Labor economics

SECOND EDITION

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•

SECOND EDITION

Labor Economics George J. Borjas Harvard University

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Labor Economics Copyright © 2000, 1996 by The McGraw-Hili Companies, lnc. All rights reserved. Printed in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. This book is printed on acid-free paper. 3 4 5 6 78 9 0 DOC DOC 9 0 98 7 6 5 4 3 21 ISBN 0-07-231198-3

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Borjas, George J. Labor economics / George J. BOIjas.- 2nd ed. p. cm Includes index. ISBN 0-07-2311 98-3 (alk. paper) 1. Labor economics. 2. Labor market-United States 1. Title. HD4901 .B6741 999 99-052902 3 3 1 --dc21 http://www_mhhe_com

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About the Author

George 1. Borjas is the Pforzheimer Professor of Public Policy at the John F. Kennedy School of Government, Harvard University. He is also a research associate at the National Bureau of Economic Research. Professor Borjas received his Ph.D. in eco­ nomics from Columbia University in 1 975. Prior to moving to Harvard in 1995, he was a professor of economics at the University of California at San Diego. Professor Borjas has written extensively on labor market issues. He is the author of several books, including Wage Policy in the Federal Bureaucracy (American Enter­ prise Institute, 1 980), Friends or Strangers: The Impact of Immigrants on the U.S. Economy (Basic Books, 1 990), and Heaven's Door: Immigration Policy and the Amer­ ican Economy (Princeton University Press, 1 999). He has published over 1 00 articles in books and scholarly journals, including the American Economic Review, the Journal of Political Economy, and the Quarterly Journal of Economics. His work also appears regularly in major magazines and newspapers, including articles in the Atlantic Monthly and National Review, as well as editorials in The New York Times, The Wall Street Journal, and Le Monde. In 1 998, Professor Borjas was elected a fellow of the Econometric Society. He is an editor of the Review of Economics and Statistics, and has been on the editorial boards of the Quarterly Journal of Economics and the International Migration Review. He has also served as a member of the Advisory Panel in Economics at the National Science Foundation and has testified frequently before congressional committees and government commissions.

v

To Sarah, Timothy, and Rebecca

Preface

The original motivation for writing Labor Economics grew out from my years of teaching labor economics to undergraduates. After trying out many of the textbooks in the market, it seemed to me that students were not being exposed to what the essence of labor economics was about-that is, they were not being given the information they needed to help them understand how labor markets work. As a result, I felt that stu­ dents did not really grasp why some persons choose to work, whereas other persons withdraw from the labor market; why some firms expand their employment at the same time that other firms are laying off workers; or why earnings are distributed unequally in most societies. The key difference between Labor Economics and other textbooks lies in its phi­ losophy. I believe that knowing the story of how labor markets work is, in the end, more important than showing off our skills at constructing elegant models of the labor market or remembering hundreds of statistics and institutional details summarizing labor market conditions at a particular point in time. I doubt that many students will (or should) remember the mechanics of deriving a labor supply curve or the way that the unemployment rate is officially calculated 10 or 20 years after they leave college. However, if students could remember the story of the way the labor market works-and, in particular, the way that workers and firms respond to changing incentives by shifting the amount of labor they supply or demand-the students would be much better prepared to make informed opinions about the many proposed government policies that can have a dramatic impact on labor market opportunities, such as a "workfare" program requiring that welfare recip­ ients work or a payroll tax assessed on employers to fund a national health care pro­ gram. The exposition in this book, therefore, stresses the ideas that labor economists use to understand how the labor market works. Although the book makes extensive use of labor market statistics and reports evi­ dence obtained from hundreds of research studies, the data and empirical findings are ix

x

Preface

not the heart of the book. These data summarize the stylized facts that a good theory of the labor market should be able to explain, as well as help shape our thinking about the way the labor market works. The main objective of the book, therefore, is to survey the field of labor economics with an emphasis on both theory and facts. As a result, the book relies much more heavily on "the economic way of thinking" than existing text­ books. I believe this approach gives a much better understanding of labor economics than an approach that minimizes the story-telling aspects of economic theory.

REQU I REMENTS The book uses economic analysis throughout the discussion. All the theoretical tools are introduced and explained within the textbook. As a result, the only prerequisite is that the student has some familiarity with the basics of microeconomics, particularly supply and demand curves. The exposure acquired in the typical introductory econom­ ics class more than satisfies this prerequisite. All other concepts (such as indifference curves, budget lines, production functions, and isoquants) are motivated, defined, and explained as they appear in our story. The book does not make use of any mathemati­ cal skills beyond those taught in high school algebra (particularly, the notion of a slope). Labor economists also make extensive use of econometric analysis in their research. Although the discussion in this book does not require any prior exposure to econometrics, the student will get a much better "feel" for the research findings if they know a little about how labor economists manipulate data to reach their conclusions. The appendix to Chapter 1 provides a simple (and very brief) introduction to econo­ metrics, and allows the student to visualize how labor economists conclude, for instance, that wealth reduces labor supply or that schooling increases earnings.

CHANGES I N THE SECO N D EDITION The second edition incorporates three major changes. First, the exposition of many of the theoretical models has been greatly simplified. Users of the previous edition will find that the models have been condensed to their bare essentials, minimizing the need for introducing additional jargon or concepts and yet maintaining the essence of what the models teach us about the way the labor market works. This simplification should considerably broaden the appeal of the book. The second edition also contains a larger repertoire of policy-relevant applications. There are now a sufficiently large number of applications that users may be able to "pick and choose," depending on the nature of the course that is being taught. The addition of these examples, I believe, has changed the feel of the book, away from a theoretical emphasis to one that is much more appli­ cations oriented. Finally, the book includes a brand new chapter, Chapter 8, "The Wage Structure." This chapter summarizes the recent (and large) empirical literature that attempts to understand why the wage distribution changed so much in the past decade in many industrialized countries, particularly in the United States.

xi

Preface Among the specific changes included in the second edition are: 1. An analysis of how the earned income tax credit affects the labor supply decisions of affected families.

2. Numerous examples of the empirical methodology of "difference-in­ differences." This easy-to-understand procedure gives students a much better grasp of the advantages and limits of state-of-the-art empirical research in labor economics. 3. A discussion of how taxes and subsidies affect labor demand. 4. An analysis of the link between affirmative action programs and the firm's costs of production. 5. The chapter on human capital now contains a unified treatment of both school and postschool investments. 6. A discussion of the intergenerational correlation in earnings and of the concept of regression toward the mean.

7. A discussion of the increased job instability that occurred in the U.S. labor market in the 1980s, and how this instability differs across skill groups. 8. A discussion of the occupational crowding hypothesis. 9. A discussion of the theory of implicit contracts and its link to structural unemployment. 10. An analysis of the link between efficiency wages and the "wage curve," the empirical relation between wages and unemployment.

ORGAN IZATION OF THE BOOK The instructor will find that this book is much shorter than other labor economics text­ books. The book contains an introductory chapter, plus 1 2 substantive chapters. If the instructor wished to cover all the material, each chapter could serve as the basis for about a week's worth of lectures in a typical undergraduate semester course. Despite the book's brevity, the instructor will find that all the key topics in labor economics are covered. The discussion, however, is kept to essentials because I have tried quite hard not to deviate into tangential material or into lO-page-long ruminations on my pet top­ ics. The book, therefore, is geared toward those who prefer their labor economics "short and sweet." Chapter 1 presents a brief introduction that exposes the student to the concepts of labor supply, labor demand, and equilibrium. The chapter uses the "real-world" exam­ ple of the Alaskan labor market during the construction of the oil pipeline to introduce these concepts. In addition, the chapter shows how labor economists contrast the theory with the evidence, as well as discusses the limits of the insights provided by both the theory and the data. The book begins the detailed analysis of the labor market with a tour of labor sup­ ply. Chapter 2 presents the static theory of labor supply (how workers allocate their

xii

Preface

time at a point in time), and Chapter 3 extends the basic model in a number of direc­ tions, including an analysis of how workers allocate their time over time as well as a discussion of household production. The book then turns to a discussion of labor demand in Chapter 4. Chapter 5 puts together the supply decisions of workers with the demand decisions of employers and shows how the market "balances out" the conflict­ ing interests of the two parties. The remainder of the book extends and generalizes the basic supply-demand framework. Chapter 6 stresses that jobs differ in their characteristics so that jobs with unpleasant working conditions may have to offer higher wages in order to attract workers. Chapter 7 stresses that workers are different, either because they differ in their educational attainment or in the amount of on-the-job training they acquire. These human capital investments help determine the economy's wage distribution. Chapter 8 discusses how changes in the rate of return to skills in the 1980s and 1990s changed the wage distribution in many industrialized economies, particularly in the United States. Chapter 9 describes a key mechanism that allows the labor market to balance out the interests of workers and firms, namely labor turnover and migration. The final section of the book discusses a number of distortions iind imperfections in labor markets. Chapter 10 analyzes how labor market discrimination affects the earnings and employment opportunities of minority workers and women. Chapter 11 discusses how labor unions affect the relationship between the firm and the worker. Chapter 12 notes that employers often find it difficult to monitor the activities of their workers so that the workers will often want to "shirk" on the job. The chapter dis­ cusses how different types of labor market contracts arise to discourage workers from misbehaving. Finally, Chapter 13 discusses how unemployment can arise and persist in labor markets. The text uses a number of pedagogical devices designed to deepen the student's understanding of labor economics. A chapter typically begins by presenting a number of stylized facts about the labor market, such as wage differentials between blacks and whites or between men and women. The chapter then presents the story that labor economists have developed to understand why these facts are observed in the labor market. The chapter then extends and applies the theory to other labor market phenom­ ena. Each chapter typically contains at least one lengthy application of the material to a major policy issue, as well as a number of illustrative boxed examples, called "Theory at Work." The end-of-chapter material also contains a number of "student-friendly" devices. There is a chapter "Summary" describing briefly the main lessons of the chapter; a "Key Concepts" section listing the major concepts introduced in the chapter (when a key concept makes its first appearance, it appears in boldface). Each chapter also includes "Review Questions" that the student can use to review the major theoretical and empirical issues. The chapter then ends with "Problems" that test the student's understanding of the material.

Acknowledgments

I am grateful to several colleagues who have graciously provided me with data from their research proj ects. I have also benefited from the comments made by many col­ leagues both on the earlier edition and on the manuscript to the Second Edition. These colleagues include: David Autor

Jean Homey

Massachusetts Institute of Technology

Furman University

Jeff Begley

Wei-chiao Huang

Furman University

Western Michigan University

Julian Betts

Mark Killingsworth

University of California, San Diego

Rutgers University

William Carrington

Thomas 1. Kniesner

Bureau of Labor Statistics

Indiana University

Janet Currie

Jaeki Lee

University of California, Los Angeles

University of Ulsan (South Korea)

Greg Delemeester

1. Peter Mattila

Marietta College

Iowa State University

Thomas Dunn

Nan Maxwell

Syracuse University

California State University-Hayward

David 1. Faurot

Bruce McClung

University of Kansas

Southwest Texas State University

Matthew Goldberg

Kenneth McLaughlin

Institute for Defense Analysis

Hunter College

James W. Henderson

H. Naci Mocan

Baylor University

University of Colorado at Denver

xiii

xiv

Acknowledgments 10m-Steffen Pischke

Charles L. Skora

Massachusetts Institute o/Technology

Boise State University

Curtis 1. Simon

Stephen Trejo

Clemson University

University o/ Texas, Austin

George f. Borjas

Contents i n Brief

Introduction

1

2

Labor Supply

3

Topics in Labor Supply

4

Labor Demand

S

Labor Market Equilibrium

6

Compensating Wage Differentials

20 103

1

Human Capital

8

The Wage Structure

9

Labor Mobility

10

II

226 303

69 159

275

Labor Market Discrimination Labor Unions

388

201

34 2

12

Labor Market Contracts and Work Incentives

13

Unemployment

INDEXES

465

432

509

xv

Contents

Introduction

1

An Economic Story of the Labor Market 2 The Actors in the Labor Market 3 W hy Do We Need a Theory? 7 The Organization of the Book 1 1 Summary 1 1 Key Concepts 1 2 Review Questions 1 2 Appendix: An Introduction to Regression Analysis 1 2 1-1 1 -2 1-3 1 -4

2

Labor Supply

20

Measuring the Labor Force 2 1 Basic Facts About Labor Supply 23 The Worker's Preferences 25 The Budget Constraint 3 1 The Hours-of-Work Decision 33 Theory at Work: Dollars and Dreams 40 2-6 To Work or Not to Work? 40 Theory at Work: Winning the LOTTO Will Change Your Life 43 2-7 The Labor Supply Curve 44 2-8 Estimates of the Labor Supply Elasticity 46 Theory at Work: The Laffer Curve 50 2-9 Labor Supply of Women 5 1 2-10 Policy Application: Welfare Programs and Work Incentives 55 2-1 1 Policy Application: The Earned Income Tax Credit 60 Summary 65 2- 1 2-2 2-3 2-4 2-5

�

xvii

xviii

Contents

Key Concepts 66 Review Questions 66 Problems 67 3

Topics in Labor Supply

3-1 3-2 3-3 3-4

3-5 3-6

4

Labor Supply over the Life Cycle 70 Labor Supply over the Business Cycle 76 Retirement 78 Policy Application: The Decline in Work Attachment Among Older Workers 82 Theory at Work: The Notch Babies 84 Household Production 87 Fertility 94 Theory at Work: Poor Relief and Fertility 98 Summary 1 00 Key Concepts 1 0 1 Review Questions 1 0 1 Problems 1 0 1

Labor Demand

103

The Production Function 1 04 The Employment Decision in the Short Run 1 07 The Employment Decision in the Long Run 1 14 The Long-Run Demand Curve for Labor 1 1 9 The Elasticity of Substitution 1 25 Theory at Work: California's Overtime Regulations and Labor Demand 1 26 4-6 Policy Application: Affirmative Action and Production Costs 128 4-7 Marshall's Rules of Derived Demand 1 3 1 4-8 Factor Demand with Many Inputs 1 34 4-9 Overview of Labor Market Equilibrium 1 36 4- 1 0 Policy Application: The Employment Effects of Minimum Wages 1 3 8 Theory a t Work: The Minimum Wage and Puerto Rico 1 48 4- 1 1 Adjustment Costs and Labor Demand 1 49 Summary 155 Key Concepts 1 56 Review Questions 1 56 Problems 1 57

4- 1 4-2 4-3 - 4-4 4-5

,

69

Contents

5

xix

Labor Market Equilibrium

5- 1 5-2 }

�

6

5-3 5-4 5-5 5-6 5-7 5-8

Equilibrium in a Single Competitive Labor Market 1 60 Competitive Equilibrium Across Labor Markets 1 6 1 Theory at Work: The Intifadah and Palestinian Wages 1 6 1 Policy Application: Payroll Taxes and Subsidies 1 66 Policy Application: Immigration 172 Theory at Work: The Clinton Health Care Program 1 73 The Cobweb Model 1 82 Noncompetitive Labor Markets: Monopsony 185 Noncompetitive Labor Markets: Monopoly 1 93 Wages and Employment in the Public Sector 1 96 Summary 1 98 Key Concepts 1 99 Review Questions 1 99 Problems 1 99

Compensating Wage Differentials

6-1 6-2 - 6-3 6-4

�.

