price of primary factor n = profit margin per unit of output Given exogenous values for TFP (t), the price of primary factors (pf), the profit margin (71), import prices (pm), and the base year I-O matrix (akj\ the model can determine simultaneously technical change for target year, as expressed by the variables a*, r, and s, and the price level variables px, p, p, p. We shall be more specific about individual equations and the causal relationship behind them. As mentioned before, the efficiency parameters (s) in the conventional RAS system are now approximated by the inverse of TFP, so that s can be easily accounted for by the change in TFP as shown in equation (4). These TFP changes are usually estimated using information relating to technology, such as R&D expenditures, diffusion of new technologies, and relative factor prices; changes in these directly affect s parameters. The r parameters, representing substitution among factor inputs, are mostly explained by the changes in relative prices as in (6), since we assume that the elasticities of substitution of a specific product are approximately equal among different users. A detailed analysis discussed later, however, indicates that additional explanatory variables, such as dummy variables representing rate of technical progress and other nonprice factors, are required. In any case, we expect that 0 > a > — 1 in most cases, where a = 6 In r/8 In p. Equations (8), (9), and (10) determine output and input prices that are affected by changes in the parameters s and r, that is, changes in the a* matrix. Therefore, our

72

Input -Output and the Analysis of Technical Progress

causal relationship indicates simultaneous interdependence between a* and p, mostly arising through changes in r. A representation of this interdependence is given below.

where

> = endogenous flows > = exogenous flows A, A* = matrices comprising akj, a*j

Rapid technical growth in high-technology products, for example, lowers their s parameters and prices, which in turn raises their r parameters due to substitution, stimulating demand for them (shown later). We now discuss the empirical implementation of this new approach, which we have called V-RAS. EMPIRICAL ASPECTS OF TECHNICAL CHANGES FROM 1970 TO 1980 In July 1985, the Japanese government published I-O tables for 1970, 1975, and 1980, including a 544 x 409 matrix on a perfectly comparable basis in both current and 1980 prices (Government of Japan, 1985). On the basis of this detailed I-O data base, employment (distinguishing between employees and others) and capital stock data were estimated on a 406 sectoral basis for these three benchmark years by the University of Tsukuba and Foundation for Advancement of International Science (FAIS) (Shishido et al., 1981). Primary input coefficients for labor and capital in both current and 1980 prices were also estimated, and the latter series in real terms served as a basis for obtaining sectoral TFP, as specified in equation (2). TFP changes for major high-technology industries are indicated in Table 6.1; full details of the changes are available on request. Although no adjustment was made for differences in the rates of capacity utilization, the table shows the rapidity of technical progress in Japan's high-technology sectors during the 1970s. In view of the fact that the average annual rate of technical progress in terms of TFP for all industries was 1.3 percent during the period 1970 to 1975 and 1.0 percent during the period 1975 to 1980, and that there was a marked tendency in the average rate of technical progress to decline in the latter half of the 1970s due to oil price increases, it is surprising that there was no such general tendency (rather signs of an acceleration) in some sectors of the high-technology industries. Technical progress is particularly conspicuous for office machinery, computers, semiconductor devices and integrated circuits, and computer rental services, which show rates of increase about ten times or more the average rate. Rapid increases are also observed for new material- and biotechnologyrelated sectors such as acrilonitrile fiber, electric wires and cables, and medicines. Table 6.2 shows a picture of the whole economy during the 1970s. The table was

Technical Progress in Japan's High-Technology Industries

73

TABLE 6.1 Total factor productivity of high-technology industries on 409-sector basis Annual Growth Rate (%)

Level

1970

1975

1980

1975/1970

1980/1975

0.844

0.909

0.995

1.49

1.82

0.789 0.213

0.845 0.502

1.007 1.018

1.38 18.70

3.57 15.19

0.767 0.502 0.469 0.670 0.302 0.731 0.510

0.865 0.736 0.723 0.839 0.583 0.820 0.714

0.990 1.089 1.156 1.078 1.086 1.055 1.073

2.43 7.95 9.04 4.60 14.06 2.32 6.96

2.74 8.15 9.84 5.14 13.25 5.17 8.49

0.254

0.528

1.111

15.76

16.04

0.624 0.743 0.609 0.547 0.592 0.755

0.809 0.857 0.700 0.728 0.751 0.863

1.016 1.025 1.004 1.024 0.985

5.33 2.90 2.82 5.88

4.66 3.65 7.48 7.06

4.87

1.135

2.71

5.57 5.63

0.185

0.324

0.564

11.86

11.72

New materials Acrilonitrile fiber Other glass and glass products Other basic nonferrous metal products Metal doors and shutters Electric wires and cables

0.480 0.666 0.786 0.691 0.622

0.787 0.784 0.917 0.953 0.884

0.986 0.945 1.071 1.014 1.111

10.39 3.32 3.13 6.64 7.28

4.61 3.81 3.15 1.25 4.68

Biotechnology Agricultural chemicals Medical preparations Toilet preparations and dentifrice

0.403 0.690 0.685

0.619 0.921 0.920

0.834 1.167 1.158

8.96 5.95 6.08

6.14 4.85 4.71

Industry Electronics Machine tools Other general industrial machinery and equipment Office machinery Sewing machines and wool knitting machinery Electric sounders Radio and television sets Electric equipment for home use Electric computers and accessory devices Other applied electronic equipment Electronic tubes Semiconductor devices and integrated circuits Telecommunication machinery and related equipment Electric measuring instruments Medical instruments Cameras Watches and clocks Musical instruments Rental and leasing of electric computers and accessory devices

obtained by aggregating the original table calculated on a 409-sector basis. Rapid technical progress is also noted for high-technology industries such as 46, light electrical applicances (mostly electronics); 49, precision instruments; and 34, other chemical products (fine chemicals), their rates of increase being four to five times the average. It should be noted that rates for these sectors tended to accelerate during the latter half of the observation period, probably as a result of higher energy prices. Also notable is the fact that several industries declined or were stagnant in terms of technical progress: agricultural crops, fisheries, crude oil and natural gas, printing and publishing, basic petrochemicals, coal products, and building construction. They all tended to marked decline after the oil price shock. It can be stated, therefore, that the oil price increase in the latter half of the period under consideration resulted in accelerating the imbalances in technical progress between different sectors, especially

Input- Output and the Analysis of Technical Progress

74

TABLE 6.2 Total factor productivity of all industry on 72-sector basis Annual Growth Rate (%)

Level Sector a 1 2 3 4 5 6 7 8 9 10 11

12 13

14 15

16b 17

18 19 20

21 22 23 24 25 26 27 28 29 30 31

32 33 34 35 36 37 38

1970

1975

1980

1975/1970

1980/1975

0.771 0.490 0.923 1.212 0.906 0.812 0.825 1.465 0.752 0.893 0.791 0.831 0.960 0.860 1.426 (2.516) 0.674 0.725 0.694 0.874 0.877 0.908 0.876 0.847 0.998 1.200 1.022 0.981 0.572 0.662 0.519 0.470 0.563 0.735 1.069 1.119 0.853 0.954

0.739 0.485 0.732 1.065 0.860 0.776 1.063 1.292 0.866 0.969 0.983 0.922 0.995 0.876 1.556 (3.307) 0.741 0.806 0.800 0.957 0.905 0.963 0.934 0.890 0.956 1.029 1.059 0.867 0.541 0.777 0.838 0.657 0.584 0.890 1.099 1.029 0.908 0.967

0.685 0.508 0.742 1.102 0.729 0.833 1.118 0.986 1.114 1.022 1.033 0.841 1.028 0.975 1.594 (3.352) 0.830 0.912 0.871 0.945 0.954 0.976 0.987 0.930 1.009 1.005 0.937 0.945 0.693 0.755 0.986 0.797 0.778 1.106 1.114 1.022 0.962 0.906

-0.84 -0.20 -4.53 -2.55 -1.04 -0.90 5.20 -2.48 2.86 1.65 4.44 2.10 0.72 0.37 1.76 (5.62) 1.91 2.14 2.88 1.83 0.63 1.23 1.29 1.13 -0.86 -3.03 0.71 -2.44 -1.10 -3.15 10.06 6.93 0.74 3.90 0.56 -1.66 1.26 0.27

-1.51 0.93 0.02 0.68 -3.25 1.12 1.01 -5.26 5.17 1.07 1.00 -1.82 0.66 2.16 0.48 (0.27) 2.29 2.50 1.72 -0.25 1.06 0.27 1.11 0.88 1.08 -0.47 -2.42 1.74 5.08 -0.57 3.31 3.94 5.90 4.44 0.27 -0.14 1.16 -1.30

between high-technology and other industries. These imbalances also affect relative prices and demand components for intermediate inputs, an effect which is discussed in the following section.

TESTING V-RAS ESTIMATES OF PRICES AND I-O COEFFICIENTS For the empirical implementation of our model for technical change, we first estimated r and s parameters of the (544 + 4) x 409 matrices for 1975 and 1980 by using

Technical Progress in Japan's High-Technology Industries TABLE 6.2

(Continued) Annual Growth Rate (%)

Level Sector a

39 40 41 42 43 44 45 46

47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

67 68 69 70

71 72 Total

75

7970

1975

1980

0.846 0.892 0.920 0.695 0.836 0.830 0.793 0.604 0.909 0.949 0.630 0.835 1.059 1.156 1.071 0.714 0.933 1.048 0.836 1.027 1.468 1.944 0.796

0.0

0.907 0.896 1.153 0.871 0.869 0.867 0.949 0.768 0.951 0.977 0.764 0.874 1.127 1.265 1.127 0.791 1.065 1.046 0.954 1.125 1.767 2.493 0.806

1.055 1.040 0.993 1.065 0.997 1.015 1.023 1.070 1.013 1.022 1.011 0.990 1.044 1.145 1.014 0.787 1.126 0.959 1.019 1.212 1.852 4.354 0.854

0.0

0.0

1.021 0.933 1.023 0.947 0.975 1.002 1.035 1.083 0.944 1.530

1.683 0.960 0.986 0.927 1.042 1.071 0.954 0.984 1.002 1.055

1.521 1.035 1.075 0.982 1.146 1.046 0.950 1.000 1.087 1.040

10.51 0.57 -0.73 3 -0.43 3 1.34 1.34 -1.62 2 -1.900 1.20 -7.177

0.909

0.970

1.021

1.31

1975/1970

1.40 0.09 4.62 4.62 0.78 0.88 3.66 4.92 0.91 0.58 3.93 0.92 1.25 1.82 1.02 2.07 2.68 0.38 2.68 1.84 3.78 5.10 0.25

0.0

1980/1975

3.07 3.03 -2.944 4.10 2.79 3.20 1.51 6.86 1.27 0.91 5.76 2.52 2 -1.527 -1.977 9 -2.09 9 -0.100 1.12 -1.722 1.33 2.00 0.94 11.80 1.16

0.0

-2.00 0 1.52 1.74 1.16 1.92 -0.47 7 -0.08 8 0.32 1.64 -0.299 1.30

a

See Table 6.6 for sectoral classification. Excluding real capital input.

b

the V-RAS method in equation (3). The primary input coefficients in the value-added matrix are composed of four row vectors: (1) real cost for business consumption, (2) real cost for employees, (3) real cost for entrepreneurs and family workers, and (4) real user cost of capital. The real cost (v) in equation (1) denotes the unit-factor cost deflated by base year prices, that is, 1980 prices.1 The results for high-technology industries are shown in Table 6.3 (full details are available on request). As can easily be seen, the s parameters are closely related to the inverse of TFP, whereas the r parameters seem to correspond to the changes in relative prices, as anticipated in our theoretical model. Broadly speaking, it is clear

76

Input -Output and the Analysis of Technical Progress

TABLe 6.3 r and s parameters of high-technology industries on 548 x 409 sectoral basisa

Industry Electronics Machine tools Other general industrial machinery and equipment Office machinery Sewing machines and wool knitting machinery Electric sounders Radio and television sets Electric equipment for home use Electric computers and accessory devices Other applied electronic equipment Electric tubes Semiconductor devices and integrated equipment Telecommunication machinery and related equipment Electric measuring instruments Medical instruments Cameras Watches and clocks Musical instruments Rental and leasing of electric computers and accessory devices

1970-1975

1975-1980

r

s

r

s

0.866 1.537 3.171 0.999 1.568 1.253 1.852 1.682 1.572 1.224 2.030 1.210 1.291 1.793 1.285 1.133 0.888

0.996 0.936 0.424 0.949 0.686 0.649 0.772 0.511 0.889 0.736 0.484 0.787 0.889 0.912 0.789 0.833 1.013

1.914 1.237 1.883 1.586 2.034 1.063 1.423 2.623 1.956 0.924 3.094 1.585 1.320 1.393 1.139 1.341 1.225

0.814 0.831 0.428 0.804 0.626 0.563 0.748 0.486 0.753 0.714 0.494 0.695 0.812 0.721 0.755 0.761 0.812

1.695

0.588

1.346

0.613

0.494 1.006 1.111 1.731

0.539 0.908 0.843 0.784 0.636

2.316 1.132 0.992 1.110

0.808 0.834 1.140 0.945 0.954

New materials Acrilonitrile fiber Other glass and glass products Other basic nonferrous metal products Metal doors and shutters Electric wires and cables Copper electric wires and cables Aluminum electric wires and cables

0.858 0.872

Biotechnology Agricultural chemicals Medical preparations Toilet preparations and dentifrice

1.898 1.375 1.146

1.364 0.956

0.680 0.790 0.777

1.025 1.586 1.201

0.753 0.805 0.798

"See equation (3) and following for explanation of r and s parameters.

that the lower the value of s, the higher the value of r becomes. (e.g., office machinery and semiconductor devices compared with electrical tubes and musical instruments). On the basis of these parameters, we estimated two types of structural equations, that is, equations (4) and (5), for the parameters s and r, respectively, on the basis of cross-sectional data for 1975 and 1980. The results are shown in Tables 6.4 and 6.5. The following specifications were used for the s and r functions.

whereZi and i zkj are industrial dummtyy variables.

TABLE 6.4 s functiona s=

a0

«! W*7S

-0.063

1.137 (78.14) *28

(3116-10) -0.198 (-2.57)

*2l

(0014-20) 0.086 (1.12) 1), many solutions make the present value of the output stream infinite. If the rate of productivity increase depends inversely on the level of productivity (i.e., e < 1), there exists a unique solution, subject to the qualification that the long-run output growth rate does not exceed the interest rate. If the rate of productivity increase is independent of the productivity level (i.e., e = 1), there exists a unique solution provided the labor growth rate (measured in terms of efficiency units allowing for PI As) is not positive: the qualification stated previously, on the relation between the growth rate and the interest rate, also applies here. If, on the other hand, the labor growth rate is positive, the solution ceases to be unique and the present value of the output stream is infinite, as in the case where e > 1. The general characteristics of the solutions can be illustrated in Table 10.1.

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Input- Output and the Analysis of Technical Progress

"Comparative Static" Properties of the Solution We conducted a detailed study of the properties of this model, and of how changes in the parameters and the initial conditions affect the solution, particularly in terms of the optimal labor allocation. Here, however, we summarize only what we consider the most important aspects of these theoretical results. These findings are incorporated into the econometric tests presented in the next section. Our theory supports the following hypotheses: 1. In the "simple" model a. The level of productivity has no effect on the optimal labor allocation ratio to PIAs (a) b. The size of the total labor force in the agricultural sector has a positive effect on the optimal labor allocation ratio to PIAs 2. In the "general" model a. The productivity level has negative effects on the optimal labor allocation ratio to PIAs b. The total labor force has a positive effect on this ratio, as in the simple model The simple model is denned as a special case of our model, when the growth rate of productivity does not depend on the productivity level (e = 1) and when labor (in efficiency units in PIA activities) is perceived as remaining constant (h = 0). This simple model should be regarded as an approximation (of lower order) of the general model, which is itself, of course, an approximation of reality.

Relation to Previous Models of Endogenous Technical Change In this subsection we will try to clarify the relationship of our model to the models of Lucas (1967) and Uzawa (1965), which we believe should be called models of endogenous technical change. In a sense, our purpose in this subsection is to make clear the contribution we have made to the field of theories of endogenous technical change through the development of our model. It is clear that our model, and the models of Lucas and Uzawa, have certain similar features. In particular each model regards a productivity increase as the output of activities that consume production factors, with the level of these activities being optimally determined to maximize the future output stream. However, these models also contain features that differ, so that each model has an advantage over the others for some purposes. In other words, none of the models includes any of the others as a special case. We would like to make the differences clear, and to search for directions in which our model should be enriched. Productivity-increasing activity in the Uzawa model is specified in a form that is more suitable as a representation of education than of R&D, in that the share of labor devoted to this activity determines the rate of productivity increase. The other feature we felt to be inadequate was that the level of productivity (or technology) has no influence on the determination of the rate of technical change (i.e., e is assumed to be unity). The Lucas model has corrected these deficiencies. His model, however, is applicable to a competitive microeconomic agent in the sense that perfectly elastic

Private-Led Technical Change in Prewar Japanese Agriculture

153

supplies of labor (and other production factors) are assumed. This assumption is not really acceptable for studying prewar Japanese agricultural development. Furthermore, we think that Lucas' assumption of constant factor prices (e.g., wage rates) over time is inadequate, even in a more general context. Our approach can be taken as being another way to remedy the shortcomings of the Uzawa model, or as a variant of the Lucas model, with perfectly inelastic factor supplies that are increasing at given constant rates. Our approach, however, also has shortcomings. First, our analysis is within the framework of constant elasticity (in fact, of Cobb-Douglas) production relations. In this characteristic our model is inferior to those of Lucas and Uzawa. Second, if our model is to be a macroeconomic growth model, we should treat savings (or investment) as a choice variable, as is done by Uzawa. If these two extensions were made to our model, we could assert that the Uzawa model is a special case of ours.

Interpretation of the Model We implicitly treat productivity-increasing activities (PIAs) as private R&D, both advancing the best practices and enhancing average practices by imitating the techniques used by neighbors. This involves an element of trial and error, an essential component of R&D activities. Yet we have no intention of confining the PIAs to private R&D. More specifically, we would like to include investment in latent capital (e.g., land improvement projects such as building and improving irrigation and drainage facilities) and private educational activities1 (such as attending farmers' meetings) as components of the PIAs.2 We can show that the latent capital model and the private education model are special cases of our PIA model. In the first of these models there is another type of capital, which is not included in the official measure of capital (and is thus latent) and is produced using production factors, notably labor. Farmers are assumed to maximize the present value of the future output stream by allocating their labor between agricultural goods production and latent capital production. In the private education model, technical change is a function of the share of labor in educational activities, rather than of the amount of labor devoted to PIAs. ECONOMETRIC TESTING Methodology In applying our theoretical model to econometric testing, two difficulties arise. These difficulties, and the way in which we overcame them, are as follows: 1. Our models cannot be transformed into linear relationships between observable quantities without assuming away the key features of the model. Hence we cannot estimate the model using ordinary least squares. We thus resorted to maximum likelihood (or nonlinear least squares) estimation. 2. The time series on inputs, as well as those on outputs, have strong time trends so that parameter estimates are very unstable (i.e., we have a serious case of multicollinearity). We thus adopted the mixed estimation technique. This method allows us to combine cross-sectional data, which are free from time trends, with the time series data, which alone can provide legitimate measures of technical change.