6-5

7

159

The Market for Risky Jobs 202 Theory at Work: W hy Do Public Interest Lawyers Earn Less? 208 The Hedonic Wage Function 209 Policy Application: How Much Is a Life Worth? 2 1 3 Policy Application: Safety and Health Regulations 2 1 6 Theory at Work: Workers' Compensation May Be Hazardous to Your Health 2 1 8 Compensating Differentials and Job Amenities 2 1 9 Summary 223 Key Concepts 224 Review Questions 224 Problems 225

Human Capital

7-1 7-2 7-3 7 -4 7 -5

7-6 7 -7 7-8

201

226

Education in the Labor Market: Some Stylized Facts 227 Present Value 228 The Schooling Model 230 The Wage Gap Among Workers Who Differ in Their Education 237 Estimating the Rate of Return to Schooling 24 1 Theory at Work: Can We Afford to Improve the Skills of High School Dropouts? 242 Do Workers Maximize Lifetime Earnings? 245 Schooling as a Signal 249 Theory at Work: Is a GED Better Than Nothing? 254 Postschool Human Capital Investments 255

xx

Contents

On-the-Job Training 257 Theory at Work: Formal Training Programs 260 7-10 On-the-Job Training and the Age-Earnings Profile 261 Theory at Work: The Labor Market Effects of Substance Abuse 7 -11 Policy Application: Evaluating Government Training Programs Summary 27 1 Key Concepts 272 Review Questions 272 Problems 273

7-9

8

The Wage Structure

8-1 8-2 8-3 8-4 8-5

9

266 268

275

The Earnings Distribution 276 Changes in the Wage Structure: Basic Facts 278 Policy Application: W hy Did Wage Inequality Increase? 282 Theory at Work: Computers, Pencils, and the Wage Structure 290 The Earnings of Superstars 293 Inequality Across Generations 296 Summary 300 Key Concepts 300 Review Questions 301 Problems 301

Labor Mobility

303

Geographic Migration as a Human Capital Investment 304 Internal Migration in the United States 305 Family Migration 309 Immigration in the United States 312 Immigrant Performance in the U.S. Labor Market 313 The Decision to Immigrate 319 Theory at Work: Visas Available CIf You Pass a Test or Pay Up!) 325 9-7 Policy Application: The Economic Benefits from Immigration 325 9-8 Job Turnover: Some Stylized Facts 328 9-9 The Job Match 330 9-10 Specific Training and Job Turnover 332 Theory at Work: Health Insurance and Job-Lock 332 9-11 Job Turnover and the Age-Earnings Profile 335 Summary 337 Key Concepts 338 Review Questions 338 Problems 339 9-1 9-2 9-3 9-4 9-5 9-6

Contents

xxi

Labor Market Discrimination

10

342

Race and Gender in the Labor Market 343 The Discrimination Coefficient 344 Employer Discrimination 345 Theory at Work: Auditing Employer Hiring Practices 347 Theory at Work: Beauty and the Beast 353 10-4 Employee Discrimination 354 10-5 Customer Discrimination 355 10-6 Statistical Discrimination 357 Theory at Work: Customer Discrimination and the NBA 358 10-7 Measuring Discrimination 362 10-8 Policy Application: Determinants of the Black-White Wage Ratio Theory at Work: Orchestrating Impartiality 366 10-9 Policy Application: Determinants of the Male-Female Wage Ratio 374 10-10 Discrimination Against Other Groups 382 Summary 384 Key Concepts 385 Review Questions 385 Problems 386

10-1 10-2 10-3

II

Labor Unions

11-1 11-2 11-3

�

11-4 11-5 11-6 11-7 11-8 11-9

388

Unions in the United States 389 Determinants of Union Membership 394 Monopoly Unions 400 Theory at Work: Airline Deregulation and the Wages of Airline Mechanics 401 Policy Application: Unions and Resource Allocation 402 Efficient Contracts 405 Strikes 411 Union Wage Effects 417 The Exit-Voice Hypothesis 423 Policy Application: Public-Sector Unions 425 Theory at Work: Lawyers and Arbitration 427 Summary 428 Key Concepts 429 Review Questions 429 Problems 430

366

xxii

Contents

12

Labor Market Contracts and Work Incentives

1 2- 1 1 2-2 1 2-3 1 2-4 1 2-5

13

432

Piece Rates and Time Rates 433 Theory at Work: Work Effort Among Navy Recruiters 439 Tournaments 440 Theory at Work: Work Effort in the PGA Tour 444 Policy Application: The Compensation of Executives 445 Work Incentives and Delayed Compensation 447 Efficiency Wages 452 Theory at Work: Did Henry Ford Pay Efficiency Wages? 457 Summary 46 1 Key Concepts 462 Review Questions 462 Problems 463

Unemployment

465

Unemployment i n the United States 466 Frictional and Structural Unemployment 472 Theory at Work: Out of Work in the Workers' Paradise 473 1 3-3 The Steady-State Rate of Unemployment 474 1 3-4 Job Search 477 Theory at Work: Jobs and Friends 480 1 3-5 Policy Application: Unemployment Compensation 484 Theory at Work: Cash Bonuses and Unemployment 485 1 3-6 The Intertemporal Substitution Hypothesis 489 1 3-7 The Sectoral Shifts Hypothesis 49 1 1 3-8 Efficiency Wages 492 1 3-9 Implicit Contracts 497 1 3 - 1 0 Policy Application: The Trade-Off Between Inflation and Unemployment 499 Summary 505 Key Concepts 506 Review Questions 506 Problems 507 1 3- 1 1 3-2

Indexes 509 Name Index 509 Subject Index 5 1 4

CHAPTER

Introd uction

1

Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house. Jules Henri Poincar

Most of us will allocate a substantial fraction of our time to the labor market. How we do in the labor market helps determine our wealth, the types of goods we can afford to consume, who we associate with, where we vacation, which schools our children attend, and even the types of persons who find us attractive. As a result, we are all eager to learn how the labor market works. Labor economics studies how labor mar­ kets work. Our deep interest in labor markets arises not only from our own personal involve­ ment, but also because many of the issues in the debate over social policy concern the labor market experiences of particular groups of workers, or question various aspects of the employment relationship between workers and firms. Among the policy issues examined by modem labor economics are: 1 . Why did the labor force participation of women rise steadily throughout the past century in many industrialized countries? 2. What is the impact of immigration on the wage and employment opportunities of native-born workers? 3. Do minimum wages increase the unemployment rate of less-skilled workers? 4. Do wage and tax subsidies encourage firms to increase their employment? 5. What is the impact of occupational safety and health regulations on employment and earnings? 6. Are government subsidies of investments in human capital an effective way to improve the economic well-being of disadvantaged workers? 7. Why did wage inequality rise much more rapidly in the United States during the 1 980s than in other industrialized economies? 8. What is the impact of affirmative action programs on the earnings of women and minorities, and on the number of women and minorities that firms hire? 9. What is the economic impact of unions both on their members and on the rest of the economy?

2

Chapter One 10. Do generous unemployment insurance benefits lengthen the duration of

unemployment spells?

This diverse list of questions clearly illustrates why the study of labor markets is intrinsically more important and more interesting than the study of the market for but­ ter (unless one happens to be in the butter business!). Labor economics helps us under­ stand and address many of the social and economic problems facing modem societies.

I-I

AN ECONOMIC STORY OF THE LABOR MARKET

This book tells the "story" of how labor markets work. Telling this story involves much more than simply recounting the history of labor law in the United States or in other countries, and presenting table after table of statistics summarizing conditions in the labor market. After all, good stories have themes, characters that come alive with vivid personalities, conflicts that have to be resolved, ground rules that limit the set of permissible actions, and events that result inevitably from the interaction among these characters. The story we will tell about the labor market contains all of these features. Labor economists typically assign motives to the various "actors" in the labor market. We typically view workers, for instance, as trying to find the best possible job and assume that firms are trying to make money. Workers and firms, therefore, enter the labor mar­ ket with different objectives-workers are often trying to sell their labor at the highest price, whereas firms are often trying to buy labor at the lowest price. The types of economic exchanges that can occur between workers and firms are limited by the set of ground rules that the government has enacted to regulate transac­ tions in the labor market. Changes in these rules and regulations would obviously lead to different outcomes. For instance, a minimum wage outlaws exchanges that pay less than a particular amount per hour worked; occupational safety regulations forbid firms from offering working conditions that are deemed too risky to the worker's health. The deals that are eventually struck between workers and firms determine the types of jobs that are offered, the skills that workers acquire, the extent of labor turnover, the struc­ ture of unemployment in the economy, and the observed earnings distribution. The story thus provides a theory, a framework for understanding, analyzing, and predicting a wide array of labor market outcomes. The underlying philosophy of this book is that modem economics provides a use­ ful story of how the labor market works. In particular, the typical assumptions we make about the behavior of workers and firms, and about the ground rules under which the labor market participants make their transactions, lead to outcomes that often mir­ ror the facts observed in "real-world" labor markets. Labor economics, therefore, helps us understand and predict why some labor market outcomes are more likely to be observed than others. The discussion is also guided by the belief that learning the story of how labor markets work is as important as knowing basic facts about the labor market. Without understanding how labor markets work-that is, without having a theory of why work­ ers and firms pursue some employment relationships and avoid others-we would be hard-pressed to predict the labor market impact of changes in government policies or

Introduction

3

of changes in the demographic composition of the labor force. Put differently, the study of facts without theory is just as empty as the study of theory without facts. The question is often asked as to which are more important, ideas or facts? The analysis presented throughout the book stresses the insight that "ideas about facts" are most important. We do not study labor economics so that we can construct elegant the­ ories of the labor market, or so that we can remember how the official unemployment rate is calculated and that the unemployment rate was 6.8 percent in 1 993. Rather, we want to understand which economic and social factors generate this level of unem­ ployment, and why. The main objective of the book, therefore, is to survey the field of labor econom-' ics with an emphasis on both theory and facts: where the theory helps us understand how the facts are generated and where the facts can help shape our thinking about the way labor markets work.

1-2

THE ACTORS I N THE LABOR MARKET

Throughout the book, we will see that there are three leading actors in the labor mar­ ket: workers, firms, and the government. As workers, we receive top casting in the story. Without us, after all, there is no "labor" in the labor market. We decide whether to work or not, how many hours to work, which skills to acquire, when to quit a job, which occupations to enter, whether to join a labor union, and how much effort to allocate to the job. Each of these decisions is motivated by the desire to optimize, to choose the best available option from the vari­ ous choices. In our story, therefore, workers will always act in ways that maximize their well-being. Adding up the decisions of millions of workers generates the economy's labor supply not only in terms of the number of persons who enter the labor market, but also in terms of the quantity and quality of skills available to employers. As we will see many times throughout the book, persons who want to maximize their well-being tend to supply more time and more effort to those activities that have a higher payoff. The labor supply curve, therefore, is often upward sloping, as illustrated in Figure 1 - 1 . The hypothetical labor supply curve drawn in the figure gives the number of engi­ neers that will be forthcoming at every wage. For example, 20,000 workers are willing to supply their services to engineering firms if the engineering wage is $40,000 per year. If the engineering wage rises to $50,000, then 30,000 workers will choose to be engineers. In other words, the higher the engineering wage, the greater the number of persons who will decide that the engineering profession is a worthwhile pursuit. More generally, the labor supply curve relates the number of person-hours supplied to the economy to the wage that is being offered. The higher the wage that is being offered, the larger the labor supplied. Firms costar in our story. Each firm must decide how many and which types of workers to hire and fire, the length of the workweek, how much capital to employ, and whether to offer safe working conditions to its workers. Like workers, firms in our story also have motives. In particular, we will often assume that firms want to maxi­ mize profits. From the firm's point of view, the consumer is king. The firm will maxi­ mize its profits by making the production decisions-and hence the hiring and firing

4 Figure I-I

Chapter One Supply and Demand in the Engineering Labor Market

The labor supply curve gives the number ofpersons who are willing to supply their services to engineering firms at a given wage. The labor demand curve gives the number ofengineers that the firms will hire at that wage. Labor market equilibrium occurs where supply equals demand. In equilibrium, 20,000 engineers are hired at a wage of $40,000. Earnings ($) Labor Supply Curve 50,000

Equjlibrium

40,000

30,000 Employment 10,000

20,000

30,000

decisions-that best serve the consumers' needs. Adding up the hiring and firing decisions of millions of employers generates the economy's labor demand. The assumption that firms want to maximize profits implies that firms will want to hire many workers when labor is cheap, but will refrain from hiring when labor is expensive. The relationship between the price of labor and how many workers firms are willing to hire is summarized by the downward-sloping labor demand curve (also illustrated in Figure 1 - 1 ). As drawn, the labor demand curve tells us that firms in the engineering industry want to hire 20,000 engineers when the wage is $40,000, but will hire only 1 0,000 engineers if the wage rises to $50,000. Workers and firms, therefore, enter the labor market with conflicting interests. Many workers are willing to supply their services when the wage is high, but few firms are willing to hire them. Conversely, few workers are willing to supply their ser­ vices when the wage is low, but many firms are looking for workers. As workers search for jobs and firms search for workers, these conflicting desires are "balanced out" and the labor market reaches an equilibrium. In a free-market economy, equilib­ rium is attained when supply equals demand. As drawn in Figure 1 - 1 , the equilibrium wage is $40,000 and 20,000 engineers will be hired in the labor market. This wage-employment combination is an equilibri­ um because it balances out the conflicting desires of workers and firms. Suppose, for example, that the engineering wage were $50,OOO--above equilibrium. Firms would then want to hire only 1 0,000 engineers, even though 30,000 engineers are looking for work. The excess number of job applicants would bid down the wage as they compete for the few jobs available. Suppose instead that the wage were $30,000-below equi­ librium. Because engineers are cheap, firms want to hire 30,000 engineers, but only

Introduction

5

1 0,000 engineers are willing to work at that wage. As finns compete for the few avail­ able engineers, they bid up the wage. There is one last major player in the labor market, the government. The government can impose taxes on a worker's earnings, subsidize the training of engineers, impose a payroll tax on finns, demand that engineering finns hire two black engineers for each white one hired, enact legislation that makes some labor market transactions illegal (such as paying engineers less than $50,000 annually), and increase the supply of engineers by encouraging their immigration from abroad. All of these actions will change the equilib­ rium that will eventually be attained in the labor market. The government regulations, therefore, set the ground rules that will guide exchanges in the labor market.