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Input-Output and the Analysis of Technical Progress

Time-Series Estimation Without Mixed Estimation Ordinary least squares estimates of Cobb-Douglas production functions, without using the mixed estimation procedure, can hardly be regarded as representing production relations3: the land coefficients were around 3 to 4, and the coefficients of nonfarm current inputs were negative, although insignificantly so. We can interpret these results if we take account of PIAs. 1. The increase in the land area is another product of PIAs4. Hence when PIAs are undertaken, the land area increases at the same time that productivity increases. The land area thus functions as a productivity indicator as well as an input for agricultural production. 2. The negative value for the coefficient of "nonfarm current inputs" is especially troublesome, since fertilizers, a major component of nonfarm current inputs, are considered leading inputs in the phase of biological-chemical technology change, in which the level of fertilizer application and the technology level are expected to more or less correspond to each other. The purchased fertilizers were almost complete substitutes for self-supplied fertilizers, which constitute self-supplied investment of "liquid" capital, as one element of latent capital. Hence when PIAs are undertaken, self-supplied capital increases to substitute for purchased fertilizers. Therefore the relation between purchased fertilizers and output becomes muted. 3. The foregoing observations can be regarded as evidence that PIAs seem to be an important component of the agricultural production relations under study. Estimation of the PIA Model To implement the mixed-estimation procedure, we first ran a cross-sectional regression, using a specification based on a straightforward Cobb-Douglas production function. The data used were those given in Akino (1972). The differences from previous studies using these data (Hayami, 1975) are that we tested the hypothesis of constant returns to scale (with the finding that decreasing returns to scale prevailed) and that we used climactic variables to improve estimation. Utilizing the cross-sectional production function estimates as prior information, we computed time-series estimates of both the simple model and the general model, applying the method of mixed estimation. 1. We first estimated an ordinary Cobb-Douglas production function, using the mixed-estimation method with and without a time-trend variable. The estimation results without a time-trend term could not be interpreted as a production relationship, even using the mixed-estimation procedure. The time trend was statistically significant, as expected, indicating the existence of technical change. 2. We then estimated our models, which incorporated PIAs into the production function. The results were statistically superior to the estimates incorporating a simple time trend. The difference between the two versions (simple and general) of our models was not statistically significant. This implies that we need more detailed data to distinguish between the contributions of diffusion, and of the advancement of best practices, to technical change at the aggregate level. 3. Because there was no guarantee that the cross-sectional and time-series production

Private-Led Technical Change in Prewar Japanese Agriculture

155

functions were the same, we investigated whether they actually were. Furthermore, the coverage of capital and "nonfarm current inputs" are not the same for crosssectional and time-series data. The cross-sectional data are less complete because of data deficiency, so there are grounds for scepticism about using cross-sectional estimates as prior information for mixed estimation of the time-series production function. Accordingly we performed the compatibility test suggested by Theil (1963). The results were well within the acceptance range for any reasonable significance level. Hence we may conclude that the incompatibility between the two data sets was not serious. 4. One question we would like to address is whether our model can explain the observed timing patterns. This is equivalent to the question whether the estimation residuals have the same pattern as the timing sequence we set out earlier. If we can explain the timing using the models, the residuals from the models should be random and have no significant pattern. Our models turned out to be powerful in this respect, in that statistically we could not discern a kink around 1920 in our residuals. In contrast, the simple time-trend model failed in this respect: there was a statistically very significant kink around 1920. 5. The estimates of the elasticity of optimum labor allocation to PIAs with regard to the total agricultural labor force were about 6 to 9, depending on the specification. These estimates may seem too high. In the period 1914 to 1920 the agricultural labor force decreased from 13.5 million to 12.0 million in terms of male equivalent workers, a decrease of 11 percent. The parameter estimates imply that the labor devoted to PIAs decreased by between 51 and 69 percent. We interpret these results as follows: a. Our theoretical model implies that these values are reasonable if the labor allocation ratio was around 5 to 10 percent and the production elasticity of labor for the PIAs was around 85 to 90 percent, or for other combinations with smaller (or larger) values for the PIA labor allocation ratio and lower (higher) PIA production elasticities. b. The PIAs are specified in net terms. For example, maintenance of irrigation and drainage facilities is not included in PIAs but rather in ordinary agricultural goods production. Therefore in the same period, the change in the labor allocation to gross PIAs was modest, but the change in net terms was drastic, as the preceding figures indicate. 6. The estimates of the production elasticities for each of the four input categories are practically identical, regardless of whether we use the simple or the general model, and are reported in Table 10.2. TABLE 10.2 Mixed-estimation production elasticity estimates Labor Land Capital Nonfarm current inputs

0.15 0.42 0.11 0.18

•Figures in parentheses are standard errors.

(0.04)°

(0.04) (0.02) (0.02)

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Input-Output and the Analysis of Technical Progress

Comparison with Previous Estimates Previous estimates of the production function for prewar Japanese agriculture are summarized in Table 10.3. Although his work was based on postwar data, Tsuchiya's estimates are also included, on the grounds that the conditions of production in 1951 were still similar to those prevailing prewar. We recognize a high degree of similarity among the estimates, including ours. The exception is the set of estimates by Akino (1972), which serve as the basis for the studies on technical change in Hayami (1975). The similarity is particularly remarkable because of the fact that their data bases are fairly independent. Ohkawa's classic study (1945) and Tsuchiya's study (1955) are based on production-cost surveys of different dates; both of Shintani's studies (1970,1971) are based on farm household economy survey data of different dates; and Akino's study and ours are based on the aggregate data, which covers all farming units. We think that this similarity indicates the soundness of our estimates. One difference that clearly distinguishes our estimates from the others is that we found decreasing returns to scale (indicated by the fact that the sum of the production function coefficients is less than unity). We should compare our results only with those of Ohkawa and Tsuchiya, because all the others simply assumed constant returns to scale without testing the hypothesis. We think that there are two sources for the difference. First, their studies cover only rice production. As Tsuchiya (1955) has shown, the degree of scale economies (or diseconomies) depends on the commodity studied: rice is subject to constant returns to scale, whereas other commodities are subject to increasing returns or decreasing returns. Our study covers aggregate agricultural production, and although rice is the main commodity, it is not a priori clear whether constant returns prevail. Second, the data on which their studies depend came from homogeneous regions, whereas our data covered all regions. Thus the irrigation and drainage facilities were rather uniform in their data base, but this latent capital is one of the main sources of decreasing returns to scale, and hence their estimates failed to capture decreasing returns to scale. This difference, however, does not necessarily indicate any inconsistency between their estimates and ours. They estimated microeconomic production functions, with the aim of comparing coefficients with factor shares and of studying the behavior of individual farmers, whereas TABLK 10.3 Previous estimates of prewar agricultural production function Shintani

Labor Land Capital Nonfarm Current input Sum Years covered Output covered

Ohkawa (1945)

(1970)

(1971)

Akino (1972)

Tsuchiya (1955)

0.23 0.56 —

0.22(0.09)" 0.63(0.10) —

0.3-0.5 0.3-0.5 0.2

0.41(0.07) 0.17(0.06) 0.14(0.04)

0.19 0.56

0.18 0.98 1937-39 Rice

0.15(0.05) 1.00 1888-1900 Rice

— 1.00 1925-36 Agri. output

0.28(0.04) 1.00 1928-37 Agri. output

0.25

"Figures in parentheses arc standard errors.

1.00 1951 Rice

Private-Led Technical Change in Prewar Japanese Agriculture

157

our aim was to estimate a time-series production function and to study the dynamic property of technical change. Akino's estimates are quite different from the others, although our data and his are basically the same: we actually used his cross-sectional data, along with time-series and climactic data. One of the most important sources of the difference between our estimates and Akino's is that we included climactic variables at the stage of crosssectional estimation. We think that the influence of climactic factors in cross-sectional estimation should be eliminated when one studies technical change. Such change appears legitimately only in time-series data and has little to do with climactic factors.

NOTES 1. Formal education can be regarded as this type of activity if the effort devoted to it is a choice variable from the private farmers' point of view. 2. Obviously these activities are interrelated. For example, in the case of imitating the practices of others, acquisition of the necessary information can be classified as the third type of activity (i.e., education), whereas trying the new techniques is an activity of the first type. But in addition, improved irrigation, an element of the second type of PIA, may also be required. 3. Straightforward time-series estimation of Cobb-Douglas functions based on Long-Term Economic Statistics (LTES) data has been tried before, but resulted in unreasonable estimates and was therefore discarded (Yamada, 1967). We report the results here because we think they are supportive to our views. 4. One purpose of land replotment projects was to increase land area, although the main purposes were to simplify operations and to improve (or to build) irrigation and drainage facilities.

REFERENCES Akino, Masakatsu. 1972. "Nogyo Seisan Kansu no Keisoku" (Estimation of the agricultural production function). Nogyo Sogo Kenkyu 26: 163-200. Fei, J. H., and G. Ranis. 1964. Development of the Labor Surplus Economy: Theory and Policy. Homewood, III.: Irwin. Hayami, Yujiro. 1975. A Century of Agricultural Growth in Japan. Minneapolis: University of Tokyo Press and University of Minnesota Press. Hayami, Yujiro, and V. W. Ruttan. 1971. Agricultural Development: An International Perspective. Baltimore: Johns Hopkins University Press. Ishikawa, Shigeru. 1967. Economic Development in Asian Perspective. Tokyo: Kinokuniya. Kelley, A. C., and J. G. Williamson. 1974. Lessons from Japanese Development: An Analytical Economic History. Chicago: University of Chicago Press. Lockwood, W. W. 1954. The Economic Development of Japan. Princeton, N.J.: Princeton University Press. Lucas, R. E. Jr. 1967. "Tests of a capital theoretic model of technical change." Review of Economic Studies 34: 175 180. Nogyo Hattatsu-shi Chosa Kai. 1953-1958. Nihon Nogyo Hattatsu Shi (History of Japanese Agricultural Development). l0vols. Tokyo: Chuokoronsha. Ohkawa, Kazushi. 1945. Shokuryo Keizai no Riron to Keisoku (Theory and Measurement of the. Food Economy). Tokyo: Nihon Hyoronsha. Ohkawa, K., M. Shinihara, with L. Meissner. 1979. Patterns of Japanese Economic Development: A Quantitative Approach. New Haven, Conn., and London: Yale University Press.

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Input Output and the Analysis of Technical Progress

Shintani, Masahiko. 1970. "Meiji Chuki Suito Seisan ni Kansuru Suryo Bunseki" (Econometric analysis of paddy rice production in the middle Meiji era). Nogyo Keizai Kenkyu 42: 97101. Shintani, Masahiko. 1971. "Senzen Nihon Nogyo no Gijutsu Shimpo to Fukyu ni Kansuru Benseki" (Technological innovation and its diffusion in prewar Japanese agriculture). Paper presented at the annual meeting of the Japanese Association of Theoretical Economics, Tokyo. Theil, H. 1963. "On the use of incomplete prior information in regression analysis." Journal of the American Statistical Association 58: 401-414. Tsuchiya, Keizo. 1955. "Nogyo ni Okeru Seisan Kansu no Kenkyu" (A study of the agricultural production function). Nogyo Sogo Kenkyu 9: 209-262. Uzawa, H. 1965. "Optimum technical change in an aggregative model of economic growth." International Economic Review 6: 18 31. Yamada, S. 1967. "Changes in output and in conventional and nonconventional inputs in Japanese agriculture since 1880." Stanford University Food Research Institute Studies 1: 371-413.

IV INPUT-OUTPUT AND THE ANALYSIS OF SOCIALIST ECONOMIES

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11 The SYRENA (SYnthesis of REgional and NAtional Models) Model Complex A. G. GRANBERG, V. E. SELIVERSTOV, V. I. SUSLOV, and A. G. RUBINSHTEIN

GENERAL PRINCIPLES Studies of multiregional input-output models and models of two-level economic systems—distinguishing between the "national economy" and the "regions"—have been conducted in the Institute of Economics and Industrial Engineering (IEIE) for more than fifteen years. During the first stage of this work, multiregional models were developed separately from regional models and were considered only as an instrument for the computation of centrally planned projections and analyses. As the studies devoted to regional models have advanced, however, the situation for a growing number of regions has changed: multiregional models have become an important instrument for the synthesis and coordinated solution of individual regional models. The main construction principle of the SYRENA (SYnthesis of REgional and NAtional economic models) model complex is as follows. A detailed description of the "central" elements (which are of special interest) is completed by an aggregated presentation of the remaining elements of the national economy (Figure 11.1). The SYRENA model complex consists of national-level models (with and without a regional specification) and models of the first-level regions (macrozones, union republics, and economic regions). There are three types of multiregional model in the SYRENA complex: 1. Different versions of the balanced multiregional input-output model (Nauka, 1983) 2. Optimizing multiregional input-output models (OMIOM) with a scalar or vector objective function (in particular cases, these models contain relationships specifying production, consumption, and incomes for the population concerned) (Granberg, 1973). 3. Models of optimal economic interaction of regions with local objective functions (Rubinshtein, 1983).

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Input-Output and the Analysis of Socialist Economies

FIGURE 11.1 Structure of the SYRENA (SYnthesis of REgional and NAtional economic models) model complex.

Moreover, within the SYRENA framework studies were conducted on the coordination of solutions for two-level systems on the basis of 1. A decomposition procedure giving the optimal multiregional distribution of centralized resources1. 2. The application of regional response functions.

OPTIMIZATION OF A MULTIREGIONAL INPUT-OUTPUT MODEL OMIOM is a result of the development and integration of the system of regional input-output balances described by

where XR, YR = gross and final output vectors of the Rth region AR = matrix of input-output coefficients in the Rth region S = number of regions This system is modified for inclusion in OMIOM by two operations: 1. The output is disaggregated into two types: output on old fixed assets set up before the plan period (denoted by a superscript °) and output on new fixed assets set up during the plan period (denoted by a superscript"). 2. Some components of final output are fixed exogenously (QR, which includes the change in stocks, the replacement of losses, the trade balance, and other elements of final output), whereas other components are endogenous (VR, UR, repairs to capital and investment for production; ZR, nonproduction consumption, the inflowoutflow balance; XRS, the outflow of production from the Rth region to the Sth region; XSR, the corresponding inflow of production).

The SYREN A Model Complex

163

The model takes into account linkages between neighboring (bordering) regions, with $(R) denoting a set of regions that are neighbors of the jRth region. The set of equations given by (1) are transformed into the following set:

where aR is the sectoral structure of nonproduction consumption and Efs, MSRR are the inflow-outflow matrices. Investment requirements are formalized as where DOR, D R are the matrices of dimension 2 x n giving machinery and construction input needed for repairs to capital. Regional balances for productive investments are given by where BOR, B R are the matrices of total investment output ratios for a period and HR is the total production investment for a period. The variables giving investment for the last year UR and total investment over a given period HR are related by a formula derived from the assumption of an exponential growth rate 0 (constant for all years of the period) for each type of investment:

The regional structure of labor resources is exogenous, and the labor constraints are where LOR, L R are the labor output ratios and LR is the projected limit on labor resources. The regional structure of nonproduction consumption is expressed as follows: where AR is the share of the Rih region in the national total of nonproduction consumption, S« = 1/1K = 1, and Z is the national total of nonproduction consumption. The volume of output on old fixed assets is limited by upper bounds: where NR is a vector of production capacities available at the beginning of the plan period. Some components of the vectors denoting output produced using new fixed assets can be limited as follows: For extractive industries the upper bounds correspond to the amount of resources available.

164

In 162 Input-Output and the Analysis of Socialist Economises

FIGURE 11.2 Structure of the model regional block. The objective function is to maximize the national total of nonproduction consumption: The structure of the regional block of the model is shown in Figure 11.2. The coefficients 7, ft are parameters of the approximation formula used for condition (5), with £t, £2 being the corresponding variables. The structure of the coordination block linking the Rth and 5th regions is shown in Figure 11.3. In the interregional block there is also a column vector As describing the allocation of consumption across regions.

BALANCED MULTIREGIONAL INPUT-OUTPUT MODELS The main assumption used in OMIOM is that units of output of the same good are substitutes, whether they are produced in the region or imported from other regions. As the sectoral and regional classifications used are highly aggregated, it is reasonable to use an alternative version of the multiregional input-output model of the balanced type (a modification of the Moses-Isard model [Moses, 1960]). In this version of the model the inflow of production to each region is considered to be noncompetitive, that is, units of output of the same good are regarded as being different if they come from different regions. The two principal equations characterizing the multiregional balances are

The SYREN A Model Complex

165

FIGURE 11.3 Structure of the model coordination block. where ARXR + YR is a vector of total consumption in the Rih region. Two types of balance models can be distinguished, denoted the W-model and the V-model. To build the W-model one defines, on the basis of equation (12), a system of so-called trade coefficients GRS (a diagonal matrix) so that Obviously, 1,RGRS = I. Since these coefficients are fixed, the VF-model equations are the result of substituting values from equation (13) for the variables XRS into equation (11) for each region: where G = block matrix, with typical block {GRS}; A= block-diagonal matrix, with typical block {AR}; X,Y = vectors composed of XR and YR, respectively. This model is known as the Moses model (Moses, 1960). To build the V-model one applies the "inverse procedure." From (11) one finds coefficients \SR (a diagonal matrix) so that

Obviously, £ S A M = /. These coefficients are also fixed so that one substitutes values for the variables XRS from equation (14) into equation (12) for each region. The Kmodel equations are where A is a block matrix with typical block {ASR}. The two models complement one another in the sense that in the first model the structure of production consumed in each region is constant for all regions acting as suppliers, and in the second the structure of production produced in each region is constant for all regions acting as consumers.

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Input-Output and the Analysis of Socialist Economies

An analysis of the productivity of the matrices in the models considered gives the following results: The matrix GA in the FF-model is productive, that is, (7 — GA) ' > 0, under every system of trade coefficients G if and only if there exists a price vector P ^ 0, with P the same for all regions, satisfying the condition PAR < P for R = 1,S. To prove that this condition is necessary a separation theorem can be applied. Let us call matrices AR, R = 1,S, possessing the property mentioned interproductive. In contrast, the matrix GA is nonproductive under every G if and only if there exists a price vector P ^ 0 satisfying PAK > P for R = 1,S. In this case let us call the matrices AR internonproductive. If the matrices AR are neither interproductive nor internonproductive, then the matrix GA can be both productive and nonproductive, with the outcome depending on G. For example, if matrices AR, R = 1,S, are productive but not interproductive, then under some G matrix GA can be nonproductive. Similarly, if the matrices AR, R = \,S, are nonproductive but not internonproductive, under some matrices G the matrix GA can be productive. The last example is a good illustration of the interaction effect: regions with nonproductive matrices AK, which cannot function under autarchy, can produce a viable system through cooperation. Similar conditions of matrix productivity were not derived for the K-model. In other words, the existence of a nonnegative solution to this model depends not only on A but also on A and Y. The importance of the concepts of interproductivity and internonproductivity goes beyond the framework of the FF-model. The concepts can be considered concepts of productivity in multiregional systems in general. Specifically, the productivity properties of the mean input^ output matrix for the system 1IRARRR (where RR is a diagonal matrix giving the weights of the Rth region in total production) are similar to those of the matrix GA. Internonproductivity of the regional matrices AR results in the nonexistence of a solution to the optimization multiregional model (under a nonnegative right-hand side). Conversely, a solution of this model can exist even if all regional matrices AR are nonproductive but are not internonproductive. The balance models can be applied both to the analysis of the hypothetical territorial proportions and for projections. In the second case, they can be used on the one hand as a "tool" for analyzing solutions of more sophisticated optimization models. On the other hand, optimization models can be added for a number of sectors and regions in the block of interregional exchange of production, with relationships describing multiregional linkages and using exogenous parameters being obtained from balance models. ECONOMIC INTERACTION MODEL By using the optimal solution generated by OMIOM one can calculate regional production exchange balances measured in shadow prices. These estimates can be used as indicative indices to measure the "pure contribution" of a region to a national aggregate of nonproduction consumption and therefore to characterize the efficiency of the regional economy. Thus, for a fixed interregional structure of nonproduction consumption, the OMIOM determines the corresponding vector of regional production exchange balances (the vector of regional pure contributions).

The SYREN A Model Complex

167

The economic interaction model (EIM) solves a problem that is precisely opposite. Under a priori given regional balances DR one is to define the interregional structure of nonproduction consumption (values A*). Thus in the EIM, the consumption of a region is a function of its pure contribution to the national aggregate of nonproduction consumption. The EIM structure is as follows. Under fixed prices Pfs and Pf* for the /th product exported from the Sth region and imported to it, respectively, each region maximizes its regional aggregate of nonproduction consumption ZR subject to the constraints given by equations (2) through (6), (8), and (9) and the supplementary conditions: The price vector P = (Pfs, P?R) is an equilibrium if there exist equilibrium optimal solutions of the regional subproblems, that is, if there are optimal solutions satisfying the conditions for all tradeable products / and trading regions S and R2. If equilibrium prices do not exist, individual regions cannot provide the given values of balances DR, that is, the a priori demand for a "pure contribution" of these regions to the national aggregate of consumption in the model framework is exaggerated. In this case one can consider quasi-equilibrium solutions in the following sense.3 Regions providing the given balances DR maximize their aggregate of nonproduction consumption, as in the initial problem, but regions that cannot provide the given DR minimize their imbalances (i.e., minimize the difference from the given DR). Thus quasi-equilibrium solutions ensure the minimum difference from the a priori given values of the resulting pure contributions of regions to the national aggregate in the case when the latter cannot be achieved. Equilibrium and quasi-equilibrium solutions of the EIM, like OMIOM optimal solutions, are Pareto optimal, that is, no region can attain a higher value for its aggregate fund of nonproduction consumption without decreasing its value in at least one other region. The EIM solutions, in contrast to the OMIOM solutions, satisfy a more strict set of requirements for optimality in problems with multiple criteria, in that they belong to the so-called feasible nondistinct core.4 The OMIOM and EIM solutions are closely related. If one fixes the balances DR obtained through the OMIOM solution in the EIM, then the EIM equilibrium or quasi-equilibrium solution coincides with one of the OMIOM optimal solutions. Moreover, equilibrium (or quasi-equilibrium) prices are proportional to the corresponding optimal dual variables of equations (2) in the OMIOM solution. The inverse relationship is the following. If one defines the interregional structure of nonproduction consumption by using the EIM solution and fixes it as the vector giving the interregional structure of consumption in the OMIOM, then the optimal OMIOM solution coincides with one of the EIM solutions. The relationship just described is applied in the algorithm used for the EIM solution, which is based on the iterative solution of problems like the OMIOM with repeated adjustment of the interregional structure of consumption described by A*.

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Input-Output and the Analysis of Socialist Economies

APPLICATION AND DEVELOPMENT OF THE SYRENA MODEL COMPLEX The main elements of the SYRENA model complex considered above have much in common. First, the models use the same data base, and the regional input-output blocks are presented in a similar way. Second, the models are formally (mathematically) interrelated and their software has many common components. We regard the different types of models described here as complementary instruments for applied investigations, and we consider that the best way to apply them is as an interrelated complex. The object that is under study using the SYRENA model complex is the process of multiregional economic interaction and the development of regions in the framework of the national economy of the Soviet Union. The SYRENA model complex is oriented to solve the following problems: 1. To estimate hypothetical territorial proportions from the point of view of improving national economic efficiency. 2. To project long-trend perspectives for territorial proportions in the Soviet Union. 3. To study trends and perspectives of the development of the large regions in the framework of the national economy. 4. To analyze processes for narrowing the gap in the levels of economic development and living standards between regions. 5. To study the territorial aspects of intensifying development and improving efficiency. 6. To study the impact of large-scale national and regional economic programs on the process of territorial development in the Soviet Union. 7. To estimate the effects, from the national economic point of view, of the formation of territorial-production complexes of national importance. The SYRENA complex has been used for a number of years to develop regional sections for the complex program of technological progress (covering a period of two decades), and to carry out preplanning studies of the problems of large regions, specifically those of the Russian Republic and Siberia, in the framework of the national economy. Recently, the organizations of a number of Union republics (the Ukraine, Kazakhstan) and regions of the Russian Republic (the Urals, the Far East, etc.) have joined the SYRENA complex as external cooperating bodies. For this purpose coordinated studies are conducted to create specialized multiregional USSR models with corresponding regional blocks (the Urals, Kazakhstan, Far East, etc.) and to install these models on the computers of the organizations mentioned. This work will lead to advanced studies on the modeling of regional development perspectives in the framework of the national economy. The construction of the SYRENA complex provided opportunities to gain a deeper insight into a number of different problems: the interaction of social and technological factors, the interaction of production and transport, the development of individual regions, and others. The principles of construction and analysis used for the SYRENA model complex were applied to the development of models of the world economy and socialist economic integration (Granberg and Menshikov, 1983; Granberg and Rubinshtein, 1984). This study was conducted in cooperation with the Projections and Perspective Studies branch of the U.N. Secretariat. In some respects

The SYREN A Model Complex

169

the studies on the modeling of world economic development and socialist economic integration were more advanced than those of interregional interactions in the USSR economy. Here we should mention: 1. 2. 3. 4.

The application of the material-value multiregional classification. The combination of global optimization and economic interaction models. The combination of input-output and macroeconomic models. The incorporation of a national economic model into the initial version of the world multiregional model.

An important line of extension of the range of application of the SYRENA model complex is the incorporation of "second level" regional models and blocks describing large regional programs. This study has started to connect blocks describing the "Krasnoyarski region" and the "Primorye region" with the operating regional blocks for East Siberia and the Far East. The lines along which the SYRENA model complex is being developed include both modification of the basic model complex (the development of material-value multiregional models, of multiregional input-output models with a financial block, of a more sophisticated presentation of dynamic and social aspects of territorial development, etc.), and improvements in the specification of the external linkages of the SYRENA complex with regional and national economic models. The intention is to construct a "buffer" between the SYRENA complex and a system of macroeconomic, econometric, material-value, material-financial, and other models that are used in the perspective studies of economic regions. To combine the SYRENA complex with operating models for Union republics, a model complex developed in Latvia has currently been chosen for a test study.

AN EXAMPLE SCENARIO The principal method of application of the SYRENA model complex is scenario analysis. A scenario is a study of an important perspective problem, or a combination of probable problem situations, which calls for specialized model projections under varying conditions and parameters. The application of the SYRENA model complex to the study of individual regional perspectives in the framework of the national economy involves two types of scenario: national and regional. The former deals with the impact of the pattern of national economic development on regional perspectives, while the latter investigates the consequences of probable changes inside a region, both for the region itself and for the national economy. A scenario studying the regional, multiregional, and national consequences of a change in the efficiency with which material resources are utilized, and the associated costs, is taken as an illustration of the application of scenario studies to the role of the Siberian region in the national economy of the Soviet Union. To investigate the consequences of possible fluctuations in the material-output ratio, a series of variants with varying input-output ratios for fuel, metals, wood, and other materials was compared with the "central" variant. Figure 11.4 characterizes the response of aggregate indices describing economic growth for Siberia and the Soviet Union as a whole to material-output ratio changes within an interval of + 20 percent. For changes in the interval +10 to —20 percent, the national economic indicators are changing monotonically (growth rates of national income and consumption are increasing, whereas the growth rate of gross product is decreasing).

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Input-Output and the Analysis of Socialist Economies

FIGURE 11.4 Changes in the material-output ratio and their effects on growth rates.

However, if the material-output ratio were to increase by more than 10 percent, the growth rate of gross product would diminish. The responses of the Siberian economy are of a more complicated nature. Siberian growth rates for gross product increase in both cases, that is, both when material-output ratios increase and when they decrease, but for essentially different reasons. In the first case the increase in material-output ratios requires enforced growth of the extractive industries and construction, resulting in a sharp increase in investment demand. In the second case the expansion is due to the accelerated growth of manufacturing in this scenario. Scenario studies enable us to conclude that in future the dependence of the growth rates and economic structure of Eastern areas on the parameters of national economic development, and in particular on the intensive development of industry in the European areas of the Soviet Union, is likely to increase. There are two reasons for this. First, the Eastern areas provide nearly all the incremental output for fuel, nonferrous metals, energy-intensive chemical products, and wood products. Second, because of limited labor resources and investment, fluctuations in traditional "Siberian" branches will lead to substantial changes in growth rates for complementary and associated industries (e.g., machine-building and light industry). If the growth rate of investment diminishes, the share of Siberia and the Far East in total investment also declines. The response of this region to the increase of investment efficiency is an acceleration of growth compared with the national economy as a whole, because Siberia receives investment released from the European area. All the variants with varying investment volumes prove the economic value of investment allocation to Siberia and the Far East in advancing growth.

The SYREN A Model Complex

171

Because of the shortage of labor in Siberia, an equal increase in labor productivity in all regions results in a higher economic effect. The gap in growth rates increases in favor of Siberia. However, labor shortage in the region becomes still more acute, and this has a negative impact on the development prospects of laborintensive industries. This phenomenon can be explained by a specific mechanism characterizing the economic interaction of Siberia with other regions (above all, with European regions): to provide for their advanced development, European regions demand ever greater increases in the extraction and processing of raw materials, which come mainly from the Eastern regions of the Russian Republic. The problem can be resolved if the growth of labor productivity in Siberia outstrips that in other regions. The effectiveness of this strategy of intensive development is much enhanced if it is supported by simultaneous measures to ensure the release of investment and economy in the use of material resources in the European area. The high efficiency of the Siberian economy is proved by computations using the Economic Interaction Model of the regions of the Soviet Union. Two types of computation were undertaken: 1. A search for situations in which the pattern of economic development is characterized by zero regional inflow-outflow balances, where these balances are calculated using the dual variables of the production problem (corresponding to the equilibrium prices). This type of situation is interpreted as a situation of balanced interregional exchange. The computations showed that in the only equilibrium solution, the national aggregate of nonproduction consumption decreases slightly compared with the OMIOM optimal solution, but the consumption share of Siberia increases considerably. 2. An analysis of the core of the economic system was conducted by considering the feasible outcomes for potential coalitions of regions. We found that the total effect of regional interaction (the emergency effect) is more than half of the final indices of national economic development; Siberia provides more than half of the total effect.

NOTES 1. This procedure was implemented for the problem "West-East" described in Granberg and Tchernishev (1970). 2. A model formulated in this way is a particular case of a problem with conventional centers. For each pair of trading regions two centers are considered: one for production exported from the Rth region to the Sth, the other for imported production. Prices Pfs and PS,K in this case correspond to the prices in these centers. 3. This definition is close to the one given in Dantzig, Eaves, and Gale (1979). 4. The core or nondistinct core is defined as a set of solutions satisfying a condition that no coalition R'eR = {1, • • • , S} or nondistinct coalition (Ekeland, 1979, pp. 101-108), which is characterized by nonempty R'eR and fixed regional shares in the coalition Hs[0,1], can improve (blockade) the corresponding vector of values of regional objective functions in the Pareto sense. These (classical) definitions can only be applied for a problem with zero balances DR. For a case with nonzero balances, feasible coalitions or nondistinct coalitions are considered as R' for which RZR. DR < 0 or fi£^. HRDR < 0. We can call solutions that cannot be blocked by feasible coalitions or nondistinct coalitions the feasible core or feasible nondistinct core, respectively.

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REFERENCES Dantzig, G. B., B. G. Eaves, and D. Gale. 1979. "An algorithm for a piecewise linear model of trade and production with negative prices and bankruptcy." Mathematical Programming 16: 190-209. Ekeland, I. 1979. Elements d'economie mathematique (in French). Paris: Hermann. Granberg, A. G. 1973. Optimization of Territorial Proportions of the National Economy (in Russian). Moscow: Ekonomika. Granberg, A. G., and S. M. Menshikov (Eds.). 1983. Interregional Inter sectoral Models of the World Economy (in Russian). Novosibirsk: Nauka. Granberg, A., and A. Rubinshtein. 1984. "Some lines of development of the United Nations global input-output model." In Proceedings of the Seventh International Conference on Input-Output Techniques. New York: United Nations, pp. 33-48. Granberg, A. G., and A. A. Tchernishev. 1970. "A problem of optimal territorial planning 'West-East'" (in Russian). Izvestya Sibirskago Otdelenya Akademii Nauk SSSR (Social Sciences series), Vol. 2, No. 6. Moses, L. 1960. "A general equilibrium model of production, interregional trade and location of industry." Review of Economics and Statistics 42: 373-397. Nauka. 1983. Multiregional Input-Output Balances (in Russian). Novosibirsk: Nauka. Rubinshtein, A. G. 1983. Modelling of the Economic Interactions in Territorial Systems (in Russian). Novosibirsk: Nauka.

12 A Planning Scheme Combining Input-Output Techniques with a Consumer Demand Analysis: A Concept and Preliminary Estimates for Poland LEON PODKAMINER, BOHDAN WYZNIKIEWICZ, and LESZEK ZIENKOWSKI Much of the actual central economic planning in the socialist (centrally planned) economies has been based on input-output techniques. Apart from planning and analytical exercises that respect literally the fundamental equation X = (/ — A ) - 1 Y , many multisectoral models of resource allocation are formulated in a more relaxed way, for example as linear programming problems allowing underutilization of capacity in some industries, expansion in others. In either form the application of input-output techniques for centrally planned economies, though undoubtedly adequate in reflecting the supply side of the economies concerned, has tended to be deficient in representing the linkages to the economies' demand side. In particular, the private consumption component C of the vector of final demand Yis usually assumed to be exogenously prescribed—and therefore may not correspond to the true notional demands implied by the circumstances. The ensuing consumer market disequilibria (shortages) may result in more than a subjective feeling of dissatisfaction with the working of the economy. Through a feedback that has been studied by many authors (see the work of Malinvaud, 1977; Muellbauer and Portes, 1978; and Podkaminer, 1986), market disequilibria may spill over into labor markets, reducing labor supply and inducing labor shortages and thereby precipitating a deterioration in production efficiency throughout the economy. If the flexibility of wages and consumer prices is low, some degree of disequilibrium in consumer markets may be unavoidable. (Also, as developments in the market situation in Poland during the period 1980-1985 have proved, high—but misguided—flexibility of prices and wages may bring about accelerating inflation without substantial equilibration of the markets.) However, the structure of the "exogenously" prescribed vector of private consumption and the resulting size of the wage fund may both significantly contribute to market disequilibria. In this chapter we try to elicit alternative policies that could have led to

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Input -Output and the Analysis of Socialist Economies

equilibrium in Poland's consumer markets in 1977. Apart from the policy of accepting the observed pattern of production and consumption while leaving the burden of adjustment to changes in consumer prices, we try to indicate policies that allow for more or less dramatic changes in the composition of output and employment. THE DEMAND SIDE Private consumer demand is assumed to conform to the ELES (extended linear expenditure system) as studied in Lluch, Powell, and Williams (1977). The notional (Marshallian) demand functions for that system are given by the following expressions:

where qi = quantity demanded of ith good. Pi = price of ith good. ci, bi = good-specific parameters (committed consumption, marginal budget share). d = parameter giving marginal propensity to consume. y = total disposable monetary endowments of consumers. m = number of goods. Although the ELES has been found to lack some theoretically desirable properties, and its estimation may entail some biases (especially when there is little variation in the observed prices), none of its rivals seems to fare much better in actual applications, especially when the level of aggregation is rather high. Following Podkaminer (1982), we specify the equations (1) for Poland on the basis of the comparative studies presented in Lluch et al. (1977). We consider m = 7 aggregates of goods consumed: 1. 2. 3. 4. 5. 6. 7.

Food, alcohol, tobacco ("food"). Clothing and footwear ("clothing"). Rent, fuel, electricity ("housing"). Furniture, domestic utensils ("furniture"). Health, personal services ("health"). Transport and communication ("transport"). All remaining services ("rest").

There are three alternative sets of parameters d, b, c that we shall apply in parallel. These three sets have been estimated on the base of statistical data relating to three West European countries: Ireland, Italy, and the Federal Republic of Germany. These "outside" sources of information reflect better, in our opinion, the "true" demand of the Polish consumer than the parameter estimates that would have been obtained using Polish data, which are affected by permanent market disequilibria. It is worth noting that when the quantities demanded qi are fixed (as equal to the supplies), it is possible to determine the corresponding equilibrium prices. These are given by the following formulae:

Planning Combining Input-Output and Consumer Demand Analysis

175

TABLE 12.1 Estimates of equilibrium prices for actual supplies of 1977 (observed 1977 prices = 1.0) Variant of ELESb Parameters Good"

Food Clothing Housing Furniture Health Transport Rest

1

2

3

0.804 1.118 1.450 3.160 0.464 2.291 2.383

0.934 0.723 2.173 1.366 1.406 1.406 1.281

0.702 0.939 2.505 3.082 1.470 1.332 2.333

a

See text for items included in each category. Extended linear expenditure system.

b

Of course, the formulae (2) are well defined as long as the supplies qi are bigger than the "substance consumption" parameters ci.

PURE STRATEGIES FOR CONSUMER MARKET EQUILIBRATION By applying the formulae (2) to the consumer's monetary endowments of 1977 and the quantities of private consumption observed in 1977 (qio) we arrive at the prices that would have equilibrated consumer markets without any reallocation of resources within the production sphere. These equilibrium prices are reported in Table 12.1. According to the estimates set out in Table 12.1, the restoration of market equilibrium in the consumer market would have required massive increases in the prices of housing, furniture, transport, and rest, while at the same time leaving room for some decrease in food prices. The other extreme equilibrating strategy would have stipulated that prices should be fixed at their actual 1977 levels, and would have computed suitable modifications in supplies to match the notional demands. By applying the formulae (1) to the actual prices of 1977 and the consumers' monetary endowments of 1977 we learn that these equilibrium supplies are rather different from the recorded ones (see Table 12.2). Table 12.2 indicates that the fixed-price strategy for the restoration of equilibrium may not have been realistic, at least in the short run. While it would not have been impossible to reduce the supplies of food and clothing, as suggested by Table 12.2, the twofold to threefold increases in the supplies of housing, transport, and rest seem totally impossible. A LINEAR-PROGRAMMING MODEL COMBINING I-O BALANCES AND MARKET EQUILIBRIUM CONDITIONS Apart from the two extremal pure strategies for the restoration of consumer market equilibrium just outlined, there are many more intermediate ones. The combination of moderate price rises and reallocations of resources from the industries supplying less heavily demanded goods (food, clothing) to those producing the goods with least adequate supplies may provide better policy options (i.e., options that are both

176

Input-Output and the Analysis of Socialist Economies TABLE 12.2 Estimates of supplies equilibrating consumer markets with unchanged 1977 prices (1000 million 1977 zlotys) Variant of ELES b Parameters I

2

3

Actual Consumption, 1977

Food Clothing Housing Furniture Health Transport Rest

484.4 170.4 153.5 134.9 18.5 203.5 87.3

539.4 118.8 215.5 67.8 83.2 113.8 113.2

442.3 156.1 144.7 116.0 50.0 114.3 186.1

560.7 151.7 111.4 47.3 35.5 94.0 91.2

Total

1353.5

1269.7

1310.0

1091.8

Gooda

a

See text for items included in each category. Extended linear expenditure system.

b

realistic, assuming moderate growth rates for individual sectors, and socially more palatable, since they limit the extent of price changes). Another factor worthy of consideration is the possibility of reducing the aggregate fund of wages through a reallocation of some labor from the sectors producing less heavily demanded goods, while paying relatively high wages and using large amounts of intermediate inputs, to other sectors that produce outputs for which there is more demand and have lower direct and full wage input costs. A simultaneous mathematical determination of the best admissible decisions over the set of consumer prices and quantities (produced and consumed) is, at least for the time being, out of our reach. Leaving to one side the purely computational difficulties inherent in such a simultaneous—and highly nonlinear—optimization, we do not feel competent to express satisfactorily the socially desirable trade-offs between price changes and greater resource (i.e., labor) mobility. The approach followed instead proceeds by determining the quantities produced and consumed, satisfying both I-O properties and market equilibrium conditions, for alternative vectors of consumer prices. More specifically, for various "reasonable" consumer price vectors P = (P1, P2, ..., P7), we build and solve versions of the linear-programming (L-P) model with the quantities as decision variables. After analyzing the solutions of these models (dual prices, sensitivity, slack variables) we can either modify the initial assumptions about the price vectors or iteratively grope for other, more promising, price changes. Constraints of Basic L-P Models Input-Output Properties where X = gross output vector. I —A = Leontief matrix. C, G,F,E = vectors of personal consumption, public consumption, fixed capital formation, and exports.