The Trans-Alaska Oil Pipeline In January 1 968, oil was discovered in Prudhoe Bay in remote Northern Alaska. The oil reserves were estimated to be greater than 1 0 billion barrels, making it the largest such discovery in North America. l There was one problem with the discovery-the oil was located in a remote and frigid area of Alaska, far from where the bulk of the consumers lived. To solve the daunting problem of transporting the oil to those consumers who wanted to buy it, the oil companies proposed that a 48-inch pipeline be built connecting the 789-rnile stretch from northern Alaska to the southern (and ice-free) port of Valdez. At Valdez, the oil would be transferred to oil supertankers. These huge ships would then cheaply deliver the oil to consumers in the United States and elsewhere. The oil companies j oined forces and fonned the Alyeska Pipeline Project. The construction project began in the spring of 1 974, after the U.S . Congress gave its approval, over the objection of environmentalists, in the wake of the 1 973 oil embargo. Construction work continued for 3 years and the pipeline was completed in 1 977. Alyeska employed about 25,000 workers during the summers of 1 974 through 1 977, and its subcontractors employed an additional 25,000 workers. Once the pipeline was built, Alyeska reduced its pipeline-related employment to a small maintenance crew. Many of the workers employed by Alyeska and its subcontractors were engineers who built pipelines across the world. Very few of these engineers were resident Alaskans. The remainder of the Alyeska workforce consisted of unskilled labor, such as truck drivers and excavators. Many of these less-skilled workers were resident Alaskans. The theoretical framework summarized by the supply and demand curves can help us understand the shifts in the labor market that should have occurred in Alaska as a result of the Trans-Alaska Pipeline System. As Figure 1 -2 shows, the Alaskan labor market was initially in an equilibrium represented by the intersection of the demand curve Do and the supply curve. The labor demand curve tells us how many workers would be hired in the Alaskan labor market at a particular wage, and the labor supply curve tells us how many workers are willing to supply their services to the Alaskan labor market at a particular wage. A total of Eo Alaskans were employed at a wage of Wo in the initial equilibrium.

lThis discussion is based on the work of William J. Carrington, "The Alaskan Labor Market During the Pipeline Era," Journal of Political Economy 104 (February 1996): 18&-218.

6

Chapter One

Figure 1 ·2

The Alaskan Labor Market and the Construction of the Oil Pipeline

The construction of the oil pipeline shifted the labor demand curve in Alaska from Do to Dl' resulting in higher wages and employment. Once the pipeline was completed, the demand curve reverted back to its original level. and wages and employment fell.

Earnings ($) Labor Supply Curve

L-____-..L.__....J.______ .

Eo

£1

Employment

The construction project clearly led to a sizable increase in the demand for labor. Figure 1 -2 illustrates this shift by showing the demand curve moving outward from D o to D!. The outward shift in the demand curve implies that-at any given wage­ Alaskan employers were looking for more workers. This theoretical framework immediately implies that the shift in demand moved the Alaskan labor market to a new equilibrium, one represented by the intersection of the new demand curve and the original supply curve. At this new equilibrium, a total of E persons were employed at a wage of WI' The theory, therefore, predicts that the l pipeline construction project would increase both employment and wages. As soon as the project was completed, however, and the temporary need for construction workers disappeared, the demand curve would have shifted back to its original position at Do' In the end, the wage would have gone back down to Wo and Eo workers would be employed. In short, the pipeline construction project should have led to a temporary increase in both wages and employment, and both the wage and employment should have fallen back to "normal" levels after the construction project was completed. Figure 1 - 3 illustrates what actually happened to Alaskan employment and earn­ ings during the 1 968- 1 983 period. Because Alaska's population grew steadily for some decades, Alaskan employment also rose steadily even before the oil discovery in Prudhoe Bay. The data clearly show, however, that employment "jumped" in 1 975, 1 976, and 1 977, and then went back to its long-run growth trend in 1 977. The earnings of Alaskan workers also rose substantially during the relevant period. After adjusting for inflation, the monthly earnings of Alaskan workers rose from an average of $2,648 in the third quarter of 1 973 to $4,140 in the third quarter of 1976, an increase of 56 percent. By 1 979, the real earnings of Alaskan workers were back to the level observed prior to the beginning of the pipeline construction project.

Introduction

7

Wages and Employment in the Alaskan Labor Market, 1968-1983

Figure 1 -3 Employment

Monthly Salary ($)

250,000

4,500

230,000 . ,

210,000 I

190,000 I

170,000

,

....

\ •

• •

'.

• •

\ •

4,000

,. 't

't

3,500

f

150,000

3,000

130,000 2,500

1 10,000 90,000 70,000

,

I

\

•

�

Wage

, \ , '" . " �

, \ • • ".

2,000

Employment

50,000

1,500 1968

1970

1972

1974

1976

1978

1980

1982

1984

Source: William 1. Carrington, "The Alaskan Labor Market During the Pipeline Era," Journal of Political Economy 104 (February 1 996): 199.

It is worth noting that the temporary increase in earnings and employment occurred because the supply curve of labor is upward sloping, so that an outward shift in the demand curve moves the labor market to a point further up on the supply curve. As we noted earlier, an upward-sloping supply curve implies that more workers are willing to work when the wage is higher. It turns out that the increase in labor supply experienced in the Alaskan labor market occurred for two distinct reasons. First, a larger fraction of Alaskans were willing to work when the wage increased. In the summer of 1 973, about 39 percent of Alaskans were working. In the summers of 1 975 and 1 976, about 50 percent of Alaskans were working. Second, the rate of population growth in Alaska accelerated between 1 974 and 1976-because persons living in the lower 48 states moved to Alaska to take advantage of the improved economic opportunities offered by the Alaskan labor market-despite the frigid weather conditions there. The increase in the rate of population growth, however, was temporary. Population growth reverted back to its long-run trend soon after the pipeline construction project was completed.

1 -3 WHY DO WE NEED A THEORY? We have just told a simple story of how the Trans-Alaska Pipeline System affected the labor market outcomes experienced by workers in Alaska-and how each of the actors

8

Chapter One

in our story played a major role. The government approved the pipeline project despite the environmental hazards involved; firms who saw income opportunities in building the pipeline increased their demand for labor; and workers responded to the change in demand by increasing the quantity of labor supplied to the Alaskan labor market. We have, in effect, constructed a simple theory or model of the Alaskan labor market. Our model is characterized by an upward-sloping labor supply curve, a downward-sloping labor demand curve, and the assumption that an equilibrium is eventually attained that resolves the conflicts between workers and firms. As we have just seen, this model predicts that the construction of the oil pipeline would temporarily increase wages and employment in the Alaskan labor market. Moreover, this prediction is testable-that is, the predictions about wages and employment can be compared with what actually happened to wages and employment. It turns out that the supply-demand model passes the test; the data are consistent with the theoretical predictions. Needless to say, the model of the labor market illustrated in Figure 1-2 does not do full justice to the complexities of the Alaskan labor market. It is easy to come up with many factors and variables that our simple model ignored and that could potentially influence our predictions. For instance, it is possible that workers care about more than just the wage when they make labor supply decisions. The ability to participate in a prestigious or cutting-edge project like the construction of the Trans-Alaska Pipeline could have attracted engineers at wages lower than those offered by firms engaged in more mundane projects- 0

;x:

40

>.

�" �

35 30 0

10,000 Per Capita GDP

20,000

55

50

•

45 40 •

35 30 0

•

•

..

.,

•

• •

• •

10,000 Per Capita GDP

.

•

-g � ""'0

45

;x:

40

i!l

::> 0

>.

�

� 20,000

50

35 30

a

1 0,000 Per Capita GDP

20,000

Introduction

17

reduces weekly hours of work by 0.0005 hour. A more meaningful way of restating this fact is that a $ 1 ,000 increase in a country's per capita GDP reduces the length of the workweek by half an hour. The intercept indicates that the workweek lasts 45 .8 hours if the country's per cap­ ita GDP is zero. We have to be very careful when we use this result. After all, no coun­ try has zero per capita GDP. We are, in effect, extrapolating the regression line to the left until it hits the vertical axis. In other words, we are using the regression line to make an "out-of-sample" prediction. It is not uncommon to get absurd results when we do this type of extrapolation: After all, what does it mean to say that a country has zero per .:apita income? An equally silly extrapolation takes the regression line and · extends it to the right until it hits the horizontal axis. This gives us the per capita GDP that would lead to zero hours of work. If we do this extrapolation, we would find that workers do not work once per capita GDP hits $9 1 ,600. One has to wonder, however, how a country where no one works generates a $9 1 ,600 per capita income. As the dis­ cussion illustrates, it is risky to predict outcomes that lie outside the range of the data. Figure 1 -7

55

The Scatter Diagram and the Regression Line

18

Chapter One Margin of Error and Statistical Significance If we plug the data reported in Table 1 - 1 into a statistics or spreadsheet program, we will find that the program reports many more numbers than just the intercept and slope of a regression line. The program also reports what are called standard errors, or a measure of the statistical precision with which the coefficients are estimated. When poll results are reported in newspapers or on television, it is said that 52 percent of the population believes that tomatoes should be bigger and redder, with a margin of error of plus or minus 3 percent. We use standard errors to calculate the margin of error of our estimated regression coefficients. In our data, it turns out that the standard error for the intercept a is 1 .4 and that the standard error for the slope [3 is 0.000 1 . The margin of error that is used commonly in econometric work is twice the standard error. The regression thus allows us to con­ clude that a $1 increase in per capita GDP reduces hours of work by 0.0005 hour per week, with a margin of error of plus or minus 0.0002 hour (or twice the standard error of 0.000 1 ) . In other words, our data are consistent with the argument that a $ 1 ,000 increase in per capita income reduces the length of the workweek by as little as 0.3 hour or by as much as 0.7 hour per week. Statistical theory indicates that the true impact of the $ 1 ,000 increase in per capita income on hours of work lies within this range with a 95 percent probability. We have to allow for a margin of error because our data are imperfect. Our data are measured with error, extraneous factors are being omitted, and our data are typically based on a random sample of the population. The regression program will also report a t statistic for each regression coefficient. The t statistic helps us assess the statistical significance of the estimated coefficients. The t statistic is defined as:

t statistic

absolute value of regression coefficient standard error of regression coefficient

( 1 -4)

If a regression coefficient has a t statistic above the "magic" number of 2, the regres­ sion coefficient is said to be significantly different from zero. In other words, it is very likely that the true value of the coefficient is not zero, so there is some correlation between the two variables that we are interested in. If a t statistic is below 2, the coeffi­ cient is said to be insignificantly different from zero, so we cannot conclude that there is a correlation between the two variables of interest. Note that the t statistic associated with our estimated slope is 5 (or 0.0005 -70.000 1 ), which is certainly above 2. Our estimate of the slope is significantly different from zero. Therefore, it is extremely likely that there is a negative correlation between the length of the workweek and per capita income. Multiple Regression Up to this point, we have focused on a regression model that contains only one inde­ pendent variable, per capita income. It is likely, however, that weekly hours of work in a given country are influenced by many other social, political, and economic factors, such as the level of unionization in the labor market, the extent to which manufactured goods are exported, and the level of aggregate demand in the economy. The simple correlation between hours of work and per capita income implied by the regression

Introduction

19

model in equation ( 1 -3) could be confounding the effect of some of these other vari­ ables. To isolate the relationship between hours of work and income (and avoid what is called omitted variable bias), it is important to control for cross-country differences in other characteristics that might influence hours of work. To provide a concrete example, suppose we believe that fInns use labor more inten­ sively in rapidly growing economies, so the length of the workweek will be positively correlated with the economy's annual growth rate. We can then write the regression model as: Hours of work

= ex

+

� per capita GDP + -y growth rate

( 1 -5)

We now wish to interpret the coefficients in this multiple regression model-a regres­ sion that contains more than one independent variable. Each coefficient in the mUltiple regression measures the impact of a particular variable on hours of work, holding other things equal. For instance, the coefficient � gives the change in hours of work resulting from a $ 1 increase in per capita GDP, holding constant the growth rate in the economy. Similarly, the coefficient -y gives the change in hours of work resulting from a 1 percentage point rise in the country's growth rate, holding constant the per capita GDP. Finally, the intercept ex gives weekly hours of work in a fIctional country that has zero per capita GDP and a zero growth rate. The last column in Table 1 - 1 reports the annual growth rate of per capita GDP in our sample of 36 countries. Because we now have two independent variables, our scat­ ter diagram is three dimensional. The regression "line," however, is still the line that best fits the data in this three-dimensional space. If we plug these data into a computer program to estimate the regression model in equation ( 1 -5), the estimated regression line is given by: Hours of work

=

45.8 ( 1 .3)

-

0.0006 per capita GDP + 1 .0 growth rate (0.000 1 ) (0.4)

( 1 -6)

where the standard error of each of the coefficients is reported in parentheses below the coefficient. Note that a $ 1 increase in the country's per capita GDP reduces the length of the workweek by 0.0006 hour even after holding constant the economy's growth rate. In other words, if we compare two countries that have the same growth rate but differ in per capita income by $ 1 ,000, the workweek is 0.6 hours shorter in the country with the larger per capita GDP. We also find that the growth rate has a positive effect on hours worked. In particular, a 1 percentage point increase in the growth rate increases week­ ly hours of work by 1 hour per week. The mUltiple regression model can, of course, be expanded to incorporate a larg­ er number of independent variables . In fact, the empirical findings reported throughout this book are typically obtained by estimating multiple regression mod­ els that isolate the correlation between the two variables of interest after controlling for all other relevant factors. Regardless of how many independent variables are included in the regression, however, all the regression models are estimated in essentially the same way: The regression line best summarizes the trends in the underlying data.

C HA P

T .E R

Labor Supply

2

In order that people may be happy in their work . . . they must not do too much of it. Herman Melville

Each of us must decide whether to work and, once employed, how many hours to work. At any point in time, the economywide labor supply is given by adding the work choices made by each person in the population. In the long run, total labor supply also depends on the fertility decisions made by earlier generations (which determine the size of the current population). The economic and social consequences of these decisions vary dramatically over time. In 1 947, 90 percent of American men and 32 percent of American women worked. By 1 997, the proportion of working men had declined to 75 percent, whereas the proportion of working women had risen to 60 percent. Over the same period, the length of the average workweek in a private-sector job fell from 40 to 35 hours. These labor supply trends have surely altered the nature of the American family as well as greatly affected the economy's productive capacity. This chapter and the next develop the framework that economists use to study labor supply decisions. In this framework, individuals seek to maximize their well­ being by consuming goods (such as fancy cars and nice homes) and leisure. Goods have to be purchased in the marketplace. Because most of us are not independently wealthy, we must work in order to earn the cash required to buy the desired goods. The economic trade-off can be clearly stated: If we do not work, we can consume a lot of leisure, but we will have to do without the cars and commodities that make life much more enjoyable. If we do work, we will be able to afford many of these goods, but we must give up some of our valuable leisure time. The model of labor-leisure choice isolates the person's wage rate and income as the key economic variables that guide the allocation of time between the labor market and leisure activities. In this chapter, we use the framework to analyze "static" labor supply decisions, the decisions that affect a person's labor supply at a point in time. In the next chapter, we extend this basic model to explore, among other things, how the timing of leisure activities changes over the life cycle and the household's fertility decision. This economic framework not only helps us understand why women's work propensities rose and hours of work declined, but also allows us to address a number of 20

21

Labor Supply

questions with important policy and social consequences. For example, do welfare pro­ grams have a disincentive effect on labor supply? Does a cut in the income tax rate increase work incentives? And why do some members of a household tend to specialize in the labor market and other members tend to specialize in "household production"?