Planning Combining Input-Output and Consumer Demand Analysis

177

The fourteen-coordinate private-consumption vector C is related to the seven consumption goods aggregates through the following linear relationship: where D is a (7,14) disaggregation (or composition) matrix. X, C, Q, and E are treated as vectors of decision variables. G and F are fixed at their 1977 levels. The only exception to this rule is the f12 component of the F vector. /12 (construction investment) is assumed to depend on the size of the demand for housing q3. The semifunctional dependence is expressed by the following continuous piecewise linear formula 1 :

Other Relationships Total employment where L = total employment. Xjj = gross output, jth sector. a] = direct unit labor requirement, jth sector. Total wages and salaries, including other labor incomes where W is the total of wages and wj is the direct unit wage rate, jth sector. Imports where M = total imports. pf = import price, jth sector. aj = unit import requirement, jth sector. Exports where e' is exports, jth sector, and pj is export price, jth sector. Foreign trade balance The magnitudes L, W, M, E, and Bal are decision variables. In various runs of the model they have, or have not been, constrained by upper (or lower) bounds. Similarly, to exclude unrealistic solutions that require radical structural changes and a degree of mobility of labor or transferability of exports that does not exist, we have often

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Input-Output and the Analysis of Socialist Economies

restricted the gross outputs of particular sectors (allowing a maximum 10 percent growth rate) and exports (allowing a maximum 15 percent change in either direction). Consumer Market Equilibrium Conditions

where qi = private consumption, ith good. ci, d, bi = fixed ELES coefficients. Pi = fixed price, ith good. 5 = that part of population's disposable monetary endowments other than wages (cash balances, grants, pensions, etc.), fixed at observed 1977 level. W = fund of wages. It should be noted that with qi and W variables, equation (11) is a system of linear inequalities with respect to the decision variables. The systems of constraints equations (3) through (11), eventually complemented by additional lower and upper bounds on particular variables, define sets of more or less realistic plans for production, consumption, exports, imports, employment, and wages which could have been implemented in 1977 without substantial violation of the basic I-O properties and without producing market disequilibria with respect to the seven major aggregates of goods. Imposing various optimization criteria that seem worthy of social approval (maximum consumption, maximum foreign trade surplus, etc.) upon the systems of constraints, and resorting to the usual simplex algorithms, we have elicited many examples of overall economic policies seemingly superior (if only in that they guarantee consumer market equilibrium) to the actual policy selected in 1977.

TWO SETS OF RESULTS The utilization of the linear-programming model defined above requires repeated runs of the computer calculations. When prices are set too low, or too-low upper production bounds are assumed, the program is likely to return the answer "no feasible solution." Since we do not intend to overwhelm the reader with a mass of confusing details, we shall report only two sets of runs executed under different assumptions. Set I

The basic assumption for this set doubled the price of housing. However that was not enough. In addition we had to allow for increases in the production of particular sectors. A 10-percent growth limit proved sufficient to produce reasonable results. (However, the necessary growth rate for the production sectors defined as "wood and glass" and "construction" appeared even higher, ranging from 20 to 36 percent). In this set we assumed that the exports of all producing sectors could grow by up to 15 percent. Because we imposed no lower limit on exports, the optimum computed

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Planning Combining Input-Output and Consumer Demand Analysis

volume of exports fell in some versions of the solutions by 80 percent, which hardly seems to be realistic. The repercussions for other variables (e.g., employment) also made their changes unrealistic in this set of results. Tables 12.3, 12.4, and 12.5 characterize the nature of the solutions to the models of Set I.

Set II The basic assumptions made here differ from those underlying Set I in that the exports of any production sector are not permitted to vary from the actual 1977 levels by more than 15 percent. In addition we "changed" the consumer prices, lowering the food price by 20 percent and raising other prices: housing by 100 percent; furniture by 90 percent; health, transport, and rest each by 30 percent. The rise in the overall price index corresponding to the assumed changes is equal to 10 percent. (This is quite modest when compared with the inflation rate we have learned to live with in the 1980s.) Total employment was assumed not to exceed the actual 1977 level by more than 1 percent. Tables 12.6, 12.7, 12.8, and 12.9 illustrate the economic nature of the solutions to the models constituting Set II.

CONCLUSIONS The research we have conducted so far is certainly more concerned with testing the model and with learning about its manifold possibilities than with actual data. Nevertheless it seems evident that, first, the restoration of equilibrium, although entailing some sacrifices (some price rises), is not out of the economy's reach. Yet at the same time the proposition, often overstressed, that equilibrium should be restored only through the reallocation of resources and the expansion of output (with consumer prices being kept constant) must be characterized as unrealistic. Second, it would be difficult to restore internal equilibrium in the consumer market and at the same time increase the volume of net exports, without a substantial decrease in the TABLE 12.3 Optimum consumption in 1977 (1000 million 1977 zlotys) (first set of assumptions, see text) Criteerion: Maximnum Perso al Consum, ption

Criteerion: Maxinmm Ba lance of Tratde

b Va iant of ELES Pammete,rs

Gooda Food Clothing Housing Furniture Health Transport Rest Total a

1

2

3

438.7 150.9 95.3 118.4 16.4 178.8 166.1

492.1 108.5 113.4 59.7 75.4 118.0 102.7

428.1 150.3 125.1 109.9 47.3 107.3 175.3

1164.6

1069.8

1143.3

See text for items included in each category. Extended linear expenditure system.

b

I

2

3

433.2

486.6

95.3 118.8 16.4 179.3 166.6

113.4 59.7 117.1 118.1 102.8

420.8 219.3 125.4 117.1 47.4 107.6 175.8

1235.6

1111.7

1221.3

219.5

108.5

Actual Consumption, 1977 560.7 151.7 111.4 47.33 35.5 94.0 91.2 1091.8

TABLE 12.4 Optimum gross output in 1977 (1000 million 1977 zlotys) (first set of assumptions, see text) Criterion: Maximum Personal Consumption

Criterion: Maximum Balance of Trade

Variant of ELES a Parameters Sector Coal and energy Fuel (without coal) Transportation equipment Other machinery Chemicals Wood and glass Light industries Food and agriculture Transport and communication Trade Housing Construction Other material goods and services Nonmaterial services Total a

Extended linear expenditure system.

Actual Output. 1977

1

2

3

1

2

3

110.3 108.4 221.3 450.6 213.6 160.0 338.2 905.3 255.3 283.2 40.2 412.7 504.3 208.3

116.3

107.2

203.6 451.9 245.6 121.4 243.1 990.9 243.2 254.9 45.3 575.7 563.3 193.1

126.3 114.8 206.3 535.7 247.0 168.7 311.1 909.8 279.4 49.5 683.5 624.5 215.0

221.4 450.2 174.7 160.0 395.9 908.8 254.6 286.9 40.3 412.4 502.5 208.4

114.3 91.3 203.6 446.9 226.1 121.2 242.3 993.0 242.6 256.6 45.3 575.7 581.2 194.5

123.2 95.7 205.6 495.3 210.4 173.6 406.8 914.2 256.9 283.8 49.7 685.7 614.1 215.0

201.4 117.6 267.2 589.5 245.7 132.0 369.8 1220.3 299.8 272.4

4211.7

4357.2

4729.9

4212.9

4334.6

4730.0

5144.2

108.9

258.1

89.6

45.6 523.3 668.4 191.2

TABLE 12.5 Optimal employment in 1977 (1000 persons) (first set of assumptions) Criterion: Maximum Balance of Trade

Criterion: Maximum Personal Consumption

Variant of ELES a Parameters Sector Coal and energy Fuel (without coal) Transportation equipment Other machinery Chemicals Wood and glass Light industries Food and agriculture Transport and communication Trade Housing Construction Other material goods and services Nonmaterial services Total a

Extended linear expenditure system.

1 262.0 46.1 439.1 1031.1 290.1 536.2 862.5 3451.0 1124.7 1230.2 93.9 1351.6 1022.3 2514.8 14255.6

2 276.4

46.3

404.0 1034.0 333.5

406.8 620.0 3777.3 1071.2 1107.4 105.7 1885.3 1141.8

3

1

300.6 48.8 409.3 1225.8

254.8 38.1 439.3 1030.0 237.3 536.2

335.5 565.2 793.3 3468.2 1137.0 1213.8

1009.6 3464.6 1121.4

1246.5

2332.3

115.6 2238.6 1265.8 2596.1

1350.5 1018.6 2516.0

14542.0

15713.6

14356.9

94.0

2 271.7

38.8 404.0 1022.5 307.0

406.2 618.0 3785.2 1068.7 1114.5 105.7 1885.3

3 292.7 40.7 407.9 1133.3 285.8 581.8 1037.3 3485.1

1131.7 1232.9

115.9

Actual Employment, 1977 478.6 50.0 530.0 1348.9 333.6 442.4 942.9

4652.1 1320.5 1183.3 106.4

1714.2

2349.0

2245.7 1244.7 2596.1

1353.9 2308.4

14554.8

15831.6

16765.2

1178.2

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Input-Output and the Analysis of Socialist Economies

TABLE 12.6 Optimum consumption in 1977 (1000 million 1977 zlotys) (second set of assumptions, see text) Criterion: Maximum Balance of Trade

Criterion: Maximum Personal Consumption

Actual Consumption,

Variant of ELESb Parameters Good" Food Clothing Housing Furniture Health Transport Rest Total

1

- -_

- -

2

3

1

2

3

1977

566.0

645.7

509.0

566.0

645.2

508.2

560.7

168.2 95.3 73.8 14.6 157.5 148.0

118.1 95.3 32.8 66.6 102.5 90.9

157.4 96.6 68.1 40.0 88.3 145.8

168.2 95.3 73.8 14.8 157.5 148.0

118.4 95.3 32.8 101.4 137.4 90.9

170.9 96.4 72.1 88.6 182.6 145.5

151.7 111.4 47.3 35.5 94.0 91.2

1223.4

1152.4

1105.3

1223.5

1221.4

1264.4

1091.8

"Sec text for items included in each category. b Extended linear expenditure system.

real level of consumption. However if one goes too far in this direction the result may be another episode of social unrest. In the future we shall be extending the scope of the alternative scenarios so as to be able to map comprehensively the eeonomy's responses to various price and other conditions. Also, we plan to repeat the whole study using data for more recent years. The whole study seems to us to be of the utmost practical importance. For, as the statistics for Poland's economic development since 1977 prove, government actions on prices and on production and consumption patterns have taken the opposite course to that which we have found rational. There have been relative increases in the prices of food with the prices of other, less well-supplied, goods falling behind. As far as the reallocation of resources is concerned, we have witnessed a major shift of all resources including the labor force from manufacturing and housing to the primary sectors. To us, therefore, it is not surprising that since 1978 the Polish economy has been displaying a major recession in production and consumption, coupled with hyperinflationary tendencies, and acute and deteriorating consumer market disequilibrium. ACKNOWLEDGMENT We thank Bozena Lopuch for programming work and computer calculations.

NOTE 1. In a static I O analysis, housing construction - an activity directly linked to the fulfilment of current consumer needs —is classified as capital formation. Without the relationship (5) it may appear incorrectly that a significant growth in the consumption of housing is possible without the construction of any new homes. Unfortunately this is not so. The specific numbers f12, q3, a, S appearing in (5) have been established in a separate study.

TABLE 12.7

Optimum gross output in 1977 (1000 million 1977 zlotys) (second set of assumptions, see text) Criterion: Maximum Balance of Trade

Criterion: Maximum Personal Consumption

Variant of ELES a Parameters

1

2

3

1

2

3

Actual Output, 1977

Coal and energy Fuel (without coal) Transportation equipment Other machinery Chemicals Wood and glass Light industries Food and agriculture Transport and communication Trade Housing Construction Other material goods and services Nonmaterial services

186.8 118.5 284.4 568.2 225.7 145.5 382.8 1212.5 314.3 306.2 41.5 438.8 633.5 206.5

193.8 119.1

186.7 117.9

188.5 118.6

285.8 584.9 262.7 115.0 312.0 1336.3 292.0 283.5 50.1 440.3 659.9 192.0

212.5 119.3 282.6 606.5 254.4 146.6 387.1 1156.2 302.0 282.8 50.1 458.2 677.0 206.8

284.4

201.4 117.6 267.2 589.5 245.7

382.8 1212.5 314.3 306.3 41.5 438.8 633.6 206.5

277.3 549.7 270.3 114.5 312.0 1337.1 306.4 291.1 41.3 439.3 665.6

191.2 123.9 293.9 573.8 270.3

193.1

389.7 1131.2 327.0 302.0 42.1 449.8 675.1 208.6

369.8 1220.3 299.8 272.4 45.6 523.3 668.4

Total

5062.2

5127.4

5142.1

5065.7

5104.8

5125.7

5144.2

Sector

a

Extended linear expenditure system.

568.1

225.8

146.5

146.6

132.0

191.2

TABLE 12.8 Optimum export, import, and balance of trade in 1977 (1000 million 1977 zlotys) (second set of assumptions, see text) Criterion: Maximum Personal Consumption

Criterion: Maximum Balance of Trade

Variant of ELES a Parameters Sector

1

2

3

1

Actual Exportsd,

2

3

1977

53.4 13.2 52.7

62.8 15.6 63.1 119.8 38.4 13,2 41.0 49.7 48.7 2.7 —

Exports: Coal and energy Fuel (without coal) Transportation equipment Other machinery Chemicals Wood and glass Light industries Food and agriculture Transport and communication Trade Housing Construction Other material goods and services Nonmaterial services

53.4 13.9 53.7 101.8 32.7 11.2 34.8 42.2 41.4 2.3 — 15.1 32.6 —

57.3 17.9 72.6 137.7 44.2 11.2 34.8 42.2 41.4 2.3 8.9 15.1

53.4 13.2 53.7 101.8 32.7 11.2 34.8 42.2 41.4 2.3 — 15.1 32.6

53.4 13.2 53.7 101.8 32.7 11.2 34.8

32.6

72.2 17.9 72.6 137.7 44.2 13.5 47.1 55.6 56.0 3.1 8.2 20.4 44.1

2.3 — 15.1 32.6

32.7 11.2 34.8 42.2 41.4 2.3 — 15.1 32.6

Total exports

435.0

518.3

592.7

434.4

434.4

434.4

511.0

Total imports

597.2

603.0

608.5

597.0

607.5

621.7

602.7

-162.2

-84.7 7

-15.8

-162.6

-173.1

-187.3

-91.7

Balance of trade a

Extended linear expenditure system.

42.2 41.4

101.8

17.8 38.3

TABLE 12.9 Optimum employment in 1977 (1000 persons) (second set of assumptions, see text) Criterion: Maximum Balance of Trade

Criterion: Maximum Personal Consumption

Variant of ELES a Parameters

Actual Employment,

Sector Coal and energy Fuel (without coal) Transportation equipment Other machinery Chemicals

1 443.8 50.4 564.3 1299.9 306.5

2 460.6 50.6 567.0 1338.2 356.8

385.4

3 504.8 50.7 560.6 1387.7 345.4 491.1 987.0

1 443.7 50.1 564.3 1299.9

2 447.9 50.4 550.2 1257.6

367.0

306.6 491.0 976.2 4622.0 1384.3

383.7 795.8 5097.1

Wood and glass

491.0

Light industries Food and agriculture Transport and communication Trade Housing Construction Other material goods and services Nonmaterial services

976.2 4622.0 1384.4 1330.3 96.9 1437.0 1284.2 2493.1

1228.7 117.0 1500.5 1372.2 2496.7

1330.5

1264.6

117.0 1442.0 1337.6 2317.8

1437.0 1284.3 2493.1

16780.0

16780.0

16780.0

16780.0

Total "Extended linear expenditure system.

795.5 5094.0

1286.1 1231.3

4407.4 1330.2

96.9

3 454.2 52.6

583.1 1312.9 367.0 491.0

993.6

1977 478.6 50.0 530.0

1348.9

333.6

442.4 942.9

1438.6 1349.3 2331.7

4312.1 1440.3 1314.3 98.2 1472.9 1368.5 2519.2

4652.1 1320.5 1183.3 106.4 1714.2

16780.0

16780.0

16765.2

1349.8

96.3

1353.9

2308.4

186

Input-Output and the Analysis of Socialist Economies

REFERENCES Lluch, C., A. A. Powell, and R. Williams. 1977. Patterns in Household Demand and Savings. Oxford: Oxford University Press. Malinvaud, E. 1977. The Theory of Unemployment Reconsidered. London: Blackwell. Muellbauer, J., and R. Portes. 1978. "Macroeconomic models with quantity rationing." Economic Journal 88: 788-821. Podkaminer, L. 1982. "Estimates of the disequilibria in Poland's consumer markets, 19651978." Review of Economics and Statistics 64: 423-431. Podkaminer, L. 1986. "Investment cycles in centrally planned economies: An explanation involving labor shortage and consumer markets' disequilibria." Acta Oeconomica 35: 133-144.

13 Some Macroeconomic Features of the Hungarian Economy Since 1970 L. HALPERN and G. MOLNAR

In introducing the "New Economic Mechanism" in 1968, the reformers of the Hungarian economy hoped to solve the problem of efficiency in a socialist economy. We show that the survival of the structure of prices and accumulation that had existed before the reform, and the interrelationship between them—among other factors— hindered the necessary transformation in the economic structure. In addition, slow adjustment, or in practice the refusal to adjust, to the explosion in world prices in the mid 1970s has led to a critical level of foreign indebtedness for the Hungarian economy. Cheap foreign loans financed investment projects of very low efficiency, while export capacity remained far below the level necessary for debt servicing. A critical point was reached in 1978, when economic policymakers decided to restrict imports, consumption, and investment to be able to service foreign debts. In 1980, simulation of world market prices was introduced to stimulate adjustment. Since then economic activity has been almost stagnant. In this chapter we present the quantitative aspects of this process, using a closed input-output model to analyze the Hungarian economy since 1970. Simultaneous analysis of the primal and dual sides of the model provides relevant results. To apply the closed model to an open economy, we have added a foreign trade sector to the model using an exogenously given export-import ratio. An index is defined to measure changes in the structural efficiency of the economy. This index helps us to demonstrate the efficiency profile of the Hungarian economy and its connection with foreign trade activity. THE MODEL The well-known primal-dual model we used is as follows: and

188

Input-Output and the Analysis of Socialist Economies

where A B X, P /

= = = =

Matrix of input-output coefficients Matrix of capital output ratios Vectors of gross output and price rate of accumulation or profit; assuming constant coefficients it can be interpreted as a long-term rate of growth

The theoretical model is derived from Brody (1970). It contains twenty sectors, fifteen commonly used sectors, foreign trade, and the labor sector, and was computed for every year from 1971 to 1983, using different A and B matrices for each year. In the case of foreign trade, input is volume of exports and output is volume of imports. Thus a closed model was used for ex-post empirical investigations of an open economy. To resolve this contradiction we used exogenous export-import ratios. Since the process describing indebtedness is nonstationary, the changing export/ import ratio reflects the external position of the economy: a ratio greater than 1 shows net debt servicing, whereas a ratio less than 1 implies net loan disbursement. It is supposed that any import surplus will be repaid using the export surplus earned in following years. For any given year the import surplus reduces the costs of total imports in the economic structure. In the opposite case the export surplus is also broken down using the import structure. This procedure reflects a special feature of the Hungarian economy—the fact that the most import-intensive sectors benefited primarily from foreign credits in the 1970s. The labor sector's input is consumption, while its output is the wage bill. A large proportion of consumption is financed by means other than wages, such as allowances and benefits. In measuring the costs of reproduction of the labor force, consumption is a better measure than wages, and therefore, while we kept the sectoral wage structure constant, we multiplied the wage vector by the consumption/wage ratio. These two modifications are sufficient to ensure that the initial data for the model are closed in the way necessary for their use.