2- 1 MEASU RI N G TH E LABOR FORCE On the first Friday of every month, the Bureau of Labor Statistics (BLS) releases its estimate of the unemployment rate for the previous month. The unemployment rate ' statistic is widely regarded as a measure of the overall health of the U.S. economy. In fact, the media often interprets the minor month-to-month blips in the unemployment rate as a sign of either a precipitous decline in economic activity or a surging recovery. The unemployment rate is tabulated from the responses to a monthly BLS survey called the Current Population Survey (CPS). In this survey, about 60,000 households are questioned about their work activities during a particular week of the month (that week is called the reference week). Almost everything we know about the size of the U.S. labor force comes from tabulations of the CPS data. The survey instrument used by the CPS has also influenced the development of surveys in many other countries. In view of the importance of this survey in the calculation of labor force statistics both in the United States and abroad, it is important to review the various definitions of labor force activities that are routinely used by the BLS to generate its statistics. The CPS classifies all persons aged 16 or older into one of three categories: the employed, the unemployed, and the residual group who is said to be out of the labor force. To be employed a worker must have been at a job with pay for at least 1 hour, or worked at least 1 5 hours on a nonpaid job such as the family farm. To be unemployed, a worker must either be on a temporary layoff from a job, or have no job but be active­ ly looking for work in the 4-week period prior to the reference week. Let E be the number of persons considered to be employed, and U the number of persons considered to be unemployed. A person participates in the labor force if he or she is either employed or unemployed. The size of the labor force (LF) is then given by:

LF = E + U

(2- 1 )

Note that the vast majority of employed persons (those who work at a job with pay) are counted as being in the labor force regardless of how many hours they work. The size of the labor force, therefore, does not say anything about the "intensity" of work. The labor force participation rate gives the fraction of the popUlation (P) that is in the labor force and is defined by: Labor force participation rate

LF

=p

(2-2)

The employment-population ratio, sometimes called the employment rate, gives the fraction of the population that is employed, or:

22

Chapter Two

Employment-population ratio

E

= -

p

(2-3)

Finally, the unemployment rate is given by the fraction of labor force partici­ pants who are unemployed: Unemployment rate

U

= -

LF

(2-4)

The Hidden Unemployed The BLS calculates an unemployment rate based on a subjective measure of what it means to be unemployed. To be considered unemployed, a person must either be on temporary layoff or claim that he or she has "actively looked for work" in the past 4 weeks. Persons who have given up and stopped looking for work are not counted as unemployed, but are considered to be "out of the labor force." The unemployment statistics, therefore, can be interpreted in different ways. Dur­ ing the 1 992 presidential campaign, for instance, it was alleged that the official unem­ ployment rate (that is, the BLS statistic) understated the depths of the recession. In particular, the Clinton campaign argued that because it was so hard to find work, many laid-off workers became discouraged with their futile job search activity, dropped out of the labor market, and stopped being unemployed. It was then argued that this army of hidden unemployed should be added to the pool of unemployed workers, so that the unemployment problem was significantly worse than it appeared from the BLS data. In fact, adding a widely used measure of hidden unemployment to the BLS sta­ tistic would have increased the unemployment rate in October 1 992 from 7.4 percent to 8.2 percent. ' Some analysts have argued that a more objective measure of aggregate economic activity may be given by the employment-population ratio. The employment­ population ratio simply indicates the fraction of the population at a job. This statistic has the obvious drawback that it lumps together persons who say they are unemployed with persons who are classified as being out of the labor force. Although the latter group includes some of the hidden unemployed, it also includes many individuals who may have little intention of working at the present time (for example, retirees, women with small children, and students emolled in school). A decrease in the employment-population ratio could then be attributed to either increases in unemployment or to umelated increases in fertility or school emollment rates. It is far from clear, therefore, that the employment-population ratio provides a better measure of fluctuations in economic activity than the unemployment rate. We

IV.S. Bureau of Labor Statistics, Employment and Earnings. Washington, D.C.: Government Printing Office, January 1993.

Labor Supply

23

shall return to some of the questions raised by the ambiguity in the interpretation of BLS labor force statistics in the next chapter.

2-2 BASIC FACTS ABOUT LABOR SUPPLY This section summarizes some of the key trends in labor supply in the United States.2 These facts have motivated much of the research on labor supply conducted in the past three decades. Table 2- 1 documents the historical trends in the labor force participa- . tion rate of men. There has been a steady fall in the labor force participation rates of men during much of the century, from over 90 percent in 1900 to 75 percent by 1 997 . Much of this decline is attributable to a precipitous drop in the labor market attach­ ment of men near or above age 65 , as an ever-larger fraction of men choose to retire earlier. The labor force participation rate of men aged 45 to 64, for example, declined by nearly 10 percentage points between 1 950 and 1 997; the participation rate of men over 65 declined from 46 to 1 7 percent over the same period. In contrast, the labor force participation rate of men in their prime working years (ages 25 to 44) declined slightly, from 97 percent in 1 950 to 93 percent in 1 997. As Table 2-2 shows, there has also been a huge increase in the labor force partici­ pation rate of women. At the beginning of the century, only about 20 percent of women were in the labor force. As late as 1 950, even after the social and economic disruptions caused by two world wars and the Great Depression, only 30 percent of women were in the labor force. During the past 40 years, however, the labor force par­ ticipation rate of women increased dramatically. By 1 997, almost 60 percent of all women were in the labor force. It is worth noting that the increase in female labor force participation was particularly steep among married women. Their labor force participation rate almost doubled in recent decades, from 32 percent in 1 960 to 62 per­ cent in 1 997. These dramatic shifts in labor force participation rates were accompanied by a siz­ able decline in average hours of work per week-with most of this decline occurring prior to 1940. Figure 2 - 1 illustrates that the typical person employed in manufacturing production worked 55 hours per week in 1 900 and 38 hours in 1 940. The length of the manufacturing workweek has remained constant at about 37 to 38 hours during the postwar era. Finally, there exist sizable differences in the various dimensions of labor supply across demographic groups at a particular point in time. As Table 2-3 shows, men not only have larger participation rates than women, but are also less likely to be employed in part-time jobs. Only 4 percent of working men are in part-time jobs, as

2For more detailed discussions of the trends in labor supply in the United States and in other countries, see John H. Pencavel, "Labor Supply of Men: A Survey;' in Orley C. Ashenfelter and Richard Layard, editors, Handbook of Labor Economics, Volume L Amsterdam: North-Holland, 1986, pp. 3-102; and Mark R. Killingsworth and James J. Heckman, "Female Labor Supply: A Survey," in Orley C. Ashenfelter and Richard Layard, editors, Handbook of Labor Economics, Volume L Amsterdam: North-Holland, 1986, pp. 1 03-204.

24

Chapter Two

TABLE 2- 1

Labor Force Participation Rates of Men, 1900-1997

Year

All Men

Men Aged 25-44

Men Aged 45-M

Men Aged over 65

1900 1920 1930 1 940 1 950 1960 1970 1980 1 990 1 997

90.9% 89.8 87.3 84.3 86.8 84.0 80.6 77.4 76. 1 75.0

98.5% 99.4 99.6 98.7 97. 1 97.7 96.8 95.4 94.3 92.8

94. 1 % 94.5 94.8 92.5 92.0 92.0 89.3 82.8 77.9 82.4

67.5% 60.0 58.4 46.2 45. 8 33. 1 26.8 1 9.0 16.4 17.1

Sources: U.S. Bureau of the Census, Historical Statistics oJ the United States, Colonial Years to 1970, Washington, DC: Government Printing Office. 1975; U.S. Bureau of the Census, Statistical Abstract oj the United States, Washington, DC: Government Printing Office, various issues.

TABLE 2-2

Labor Force Participation Rates of Women, 1900-1996

Year

All Women

Single Women

Married Women

Widowed, Divorced, or Separated

1900 1910 1930 1940 1 950 1960 1 970 1980 1 990 1997

20.6% 25.5 25.3 26.7 29.7 37.7 43.3 5 1 .5 57.5 59.8

45.9% 54.0 55.2 53.1 53.6 58.6 56.8 64.4 66.7 67.9

32.5% 34. 1 34.4 33.7 35.5 3 1 .9 40.5 49.8 58.4 6 \ .6

5.6% 1 0.7 1 \ ,7 13.8 2 1 .6 4 1 .6 40.3 43.6 47.2 48.6

Sources: Clarence D. Long, The Labor Force Under Changing Income and Employment. Princeton, NJ: Princeton University Press. 1958, Table A-6; and U.S. Department of Commerce. Statistical Abstract oj the United States, 1997. WaShington, DC: Government Printing Office, 1998, p. 408.

' compared to 1 6 percent of working women, The table also documents a strong positive correlation between labor supply and educational attainment for both men and women. In 1 997, 88 percent of male college graduates and 83 percent of female college gradu­ ates were in the labor force, as compared to only 75 and 47 percent of male and female high school dropouts, respectively. There are also racial differences in labor supply, particularly among men. White men have higher participation rates and work more hours than black men. The data presented in this section provide the basic "stylized facts" that have motivated much of the work on the economics of labor supply, As we will see below,

2S

Labor Supply Figure 2-1

Hours of Work in the United States, 1900-1990

55

3 5 +-----�----+--;_--�--� 1900

1910

1920

1930

1 940

1950

1960

1970

1980

1990

Year

Sources: Ethel Jones, "New Estimates of Hours of Work per Week and Hourly Earnings, 1900-1957," Review of Economics and Statistics 45 (November 1%3): 374-385; and Annual Survey ofManufacturers, Washington, D.C.: Government Printing Office, various issues.

the evidence suggests that changes in the economic environment-particularly in wage rates and incomes- 58

Chapter Two

The budget line created by this type of welfare program is illustrated in Figure 2- 1 5 . As before, in the absence of the welfare program, the budget line is given by FE, and the woman would choose the consumption bundle given by point P. She would then consume 70 hours of leisure and work 40 hours. The welfare program shifts the budget line in two important ways. Because of the $500 monthly grant when the woman does not work, the endowment point changes from point E to point G. In addition, the program changes the slope of the budget line. We have seen that the reduction of the grant by 50 cents for every dollar earned in the labor market is equivalent to a 50 percent tax rate on her earnings. The slope of the budget line, therefore, is the net wage rate. Hence the welfare program cuts the (absolute value of the) slope by half, from $ 1 0 to $5. The budget line associated with the welfare program is then given by HG. As drawn, when given the choice between the budget line FE and the budget line HG, the woman opts for the welfare system, and chooses the consumption bundle given by point R. She consumes 1 00 hours of leisure, and works 1 0 hours. Even this liberal "work-fare" program, therefore, seems to have work disincentives because she works fewer hours than she would have worked in the absence of welfare. In fact, it can be demonstrated that a welfare program that includes a cash grant and a tax on labor earnings must reduce labor supply. In particular, point R must be to the right of point P. To see why, draw a hypothetical budget line parallel to the prewelFigure 2- 1 5

Effect of a Welfare Program on Hours of Work

A welfare program that gives the worker a cash grant of $500 and imposes a 50 percent tax on labor earnings reduces work incentives. In the absence of welfare, the worker is at point P. The income effect resulting from the program moves the worker to point Q; the substitution effect moves the worker to point R. Both income and substitution effects reduce hours of work. Consumption ($) F

Slope = - $10

�

H

Slope

$500

=

- $5

G

E

'----+--L---4IIJ- Hours of o Leisure 100 70 1 10

Labor Supply

59

fare budget line, but tangent to the new indifference curve. This line is labeled DD in Figure 2- 15. It is easy to see that the move from point P to point Q is an income effect, and represents the impact of the cash grant on hours of work. This income effect increas­ es the demand for leisure. In terms of the figure, point Q must be to the right of point P. The move from point Q to point R represents the substitution effect induced by the 50 percent tax rate on labor earnings, and point R must be to the right of point Q. The tax cuts the price of leisure by half for welfare recipients. As a consequence, the wel­ fare recipient will demand even more leisure. This stylized example vividly describes the work incentive problems introduced by welfare programs. If our model adequately represents how persons make their work decisions, it may be impossible to develop relatively generous welfare programs with­ out substantially reducing work incentives. Awarding cash grants to recipients, as wel­ fare programs unavoidably do, reduces both the probability of a person working, as well as the number of hours worked by those who remain on the job. In addition, efforts to recover some of the grant money from working welfare recipients are, in effect, a tax on work activities. This tax reduces the price of leisure and further lowers the number of hours that the welfare recipient will work. The study of how welfare programs affect work incentives also illustrates that the basic framework provided by the neoclassical model of labor-leisure choice is only a point of departure. By specifying in more detail how a person's opportunities are affected by government policies, we can easily expand the model to analyze important social questions. The "beauty" of the economic approach, therefore, is that we do not need different models to analyze labor supply decisions under alternative government policies or social institutions. In the end, we are always analyzing the same model­ how workers allocate their limited time and money so as to maximize their utility-but we keep feeding the model more detail about the person's opportunity set. Evidence on the Labor Supply Effects of Welfare Programs

As we saw earlier, the theory predicts that welfare programs create work disincentives. A simple way of forecasting the impact of welfare programs on labor supply is to use the estimated labor supply elasticities (and associated income and substitution effects) to predict how changes in welfare program parameters affect work incentives. If we accept the earlier conclusion that the labor supply elasticity is on the order of - 0. 1 , for instance, a welfare program with an income guarantee of $9,700 (in 1 992 dollars) and a 50 percent tax rate on labor earnings would reduce male labor supply by about 8 per­ cent among recipient households.34 34George 1. Borjas and James J. Heckman, "Labor Supply Estimates for Public Policy Evaluation:' in Indus­ trial Relations and Research Association, Proceedings of the Thirty-First Annual Meeting. Madison, WI: Industrial Relations Research Association, 1979, pp. 320-33 1 . There is also evidence suggesting that one particular variation of the Aid to Families with Dependent Children (AFDC) welfare program had sizable work disincentives. During the 1 980s, some states allowed two-parent households where one of the parents was unemployed to qualify for AFDC benefits and participate in what was called the AFDC-UP program. It has been estimated that if this program had not been in effect, the employment rate of the husbands in par­ ticipating households would have risen from 8 to 59 percent, and that of wives from 5 to 36 percent; see Hilary Williamson Haynes, "Welfare Transfers in Two-Parent Families: Labor Supply and Welfare Partici­ pation Under AFDC-UP," Econometrica 64 (March 1 996): 295-332.

60

Chapter Two

The validity of this conclusion, however, is somewhat debatable because there is so much variation in the estimated responses of labor supply to changes in the wage. To better determine how work incentives respond to changes in welfare program para­ meters, the U.S. federal government sponsored four "negative income tax experi­ ments" between 1 968 and 1 982.35 These experiments were conducted in a number of areas of the country, including New Jersey, Indiana, Seattle, and Denver. The total cost of these experiments was over $285 million. All of the experiments had the same basic format: eligible households were ran­ domly offered a variety of cash grants and tax rates. For instance, in the largest of these experiments (conducted in Seattle and Denver), some of the 4,800 enrolled fami­ lies were offered cash grants that guaranteed 95 percent of the income associated with the poverty line, whereas other families were offered cash grants that guaranteed 1 40 percent of the poverty line. Similarly, the implicit tax rate on labor earnings was set at 50 percent for some families, but at 70 percent for others. There have been many studies that attempt to measure the impact of these experiments on the labor supply of the affected households.36 Overall, the experi­ ments had precisely the expected effect on labor supply variables. Among house­ holds participating in the negative income tax experiments, the probability of employment fell by 3 percentage points for the typical husband and by 7 percentage points for the typical wife. In addition, working men reduced their hours of work by 5 percent, and working women reduced their hours by 2 1 percent. The evidence from the negative income tax experiments, therefore, is consistent with the implica­ tions of our theoretical framework: welfare programs reduce labor supply, both in terms of employment probabilities and in terms of hours worked.

2- 1 1 POLICY APPLICATIO N : THE EARN ED I NCOME TAX CREDIT An alternative approach to improving the economic status of low-income persons is given by the Earned Income Tax Credit (EITC). This program began in 1 975 and has been expanded substantially since. By the late 1 990s, the EITC was the largest cash­ benefit entitlement program in the United States, granting over $25 billion to low­ income households. To illustrate how the EITC works, consider a household composed of a working mother with two qualifying children. In 1 996, this woman could claim a tax credit of up to 40 percent of her earnings as long as she earned less than $8,890 per year, result­ ing in a maximum credit of $3,556. This maximum credit would be available as long as she earned between $8,890 and $ 1 1 ,6 1 0. After reaching the $ 1 1 ,6 1 0 threshold, the 35The programs are typically called "negative income tax" programs because low-income workers, in effect, face a negative income tax rate (that is, they receive income from the government). 36Surveys of the literature are given by Philip K. Robins, "A Comparison of the Labor Supply Findings from the Four Negative Income Tax Experiments," Journal of Humall Resources 20 (Fall 1 985): 567-582; and Robert Moffitt and Kenneth Kehrer, "The Effect of Tax and Transfer Programs on Labor Supply: The Evi­ dence from the Income Maintenance Programs," Research in Labor Economics 4 ( 198 1 ) : 103-150.

Labor Supply

61

credit would begin to be phased out. In particular, each additional dollar earned reduces the credit by 2 1 .06 cents, This formula implies that the credit completely dis­ appears once the woman earns $28,495, Figure 2- 1 6 illustrates how the EITC alters the worker's budget line in a number of important ways-introducing a number of "kinks" and "spikes" into the opportunity set. The figure assumes that the worker does not have any nonlabor income, In the absence of the EITC, the worker faces the straight budget line given by FE. The EITC alters the net wage associated with an additional hour of work, As long as the worker earns less than $8,890 an hour, the worker can claim a tax credit of up to 40 percent of earnings, Suppose, for instance, that the wage rate is $ 1 0 an hour and that the worker decides to work only 1 hour during the entire year. She can then file a tax return that figure 2-16

The EITC and the Budget Line (Not Drawn to Scale)

In the absence of the tax credit, the budget line is given by FE. The EITC grants the worker a credit of 40 percent on labor earnings as long she earns less than $8,890, The credit is capped at $3,556, The worker receives this maximum amount as long as she earns between $8,890 and $11,610. The tax credit is then phased out gradual/yo The worker's "net" wage is 21.06 percent below her actual wage whenever she earns between $11,610 and $28,495.

Consumption ($) F

28,495

Net wage is 2 1 .06% below the actual wage.

1 5 , 1 66

1 2,446

Net wage equals the actual wage.

�------�-+--�

J

1 1 ,6 10 Net wage is 40% above the actual wage.

8,890 E

�------�-- Hours of Leisure 1 10

62

Chapter Two

would grant her a $4 tax credit. Therefore, the EITC implies that the worker's net wage is $ 14, a 40 percent raise. This 40 percent tax credit steepens the budget line, as illustrated by the segment lE in Figure 2- 1 6. If the woman earns $8,890, she receives the maximum tax credit, or $3,556. In fact, she is eligible for this maximum credit as long as she earns anywhere between $8,890 and $ 1 1 ,6 1 0. As long as the worker is in this range, therefore, the EITC does not change the net wage. It simply generates an increase in the worker's income of $3,556-as illustrated by the segment Hl in Figure 2- 1 6, which effectively illustrates that the EITC generates a pure income effect in this range of the program. If the worker's annual earnings exceed $ 1 1 ,6 1 0, the EITC begins to be phased out at a rate of 2 1 .06 cents for every dollar earned. Suppose, for example, that the worker is earning exactly $ 1 1 , 6 1 0 and decides to work an additional hour at $ 1 0 an hour. The tax credit is then cut back by about $2. 1 1 , implying that the worker's net wage is only $7.89 an hour. The EITC, therefore, acts like a wage cut, flattening out the budget line as illustrated by segment GH in Figure 2- 1 6. Once the worker earns $28,495 during the year, she no longer qualifies for the EITC and her budget line reverts back to the original budget line (as in segment FG). This detailed illustration of how the EITC works illustrates how government pro­ grams can generate substantial changes in the worker's opportunity sets-creating var­ ious kinks in the budget line. These kinks can have important effects on the worker's labor supply decision. So how does the EITC affect labor supply? The various panels of Figure 2- 1 7 illustrate a number of possibilities. In Figure 2- 1 7a, the worker would not be in the labor force in the absence of the EITC program (she maximizes her utility by being at the endowment point P). The increase in the net wage associated with the EITC draws the woman into the labor force, and she maximizes her utility by moving to point R. The reason for the increased propensity to work should be clear from our previous dis­ cussion. The EITC increases the net wage for nonworkers, making it more likely that the labor market can match their reservation wages and hence encouraging these per­ sons to join the labor force. The theory, therefore, has a clear and important prediction: the EITC should increase the labor force participation of nonworkers in the targeted groups. In Figure 2- 1 7b, the person would be in the labor force even if the EITC were not in effect (at point P). This worker's annual income implies that the EITC generates, in effect, an income effect-without affecting the net wage. The worker maximizes her utility by moving to point R, and she would be working fewer hours. Finally, in Figure 2- 1 7 c, the person would work a relatively large number of hours in the absence of the EITC (at point P). The EITC cuts her net wage, and she maxi­ mizes her utility by cutting hours and moving to the kink at point R. The theory, therefore, suggests that the EITC has two distinct effects on labor sup­ ply. First, the EITC increases the number of labor force participants. Because the tax credit is granted only to persons who work, more persons will enter the labor force to take advantage of this program. Second, the EITC may change the number of hours worked by persons who would have been in the labor force even in the absence of the program. As drawn in the various panels of Figure 2- 1 7, the EITC motivated workers

Labor Supply Figure 2- 1 7

63

The Impact of the EITe on Labor Supply

The EITC shifts the budget line and will draw new workers into the labor market. In (a), the person enters the labor market by moving from point P to point R. The impact of the EITC on the labor supply ofpersons already in the labor market is less clear. In the shifts illustrated in (b) and (c), the worker reduced hours of work. Consumption ($)

Consumption ($)

p

Hours of Leisure

(a ) EITC Draws Worker into Labor Market

Hours of Leisure ( b ) EITC Reduces Hours of Work

Consumption ($)

Hours of Leisure ( c ) EITC Reduces Hours of Work

Chapter Two

64

to work fewer hours-but the change in the net wage generates both income and sub­ stitution effects and the impact of the EITC on hours worked will depend on the rela­ tive importance of these two effects. The available evidence confirms the theoretical prediction that the EITC draws many new workers into the labor force.37 Some of this evidence is summarized in Table 2-5. The Tax Reform Act of 1 986 substantially expanded the benefits available through the EITe. The theory suggests that this legislative change should have increased the labor force participation rates of the targeted groups. Consider the popu­ lation of unmarried women in the United States. Those who have at least one child potentially qualify for the EITC (depending on how much they earn), whereas those without children do not qualify. Table 2-5 shows that the labor force participation rate of the eligible women increased from 72.9 percent to 75.3 percent before and after the 1 986 tax reform went into effect, an increase of 2.4 percentage points. Before one can conclude that this change in labor force participation rates can be attributed to the EITC, one must consider the possibility that other factors might account for the 2.4 percentage point increase in labor force participation rates observed during that period. A booming economy, for instance, could have easily drawn more women into the labor market even in the absence of the EITe. Or there could exist long-run demographic and social trends that might account for the increas­ ing propensity for these women to enter the labor force. As in the typical experiment conducted in the natural sciences, we need a "control group"-a group of workers who would have experienced the same types of macro­ economic or demographic changes but who were not "injected" with the benefits pro­ vided by the EITe. Such a group could be the group of unmarried women without

TABLE 2-5

The Impact of the Earned Income Tax Credit on Labor Force Participation Participation Rate After Legislation (%)

Participation Rate Before Legislation (%)

Treatment group---t;ligible for the EITC: Unmarried women with children 72.9 Control group-not eligible for the EITC: Unmarried women without children

75.3 95.2

2.4

Difference (%)

Difference­ incDifferences (%)

2.4 95.2

0.0

Source: Nada Eissa and Jeffrey B . Liebman. "Labor Supply Response to the Earned Income Tax Credit," Quarterly Journal of Economics I I I (May 1 996): 617.

37Analyses of the impact of the EITC include John Karl Scholz, "In-Work Benefits in the United States: The Earned Income Tax Credit," Economic }ournal l 06 (January 1996): 156-169; and Nada Eissa and Jeffrey B. Liebman, "Labor Supply Response to the Earned Income Tax Credit," Quarterly Journal of Economics I I I (May 1 996): 605-637.

Labor Supply

65

children. It turns out that their labor force participation did not change at all as a result of the Tax Reform Act of 1 986-it stood at 95.2 percent both before and after the tax reform legislation. The impact of the EITC on labor force participation, therefore, can be netted out by comparing the trend in the "treatment group"-the unmarried women with chil­ dren-with the trend in the "control group"-the unmarried women without children. The labor force participation rate changed by 2.4 percentage points in the treatment group, and by 0 percentage points in the control group. One can then estimate the net impact of the EITC on labor force participation by taking a "difference-in­ differences": 2.4 percentage points minus 0 percentage points, or 2.4 percentage points. This methodology for uncovering the impact of specific policy changes or eco­ nomic shocks on labor market outcomes is known as the difference-in-differences estimator and has become quite popular in recent years. The approach provides a sim­ ple and convincing way of measuring how particular events can alter labor market opportunities. At the same time, however, it is important to recognize that the validity of the conclusion depends crucially on our having chosen a correct control group that nets out the impact of other factors on the trends that we are interested in. It is worth concluding by remarking briefly on the labor supply consequences of the two distinct approaches that we have discussed for subsidizing disadvantaged workers. The typical welfare program uses a "cash grant"-granting income grants to persons who do not or cannot work. As we have seen, these grants can greatly reduce work incentives, and make it more likely that program participants do not enter the labor force. The earned income tax credit, in contrast, subsidizes work. It does not pro­ vide a cash grant, and instead increases the net wage for nonworkers who enter the labor force. As a result, it can greatly increase work incentives, and makes it more likely that eligible persons work.

Summary •

The reservation wage is the wage that makes a person indifferent between working and not working. A person enters the labor market when the market wage rate exceeds the reservation wage. An increase in nonlabor income raises the reservation wage and thus lowers the probability that a person enters the labor market; an increase in the wage rate raises the probability that a person works.

•

Utility-maximizing workers allocate their time so that the last dollar spent on leisure activities yields the same utility as the last dollar spent on goods.

•

An increase in nonlabor income reduces hours of work of workers.

•

An increase in the wage generates both an income and a substitution effect among persons who work. The income effect reduces hours of work; the substitution effect increases hours of work. The labor supply curve, therefore, is upward sloping if substitution effects dominate, and is downward sloping if income effects dominate.

66

Chapter Two •

An increase in nonlabor income reduces the likelihood that a person enters the labor force. An increase in the wage increases the likelihood that a person enters the labor force.

•

The labor supply elasticity for men is on the order of -0. 1 ; the labor supply elasticity for women is on the order of + 0.2.

•

Welfare programs create work disincentives because they provide cash grants to participants as well as tax those recipients who enter the labor market. In contrast, tax credits on earned income create work incentives and draw many persons into the labor force.

Key Concepts budget constraint budget line difference-in-differences estimator employment-population ratio hidden unemployed income effect indifference curve labor force labor force participation rate labor supply curve

labor supply elasticity marginal rate of substitution in consumption marginal utility opportunity set reservation wage substitution effect unemployment rate utility function

Review Questions 1. What happens to the reservation wage if nonlabor income increases, and why? 2. What economic factors determine whether a person participates in the labor force? 3. How does a typical worker decide how many hours to allocate to the labor

market? 4. What happens to hours of work when nonlabor income decreases? 5. What happens to hours of work when the wage rate falls? Decompose the change

in hours of work into income and substitution effects. 6. What happens to the probability that a particular person works when the wage

rises? Does such a wage increase generate an income effect? 7. Why do welfare programs create work disincentives? 8. Why does the earned income tax credit increase the labor force participation rate

of targeted groups? 9 . Why have average hours worked per week declined? 1 0. Why did the labor force participation rate of women increase so much in the past

century?

Labor Supply

67

Problems 1 . Suppose that the indifference curves between consumption and leisure are concave to the origin. How many hours will a person allocate to leisure activities? 2. Suppose that the price of goods purchased in the marketplace rises. What is the impact of this price increase on the worker's reservation wage, on the worker's probability of entering the labor force, and on hours of work? 3. What happens to a worker's desired hours of work if employers pay an overtime premium equal to "time and a half'(that is, 1 .5 times the straight-time wage) for any hours worked in excess of 40 hours? What would happen to hours of work if the overtime premium were raised to double the straight-time wage?