COMPUTED PRICES The most characteristic feature of the computed prices, which are shown in Table 13.1, is that they showed high stability all through the period under examination, whereas differences are considerable between the sectors. The same sectors that were overvalued or undervalued 1 in 1971 remained so in 1979. What is more, only three sectors changed their character during the whole period: Mining, undervalued between 1972 and 1974, overvalued in other years Food-processing industry, slightly overvalued in 1973, undervalued in other years Home trade, slightly overvalued in 1981, undervalued in other years All the other sectors were either overvalued or undervalued throughout the period. Furthermore the comparative levels hardly changed either. If, omitting mining, the sectoral price indices were ranked for 1971 and 1979, the ranking of the sectors would be identical, except for two changes of position. It follows, clearly, that while prices deviated permanently from costs during the 1970s, nevertheless they were in some way related to the latter, since prices and costs

TABLE 13.1 Computed prices by sectora (actual price = 1) Sector

1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

Mining Electricity Metallurgy Machinery Building material industry Chemical industry Light industry Food-processing industry Industry (aggregate) Construction Agriculture Transport, communication Home trade Foreign trade management Water management Material services Material sectors Personal, etc., services Health, etc., services Communal, etc., services Nonmaterial services Services (aggregate) Consumption Accumulation Exports

0.98 0.81 0.79 0.78 0.88 0.71 0.84 1.03 0.85 0.90 1.18 1.13 0.82

1.02 0.79 0.86 0.82 0.85 0.76 0.89 1.03 0.88 0.90 1.17 1.14 0.79

1.09 0.82 0.87 0.83 0.87 0.81 0.92

1.14 0.84 0.77 0.77 0.86 0.82

0.94

0.86 0.88 0.85 0.80 0.87

0.83 0.90 0.88

0.82 0.84 0.81

0.63 0.73 0.77

0.77

0.77

0.88

0.69

0.71 0.87

0.89 0.69 0.85 1.09 0.84 0.91

0.84 0.86 0.80 0.79 0.89 0.73

0.58 0.68 0.82 0.89 0.87 0.66 0.97

0.56 0.68 0.86 0.88 0.87 0.70 1.00 1.10 0.86 1.00

0.70

0.60

1.93 1.00 0.94 2.04 1.32

1.64 0.96

0.56 0.67 0.85 0.89 0.89 0.66 0.99 1.09 0.86 1.00 1.10 1.08 1.01 0.99 1.48 1.08 0.95 1.64 1.33 1.25

a

1.19 1.48 1.20 1.12 0.93 0.89

0.95 1.82 1.30 1.22 1.43 1.15

1.10 0.95

0.91

0.98

0.89 0.91 1.14 1.11 0.79

0.63 1.74 0.96 0.95 1.77

1.31 1.25 1.42 1.15 1.08 0.95 0.93

0.90 1.04 0.87 0.89 1.18 1.14 0.79 0.53 2.14 0.97 0.95 1.84

1.35 1.22 1.45 1.17 1.10 0.94 0.91

0.92 0.82 0.78 0.87 0.73

0.85 1.08 0.86 0.91 1.19 1.14 0.86 0.51

2.28 1.01

0.95 1.90 1.37 1.20 1.47 1.20 1.11

0.95 0.90

Weighted by gross output at actual current prices: The producers' price level is 1.

0.87 1.06 0.86 0.92 1.17 1.12 0.88 0.59

2.11 1.03 0.95 1.85

1.39 1.25

1.49 1.22 1.12 0.95 0.89

1.10 0.87 0.90 1.15 1.12 0.88 0.52

2.23 1.02

0.95 1.82 1.40 1.26 1.49 1.21 1.12 0.93 0.89

1.17

1.13 0.89 0.50 2.27 1.04 0.94 1.92

1.43 1.24 1.52 1.24

1.14 0.93 0.88

0.89 1.11 0.86 0.91 1.17 1.11

0.88 0.62 1.92 1.02 0.95 1.74 1.38 1.21 1.44 1.20 1.12 0.93 0.89

0.90 0.88

0.63 0.96 1.09 0.85 0.98 1.13 1.15 0.97 0.84 1.40 1.07 0.95 1.72

1.31 1.25 1.42 1.24 1.13

0.98 0.92

1.08 0.85

1.00 1.12 1.11 1.00 0.85 1.50 1.08

0.95 1.64 1.33 1.25 1.40 1.23

1.13 0.98 0.93

1.41

1.23 1.13 0.99 0.93

1.12

1.08 0.98 0.93 1.32 1.05 0.95 1.54 1.33 1.21 1.36 1.20 1.12 0.98 0.93

190

Input-Output and the Analysis of Socialist Economies

moved "in parallel" in a certain sense. The computed price indices changed in a relatively stable fashion between the two extreme points of the period. With a few exceptions, these changes began by a reduction in the undervaluation or overvaluation, and then price indices went back to near to their initial values. During the 1980s there have been considerable changes in industry. Overvaluation has increased in mining, electricity, and (to a smaller extent) the chemical industry. The position for industry as a whole has not changed, since overvaluation in machinery and light industry has decreased. Another change, compared with the 1970s, is that the computed price of construction is equal to the actual price. These changes are due to the introduction of so-called competitive pricing in 1980. This means the simulation of world market prices, implying that enterprises with considerable hard currency exports can use the microprofitability ratio achieved on Western markets on home markets. In the case of primary goods, world market prices were introduced. This led to the reduction of micro and macro profitability for enterprises in the processing industry, and an increase in the relative income of the primary sectors. This is reflected in the changed valuation of the industrial sectors mentioned above. Chemical Industry as an Example of an Overvalued Sector The overvaluation of the chemical industry fell by 11 percent between 1971 and 1974, and then went back to near the original level within a year. At that time the chemical industry was again the most overvalued sector, if foreign trade management, of peripheral importance, is not considered. In 1976 the overvaluation grew further, and then fluctuated gently around the level that had been reached. The reduction in overvaluation between 1971 and 1973 can be explained largely by the fact that the import surplus of the national economy was transformed into an export surplus, and therefore the chemical industry (with the highest intermediate import coefficient) lost some of its relative advantages over the other sectors. The further rise in the computed price index in 1973-1974 was the consequence of the rising costs of imported materials because of changes in foreign prices. In one year, the coefficient of intermediate imported inputs into the chemical industry rose from 30.6 to 40.2 percent. Some factors acted against the reduction in overvaluation. The ratio of fixed capital to output fell considerably, and the actual chemical industry price grew faster than the industrial average from 1973 to 1974. All in all the macro profitability of the chemical industry fell to its lowest level in 1974, but even so it was still among the most profitable industries. The reduction in overvaluation was followed by a considerable price increase, of 17.7 percent, from 1974 to 1975, which restored at one stroke the initial level of overvaluation. The changes in the second half of the 1970s were much smaller, and were related to fluctuations in output prices and the import surplus. In 1980 the introduction of competitive pricing, with a 24-percent price increase, implied a rise of 11 percent in overvaluation. During the early 1980s there was considerable import substitution. Intermediate import costs were practically stagnant, while intermediate domestic input costs rose very fast. By 1983 the level of overvaluation reached 70 percent, a level characteristic of the second half of the 1970s.

Some Macroeconomic Features of the Hungarian Economy Since 1970

191

Agriculture as an Example of an Undervalued Sector The undervaluation of agriculture fluctuated around a level of 18 percent. By 1973 its undervaluation had fallen a little, due partly to a low rate of price increase and partly to reduced relative wage costs. In 1974 its intermediate import costs grew suddenly, although still not reaching half of the industrial average (and compensated by price subsidy). In the following year, however, agricultural prices did not grow—as was the case with the majority of industrial prices—but fell. And yet the extent of undervaluation barely grew, since the industry adjusted successfully, and the intermediate import coefficient was reduced. In 1975 agricultural profitability dropped to a very low level. The price increase of 1976 restored the earlier level of undervaluation, and some of the price subsidies were stopped. The slight price reductions during the rest of the period were neutralized by technological change, which was characteristic not only of these three years but of the whole of the 1970s. The wage coefficient fell from 45 to 37 percent in the course of nine years, the coefficient of intermediate input costs grew from 55.4 to 63 percent, while both wages and the prices of inputs used in agriculture grew faster than agricultural output prices. To sum up the analysis of the computed price indices, we can state that at the beginning of the period, the level of overvaluation in the overvalued sectors, as well as the level of undervaluation in the undervalued sectors, generally fell, implying that the price scissors closed. In the following years this process was reversed and the computed prices stabilized at the level that characterized the early period. We have shown (Halpern and Molnar, 1985) that if the price scissors narrow at the same time that import prices grow and the rate of accumulation starts to increase, the system of income redistribution gets into a difficult situation. In such a case, either this system has to be adjusted flexibly to conform with the new conditions or, more simply, the price scissors must be opened again, implying that the prices of the overvalued sectors should be raised. It is the latter policy that was put into practice. In this interpretation it was the policy of maintaining the trends and proportions of the income redistribution system that led to the increase in the prices of the overvalued sectors. Thus the pattern of sectoral income, accumulation, and prices—closely linked by income redistribution—reproduced itself, resisting changes and ensuring that every effort at a structural transformation directed at one or another component of the complex system was doomed to fail.

COMPUTED PRODUCTION PATTERN At our computed prices, the sectors earn income proportional to their capital, and this enables them to enlarge their capital steadily. For this expansion to be carried out, the pattern of accumulation has to be transformed as well. The computed production pattern obtained as a result of solving the primal problem (1) indicates the direction and dimensions of this transformation. In a simple formulation, sectors whose actual production is larger than their computed production, that is, sectors with an index below 1, are called overproducing sectors, and those whose production is smaller are called underproducing sectors. Table 13.2 presents actual and computed production indices. The sector with the

TABLE 13.2 Computed production by sectora (actual production = 1) Sector

1971

1972

1973

1974

1975

1976

Mining Electricity Metallurgy Machinery Building material industry Chemical industry Light industry Food-processing industry Industry (aggregate) Construction Agriculture Transport, communication Home trade Foreign trade management Water management Material services Material sectors Personal, etc., services Health, etc., services Communal, etc., services Nonmaterial services Services (aggregate) Consumption Exports

0.95 1.01 0.92

0.97 1.00 1.03 0.88 1.09 0.98 1.01 0.98 0.97 1.14 0.99 1.07 1.00 0.97 1.15

0.99 1.00 1.02 0.89 1.03 0.99 0.99 1.00 0.97 1.10 1.01 1.06 0.98 0.98 1.10 1.02 1.00 1.02 1.01 1.00 1.01 1.02 1.01 0.93

0.92 0.99 0.98 0.88 1.02 0.97 0.97 0.99 0.95 1.18 1.02 1.08 0.98 0.96 1.34 1.04 1.00 1.03 1.02 1.01 1.02 1.03 1.01 0.90

0.97 0.98 0.94 0.88 1.01 0.98 0.99 1.02 0.96 1.15 1.01 1.05 0.99 0.97 1.34 1.04 1.00 1.03 1.02 1.01 1.02 1.03 1.01 0.92

3.01 0.99 0.96 0.89 1.07 0.98 0.99 0.97 0.96 1.10 1.03 1.08 0.97 0.96 1.41 1.04 1.00 1.02 1.02 1.01 1.02 1.03 1.02 0.91

a

0.82 0.98

0.95 0.96 0.99 0.93

1.28

1.00 1.11 1.02 0.96 1.38 1.07 1.00 1.05 1.02 1.02 1.03 1.05 1.02 0.91

1.03 1.00 1.03 1.01 1.01

1.02 1.03

1.01

0.92

Computed gross output at the Macro Level is equal to actual gross output.

1977

1978

1979

1980

1981

1982

1983

1.00

1.01 1.00 0.93 0.89 1.03 0.94 0.94 0.96 0.94 1.19 1.02 1.10 1.00 0.93 1.56 1.07 1.00 1.04 1.02 1.02 1.03 1.05 1.02 0.87

1.02 1.01 0.93 0.88 1.02 1.00 1.03 0.99 0.97 1.05 1.03 1.06 1.02 0.98 1.25 1.05 1.00 1.02 1.01 1.00 1.01 1.03 1.01 0.93

0.96 0.97 0.97 0.88 1.04

0.97 0.99 0.97 0.90 1.05 1.00 0.99 0.98 0.97 1.13 1.01 1.04 1.00 0.96 1.29 1.04 1.00 1.02 1.01 1.01 1.01 1.03

0.98 1.01

0.97 1.00 0.98 0.90 1.04 1.01 0.99 1.00 0.97 1.07 1.01 1.04 1.00 0.97 1.22 1.03

0.99

0.95 0.89 1.05 0.98 0.99 0.95 0.95 1.09 1.04 1.08

0.99

0.96 1.48 1.05 1.00 1.03 1.02 1.01 1.02 1.04 1.02 0.89

0.99 0.98

1.00 0.96 1.14 1.00 1.04 1.05 0.98 1.14 1.05 1.00 1.02 1.01 1.01 1.01 1.03 1.01 0.93

1.01 0.94

0.99 0.90 1.04 1.00 0.99 0.98 0.97 1.14 0.99 1.04 1.00 0.97 1.27 1.04 1.00 1.02 1.01 1.01 1.01 1.03 1.01 0.94

1.00

1.04 1.00 1.00 1.02 1.03 1.01 0.97

Some Macroeconomic Features of the Hungarian Economy Since 1970

193

greatest level of overproduction is machinery; that with the greatest level of underproduction, apart from water management, is construction. Additional overproducing sectors, for the whole or a considerable part of this period, are metallurgy, chemical industry, light industry, food-processing industry, and foreign trade management; while permanently underproducing sectors are building material industry, agriculture, transport and communication, water management, and nonmaterial services. The indices of electricity and the home trade sector fluctuate, tending toward overproduction, whereas the mining industry, initially overproducing, becomes an underproducer after 1975 and an overproducer again after 1980. The majority of indices fluctuate rather sharply from one year to another. This fluctuation is mainly influenced by the changing ratio of accumulation and fixed capital formation drawing on the output of the given sector (where the sector concerned delivers to capital formation), since for several reasons this ratio is highly variable. In the case of sectors with a considerable output of such products (equipment, buildings) or sectors closely related to these, the relative extent of accumulation is determined by the investment cycle, which implies, for example, that if machinery output for investment purposes increases significantly the production index of machinery will fall correspondingly. In the sectors where output for accumulation consists mainly of changes in the stocks of the products of the sector concerned—which sometimes even results in a negative demand for accumulation purposes—obviously fluctuations in the index are even more closely linked to the cycle. What interests us primarily is, however, not the cyclical variation of the production indices but their level, which, as with the price indices though to a lesser extent, is rather stable for most sectors. The picture given by the production indices agrees in several of its features with what we know about development preferences. Nonmaterial services, transport and communication, and water management, that is, all services apart from trade, are permanently and to a considerable extent underproducers, so that their economic development (measured by the rate of accumulation relative to the capital stock) is not favored. More information about the preference structure can be found in Halpern and Molnar (1985). There are also important differences that can be observed when indirect interrelationships are taken into account. The most conspicuous feature is the great extent of underproduction in construction, which arises because in the neglected service sectors on average more than three quarters of the fixed capital consists of buildings (in nonmaterial services the figure is more than 90 percent), while in industry this proportion is less than a third. If, therefore, services were to grow in proportion, demand for the output of construction would suddenly grow, while demand for output of machinery would fall. This explains why the production index for machinery is particularly low. It is mainly the underproduction of consumption goods that ensures that agriculture is a considerable underproducer and brings the index for the foodprocessing industry, which appears to have developed faster than average, close to 1. The difference is in the opposite direction for metallurgy, which is an overproducer according to the figures given, although in the late 1970s it experienced a rate of accumulation less than the average. This is because, in spite of a low rate of accumulation, its actual production level is judged to be too high by the model. The computed production pattern consumes fewer imports and more labor than the actual production pattern.

194

Input-Output and the Analysis of Socialist Economies

With a few exceptions the overproducing sectors coincide with the overvalued sectors and the underproducing sectors with the undervalued sectors: this is confirmed by Table 13.3. This rule is the consequence of economic policy toward development and pricing rather than of the characteristics of the model we have applied. The development policy side of this rule during the 1970s was as follows: When accumulation decreases or is growing slowly, the share of industry is low and that of services (especially of nonmaterial services) high. On the other hand, when accumulation grows rapidly, the share of industry (needed for accumulation) is high or increases, while that of services, especially of nonmaterial services, falls. In simple terms this implies that, as a rule, services have a larger share when the volume of accumulation is smaller, while industry's share is higher when accumulation is greater. If, therefore, changes in sectoral growth rates or the sectoral pattern of accumulation are used as distinct arguments or counterarguments in the course of the analysis or formation of macroeconomic policy, this must disguise an intention to promote or hold back the development of one or the other sector. Pricing policy is a necessary tool for the implementation of such a development policy. During the period of socialist industrialization, pricing policy's main function was to ensure the redistribution of incomes. For the most part this role has been maintained. After allocating the resources necessary for the development of the favored industrial sectors, the remaining industrial revenues are reallocated to finance the lower level of development of the other sectors. This linkage between development

TABLE 13.3 Correspondence between valuation and production during years 1971-1983a Overproducer

Overvalued

Mining (71, 75, 80-83) Electricity (73-77, 80-81, 83) Metallurgy (71, 74-83) Machinery Building material industry (72) Chemical industry (71-81) Light industry (71, 73-78, 80-83) Home trade (72-77, 83) Foreign trade management

Mining (72-74) Food-processing industry (71-72, 74, 76-79, 81-83) Agriculture (72, 82) Undervalued
fu.