4.

a. Suppose that a worker's commute involves traveling a long distance on a highway that is about to start charging toll fees of $Y. There is no other way for the person to get to her job. What will happen to hours of work as a result of this increase in commuting costs? h. Suppose a worker's current job is located very near her house, so that the time it takes to commute to work is essentially zero. The firm is considering a move to another town, and it will then take the worker 10 hours per week to get to and from work, regardless of how many hours the worker actually decides to work. What will happen to the worker's hours of work (defined as hours actually spent on the job) as a result of this increase in commuting costs? c . Compare the answers in the two parts of this problem, and discuss why the difference arises.

5. You own a small farm near a large city, and you are about to decide whether to work on that small farm or take a job in the city. Your utility depends on your income per day (Y) and on hours of leisure (L). Your daily income from farm work is:

where hr is hours of work on the farm, and your daily income from the city job is: Ye

=

1 4hc

where he is hours of work in the city.

a. If you can work either on the farm or in the city, but not both, which sector would you choose? h. If you can work both on the farm and in the city, how would you allocate your time?

6. The utility function of a worker is represented by U(C, L) = C X L. The marginal utility of leisure is then given by MUL = C and the marginal utility of consumption is given by MUc = L. Suppose that this person currently has a weekly income of $600 and enjoys 70 hours of leisure per week. How many additional dollars of income would it take to make a nonworker give up 10 hours of leisure time?

68

Chapter Two 7. You can either take a bus or drive your car to get to work. A bus pass costs $5 per week, and the weekly costs associated with driving the car to work are $60 (including parking, gas, etc.). You spend half an hour less on a one-way trip if you drive the car than if you take the bus. Suppose your wage rate were $ 1 0 per hour, how would you prefer to get to work? Will you change your preferred mode of transportation if your wage rate rises to $20 per hour? Assume you work 5 days a week and that the time spent riding on a bus or driving a car does not enter your utility directly.

i l"

, J! !

C H A P T E R

3

Topics i n Labor Supply

We see which way the stream of time doth run And are enforced from our most quiet sphere By the rough torrent of occasion. Will iam Shakespeare

In the last chapter, we analyzed "static" models of labor supply. Those models described how persons allocate their time among the labor market, the nonmarket sec­ tor, and leisure activities at a given point in time. The framework helped us understand how some economic variables, such as income and wage rates, influence the decisions of whether to work and how many hours to work. Despite its usefulness, the static model of labor supply does not provide a completely satisfying story of how we allo­ cate our time. After all, we make labor supply decisions continuously over the life cycle, and our current decisions influence economic opportunities in the future and are obviously influenced by the decisions we made in the past. It is evident that we allocate our time in different ways at different stages of our life cycle. In 1 996, for instance, only about 50 percent of men and women aged 1 6 to 19 participated in the labor force. I Among workers aged 35 to 44, however, the partici­ pation rate had risen to 92 percent for men and 78 percent for women. By the time workers reached their late fifties and early sixties, the participation rate declined to 67 percent for men and 50 percent for women. By extending the neoclassical model of labor-leisure choice to incorporate the links between the labor supply decisions we make at different times, we can tell a simple story of how we allocate our time over time. The first part of this chapter describes how labor supply is determined in the long run. This analysis helps us understand how our allocation of time takes advantage of changes in economic opportunities over the life cycle, how labor supply responds to the business cycle, and how economic factors influence the timing of the retirement decision. The chapter also extends the labor-leisure model to account for linkages among the labor supply decisions of household members. For instance, the labor supply 'V.S. Bureau of the Census, Statistical Abstract of the United States, 1997. Washington, DC: Government Printing Office, 1 997, p. 397.

69

i'

I Ii I

Chapter Three

70

decisions of both husbands and wives will likely be influenced by the spouse's eco­ nomic opportunities. The chapter then concludes by showing how economic variables influence the household's fertility decision. The joint fertility decisions of the house­ holds in the economy determine the size of the popUlation-and hence of aggregate labor supply-in the next generation. The extensions of the static labor supply model considered in this chapter, therefore, allow us to address a number of questions that have significant policy rel­ evance: Why have the labor force participation rates of older workers declined so rapidly in the past few decades? How does labor supply respond to changes in the parameters of social security systems (in the United States as well as in other countries)? And how do changes in the wage influence the fertility decisions of families?

3- 1 LABOR S UPPLY OVER TH E LI FE CYCLE

, I

The model of labor supply we presented in the last chapter analyzes the decisions of whether to work and how many hours to work from the point of view of a worker who allocates his time in a single time period, and who ignores the fact that he will have to make similar choices continuously over many years. In fact, because con­ sumption and leisure decisions are made over the entire working life, workers can "trade" some leisure time today in return for additional consumption tomorrow. For instance, a person who devotes a great deal of time to his job today can save some of the additional earnings, and use these savings to increase his consumption of goods in the future. As we will see in Chapter 7, a great deal of evidence suggests that the typical worker's age-earnings profile-the path of wages over the life cycle-has a pre­ dictable path: wages tend to be low when the worker is young; they rise as the worker ages, peaking at about age 50; and the wage rate tends to remain stable or decline slightly after age 50. The path of this typical age-earnings profile is illustrated in Fig­ ure 3- 1 a. This age-earnings profile implies that the price of leisure is relatively low for younger and older workers, and is highest for workers in their prime-age working years. Consider how the worker's labor supply should respond to the wage increase that occurs between ages 20 and 30, or to the wage decline that might occur as the worker nears retirement age. It is important to note that these types of wage changes are part of the aging process for a given worker. A change in the wage along the worker's wage profile is called an "evolutionary" wage change, for it indicates how the wages of a particular worker evolve over time. It is crucial to note that an evolutionary wage change has no impact whatsoever on the worker's total lifetime income. The worker fully expected his wage to go up as he matured, and to go down as he got nearer retire. ment age. As a result, an evolutionary wage change alters the price of leisure-but does not alter the value of the total opportunity set available to the worker over his life cycle. In other words, if we knew that our life cycle age-earnings profile took on the

Topics in Labor Supply Figu re 3-1

71

The Life Cycle Path of Wages and Hours for a Typical Worker

(a) The age-earnings profile of a typical worker rises rapidly when the worker is young, reaches a peak at around age 50, and then wages either stop growing or decline slightly. (b) The changing price of leisure over the life cycle implies that the worker will devote relatively more hours to the labor market when the wage is high andfewer hours when the wage is low. Wage Rate

Hours of Work

50 (a)

Age

50

Age

(b )

precise shape illustrated in Figure 3- 1 a, the fact that our wage would rise from age 37 to age 38 does not increase our lifetime wealth: We already expected this wage increase to occur and would have already incorporated that fact in the calculation of lifetime wealth. Suppose then that the wage falls as a worker nears retirement age. And consider the following question: Would the worker be better off by working a lot of hours at age 50 and consuming leisure in his sixties, or would the worker be better off by working relatively few hours at age 50, and devoting a great deal of time to his job in his six­ ties? The worker will clearly find it worthwhile to work more hours at age 50, invest the money, and buy consumption goods and leisure at some point in the future when the wage is lower and leisure is not as expensive. After all, this type of labor supply decision would increase the worker's lifetime wealth, and allow him to consume many more goods than if the person were to work "excess" hours in his sixties when the wage is low, and consume a great deal of leisure in his fifties when the wage is high. A very young worker faces the same type of situation. His wage is quite low-and he wil1 find it optimal to consume leisure activities when he is very young, rather than in his thirties and forties, when the price of those leisure activities will be very high. The argument, therefore, suggests that we will generally find it optimal to concentrate

\

Chapter Three

72

� \,0 (.;�V -

\)I}� �-

Y\{ \ � �

. SR

=

!1ESR . W !1w ESR

percent change in employment ---'---" -� ---' '--"---

--

percent change in the wage

(4-6)

-

Because the short-run demand curve for labor is downward sloping, it must be the case that the elasticity is negative. In our example, we saw that the industry hires thirty workers when the wage is $20 and hires 56 workers if the wage falls to $30. The short­ run elasticity is:

?>SR

=

in employment percent change "-----'---" � ---' '---

­

percent change in the wage

(56

30)/30 (10 - 20)/20 -

(4-7 )

- 1 .733

Labor demand is said to be elastic if the labor demand curve has an elasticity greater than one in absolute value. Labor demand is said to be inelastic if the elasticity is less than one in absolute value. An Alternative Interpretation of the Marginal Productivity Condition

The requirement that firms hire workers up to the point where the value of marginal product of labor equals the wage gives the firm's "stopping rule" in its hiring decision; that is, the rule that tells the firm when to stop hiring. This hiring rule is also known as the marginal productivity coudition. An alternative and more familiar way of describing profit-maximizing behavior refers to the stopping rule for the firm's output: A profit-maximizing firm should produce up to the point where the cost of producing an additional unit of output (or marginal cost) equals the revenue obtained from sell­ ing that output (or marginal revenue). This condition is illustrated in Figure 4-5. The marginal cost (Me) curve is upward sloping-as the firm expands, costs increase at an increasing rate. For a com­ petitive firm, the revenue from selling an additional unit of output is given by the con­ stant output price p. The equality of price and marginal cost occurs at output q If the firm were to produce fewer than q* units of output, it would increase its profits by expanding production. After all, the revenue from selling an extra unit of output exceeds the costs of producing that unit. In contrast, if the firm were to produce more than q* units, it would increase its profits by shrinking. The marginal cost of producing these units exceeds the marginal revenue. It turns out that the profit-maximizing condition equating price and marginal cost (which gives the optimal level of output to be produced) is identical to the profit­ maximizing condition equating the wage and the value of marginal product of labor (which gives the optimal number of workers to hire). Recall that MPE tells us how many 5. units of output an additional worker produces. Suppose, for instance, that MPE *.

=

Labor Demand Figure 4-5

1 13

The Firm's Output Decision

A profit-maximizing firm produces up to the point where the output price equals the marginal

cost ofproduction. This profit-maximizing condition is the same as the one requiring firms to hire workers up to the point where the wage equals the value of marginal product. Dollars Me

p �------�'-- Output Price

'--

,-- Output

--'"::-

----------

q*

--,--

-

This implies that it takes one-fifth of a worker to produce one extra unit of output. More generally, if one additional worker produces MPE units of output, then liMPE workers will produce one unit of output. Each of these workers gets paid a wage of w dollars. Hence the cost of producing an extra unit of output is equal to:

Me

= w x

1

MPE -­

(4-8)

The condition that the firm produces up to the point where marginal cost equals price can then be written as: w X

1

MPE

= P

(4-9)

By rearranging terms in equation (4-9), we obtain the marginal productivity condition: w = p X MPE' In short, the condition telling the profit-maximizing firm when to stop producing output is exactly the same as the condition telling the firm when to stop hir­ ing workers.

Criticisms of Marginal Productivity Theory

A commonly heard criticism of marginal productivity theory is that it bears little rela­ tion to the way that employers actually make hiring decisions. Most employers have probably never even heard of the concept of value of marginal product-let alone ask

i I I I

1 14

Chapter Four

their personnel managers to conduct detailed and complex calculations that equate this quantity to the wage rate, and thereby determine how many workers they should hire. Proponents of the theory do not take this criticism seriously. One obvious response to the criticism is that if employers did not behave the way that marginal pro­ ductivity theory says they should behave, the employers would not last long in the marketplace. Only the fittest-that is, the most profitable-survive in the competitive market. And if a particular employer is not hiring workers optimally, some other firm will undercut the inefficient employer. One could also argue that the value of the theory of marginal productivity does not necessarily depend on the validity of the assumptions--or on whether it provides a "realistic" depiction of the real world. Tiger Woods and Mark McGwire, for example, surely have not memorized all the physical laws that dictate how golf balls or baseballs react to being hit by a golf club or a bat, and how the laws of gravity and motion deter­ mine how these balls travel through the air. Nevertheless, they have clearly learned­ through innate ability and acquired skills-the implications of these laws for putting a birdie or hitting a home run. In other words, Tiger Woods and Mark McGuire surely act as if they know all the relevant laws of physics. In the same vein, employers probably do not know how to solve the mathematical equations that are required to equate the value of marginal product to the wage rate. Nevertheless, the pressures of a competitive market have forced them to learn the rules of thumb implied by these equations: how to make the hiring decisions that ensure that they can make money and that their business will survive. In short, employers in a competitive labor market must act as if they know the implications of marginal pro­ ductivity theory.

4-3 TH E EMPLOYM ENT DECISION I N TH E LONG RU N In the long run, the firm's capital stock is not fixed. The firm can expand or shrink its plant size and equipment. Therefore, in the long run the firm maximizes profits by choos­ ing both how many workers to hire and how much plant and equipment to invest in. Isoquants

An isoquant describes the possible combinations of labor and capital that produce the same level of output. The isoquant, therefore, describes the production function in exactly the same way that indifference curves describe a worker's utility function. Fig­ ure 4-6 illustrates the isoquants associated with the production function q = feE, K) . The isoquant labeled qo gives all the capital-labor combinations that produce exactly qo units of output, and the isoquant labeled q j gives all the capital-labor combinations yielding q j units. Figure 4-6 illustrates the properties of these constant-output curves:

1. Isoquants must be downward sloping. 2. Isoquants do not intersect.

Labor Demand

figure 4-6

l IS

Isoquant Curves

All capital-labor combinations that lie along a single isoquant produce the same level of output. The input combinations at points X and Y produce '10 units of output. Input combinations that lie on higher isoquants produce more output. Capital

Employment

3. Higher isoquants are associated with higher levels of output. 4. Isoquants are convex to the origin. These properties of isoquants correspond exactly to the properties of indifference curves. Finally, just.as the slope of an indifference curve is given by the negative of the ratio of marginal utilities, the slope of an isoquant is given by the negative of the ratio of marginal products. In particular2:

�K �E

(4-10)

2To prove this, let's calculate the slope of the isoquant between points X and Y in Figure 4-6. In going from point X (0 point Y. the firm hires AE more workers, and each of these workers produces MPE units of output. Hence the gain in output is given by the product AE x MPE. In going from point X to point Y. however, the firm is also getting rid of AK units of capital. Each of these units has a marginal product of MPK. The decrease in output is then given by AK x MPK. Because output is the same at all points along the isoquant, the gain in output resulting from hiring more workers must equal the reduction in output attributable to the cutback in the capital stock so that (AE X MPE) + (AK X MPK) = O. Equation (4-10) is obtained by rear­ ranging the terms in this equation.

Chapter Four

1 16

'\ I,

I) I

The absolute value of this slope is called the marginal rate of technical substitu­

tion. The assumption that isoquants are convex to the origin is an assumption about how the marginal rate of technical substitution changes as the firm switches from capital to labor. In particular, the convexity assumption implies

diminishing marginal

rate of technical substitution (or a flatter isoquant) as the firm substitutes more labor for capital.