Application of Lemma 1 yields the result that the total import elasticity is no smaller in absolute value than its direct counterpart, that is, Let us now turn to the concept of direct import substitution. Without going into AND T = 0,1,IN EXPRESSION (14) AND DERIVE THE DIRECT IMPORT SUBSTITUTION IN SECTOR I AS

DETAILS, WE REPLACE

stitution is expressed in terms of a direct supply effect («01) and a demand effect (v0i). Our previous remarks on the direction of total effects also hold good here. Several points of interest now crop up. Will s01 and s01 be identical in direction? Which one will be larger in absolute value? Will the ranking of the sectors be independent of the type of substitution? Equation (15), when divided by equation (18), becomes

which entails the following: 1. sfVs? 1 > 0: direct and total substitution will be identical in direction. 2. s?1/^1 | 1» provided (4/r?-) | (r}Jr§. The relative strength of direct and total substitution depends on the nature and degree of interrelationship among the sectors. 3. Since the ranking of the sectors depends on both direction and magnitude, it may not be independent of the type of import substitution. 4. Indirect import substitution is s?1 = s?1 — s?1 = v01(u01 — u01), which is not independent of the degree of sectoral interrelatedness. ESTIMATES The input-output tables of India for the years 1953-1954, 1960-1961, and 19641965 have been used. All the I-O tables are in 1960-1961 producers' prices. Import

TABLE 15.1 Total import substitution in India (at relative level)

No. a 1 2 3 4 5

6

7 8 9 10 11

12

13 14 a b

u01 0.7926(1 3)b 0.9509(11) 1.0222(3) 0.9772(8) 0.9701(9) 1.0685(2) 1.0114(5) 0.8943(12) 0.9781(7) 1.0170(4) 0.9697(10) 0.7762(14) 0.9841(6) 1.1659(1)

v01 0.0264 0.0429 -0.0092 0.0871 0.2567 0.5500 -0.0252 0.1039 -0.1063 0.0168 -0.0112 -0.0728 -0.0011 0.0109

See text for description of sectors. Figures in parentheses are sector ranks.

1960-61 to 1964-65

1953-54 to 1964-65

1953-54 to 1960-61

cector

s01 0.0209(9) 0.0406(10) -0.0094(5) 0.2806(13) 0.2490(12) 0.5878(14) -0.0255(2) 0.0929(11) -0.0159(3) 0.0171(8) -0.0109(4) -0.0565(1) -0.0011(6) 0.0127(7)

u01 0.8518(14) 0.9526(12) 1.0245(6) 0.9765(10) 1.0522(5) 1.1711(2) 1.0959(4) 0.9278(13) 1.0018(8) 1.0081(7) 0.9852(9) 1.1575(3)

0.9632(11) 1.2429(1)

u01 0.0203 -0.0005 -0.0101 0.1187 0.0143 0.0243 -0.0720 -0.0218 -0.0182 0.0019 -0.0024 -0.0710 -0.0018 0.0132

s01 0.0173(12) -0.0005(8) -0.0103(5) 0.1159(14) 0.0150(10) 0.0285(13) -0.0789(2) -0.0202(3) -0.0182(4) 0.0019(9) -0.0024(6)

-0.0822(1)

-0.0017(7) 0.0164(11)

uo1 1.0746(5) 1.0019(11) 1.0022(10) 0.9993(12) 1.0846(3) 1.0961(2) 1.0835(4) 1.0375(7) 1.0243(8) 0.9852(13) 1.0159(9) 1.4913(1) 0.9787(14) 1.0660(6)

vm -0.0090 -0.0398 -0.0009 -0.0872 -0.1459 -0.1456 -0.0507 -0.0989 -0.0019 -0.0145 0.0089 0.0021 -0.0008 0.0022

s01 -0.0097(8) -0.0399(6) -0.009(10) -0.0871(4) -0.1582(2) -0.1596(1) -0.0549(5) -0.1020(3) -0.0019(9) -0.0143(7) 0.0090(14) 0.0032(13) -0.0008(11) 0.0024(12)

TABLE 15.2 Direct import substitution in India (at relative level) 1953-54 to 1964-65

1953-54 to 1960-61

c* ector

No."

S01

1 2 3 4 5 6

0.7905(13)* 0.9526(11) 1.0209(3) 0.9474(8)

0.9739(9) 1.0746(2)

7 8

1.0080(5) 0.8916(12)

9 10 11 12 13 14

0.9781(7) 1.0164(4) 0.9689(10) 0.7771(14)

0.9842(6) 1.1656(1)

v01 0.0264(9) 0.0429(10) -0.0092(5) 0.2871(13) 0.2567(12) 0.5500(14) -0.0252(2) 0.1039(11)

-0.0163(3) 0.0168(8)

-0.0112(4) -0.0728(1) -0.0011(6) 0.0109(7)

"See text for description of sectors. 'Figures in parentheses indicate sector ranks.

s01 0.0209(9)

0.0409(10) -0.0094(5) 0.2806(13) 0.2500(12) 0.5910(14) -0.0254(2)

0.0926(11)

-0.0159(3) 0.0171(8) -0.0109(4) -0.0566(1) -0.0011(6)

0.0127(7)

S01

0.8486(14) 0.9543(12) 1.0213(5) 0.9774(10) 1.0570(5)

1.1761(2) 1.0973(4)

0.9246(13) 1.0018(7) 1.0016(8) 0.9821(9) 1.1592(3)

0.9634(11) 1.2429(1)

v01

1960-61 to 1964-65

s01

0.0203 -0.0005 -0.0101 0.1187 0.0143 0.0243

0.0172(12) -0.0005(8) -0.0103(5) 0.1160(14)

-0.0182 0.0019

-0.0182(4)

-0.0720 -0.0218 -0.0024 -0.0710 -0.0018 0.0132

0.0151(10) 0.0286(13) -0.0790(2) -0.0202(3)

0.0019(9) -0.0024(6) -0.0823(1) -0.0017(7) 0.0164(11)

u01 1.0735(5) 1.0019(10) 1.0003(11) 1.0000(12) 1.0853(4) 1.0944(2) 1.0886(3) 1.0370(7) 1.0243(8)

0.9854(13) 1.0136(9) 1.4916(1) 0.9616(14)

1.0663(6)

V0i

-0.0090 -0.0398 -0.0009 -0.0872 -0.1459 -0.1456 -0.0507

-0.0989 -0.0019 -0.0145

0.0089 0.0021

-0.0008 0.0022

s01

-0.0097(8) -0.0399(6) -0.0009(10) -0.0872(4) -0.1583(2) -0.1594(1) -0.0552(5)

-0.1026(3) -0.0019(9) -0.0143(7) 0.0090(14) 0.0031(13) -0.0008(11) 0.0023(12)

218

Input -Output and Developing Countries

substitution measures at the relative level (both direct, total, and indirect) experienced by fourteen different aggregated sectors are estimated for three periods: I II III

1953-54 to 1960-61 1960-61 to 1964-65 1953-54 to 1964-65

The aggregated sectors are 1. Agriculture 2. Plantation 3. Coal and coke 4. All other mining 5. Iron and steel 6. Nonferrous metals 7. Engineering 8. Chemicals 9. Cement 10. Glass, wood, and nonmetallic products 11. Food, drink, and tobacco 12. Cotton and other textiles 13. Jute textiles 14. Leather, rubber, and products Table 15.1 gives the estimates of total import substitution, broken down by components, and Table 15.2 the estimates of direct import substitution. The estimates of indirect substitution arc presented in Table 15.3. The following points should be noted. 1. Direct and total import substitution have been identical in direction for all periods. 2. The producing sectors have displayed identical rank ordering with respect to direct and total substitution. TABle 15.3 Sector No.a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 a

Indirect import substitution (s) in India (at relative level)

1953 54 to 1960-61

1953 54 to 1964-65

1960-61 to 1964-65

0.0001 -0.0003 0 0 -0.0010 -0.0032 -0.0001 0.0003 0 0 0 0.0001 0 0

0.0001 0 0 -0.0001 -0.0001 -0.0001 0.0001 0

0 0 0 0.0001 0.0001 -0.0002 0.0003 0.0006 0 0 0 0.0001 0 0.0001

See text for description of sectors.

0 0 0 0.0001 0 0

Import Substitution and Changes in Structural Interdependence

219

3. Import substitution has varied both by sector and by period. During 1953-54 to 1960-61, only six of fourteen sectors enjoyed positive import substitution (both direct and total): coal and coke (sector 3), engineering (sector 7), cement (sector 9), food (sector 11), cotton and other textiles (sector 12), and jute textiles (sector 13). The number increases to eight and eleven during the periods 1953-1954 to 19641965 and 1960-1961 to 1964-1965, respectively. This clearly indicates an increasing tendency over time in the economy toward import substitution. 4. The structural component of import substitution (u01 in the case of total substitution and w01 in the case of direct substitution) has also varied from sector to sector and from period to period. During the first period, 1953-1954 to 1960-1961, w01 and w01 both exceeded unity in the case of only five sectors: coal and coke (sector 3), nonferrous metals (sector 6), engineering (sector 7), glass, wood, and nonmetallic products (sector 10), and leather, rubber, and products (sector 14). Only these five sectors, therefore, have gained from a favorable technological effect on import substitution, leather, rubber, and products (sector 14) being ranked first. But during the period 1960-1961 to 1964-1965, u01 and u01 exceeded unity in the case of twelve sectors, and thus almost all the sectors attained a favorable technological effect on import substitution (direct and total), cotton and other textiles (sector 12) being ranked first. 5. Indirect import substitution for most of the sectors has been either nil or insignificant, as can be seen from Table 15.3. Nonferrous metals (sector 6) deserves special attention. Interestingly, and to an appreciable extent, it has displayed significant positive indirect substitution, although its direct and total substitution have both been negative. CONCLUDING REMARKS First, in this chapter import substitution is estimated only at the relative level. Absolute import substitution is not estimated. Second, imports are taken as perfect substitutes for domestic goods. This is quite consistent with the characteristics of the Indian economy, where all types of imports have domestic substitutes. However, the case of imperfect substitutes may be examined along the lines developed here. Third, competitive imports and domestic outputs are lumped together without distinction, in final demand and intermediate demand, and hence in the input-output balance equations. Intermediate transactions may be decomposed into (1) intermediate transactions of domestic outputs and (2) intermediate transactions of imports, and two separate interindustry transactions matrices may be built, one relating to the interindustry domestic transactions and the other to the interindustry import transactions. Import substitution may then be examined in terms of the "pure" domestic technology matrix (which is formed from the interindustry domestic transaction matrix). We have not experimented with this approach because such a matrix is not available over time for India. NOTE 1. In the case where A is strictly indecomposable so that rj; > 0, Etj = 0 only when nij = 0.

220

Input-Output and Developing Countries

REFERENCES Chenery, H. B., S. Shishido, and T. Watanabe. 1962. "The pattern of Japanese growth, 19141954." Econometrica 30: 98 139. Chenery, H., and M. Syrquin. 1977. "A comparative analysis of industrial growth." Paper presented at 5th World Congress of the International Economic Association, Tokyo. Guillaumont, P. 1979. "More on consistent measures of import substitution." Oxford Economic Papers 31: 324-329. Kubo, Y., and S. Robinson. 1979. "Sources of industrial growth and structural change." Paper presented at 7th International Conference on Input-Output Techniques, Innsbruck, Austria. Morlcy, S., and G. W. Smith. 1970. "On the measurement of import substitution." American Economic Review 60: 728 735. Pal, D. P. 1981. "Structural interdependence in India's economy-an intertemporal analysis." Ph.D. diss., Kalyani University, Kalyani, India. Syrquin, M. 1976. "Sources of industrial growth and change: An alternative measure." Paper presented at the European Meeting of the Econometric Society, Helsinki.

VI THE ANALYSIS OF SOCIAL AND ENVIRONMENTAL PROBLEMS

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16 A Long-Term Projection of the Industrial and Environmental Aspects of the Hokkaido Economy: 1985-2005 FUMIMASA HAMADA

This chapter describes a study that attempts to predict industrial activity and its environmental effects in the central area of Hokkaido for the period 1985 through 2005. An input-output model linked with a small-scale macroeconometric model of Hokkaido was constructed and environmental changes in terms of biological oxygen demand (BOD), nitrogen oxides (NOX), sulfur oxides (SOX), and carbon dioxide (COD) to be emitted by the industrial activities and also by the residents were estimated, to predict the degree of resulting environmental pollution. The study also estimated industrial demands for space, water, fuels, electric power, and workers by individual industries, and the demand of residents in this area for various public utilities. Although many empirical studies of input-output structures have been reported and published since the seminal work of Leontief (1941), an application of inputoutput techniques to industrial and environmental development in a specific area, for which data on economic and environmental circumstances are very limited, is rare. The study reported here is an attempt to develop an analytical method for this type of work, since it is required for the analysis of regional development. First, a macroeconometric model of Hokkaido consisting of seventeen structural equations was constructed. This model determines final demands, such as consumption, investment, and interregional trade, with the levels of local and central government consumption and investment and the real growth rate of the national economy as given. Second, a Hokkaido input-output model was used to determine final demands by fifteen industries. The classification of these industries (Table 16.1) reflects the characteristics of changes in the industrial structure of the Hokkaido area from the viewpoint of the technological production process, such as integrated and nonintegrated, processing and combining, basic and nonbasic transformation, and so forth. This model also determines the real output by these fifteen industries as a whole. Third, by estimating shares of the central area of Hokkaido by industry, real

224

The Analysis of Social and Environmental Problems TABLE 16.1

Industrial classification used in study of Hokkaido-area industries

Name

No.

Industries Included

1

Primary industry

Agriculture, forestry, and fishery

2

Integrated basic materials

Chemicals and petroleum products

3

Nonintegrated basic materials

Textiles, paper and pulps, and ferrous and nonferrous products

4

Integrated process combining

Metal products and general machines

5

Nonintegrated process combining

Transportation and precision machines

6

Integrated other manufactures

Food and wood products

7

Nonintegrated other manufactures

Clothing, printing, leather products, rubber products, etc.

8

Energy

Electric power, gas, and water

Transportation

Transportation

10

Commercial trade

Wholesale and retail

9 11

Services

Services

12

Public services

Public services

13

Financial institutions

Financial intermediaries, insurance, and unclassified

14

Construction

Construction and civil enginering

15

Mining

Mining

output in this area was obtained. Finally, using these estimates for real output by industries, economic and environmental activity levels in this area were predicted on the basis of the assumed growth path of the Japanese economy as a whole for the period 1985 through 2005. OUTLINE OF THE WHOLE SYSTEM As already noted, the aim of this study is to predict the level and structure of industrial activity in the central area of Hokkaido, and its relation to environmental changes. The long prediction horizon (1985-2005) implies that technology will change, as will the tastes and values of consumers, the supply conditions of natural resources, and other locational factors that influence economic activities in this area. The prediction is based on a set of assumptions about the macroeconomic system and technological progress in the field of pollution abatement as well as in the industrial production process. A Macroeconomic Model of Hokkaido A complete system for the determination of income, prices, and output should ideally be constructed as a set of dynamic and interdependent relations between supply of

Industrial and Environmental Aspects of the Hokkaido Economy

225

and demand for outputs. I will, however, assume that the supply elasticity is infinite, and that the scale of the Hokkaido economy is determined from the demand side. I also assume that the volume of final demand depends on that of the Japanese economy as a whole, as well as on the consumption and investment of the Hokkaido government. The price level is assumed to be determined by the national economy through arbitrage. The macroeconomic model of Hokkaido was estimated by ordinary least squares for the sample period 1965 through 1982. The estimated model is as follows: Consumption (CP)

Housing Investment (h)

Fixed Investment (i)

Inventory Investment (j)

Exports to Other Domestic Areas and Abroad (e)

Imports from Other Domestic Areas and Abroad (m)

Implicit Price Deflator for Consumption (pc): 1975 = 1

Implicit Price Deflator for Housing Investment (ph): 1975 = 1

Wholesale Price Index (p w ): 1975 = 1

226

The Analysis of Social and Environmental Problems

Personal Disposable Income (y) at 1975 Constant Prices where pc, ph, and pw are the rate of change in the consumption deflator, housing investment deflator, and wholesale prices, respectively. ra is the long-term rate of interest. Data on the Japanese macro and Hokkaido macro variables for the national and regional accounts produced by the Economic Planning Agency (annual) were used. Other price indices were available from the Bank of Japan (monthly). This macromodel determines real disposable income y, real consumption CP, real housing investment h, real fixed investment i, real inventory investment j, real exports e, real imports m, and consequently real gross output x, which is given by an identity where gc, gi, and gj are the government's consumption, capital formation, and inventory investment, respectively and are assumed to be exogenously determined. As easily seen, this system is basically demand led, so that the level and movement of exogenous demand are very important in determining the course of the economy in question. Among other factors, the scale of the Japanese economy as a whole and its growth rate regulate the scale and growth rate of the Hokkaido economy. This assumption seems too strong to govern the analysis of the actual economic performance of Hokkaido, but by keeping in mind the fact that the relative share of the Hokkaido economy in the Japanese economy as a whole is about 4 percent (on the basis of GNP), and that the main purpose of this study is not to make an intensive investigation of the industrial structure of Hokkaido but to predict what will take place in this area for the next twenty years, this simplification can be permitted as a first step. Since the Hokkaido economy has its own regional characteristics, the composition of final demand may be different from that in other regions, and this difference should be reflected in the industrial structure in Hokkaido. This is a minimum requirement for a macromodel in this study.

An Industrial Model of Hokkaido and Its Central Area Before determining the industrial structure of the central area of Hokkaido, it is necessary first to construct an industrial model of the Hokkaido economy. Final demands by item are decomposed into demands by fifteen industries, using a converter that is a column vector of dimension 15 x 1. Let Xc be a consumption vector and Vc its converter. Then the consumption vector can be written In the same way, the investment vectors and other final demand vectors are written as follows:

Industrial and Environmental Aspects of the Hokkaido Economy

227

where Xt is a final demand vector for the sum of housing investment, fixed investment, and inventory investment; Xe is a final demand vector for exports outside of Hokkaido; and X0 is the sum of other final demands. Ve and V0 are the corresponding converters. Next, real output levels by fifteen industries are determined, using an inverse matrix for the Hokkaido economy:

where X is a real output vector for the Hokkaido industries (15 x 1), and R is the inverse matrix (15 x 15), the classification of which is seen in Table 16.1. Since we do not have any reliable data on the input-output relationships specific to the central area of Hokkaido, the only thing we can do is estimate the relative share of real output by industry in this area to that of Hokkaido, and compute real output by industry in this area by multiplying those relative shares by the real outputs by industries for Hokkaido as a whole. Let [Ski] be the relative share matrix for the central area of Hokkaido, where Ski = RXSki/RXk and RXSki is the real output of the kth industry for the ith city; and Skj = RXj/RX where RXj is total real output for the jth town or village and RX is total real output for the Hokkaido economy. Real output by industry and by area can be determined as follows:

Summing up those real outputs by industries and by areas with respect to the areas located in the central area of Hokkaido, real output by industry k for central Hokkaido can be determined as

Calculation for the primary industry (agriculture, forestry, and fishery) and the last industry (mining) turned out to be impossible because of lack of reliable data. Once real output by industry for the area in question is obtained, the number of workers and the demands for space, water, and energy (including fuel and electric power) can be computed by multiplying the corresponding coefficients by real output by industries:

228

The Analysis of Social and Environmental Problems

where SPk is demand for space (square meters), WTk is demand for water (cubic meters per day), EPk is demand for electric power (1975 constant million yen), FEk is demand for fuel (1975 constant million yen), and LBk is demand for workers (persons) by industry k. a, /?, y, e, and r\ are coefficients corresponding to those demands, and n and v are the rates of increase in efficiency and productivity, respectively. Demand for space by the residents LRESD,, and demand for water by the residents WTLIF,, can be written as follows:

where NPOP, is the number of residents and a and /? are constants. The number of residents is assumed to grow at a constant annual rate, so that

where NPOP 0 is the number of residents at the beginning of the prediction period and 7 is an annual rate of increase in the number of residents in the area in question.

An Environmental System for the Central Area of Hokkaido The environmental profile is assumed to be formed through the degree of air pollution by the quantities of BOD, NOX, SOX, and COD that industrial activities and residents will emit in this area. Technological progress will reduce the quantity of these materials per unit of output and per capita, so that the speed of technical progress should be taken into account. The only information on technological progress in this field is available from the reports of some nonprofit institutions and from the Hokkaido Government Office. The procedure used to estimate the quantities of these materials to be emitted is multiplication of the coefficients by real output by industry and by number of residents in the area. We define t;sk as the coefficient for the quantity of the sth material to be emitted per unit of real output by industry k, and £s as the coefficient for the quantity of the sth material to be emitted by one resident. Then the quantity of materials to be emitted by industry k in period t, Skt, is determined as

where /t is an annual rate of technical progress which reduces the quantity of the polluting materials emitted per unit of output by industry k. The quantity of material s to be emitted by the residents, Spt, can be written as

where NPOP, is the number of residents in period t.

Industrial and Environmental Aspects of the Hokkaido Economy

229

A LONG-RANGE PROJECTION: 1985-2005 This section presents a set of computed results of a long-range projection using the combined macroeconomic, industrial, and environmental models discussed in the previous section. First, however, some basic preconditions of the projection developed here should be stated. Basic Preconditions As already mentioned in the introduction, the whole system used in this study is basically demand led. The leading or exogenous demands of the Hokkaido economy are, among others, the rate of growth of the Japanese economy as a whole, the consumption and investment of the Hokkaido government, and exports outside of Hokkaido. The main features are as follows: 1. The annual growth rate of the Japanese economy is about 3.7 percent during the period 1985 through 1991 and is about 4.5 percent after 1992. 2. The growth rate of Hokkaido government consumption is about 3 to 4 percent through the period of projection. 3. The rate of growth of Hokkaido government investment is about 3 to 4 percent during the same period. 4. The rate of inflation is about 1.5 to 3 percent during the same period. These preconditions seem to agree with the general consensus on the present and future state of the Japanese economy. Summary figures are omitted here, but data in more detail are available on request. An Economic Profile On the basis of the preconditions, and using the whole system together with the figures shown in Tables 16.2, 16.3, and 16.4, the time paths of the control solutions for all the endogenous variables were obtained for the period 1976 through 2005. To save space, only the main features of the computed results will be shown here. Figure 16.1 summarizes the time paths of real output by industry in the central area of Hokkaido in terms of growth rates. In the coming twenty years the growth rate will turn out to be higher in the process combining industries such as general machines, transportation machines, and precision machines; in the nonintegrated light industries such as clothing, printing, rubber, paper and pulps; and in ferrous and nonferrous products and construction. This implies that, contrary to a trend on the mainland, the development of manufacturing industries will dominate in the central area of Hokkaido, so that the demand for labor will increase at rather a high rate in this area compared with the mainland. Figure 16.2 shows this feature very clearly—that labor demands will increase in the same industries as those listed here despite increases in labor productivity in these industries. Figure 16.3 shows movements in the growth rates of total demand for fuel, space, and water during the same period. These three are interesting in that the growth rates seem to follow a similar pattern, despite the fact that the demand for these inputs by industries varies considerably: detailed figures showing this are omitted here because of space restrictions.

TABLE 16.2 Induced production coefficients and share coefficients'I Industry No.b

1 2 3 4 5 6 7

8 9 10 11 12 13 14 15

Rc

R1

Re

K»

RXSk/RXk

0.04627 0.03837 0.01696 0.01849 0.00785 0.06255 0.02061 0.03564 0.03655 0.08947 0.11131 0.00142 0.08914 0.00916 0.01932

0.00702 0.01312 0.11335 0.09988 0.03454 0.01746 0.03003 0.03090 0.03050 0.04786 0.01716 0.00000 0.03203 0.27739 0.03023

0.11603 0.05906 0.20855 0.01730 0.01181 0.07891 0.01107 0.03806 0.04068 0.02507 0.03577 0.00006 0.02682 0.00218 0.05017

0.00065 0.01943 0.02308 0.00788 0.00978 0.01435 0.01296 0.04530 0.02815 0.02255 0.17290 0.17857 0.02269 0.00308 0.01405

— 0.46373 0.77773 0.88273 0.69973 0.65073 0.85173 0.45960 0.45960 0.63751 0.45960 0.45960 0.45960 0.45960 _.

"Input-output table for the Hokkaido economy is available in the report of the Hokkaido government (1984); the 1980 table was used in computing the inverse matrix R and the final demands converters Vc, V1, Ve, and V0. See text for description of these converters. 'See Table 16.1 for names of industries.

TABLE 16.3 Environmental coefficients: annual basis" Industry No. b

2 3 4 5 6 7 8

9

10 11 12

13

14

Residents

BOD c (ton)

COD

NOX

SOX

(ton)

(ton)

(ton)

2.963 11.960 0.507 0.246 12.100 7.940

6.749 30.827 0.449 0.199 11.288 7.126 0.811

32.060 48.390 1.857 1.235 10.466 10.585 125.100 81.510 22.240

— — — — — — 18.250

— — ._. -— .._ —

19.600 17.350

23.630 8.690 0.97

25.0100 38.8400 3.4940 4.9420 9.7030 16.5530 302.5000 287.0000 78.5000 69.1700 61.2400 83.4100 30.8600 0.0600

"All coefficients are per unit of real output in 1975 constant million yen. Figures for the residents are per 1000 persons for one year. The annual rate of technical progress to reduce public pollution is assumed to be 0.076 in all cases. b See Table 16.1 for names of industries. c BOD = biological oxygen demand COD = carbon dioxide NOX = nitrogen oxides SOX = sulfur oxides

230

231

Industrial and Environmental Aspects of the Hokkaido Economy TABLE 16.4 Other economic factor coefficientsa Industry Noh

2 3 4 5 6 7 8 9

10 11 12 13 14

Residents

Labor (persons)

Space (m2)

Water (m3/day)

Electric Powerc

Fuel

0.01517 (0.05)11 0.05752 (0.04) 0.11047 (0.04) 0.12099 (0.06) 0.09097 (0.03) 0.18904 (0.02) 0.03573 (0.04) 0.55534 (0.04) 0.89928 (0.03) 0.46192 (0.03) 0.30276 (0.02) 0.23058 (0.07) 0.61248 (0.06) —

22.49

0.2408

0.01791

0.07562

30.70

2.4685

0.10872

0.11383

16.68

0.1528

0.02040

0.03010

13.26

0.0646

0.01470

0.00680

19.80

0.4450

0.01290

0.02960

6.57

0.0558

0.01240

0.00990

16.90

0.0698

—

—

0.8400

—

3.588

0.0866

—

3.162

0.0763

—

2.799

0.0676

—

3.813

0.0920

—

—

0.0457

—

0.15

10.6

—

"Coefficients in all columns are per unit of real output in 1975 constant million yen. b See Table 16.1 for names of industries. c Unit of coefficients is neutral. d Figures in parentheses are the annual rates of technical progress obtained from direct estimation of the production functions by industry as given by Hamada and Chido (1983). The coefficient of space for residents is km2 per 1000 persons, and the coefficient of water for residents is 10,000 ton per 1000 persons. Annual rate of technical progress to save space, water, electric power, and energy is assumed to be 0.03. Sources: Industries 2-7, Japan Spacing Center, 1984; industries 8 14, Japan Industrial Planning and Research Institute, 1977; Columns 1 and 2, Association for Industrial Pollution Problem, 1974; columns 3 and 4, Osaka Prefectural Government, 1982; coefficient for residents, Hokkaido Government, 1984; Japan Sewerage Association, 1980.

An Environmental Profile The environmental profile for the central area of Hokkaido obtained in this study is summarized in Figure 16.4, where the annual rates of growth in total quantity of BOD, COD, NOX, and SOX to be emitted by all industries and residents during the coming twenty years are shown. Although until the first half of the 1980s output of these four materials had been decreasing, the rate of decline has become smaller with

232

The Analysis of Social and Environmental Problems

FIGURE 16.1 Movements of growth rates of real output by industry. Numbers on curves refer to industrial classification; see Table 16.1.

time, because of the increasing growth rate of industrial activities. This tendency is marked for COD, NOX, and SOX. It should be noted however, that if the assumption about technical progress reducing environmental pollution is correct, the area under study will be no problem in the future. Thus the outcome depends on whether this assumption is realistic. Finally, let us sum up the prospect for the Hokkaido economy as a whole. According to the prediction made using a macroeconometric model of Hokkaido, the rate of economic growth in this area will be slightly higher than that on the mainland. The most remarkable feature is the growth in housing investment, at a rate of about 10 percent annually. This growth can be thought to have brought about industrial development in Hokkaido, together with the growth rate of more than 5 percent in private fixed investment and exports.

Industrial and Environmental Aspects of the Hokkaido Economy

233

FIGURE 16.2 Movements of growth rates of demands for labor by industry. Numbers on curves refer to industrial classification; see Table 16.1.

ACKNOWLEDGMENTS I am grateful to S. Nakamura and K. Miyamoto, University of Tokyo, and J. Takahashi, Keio University, for their useful comments. I also thank A. Kubo and Y. Shinozaki of The Institute of Industrial Studies for their assistance in gathering data on the environmental variables and coefficients. Y. Maeda assisted in the data processing and estimation of the inverse matrix for the Hokkaido economy.

REFERENCES Association for Industrial Pollution Problem (Sangyo Kogai Boshi Kyokai). 1974. "General feature of pollution load factor on emitted smoke." (Haien ni Kansuri Osen Fukaryo Gentani Chosa Kekka Gaiyo). Tokyo, Japan.

234

The Analysis of Social and Environmental Problems

FIGURE 16.3 Movements of growth rates of demands for space (SP), water (WT), and fuel (FE).

FIGURE 16.4 Movements of growth rates of polluting materials. COD, carbon dioxide; SOX, sulfur oxides; NOX, Nitrogen oxides; BOD, biological oxygen demand.

Bank of Japan. (Monthly). Economic Statistics Monthly (Kleiziai Toukei Geppo). Tokyo: Bank of Japan. Economic Planning Agency. (Annual). Annual Report on National Accounts. Tokyo, Japan. Hamada, F. 1984. A Macroeconometric Analysis of Japan (Nihon-Keizai no Macro Bunskei). Tokyo: Nihon-hyoron Sha. Hamada. F'., and R. Chido. 1983. "Direct estimation of production function by industry." Keio Economic Studies 20: 33 66.

Industrial and Environmental Aspects of the Hokkaido Economy

235

Hokkaido Government. 1984. Input Output Tables of Hokkaido: 1980. Hokkaido, Japan. Japan Industrial Planning and Research Institute (Sangyo Kenkyu Sho). Tokutei Chiiki 0 Taisho To Sum Chiikikankyo Keizai Sogo Model. Tokyo, Japan. Japan Sewerage Association (Nihon Gesuido Kyokai). 1980. Report on Global Planning of Sewerage Construction by Basin (Ryuiki Betsu Gesuido Seibi Sogo-Keikaku Chosa). Tokyo, Japan. Japan Spacing Center (Nihon Ricchi Sentaa). 1984. Report on Manufacture Locational Unit Survey (Kogyo Ricchi Gentani Chosa Hohkoku). Tokyo, Japan. Leontief, W. 1941. The Structure of the American Economy, 1919-39. New York: Oxford University Press. Osaka Prefectural Government (Osaka Fu). 1982. A Brief Outline of Global Planning of Osaka Living Environment (Osaka Fu Kankyo Sogo Keikaku Gaian Kisoshiryo). Osaka, Japan.

17 An Application of Input-Output Techniques to Labor Force Allocation in the Health and Medical and the Social Welfare Service Sectors YOSHIKO KIDO

The ageing of Japanese society had been and will continue to be very rapid compared with other developed countries. The proportion of the elderly (65 years old and over) to the total population in 1970, 1980, and 1985 was 7.1, 9.0, and 10.1 percent, respectively. The Ministry of Health and Welfare forecasts that this proportion will be 14 percent in 1996. This implies that the time needed for the proportion to change from 7 to 14 percent is only twenty-six years in Japan. In contrast, in West Germany and the United Kingdom forty-five years are needed; in Sweden eighty-five years; and in France (the slowest case) 115 years are needed for such a change in the age structure of the population. The same estimates show that the proportion of elderly people in the year 2000 will be 15.6 percent and that the number will peak in 2020 at 21.8 percent. This will be the highest proportion among the developed countries. The increase in number of elderly, especially those seventy five years old and over, causes an increase of demand for health, medical, and social welfare services. The increase in demand for these services usually leads to an increase in demand for labor in these sectors. At the same time Japan will face a decrease in the population of working age (fifteen to sixty four years old), as well as ageing of the working population, since the proportion of those aged forty and over in the work force will increase. Therefore the allocation of the labor force across industries, and the application of technological innovation in all industries, especially in the health and medical and the social welfare sectors, are now becoming very important problems. In general it is very difficult to make a quantitative analysis of manpower needs in the social policy field (the health and medical and social welfare service sectors). However in this chapter we treat the requirement for workers in these sectors in the same way as the demand for labor in ordinary industries, and we analyze the industrial characteristics of these sectors, consider their interrelations with other industries, and try as far as possible to set out a quantitative analysis. For this purpose we apply input -output techniques to the problem of labor force allocation.

237

Application of Input-Output Techniques to Labor Force Allocation

LABOR INPUT COEFFICIENTS IN THE SOCIAL POLICY SECTOR The application of input -output techniques to labor force allocation is based on the usual principles of I-O analysis for goods and services. It aims at measuring how much additional labor is needed in a specific industry, elsewhere in the economy, and in total in response to a unit increase in the demand for the good and service produced by that specific industry, or a unit increase in one of the final demand components (e.g., private consumption expenditure or government expenditure). This technique of analysis takes into consideration, therefore, the direct and indirect effects on the demand for labor generated in one of the industries. As a preparatory step for such an analysis of the close interrelations between industries, we consider the coefficient showing the amount of labor input needed for the production of a unit of output in each industry, and we discuss the characteristics of industrial activity in the health and medical and the social welfare sectors. The labor input coefficient considered here is the amount of labor input per unit of output, defined as the total number of workers in each industry divided by the corresponding total volume of output. Table 17.1 shows the labor input coefficient in both sectors, calculated at 1980 constant prices, for the years 1970, 1975, and 1980. These years are chosen because we will use the 1970-1975-1980 Link Input-Output Table, recently published by the TABLE 17.1 Labor input coefficients (persons/billion yen) and labor productivity (index 1970 = 100.0) Health and Medical

Social Insurance and Welfare

Subtotal Social Policy Sector

Aggregate Economy

230.1 243.0 208.8

214.0 173.4 137.3 40.4 27.3 14.4 179.4 148.5 123.8

152.5 130.5 107.8 53.1 39.7 29.2 94.3 85.2 74.3

100.0 105.7 90.0 — — — 100.0 105.6 90.7

100.0 81.0 64.2 100.0 67.6 35.6 100.0 82.8 69.0

100.0 85.6 70.7 100.0 74.8 55.0 100.0 90.3 78.8

Input

Total Self-employed

Employees

1970 1975 1980 1970 1975 1980 1970 1975 1980

208.9 160.7 126.6 40.4 27.3 14.4 166.8 132.1 111.5

234.7 248.1 211.2

— — —

Productivity Total

Self-employed

Employees

1970 1975 1980 1970 1975 1980 1970 1975 1980

100.0 76.9 60.6 100.0 67.6 35.6 100.0 79.2 66.8

238

Analysis of Social and Environmental Problemsems

Japanese government, later in this chapter. The labor input coefficient in this table is expressed in terms of labor requirements per billion yen of output for the health and medical and the social insurance and social welfare sectors, for a subtotal relating to the social policy sector as a whole, and for an aggregate of 158 industries that is added for the purpose of comparison. Separate coefficients are shown for all workers, for the employed, and for the self-employed; the latter defined as entrepreneurs and their family members working together. By definition, the labor input coefficient is the inverse of the productivity of labor measured in terms of output, so that the size of the labor input coefficient indicates the degree of labor productivity. In the case of manufacturing industry, when the labor input coefficient is small, labor productivity is high. In the case of the health and medical and the social insurance and social welfare sectors, however, the validity of this interpretation is restricted. This is because output for these sectors is measured only in terms of expenditures and, especially in the case of the social insurance and social welfare sectors, an important part of expenditure consists of general government consumption. It is therefore impossible to evaluate the volume of output, and labor productivity, in this sector in the same manner as in manufacturing industry. In spite of this restriction we can point out some findings from the table. First, the labor input coefficient in the social policy sector is larger than that for aggregate industry, except in the case of the self-employed, which implies that the social policy sector is more labor intensive than ordinary industry, with the social welfare and social insurance sector being an extreme case. This finding is in accordance with our daily experience and with common sense: In both of the social policy subsectors, close person-to-person services are still expected, as is the help provided by new technologies. Second, the difference in labor input coefficient between the social policy sector and aggregate industry has decreased during the last ten years. This is a result of the large reduction of the labor input coefficient in the former, due principally to a remarkable decline in the health and medical sector. The labor input coefficient in the social insurance and social welfare sector increased at first and then fell by a small proportion. As a result this coefficient remains much higher in 1980 than in the health and medical sector and than in aggregate industry. The reasons this input coefficient increased were institutional factors, such as the increase of the statutory staff/beneficiary ratio in various social welfare facilities and the growth of nursing homes for the elderly and home helpers in the early 1970s. The increase in statutory TABU; 17.2

1970 1975 1980

Labor force inducement effects (persons/billion yen)

Health and medical Social ins. and welfare Health and medical Social ins. and welfare Health and medical Social ins. and welfare

Inducement Direct Total

Ratio

326.2 285.1 243.5 308.7 201.8 276.4

0.6274 0.7641 0.6600 0.8037 0.6404 0.8232

208.9 234.7 160.7 248.1 126.6 211.2

Sensitivity 214.5 234.7 170.8 248.1 139.4 211.2

Labor Input Coefficient 0.7291 0.7978 0.7000 1.0168 0.7062 1.0699

Application of Input-Output Techniques to Labor Force Allocation

239

staff/beneficiary ratios is intended to provide better services to the users of social welfare facilities, so that the quality of output in this sector should have improved at the same time that, the labor input coefficient increased. This discussion indicates the need to be very careful in interpreting the magnitude of labor input coefficients in this sector. In addition, we would expect the labor input coefficient in this sector to be reduced by the usual factors, such as mechanization, the use of better facilities, and improvements to buildings and the environment. These factors are likely to be still more important in the future. In the health and medical sector as well, personal service is the basis of the activity, but increases in labor productivity through new technologies are important as well. TOTAL AND DIRECT INDUCEMENT EFFECTS FOR LABOR The labor input coefficient measures the additional number of workers directly employed for a unit increase in the demand for output (measured in billion yen in this case). However, a unit increase in output demand for a specific industry induces demand for labor in other sectors as well, because of the interdependence of industries. Similarly a unit increase in output demand for all industries induces additional demand for labor in a specific industry such as the health and medical sector. Table 17.2 summarizes these inducement effects caused by industrial interdependence, using the 1970-1975-1980 Link Input-Output Table with 158 industries. The total inducement indicates the total of each column (i.e., those corresponding to the health and medical and the social insurance and social welfare sectors) in the inverse matrix multiplied by the labor input coefficient for each of the 158 industries. Each component of the Leontief inverse of an input-output table is a technical coefficient indicating the amount of additional output in an industry induced by a unit increase in final demand, so the number of workers required to produce the additional output can easily be calculated by multiplying the labor input coefficient by the amount of output induced in each industry. If we compare the total inducement effect of the two subsectors in the social policy field, that of the health and medical sector was larger in 1970. But since the reduction in the labor input coefficient in the health and medical sector has been remarkable, especially between 1970 and 1975, the inducement effect in the health and medical sector became much smaller than that in the social insurance and social welfare sector in 1980. On the other hand, the total inducement effect in the social insurance and social welfare sector has fallen by only a little during the ten-year period, and indeed it increased during the first half of the 1970s. As far as this sector is concerned, a major part of the total inducement effect is a direct effect, and the demand for labor in this sector is derived almost entirely from the increase in output of the sector itself. The direct inducement effect is merely another name for the labor input coefficient; the direct inducement ratio denotes the ratio of the labor input coefficient to the total labor inducement. It indicates, therefore, the degree of influence of a unit increase in the demand for output in a specific sector on the increased demand for labor in other industries, and the subsequent repercussions on the demand for labor in the original sector. The larger the ratio, the smaller the influence on other industries and the repercussions for the original sector. In this respect the health and medical sector has more influence on the demand for labor in other industries, and more

240

The Analysis of Social and Environmental Problems

repercussions on the demand for labor in the health and medical sector itself, than the social insurance and social welfare sector. Furthermore this ratio has tended to increase during the ten-year period for both social policy subsectors, which implies that their influences on other industries, and their repercussions for their own sectors, have weakened during the period. The sensitivity indicates the total effect summing along each row (i.e., those corresponding to the health and medical and the social insurance and social welfare sectors in the inverse matrix) multiplied by the labor input coefficient for each of the two sectors. Thus the figures indicate the effects on the demand for labor in both sectors arising from the change in output demand for the industries themselves and other industries. At first sight, the social insurance and social welfare sector seems to be more sensitive than the health and medical sector to a uniform increase in output demand for all industries, but it is sensitive only to the level of output demand for the sector itself. Finally, on the basis of this discussion we can say that the influence of the two sectors on labor demand in other industries can to some extent be analyzed using I-O techniques. However, since the effects from other industries on the demand for labor in the two sectors are very small, this application of I-O techniques is subject to limitations. This results from a peculiarity of these sectors, which is that their output consists almost entirely of final demand and not of intermediate input.