Isocosts The firm's costs of production, which we denote by

C, are given by;

C = wE + rK

(4- 1 1 )

Co. The Cr/r units of capital,

Let's consider how the firm can spend a particular amount of money, call it firm could decide to hire only capital, in which case it could hire or it could hire only labor, in which case it would hire

Cr/w workers. The line connect­

ing all the various combinations of labor and capital that the firm could hire with a cost outlay of Co dollars is called an isocost line, and is illustrated in Figure 4-7.

A

number of properties of isocost lines are worth noting. In particular, note that

the isocost line gives the menu of different combinations of labor and capital that are equally costly. Second, higher isocost lines imply higher costs. Figure

Fig",re 4-7

4-7 illustrates

Isocost Lines

All capital-labor combinations that lie along a single isocost curve are equally costly. Capital­ labor combinations that lie on a higher isocost curve are more costly. The slope of an isoquant equals the ratio of input prices (-w/r). Capital

/

i

�:

Isocost with Cost Outlay C,

Isocost with Cost Outlay Co

Employment

Labor Demand

1 17

the isocost lines associated with cost outlays Co and Cl ' where Cj > Co' Finally, one can easily derive the slope of an isocost line by rewriting equation (4- 1 1 ) as:

K

=

C

-

r

w - -E

(4-12)

r

This equation is of the form y a + bx, with intercept Clr and slope - wlr. The slope of the isocost line, therefore, is the negative of the ratio of input prices. =

Cost Minimization

A profit-maximizing firm that is producing qo units of output obviously wants to pro­ duce these units at the lowest possible cost. Figure 4-8 illustrates the solution to this cost-minimization problem. In particular, the firm chooses the combination of labor and capital ( 1 00 workers and 175 machines) given by point P, where the isocost is tan­ gent to the isoquant. At point P, the firm produces % units of output at the lowest pos­ sible cost because it uses a capital-labor combination that lies on the lowest possible

Figure 4-8

The Firm's Optimal Combination of Inputs

A finn minimizes the costs ofproducing qo units of output by using the capital-labor combination at point P, where the isoquant is tangent to the isocost. All other capital-labor combinations (such as those given by points A and B) lie on a higher isocost curve. Capital

Crlr

1 75

100

Employment

1 18

Chapter Four isocost. The firm can produce qo units of output using other capital-labor combina­ tions, such as points A or B on the isoquant. This choice, however, would be more costly because it places the firm on a higher isocost line (with a cost outlay of C, dol­ lars). Note that the firm minimizes costs when it uses the capital-labor combination where the isocost is tangent to the isoquant. This implies that the slope of the isocost equals the slope of the isoquant, or:

(4-1 3) Cost-minimization, therefore, requires that the marginal rate of technical substitution equal the ratio of prices. The intuition behind this condition is easily grasped if we rewrite it as:

w

(4- 14)

r

The last worker hired produces MPE units of output for the firm at a cost of w dollars. If the marginal product of labor is 20 units and the wage is $ 1 0, the ratio MPElw implies that the last dollar spent on labor yields two units of output. Similarly, the ratio MPKlr gives the output yield of the last dollar spent on capital. Cost-minimization requires that the last dollar spent on labor yield as much output as the last dollar spent on capital. In other words, the last dollar spent on each input gives the same "bang for the buck." The hypothesis that firms minimize the cost of producing a particular level of out­ put is often confused with the hypothesis that firms maximize profits. It should be clear that !L�e constrain the firm to produce qo units of output, the firm must produce this level of output in a cost-minimizing way in order to maximize profits. Profit­ maximizing firms, therefore, will always use the combination of labor and capital that equates the ratio of marginal products to the ratio of input prices. This condition alone, ..b9.wever, does not describe the behavior of profit-maximizing firms. After all, the equality of ratios in equation (4- 1 3) was derived by assuming that the firm was going to produce % units of output, regardless of any other considerations. A profit­ maximizing firm will not choose to produce just any level of output. .Rather, a profit­ maximizing firm will choose to produce the optimal level of output-that is, the level of output that maximizes profits, where the !lli!fginal cost of prod��tion equals the * .price of th.�,q!!Jput (or q units in Figure 4-5). . Therefore, the condition that the ratio of marginal products equals the ratio of prices does not tell us everything we need to know about the behavior of profit­ maximizing firms in the long run . We saw earlier that for a given level of capital­ including the optimal level of capital-the firm's employment is determined by equating the wage with the value of marginal product of labor. By analogy, the profit­ maximizing condition that tells the firm how much capital to hire is obtained by equating the price of capital (r) and the value of marginal product of capital VMPK' ' ''No''

.-

Labor Demand

1 19

Therefore, long-run profit maximization also requires that labor and capital be hired . up to the point where:

w = p X MPE

and

r = p X MPK

(4- 15)

These profit-maximizing conditions imply cost minimization. After all, the ratio of the two marginal productivity conditions in equation (4- 1 5) implies that the ratio of input prices equals the ratio of marginal products.3

4-4 THE LON G-RU N DEMAND CURVE FOR LABOR We can now determine what happens to the firm's long-run demand for labor when the wage changes. We are going to consider a firm that is initially producing qo units of output. We assume that this output is the profit-maximizing level of output, in the sense that at that level of production output price equals marginal cost. A profit­ maximizing firm will produce this output at the lowest cost possible, so it uses a mix of labor and capital where the ratio of marginal products equals the ratio of input prices. The wage is initially equal to wo0 The optimal combination of inputs for this firm is illustrated in Figure 4-9, where the firm uses 75 units of capital and 25 workers to produce the qo units of output. Note that the cost outlay associated with producing this level of output equals Co dollars. Suppose that the market wage falls to w ' how will the firm respond? The absolute I value of the slope of the isocost line is equal to the ratio of input prices (or w/r) so that the isocost line will be flattened by the wage cut. Because of the resemblance between the wage change in Figure 4-9 and the wage change in the neoclassical model of labor-leisure choice that we discussed in Chapter 2, there is a strong inclination to duplicate the various steps of our earlier geometric analysis. We have to be extremely careful when drawing the new isocost line, however, because the obvious way of shifting the isocost line is also the wrong way of shifting it. As illustrated in Figure 4-9, we may want to shift the isocost by rotating it around the original intercept Cofr. If this rotation of the isocost line were "legal," the firm would move from point P to point R. The wage reduction increases the firm's employment . . - - .----.. from 25 to 40 workers and increases output from qo to q� units. Although we are tempted to draw Figure 4-9, the analysis is simply wrong! The rotation of the isocost around the original intercept Ca'r implies that the firm's cost outlay is being held constant, at Co dollars. There is nothing in the theory of profit

J

.",

" \

maximization to require that the firm incur the same costs before and after the wage change. The long-run constraints of the firm are given by the technology (as summa­

rized by the production function) and by the constant price of the output and other inputs (p and r). In general, the firm will not maximize its profits by constraining itself to incur the same costs before and after a wage change.

3To restate the point, profit maximization implies cost minimization, but cost minimization need not imply profit maximization.

'\ ! ,......

.

ff?. ...,,- . V'

1 20

Chapter Four

Figure 4-9

The Impact of a Wage Reduction, Holding Constant Initial Cost Outlay at eo

A wage reduction flattens the isocost curve. If thefirm were to hold the initial cost outlay constant at Co dollars, the isocost would rotate around Co and the firm would move from point P to point R. A profit-maximizing firm, however, will not generally want to hold the cost outlay constant when the wage changes. Capital

CrJr

7S �--- q6

e-- Wage Is Wo

2S

40

Employment

Will the Firm Expand If the Wage Falls? '1.

',,-

The decline in the wage will typically cut the marginal cost of producing the firm's output.4 In other words, it is cheaper to produce an additional unit of output when labor is cheap than when labor is expensive. We-then-expect that the drop in the wage �eJ.lcourage the firm to expand prgqIJEtiQ!,l. Figure 4-1 0a illustrates the impact of ; this reduction in marginal cost on the firm s scale (that is, on the size of the firm). Because the marginal cost curve drops from Mea to Mel' the wage cut encourages the firm to produce 200 units of output rather than 100 units. Therefore, the fmn will "jump" to a higher isoquant, as illustrated in Figure 4- l Ob. As noted earlier, the total costs of producing 200 units of output need not be the same as the costs of producing only 100 units. In particular, the new isocost line net!� not 4It can be shown that the marginal cost of productioIlJaljs. when the inputs used in the production process are "normal" inputs-in the sense that \!li:!)'\pn u.s�s_.!II0reJ.aho.r anJJJnQr� J:_aJ?i!,!����!.hoWingJ.!!� l!!i£es- of labor and capital constant. The key result of the theory-that tbe long-run labor demand curve is dow���d-�ioping-al so holds even if labor were an inferior input.

___

,. .

Labor Demand Figure 4- 1 0

121

The Impact of a Wage Reduction on the Output and Employment of a Profit-Maximizing Firm

(a) A .11lilfl£..at.e.cluC£S-. t.r theJnargirwl co� ofW:otjlJction..q,nd encourages the firm to expand (from producing 100 to 200 units). (b) Thefirm moves from point P to point R, increasing the number of workers hiredfrom 25 to 50.

Dollars

Capital

p

1

200

100 100

200

Output

(a) Firm's Output Decision

25

Employment

50

(b) Firm's Hiring Decision

,�!nate. fr()m the same point on the vertical axis as the old isocost line. We do know, however, that a profit-maximizing firm will produce the 200 units of output efficiently; that is, this output will be produced using the cost-minimizing mix of labor and capi­ tal. The optimal mix of inputs, therefore, is given by the point on the higher isoquant where the isoquant is tangent to a new isocost line, which has a slope equal to (and hence is flatter than the original isocost line). The solution is given by point

w

/r

R in

Figure 4- l Ob. As drawn, the firm's employment increases from 25 to 50 workers. We will see below that the firm will

always hire more workers when the wage falls. The position- :

ing of point R in Figure 4- 1 0b also implies that the firm will use more capital. We will see below that this need not always be the case. In general, a wage cut can either increase or decrease the amount of capital demanded. The long-run demand curve for labor (or

DLR) is illustrated in Figure 4- 1 1 . At the

initial wage of wo' the firm hired 25 workers. When the wage falls to

wI'

the firm hires

50 workers. We will now show that the long-run demand curve for labor must be

downward sloping.

1 22

Chapter Four

Figure 4- 1 1

The Long-Run Demand Curve for Labor

The long-run demand curve for labo!' gives the firm 's employment at a given wage and is downward sloping. Dollars

25

50

Employment

Substitution and Scale Effects In our derivation of a worker's labor supply curve, we decomposed the impact of a wage change on hours of work into income and substitution effects. This section uses a siririlar decomposition to assess the impact of a wage change on the firm's employ­ ment. In particular, the wage cut reduces the price of labor relative to that of capital. The decline in the wage encourages the firm to readjust its input mix so that it is more labor intensive (and thus takes advantage of the now-cheaper labor). In addition, the wage cut reduces the marginal cost of production and encourages the firm to expand. As the firm expands, it wants to hire even more workers. These two effects are illustrated in Figure 4-1 2. The firm is initially at point P, where it faces a wage equal to wo' produces 100 units of output, and hires 25 workers. When the wage falls .to w I ' the firm moves to point R, producing 200 units of output and hiring 50 workers. It is useful to view the move from point P to point R as a two-stage move. In the first stage, the firm takes advantage of the lower price of labor by expanding produc­ tion. In the second stage, the firm takes advantage of the wage change by rearranging its mix of inputs (that is, by switching from capital to labor), while holding output con­

stant.

Labor Demand

1 23

I

i

Figure 4- 1 2

Substitution and Scale Effects

A wage cut generates substitution and scale effects. The scale effect (the move from point P to point Q) encourages the firm to expand, increasing the firm 's employment. The substitution effect (from Q to R) encourages the firm to use a more labor-intensive method ofproduction, further increasing employment. Capital D

Celr

Wage Is Wo

25

40

50

To conduct this decomposition, Figure

Employment

4- 1 2 introduces a new isocost line, labeled

DD. This isocost line is tangent to the new isoquant (which produces 200 units of out­

put), but is parallel to the isocost that the firm faced before the wage reduction. In other words, the absolute value of the slope of the DD isocost is equal to wrlr, the original price ratio. The tangency point between this new isocost and the original iso­ quant is given by point Q. We define the move from point P to point Q as the scale effect. The scale effect indicates what happens to the demand for the firm's inputs as the firm expands produc­ tion. As long as capital and labor are "normal inputs," the scale effect increases both the firm's employment (from 25 to 40 workers) and the capital stock.5

5Note that the definition of normal inputs is analogous to that of normal goods in Chapter 2.

I I.

1 24

Chapter Four In addition to expanding its scale, the wage cut encourages the firm to adopt a dif­ ferent method of production, one that is more labor intensive to take advantage of the now-cheaper labor. The substitution effect indicates what happens to the firm's employment as the wage changes, holding output constant, and is given by the move from Q to R in Figure 4- 1 2. Holding output constant at 200 units, the firm adopts a more labor-intensive input mix, substituting away from capital and toward labor. As drawn, the substitution effect raises the flrm's employment from 40 to 50 workers. Note that the substitution effect must decrease the firm's demand for capitaL Both the substitution and scale effects induce the firm to hire more workers as the wage falls. As drawn, Figure 4-1 2 indicates that the firm hires more capital when the wage falls, so that the scale effect (which increases the demand for capital) outweighs the substitution effect (which reduces the demand for capital) . The firm would use less capital if the substitution effect dominated the scale effect. As usual, we use the concept of an elasticity to measure the responsiveness of changes in long-run employment (ELR) to changes in the wage. The long-run elasticity of labor demand is given by:

OLR =

percentage change in employment -=---=---=---=----=--

percentage change in the wage

flELR . W flw ELR

--

-

(4- 1 6)

Because the long-run labor demand curve is downward sloping, the long-run elasticity of labor demand is negative. An important principle in economics states that consumers and firms can respond more easily to changes in the economic environment when they face fewer constraints. Put differently, extraneous constraints prevent us from fully taking advantage of the opportunities presented by changing prices. In terms of our analysis, this principle states that the long-run demand curve for labor is more elastic than the short-run demand curve for labor, as illustrated in Figure 4-1 3 . In the long run, firms can adjust both capital and labor and can fully take advantage of changes in the price of labor. In the short run, the firm is "stuck" with a fixed capital stock and cannot adjust its size optimally.

Estimates of the Labor Demand Elasticity Many empirical studies attempt to estimate the elasticity of labor demand.6 Given our earlier discussion of the problems encountered in estimating the labor supply elastic­ ity, it should not be too surprising that there is a huge range of variation in the esti­ mates of the labor demand elasticity. Although most of the estimates indicate that the labor demand curve is downward sloping, the range of the estimates is very wide. Despite the dispersion in the estimates of the short-nih labor demand elasticity, there is some consensus that the elasticity lies between -0.4 and -0.5. In other words, a 10 percent increase in the wage reduces employment by perhaps 4 to 5 per­ centage points in the short run. The evidence also suggests that the estimates of the

6An encyclopedic survey of this literature is given by Daniel S. Hamennesh, Labor Demand. Princeton, NJ: Princeton University Press, 1993.