DEPENDENCE OF LABOR DEMAND ON COMPONENTS OF FINAL DEMAND

We have looked at the industrial characteristics of each of the two subsectors in the social policy field, and at their interrelations with or interdependence on other industries. Next we consider which component of final demand causes the largest increase in the demand for labor in these two sectors. This is shown by the so-called dependency ratio of labor force demand on the components of final demand. This ratio measures the relative magnitudes of the labor force increase in each industry induced by a unit increase (here of one billion yen) in each of the components of final demand (e.g., private consumption expenditure, general government consumption, etc). Table 17.3 shows the dependency ratio of the demand for labor for the two subsectors in the social policy field. Increases in stocks, gross domestic private fixed capital formation, exports, and imports have few effects on the demand for labor in the social policy field, nor does gross domestic government fixed capital formation. Economic activities in the social policy field are really types of consumption. Summarizing, a unit increase in private consumption expenditure causes almost all of the increase in the demand for labor in the health and medical sector, whereas a unit increase in general government consumption causes most of the increase in the demand for labor in the social insurance and social welfare sector in 1980. The consumption of private nonprofit organizations also plays an important role in increasing the demand for labor in the latter sector in the same year. A unit increase in private consumption expenditure causes only 20 percent of the total increase in the demand for labor in this sector in 1980, whereas in 1975 a unit increase in private consumption expenditure caused 61.1 percent of the total increase, and in 1970 the

Application of Input-Output Techniques to Labor Force Allocation

241

TABLE 17.3 Dependency ratio of labor-force demand on final demand (%) Consumption

Private Total industry Health and medical Social insurance and welfare

1970 1975 1980 1970 1975 1980 1970 1975 1980

58.7 60.9 60.2 93.0 95.7 96.2 67.4 61.1 20.0

Nonprofit Bodies

0.9 0.6 0.7 1.3 -0.3 -0.1 15.6 18.7 36.8

General Government

9.3 9.7 9.5 5.6 4.6 0.1 17.0 20.2 43.2

Government Capital Formation

Total Final Demand

10.1

100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0

9.4 9.3 0.0 0.0 0.0 — — —

figure was even larger. Thus the dependence of labor force demand in this sector on general government consumption, and on the consumption of private nonprofit organizations, has tended to rise over the same period, and has undergone a remarkable increase since 1975, implying a complete change in the consumption pattern during the period observed. The importance of consumption by private nonprofit organizations in the social insurance and social welfare sector in recent years is based on the fact that many of the social welfare facilities in Japan are owned and managed by private nonprofit organizations. The importance of private consumption expenditure in the health and medical sector has not changed much throughout the period, although there has been a small increase. Private consumption expenditure is important in this sector because of the existence of compulsory private medical insurance schemes, which provide a system of private doctors covering the whole nation, and because many hospitals also belong to private doctors. Thus most health and medical expenditures take the form of private consumption, financed by general government current transfers to households.

FACTORS AFFECTING THE NUMBER OF WORKERS IN THE SOCIAL POLICY FIELD As we have already stated, Japan has been ageing very rapidly during the past ten or fifteen years. The increase in the number of elderly persons has increased the demand for health and medical and for social welfare services during the period. According to the 1970-1975-1980 Link Input-Output Table, final demand for health and medical services, measured at 1980 constant prices, increased by 68.7 percent from 1970 to 1975 and by 50.4 percent from 1975 to 1980 (figures that imply a 154.1% increase from 1970 to 1980). At the same time the proportion of the elderly increased from 7.1 percent in 1970 through 7.9 percent in 1975 to 9.0 percent in 1980. Similarly, final demand for social insurance and social welfare services increased by 17.5 percent from 1970 to 1975 and by 25.8 percent from 1975 to 1980 (implying an increase of 47.8 percent from 1970 to 1980). There was a much smaller increase in the number of workers in these sectors over the same period: 29.4 percent from 1970 to 1975 and 18.5 percent from 1975 to 1980

242

The Analysis of Social and Environmental Problems

(53.4 percent for 1970 to 1980) in the health and medical sector, and 24.2 percent from 1970 to 1975 and 7.0 percent from 1975 to 1980 (33.0% from 1970 to 1980) in the social insurance and social welfare sector. The main reason why the increase in the number of workers in these sectors is smaller than the increase in final demand for these services is the impact of labor-saving measures in these sectors. Table 17.4 presents an analysis of the factors causing changes in the number of workers in both sectors. These changes are decomposed into the demand effect, the labor-saving effect, and the technological change effect (change in the technological relationships between raw materials and output). The table also gives the total effect and the number of workers, expressed as an index number. The demand effect is defined to be the change in the number of workers that can be attributed to the change in final demand, that is l 0 B 0 AF, where l0 denotes the labor input coefficient in the base year, B0 denotes the Leontief inverse matrix in the base year, and AF denotes the change in final demand between the two time points. The labor-saving effect is defined as the estimated change in the number of workers attributable to change in the labor input coefficient, written as AIB0F1, where A/ denotes the change in labor input coefficient and F1 the level of final demand in the year of comparison. Similarly, the technical change effect is defined as the estimated change in the number of workers caused by change in the technological structure, that is l}ABFlt where /j denotes the labor input coefficient in the comparison year and AB denotes the change in the technological relationship between raw materials and output. The total effect is the sum of these three effects. The numbers in the first four columns of Table 17.4 are expressed as percentages of the total number of workers in the base year. As can be seen from the table, the technological effect has been very small during the period. In contrast, the demand effect has been remarkable, as we would expect from our earlier discussion, particularly in the health and medical sector. The demand effect in the social insurance and social welfare sector has not been as large, especially during the first five years. The larger demand effect in this sector in the latter half of TABLE 17.4

Factors affecting number of workers in social policy-related sectors Demand Effect t

Labor-Saving Effect ct

Technology Effect ct

Total Effect

ct

1970- 1975

1970

Health and medical Social ins. and welfare Subtotal % elderly

68.7 17.5 57.4

-38.8 6.7 -28.8

-0.5 0.0 -0.4

29.4 24.2 28.2

Total industries

27.2

-18.4

-6.3

2.6

8

8

4

No. of Workers

5

4

3

1975 -1980

1975

100.0 129 .4 100.0 124.2 100.0 128.2 7.1 7.9 100.0

126.2

1975

1980

Health and medical Social ins. and welfare Subtotal % elderly

50.4 25.8 45.2

-31.8 -18.8 -29.0

-0.1 0.0 -0.1

18.5 7.0 16.1

100.0 118.5 100.0 107.0 100.0 116.1 7.9 9.0

Total industries

24.8

-21.7

1.4

4.5

100.0 104.5

Application of input-Output Techniques to Labor Force Allocation

243

the period seems to reflect the more rapid ageing of the population from 1975 to 1980 relative to the earlier years. This development has important implications for the problem of labor force allocation across industry, since it is clear that a much larger labor force will be needed in this sector in the future. The demand effect in the social policy field as a whole during the late 1970s has been much larger than the effect for aggregate industry. In this sense the labor-saving effect in these sectors is much more important than in other industries. The labor-saving effect in the health and medical sector has been very large throughout the period, and much larger than the corresponding effect for aggregate industry. If we consider the social insurance and social welfare sector, the labor-saving effect has been small, and was positive (indicating increased labor requirements from this factor) during the first five years of the period. Since the laborsaving effect is related to changes in the labor input coefficient, and we have already discussed the meaning of these changes in the social policy field, we shall not repeat the discussion here. But it is necessary to stress the importance of applying new technologies to these fields and of improving the environment of social welfare services in the future. Because of the magnitude of the labor-saving effect, the total effect and the actual increase in the number of workers in these two sectors have not been as substantial as we feared, in spite of the huge contribution of the demand effect during the period. But this large increase in demand also has meant that the increase in number of workers has been proportionately greater in these sectors than in aggregate industry, in spite of the significant labor-saving effect.

CONCLUSION In this chapter we have discussed the problem of labor force allocation in the social policy field using input-output techniques. Although there are some limitations that affect the application of I-O techniques to this problem, we can draw two policy implications from this discussion. First, since we are sure of a large increase in the demand for labor in the social policy sector from now on, we should try to maintain a large labor-saving effect in these sectors, as has been done in the health and medical sector with the help of new technologies. We should make much more effort to increase labor productivity, particularly in the case of social welfare services, as well as trying to offer an improved and more humane service. Second, as far as health and medical services are concerned, there has been an excessive tendency to depend on the private sector. From now on, particularly in the fields of prevention and primary care, we need more direct government intervention and government supply of a basic minimum level of services.

Index

Agriculture in Japan, 9, 149-57 Allocation coefficients, 26- 28. Aluminum industry, in Taiwan, 29-32 Australia, 101-3 Autarchy, 166 Balance of trade, 10, 177, 203 Banks, 124-25, 128, 130 Battelle Institute, 142 Biological oxygen demand, 223, 228, 231-32 Business cycles, 127, 137 Juglar, 137 Kitchin, 137 Kuznets, 137 Kondratieff. See Long wave Business forecasting, 3 By-products, 44, 46 48, 50. See also Joint production Capital coefficients, 22-23, 122, 204. See also Investment output ratio Carbon dioxide, 223, 228, 231-32 Cobb-Douglas production function. See Production function Commodity technology, 44 Comparative advantage, 11, 203-4, 208 indices of, 204-5 Comparative cost differences, 8, 113-19, 203 Competitive industry, 121, 123, 131-32 Computable general equilibrium models, 10 Concentration ratio, 9, 133-35 Conglomerate firms, 7 Consumer-demand systems, 10, 143, 174-75 Consumption function, 143 Consumption table. See Final demand tables Core, 167, 171, 171n.4 Cost function, 108-11, 142 Denmark, 58, 63 Developing countries. See Less-developed countries Disequilibrium, in consumer markets, 10, 174, 182 Dual prices, 10, 167, 176. See also Equilibrium prices EC. See European Community

Economic development, 11, 149. See also Lessdeveloped countries and "long waves," 9, 137-38 Economic policy, 3 Education, 152-53 Effective demand, 4 Effective protection, 11 Elasticity of substitution, 71, 81, 153 ELES. See Extended Linear Expenditure System Employment linkages, 200-203 Environment, 12, 138, 223-24, 228-32 Equilibrium prices, 171, 174-75 ESA. See European System of Integrated Economic Accounts European Community, 11, 199-200, 205-8 European System of Integrated Economic Accounts (ESA), 6, 39, 44-48, 50-51 Exchange rates, 112 Extended Linear Expenditure System, 174-75, 178 Factor intensities, indices of, 203-4, 209 Fixed capital formation, 10 Final demand tables, 141—43 Foreign debt, 187-88 Foreign trade, 187-88. See also International trade France, 9, 101-3, 145-47 General equilibrium, 10 Germany. See West Germany Gibson paradox, 127 Harrod-Domar model, 194 Health care, 12, 236-43 High-technology industry, 7, 69, 72-74, 88, 90, 101-3 Hokkaido, 12, 223-33 Households, 124 Hungary, 10, 187-88, 194-95 Imports coefficient, 211, 212-13 Import substitution, 11, 190, 211-19 Imports, and concentration ratio, 135 Income distribution, 11, 127-28, 138, 191, 194

Index Index numbers, exact, 109 Laspeyres, 53 Paasche, 54 Tornqvist, 111 India, 11,215-19 Indonesia, 199-200, 201, 205-8 Industrial organization, 5 Industrial structure, 3, 10, 12 Industrialization, 194 Industry technology, 44 Inflation, 128, 174, 179 Innovation, clustering of, 138-39, 142 Input-output coefficients changes in, 22, 26, 32, 140, 169-70, 204-5 extrapolation of, 5, 70-72, 83, 103 interregional comparisons, 5, 24 stability of, 25-33 Input-output matrix and intersectoral linkages, 11, 25, 139, 199-203 and similarity transforms, 5, 17-24 balancing of, 53, 55, 58-59, 62-64 compilation of, 6-7, 43-44, 4>-51, 53-65 productivity of, 166 Input-output system environmental models, 12, 226-28 integration with national accounts, 40 regional models, 10, 25, 161-69 supply-driven, 6, 25-26, 200 Interest rate, 122, 127-28, 130 International trade, 8, 11, 199, 203-8 Investment cycle, 193 Investment output ratio, 163. See also Capital coefficients Investment table. See Final demand tables Ireland, 175 Irrigation, 155-56 Italy, 175 Japan, 7, 8, 12, 128, 224-26, 229 comparative costs, 108-9, 113-19 high-technology industries, 69-70, 72, 83, 8890, 101-3 technical change in agriculture, 149-57 welfare services in, 236-43 Joint production, 7 Joint stability, 27-29, 33-35 Kazakhstan, 168 Keynes, J. M., 126, 130 Korea. See South Korea Labor coefficients, in social policy sector, 237-39 Labor supply, 174 Land, 154-55 Latvia, 169 LDCs. See Less-developed countries Leontief inverse, 17-18, 200, 214-15, 239, 242 Leontief paradox, 11 Less-developed countries (LDCs), 149-50, 199200, 206-8 Linear programming, 10, 34n.6-8, 174, 176 Linkages, indices of, 200, 202-3, 208-9 Long wave (Kondratieff cycle), 137-38, 142-43, 146-47

245 Macroeconomic models, 3-4, 9, 10, 83, 88-89, 223-26 Macroeconomic policy, 194 Macroeconomic theory, 3 Make matrix, 41, 45-46, 50, 55, 58, 59-65 Malaysia, 206 Marginal cost, 123, 125 Marginal propensity to consume, 175 Maryland, University of, 142 Material Product System, 39 Medical services, 236-43 Mexico, 199-200, 205-8 Mitchell, W. C, 127, 130 Mixed estimation, 153-55 Moses-Isard model, 164-65 MPS. See Material Product System Monopoly, 121, 123, 130-32 Monopoly power, in U.S., 132-36 Moving equilibrium. See Temporary equilibrium Multiplier, 129 Multiunit firm, 44, 49 National accounts, 6-7, 39-51, 56-57, 64-65 Netherlands, 53, 55, 61, 63-64 New Economic Mechanism, 11, 187 Nitrogen oxides, 223, 228, 231-32 Nonmarket production, 43 Nonsubstitution theorem, 4, 6 Nontariff barriers, 206 North-South trade, 206 Norway, 63 Objective function, 161, 164, 178 Obsolescence, 122 OECD. See Organization for Economic Cooperation and Development Okun's Law, 126-27 Oligopoly, 9 OPEC. See Organization of Petroleum Exporting Countries Optimizing behavior, 4 Organization for Economic Cooperation and Development (OECD), 103 Organization of Petroleum Exporting Countries (OPEC), 101, 103 Overproduction, by industrial sectors, 191-95 Overvaluation, of industrial sectors, 188-91 Pakistan, 199-200, 205-8 Pareto optimality, 167 Pennsylvania, University of, 83, 103 Planned economies, 10, 25, 174, 187 Planning, 6, 9-11, 26, 161, 174 Poland, 10, 174-75, 182 Pollution. See Environment Pontryagin's Maximum Principle, 151 Price behavior, J23, 130 Pricing of commodities, 123 Primary production, 202-3, 208 Prime cost, 122, 125-26 Production, vintage model of, 8, 121-22 Production coefficients. See Input-output coefficients

246 Production function, 108, 138, 140, 151 52 estimation of, 9, 151, 153-57 Productivity-increasing activities, 9, 150-55 Profit expectations, 122 Profit margins, 5 Profitability, 8 Profits, 121-22, 124, 130-32 Purchasing power parity, 8, 108, 112 Quasi-equilibrium solutions, 167 R & D expenditure, 71, 143, 152-53 RAS technique, 5, 8, 69-72. See also V-RAS technique Rationing, 6, 26, 29-32 Real wage rate, 122, 127-28, 130 Regional balances, 164-67, 171 Regional development, 223 Regional models. See Input-output system, regional models Regression, and similarity transforms, 18-21 Residual income. See Profits Russian Republic, 168, 171 Saving propensity, 128 Savings, 122, 153 Scenario analysis, 169 Separation theorem, 166 Shadow prices, 166 Shephard s lemma, 109 Siberia, 168-71 SNA. See United Nations System of National Accounts Social services, 12, 236-43 Socialist economies. See Planned economies South Korea, 199-200, 202, 205-8 Soviet Union, 10, 168 71 Spain, 142 Statistical unit, choice of, 39, 41-43, 48, 49 Stockholders, 125-26, 129-30 Stocks, valuation of, 57 Structural change, 69, 214 Structural efficiency, index of, 187, 194-95 Structural interdependence, 212, 239-40 Sulfur oxides, 223, 228, 231-32 Supply restrictions. See Rationing Supply side, 174

Index Taiwan, 29-32 Tariffs, 206 Technical change, 7-9, 69-103, 121 22, 131-32, 150-53, 191, 228, 232, 242-43 Technical progress. See Technical change Technological substitution, 6, 26-27, 71-72, 140 Technology, dissemination of, 9, 71, 138-39, 14243, 149-50 Temporary equilibrium, 123, 126-27 Total factor productivity, 7-8, 141-42, 143-45 in France, 145-47 in Japan, 69-71, 73-76, 83, 89-90 in Japanese agriculture, 149-57 international comparisons, 108-11 Trade coefficients, 165 Trade margins, 58, 59-61 Tsukuba, University of, 72 Ukraine, 168 Underproduction, by industrial sectors, 191-95 Undervaluation, of industrial sectors, 188-91 Unemployment, 130 United Nations Industrial Development Organization (UNIDO), 3, 11 United Nations Statistical Office, 207 United Nations System of National Accounts (SNA), 6-7, 39, 41-44, 49-50, 55 United Kingdom, 101-3, 128 United States, 8, 101-3, 137 comparative costs, 108-9, 113 19, 128 competitive and noncompetitive industries, 132-36 Use matrix, 41, 55, 58, 59-65 Utility function, 124 V-RAS technique, 69 72, 75-83, 103 Wage bill. See Wage fund Wage fund, 174, 176, 178, 188 Washington, state of, 34n.l2 West Germany, 8, 101-3, 175, 206 comparative costs, 108-9, 113-19, 128 Working capital, 128-30 World market prices, in Hungary, 188-91