Labor Demand F igure

4- 1 3

12S

The Short- and Long-Run Demand Curves for Labor

In the long run, the firm can takefull advantage of the economic opportunities introduced by a change in the wage. As a result, the long-run demand curve is more elastic than the short-run demand curve. Dollars

vi

Long-Run Demand Curve

Employment

long-run labor demand elasticity cluster around - 1 , so the long-run labor demand curve is indeed more elastic than the short-run curve. In the long run, a 1 0 percent change in the wage leads to a 10 percent change in employment. About one-third of the long-run elasticity can be attributed to the substitution effect and about two-thirds is due to the scale effect.

4-5 THE ELASTI CITY OF SUBSTITUTION The magnitude of the firm's substitution effect depends on the curvature of the iso­ quant. Two extreme situations are illustrated in Figure 4- 14. In Figure 4- 1 4a, the iso­ quant is a straight line, with a slope equal to -0.5. In other words, output remains con­ stant whenever the firm lays off two workers and replaces them with one machine. This "rate of exchange" between labor and capital is the same regardless of how many workers or how much capital the firm already has. The marginal rate of technical sub­ stitution is constant when the isoquant is a line. Whenever any two inputs in produc­ tion can be substituted at a constant rate, the two inputs are called perfect substitutes. 7

7Note that our definition of perfect substitution does not imply that the two inputs have to be exchanged on a one-to-one basis; that is, one machine hired for each worker laid off. Our definition only implies that the rate at which capital can be replaced for labor is constant.

1 26

Chapter Four

Theory at Work

California's Overtime Regulations and Labor Demand The Fair Labor Standard Act of 1 938 requires that covered workers be paid 1 . 5 times the wage for any hours worked in excess of 40 hours per week. Unlike most states, Califor­ nia imposes additional regulations on overtime pay. Workers in California must be paid 1 .5 times the wage for any hours worked in excess of 8 hours per day--even if they work fewer than 40 hours during the week. Before 1 974, California's legislation applied only to female workers. After 1 980, the legislation covers both men and women. The theory of labor demand makes a clear prediction about how this legislation should affect the probability that California's workers work more than 8 hours per day. In particu­ lar, the probability that

men

work more than 8 hours per day in California should have

declined between the 1 970s and the 1 980s-because the overtime-per-day regulation was extended to cover men and employers switched to cheaper methods of production. Table 4-2 shows that 1 7 . 1 percent of California's working men worked more than 8 hours per day in 1 973. By 1 985, only 1 6.9 percent of working men worked more than 8 hours per day. Before we can attribute this slight reduction in the length of the workday to the increasing coverage of the overtime legislation, we need to know what would have hap­ pened to the length of the workday for California's men in the absence of the legislation. In other words, we need a control group. One possible control group are the working men in other states-men whose workday was unaffected by the change in California's poli­ cies. It turns out that the fraction of men in other states working more than 8 hours per day

rose

during the same period, from 20. 1

to 22.8 percent. The "difference-in­

differences" estimate of the impact of California's overtime legislation was a substantial reduction of 2.9 percentage points on the probability of working more than 8 hours per day. Alternatively, the control group could be California's working women-who had always been covered by the legislation. The probability that their workday lasted more than 8 hours also rose during the period, from 4.0 to 7.2 percent. Again, the difference­ in-differences approach implies that California's overtime legislation reduced the proba­ bility that working men worked more than 8 hours per day by 3.4 percentage points.

TABLE 4-2

Employment Effects of Overtime Regulation in Califorllia Treatment Group

Control Group

Working Men in California (%)

Working Men in Other Slales (%)

17.1 1 6.9 - 0.2

20. 1 22.S 2.7 - 2.9

Working Women in California (%)

Workers working more than 8 hours per day in:

1 973 1 985 Ditference Difference-in-d ifferences

4.0 7.2 3.2 -3.4

Source: Daniel S. Hamennesh and Stephen J. Trejo, "The Demand for Hours of Labor: Direct Estimates from Califomia," Review ofEconomics and Statistics, forthcoming 2000.

Labor Demand Figure 4 - 1 4

1 27

Isoquants When Inputs Are Either Perfect Substitutes or Perfect Complements

Capital and labor are perfect substitutes if the isoquant is linear (so two workers can always be substitutedfor one machine). The two inputs are perfect complements if the isoquant is right­ angled. The firm then gets the same output when it hires 5 machines and 20 workers as when it hires 5 machines and 25 workers. Capital

(i i

Ii

Capital

100

/' qo Isoquant

5

200 (a) Perfect Substitutes

Employment

20

Employment

(b) Perfect Complements

The other extreme is illustrated in Figure 4-14b. The right-angled isoquant implies that using 20 workers and 5 machines yields qo units of output. If we hold capital con­ stant at five units, adding more workers has no impact on output. Similarly, if we hold labor constant at 20 workers, adding more machines has no impact on output. A firm that does not wish to throw away money has only one recipe for producing qo units of output: use 20 workers and 5 machines. When the isoquant between any two inputs is right-angled, the two inputs are called perfect complements. The substitution effect is very large when labor and capital are perfect substitutes. When the isoquant is linear, the firm minimizes the costs of producing % units of out­ put by hiring either 100 machines or 200 workers, depending on which of these two alternatives is cheaper.s If the prices of the inputs change sufficiently, the firm will "jump" from one extreme to the other. In contrast, t�ere is no substitution effect when the two inputs are perfect comple­ ments. Because there is only one recipe for producing % units of output, a change in 'the wage does not alter the input mix at all. The firm must always use 20 workers and 5 machines to produce qo units of output, regardless of the price of labor and capital. In between these two extremes, there are a great number of substitution possibili­ ties, depending on the curvature of the isoquant. The more curved the isoquant, the

8The student is asked to elaborate on this point in Problem 1 .

" ',"Ii ' ,

:'

!'

1

Ii

"

,I

, I

1 28

Chapter Four smaller the size of the substitution effect. To measure the curvature of the isoquant, we typically use a number called the elasticity of substitution. The elasticity of substitu­ tion between capital and labor (holding output constant) is defined by: Elasticty of substitution

percent change in K/L =

percent change III W/ r

(4- l7)

.

The elasticity of substitution gives the percentage change in the capitalflabor ratio resulting from a 1 percent change in the relative price of labor. As the relative price of labor increases, the substitution effect tells us that the capitalflabor ratio increases (that is, the firm gets rid of labor and replaces it with capital). The elasticity of substitution, therefore, is defined so that it is a positive number. It turns out that the elasticity of substitution is zero if the isoquant is right-angled as in Figure 4- 1 4b, and is infinite if the isoquant is linear as in Figure 4- 14a. The size of the substitution effect, therefore, directly depends on the magnitude of the elasticity of substitution.

4-6 POLICY APPLICATIO N : AFFIRM ATIVE ACTIO N A N D PRODUCTION COSTS There has been a great deal of debate about the economic impact of affirmative action programs in the labor market. These programs typically "encourage" firms to alter the race, ethnicity, or gender of their workforce by hiring relatively more of those workers who have been underrepresented in the firm's hiring in the past. A particular affirma­ tive action plan, for instance, might require that the firm hire one black worker for every two workers hired. Our theory of how firms choose the optimal mix of inputs in the production process helps us understand the nature of the debate over the employment impact of these programs. To simplify the discussion, suppose there are two inputs in the pro­ duction process, black workers and white workers. In this example, therefore, we will ignore the role that capital plays in the firm's production function. This simplification allows us to represent the firm's hiring choices in terms of the two-dimensional iso­ costs and isoquants that we derived in the earlier sections. Suppose further that black and white workers are not perfect substitutes in production, so the isoquants between these two inputs have the usual convex shape, as illustrated in Figure 4- 1 5a. The two groups of workers might have different productivities because they may differ in the amount and quality of educational attainment or because they might have been employed in different occupations and hence are entering this firm with different types of job training. A competitive firm can hire as many black workers as it wants at the going wage of wB and can hire as many white workers as it wants at the going wage of W w. A firm is "color-blind" if the race of the workers does not enter the hiring decision at all. A profit-maximizing color-blind firm would then want to produce q* units of output in the most efficient way possible, where the isoquant is tangent to the isocost. This hir­ ing mix is illustrated by point Q in Figure 4- 1 5a.

Labor Demand Figu re 4- 1 5

1 29

Affirmative Action and the Costs of Production

(a) The discriminatory firm chooses the input mix at point P, ignoring the cost-minimizing rule that the isoquant be tangent to the isocost. An affirmative action program can force the firm to move to point Q, resulting in more efficient production and lower costs. (b) A color-blindfirm is at point P, hiring relatively more whites because of the shape of the isoquants. An affirmative action program increases this firm's costs. Black Labor

Black Labor

q*

White Labor

q*

White Labor

(a) Affirmative Action Reduces Cost of Discriminatory Firm

(b) Affirmative Action Increases Cost of Color-Blind Firm

Suppose, however, that the finn. discriminates against black workers. In other words, the finn's management gets disutility from hiring blacks, and would rather see whites filling most jobs in the finn. The finn's prejudice alters its hiring decision. A

ry finn will not want to be at point Q, but will instead choose an input mix

discriminato

that has more white ·workers and fewer black workers to produce the same q* units of output, such as point

P in the figure.

Note that employment discrimination has moved the finn away from the input

mix where the isoquant is tangent to the isocost. The prejudiced finn has simply de­

cided that it is going to ignore the cost-minimizing rule that the ratio of marginal products

1 30

Chapter Four equals the ratio of input prices because that rule generates the "wrong" color mix for ' the firm's workforce. As a result, the input mix chosen by the firm (or point P) is no longer a point where the isoquant is tangent to the isocost. After all, the slope of the isocost is given by the ratio of wage rates (or -WwfWB)' and a competitive firm cannot influence wages. Therefore, point P does not lie on the lowest isocost that would allow the firm to produce q* units of output, and the prejudiced firm uses an input combina­ tion that costs more than the input combination it would have chosen had it been a color-blind firm. Our theoretical framework, therefore, leads to a very simple-and surprising-conclusion: Discrimination is not profitable.9 Suppose that the government forces the firm to adopt an affirmative action pro­ gram that mandates the firm to hire relatively more blacks. This policy moves the firm's employment decision closer to the input mix that a color-blind firm would have chosen. In fact, if the government fine-tunes the employment quota "just right," it could force the discriminatory firm to hire the same input mix as a color-blind firm (or point Q). This type of affirmative action policy has two interesting consequences. First, the firm's workforce has relatively more blacks. And, second, because it costs less to pro­ duce a particular level of output, the firm is more profitable. lo In short, this type of affirmative action policy leads to a more efficient allocation of resources. The reason is that discriminatory firms are ignoring the underlying economic fundamentals. In par­ ticular, they disregard the information provided by the cost of hiring black and white workers when they make their hiring decisions, and instead go with their "feelings." Affirmative action policies would then force discriminatory firms to ignore those feel­ ings and to pay more attention to prices. Before we conclude that the widespread adoption of affirmative action programs would be a boon to a competitive economy, it is important to recognize that the exam­ ple illustrated in Figure 4- 1 5a adopted a particular prism through which to view the world. In particular, the analysis assumed that the competitive firm is prejudiced, so that the firm's hiring decisions are affected by discrimination. Needless to say, there is an alternative point of view, one that leads to very differ­ ent implications. Suppose, in particular, that firms in the l abor market do not discrimi­ nate at all against black workers. And suppose further that the shape of the firm's iso­ quants is such that the firm hires relatively fewer black workers, even if blacks and whites are equally costly. This situation is illustrated in Figure 14- 15b, where the slope of the isocost is minus one. The color-blind profit-maximizing firm then chooses the input mix at point P in the figure, where the isoquant is tangent to the isocost and the * firm is producing output q in the cheapest way possible. Because of productivity dif­ ferences between the two groups, this color-blind firm hires a workforce that has many white workers and relatively few black workers. 9Chapter 10 presents a much more detailed discussion of discrimination in the labor market. In this section, we use the context of discrimination to show how our approach to modeling the firm's employment decision can inform us about the nature of the debate over many policy-relevant issues. IOBecause tbe affirmative action program increases the demand for black workers and reduces the demand for white workers, the program will also tend to equalize the wages of black and white workers in the labor market.

r .

Labor Demand

131

Suppose the government again mandates that firms hire relatively more blacks. This policy forces the firm to move from point P, the cost-minimizing solution, to point Q, a point where the isoquant is not tangent to the isocost. Therefore, this affir­ mative action program increases the firm's costs of production. It is clear, therefore, that the "initial conditions" assumed in the exercise deter­ mine the inferences that one draws about the labor market impact of affirmative action programs. If one assumes that the typical competitive firm discriminates against black workers, an affirmative action program can force the firm to pay more attention to the economic fundamentals and increase the firm's profits. In contrast, if one assumes that the typical firm does not discriminate, an affirmative action program may substantially reduce the profitability of competitive firms and perhaps drive many of them out of business. As this discussion shows, our perception about the "real world" can greatly influ­ ence the position that we take in the debate over the labor market impacts of affirma­ tive action. ! I This fact reinforces the importance of couching the debate in the context of the empirical evidence about the existence and prevalence of labor market discrimi­ nation. As we will see in Chapter 1 0, labor economists have made a great deal of progress in trying to understand the factors that encourage firms to take race into account when they make hiring decisions, and have derived widely used methodolo­ gies to measure the extent of labor market discrimination.

4-7 MARSHALL S RULES OF DERIVED DEMAND The famous Marshall's rules of derived demand describe the factors that are likely to generate elastic labor demand curves in a particular industry. 1 2 In particular: •

Labor demand is more elastic the greater the elasticity of substitution. This rule

follows from the fact that the size of the substitution effect depends on the curvature of the isoquant. The greater the elasticity of substitution, the more the isoquant looks like a straight line, and the more "similar" labor and capital are in the production process. This allows the firm to easily substitute labor for capital as the wage changes. •

Labor demand is more elastic the greater the elasticity of demandfor the output. When the wage rises, the marginal cost of production increases. A wage

increase, therefore, raises the industry's price and reduces consumers' demand for the product. Because less �Utput is being sold, firms cut employment. The greater the reduction in consumer demand (that is, the more elastic the demand

" Peter Griffin, "The Impact of Affirmative Action on Labor Demand: A Test of Some Implications of the Le Chatelier Principle," Review ofEconomics and Statistics 74 (May 1 992): 251-260, provides a rare empir­ ical study that tries to determine how affirmative action shifts the firm's isocost curve. He finds that the cost of production rises by almost 7 percent among firms subject to affirmative action programs. 12For a technical derivation of Marshall's rules, see Daniel S. Hamermesh, Labor Demand. Princeton, NJ: Princeton University Press, 1993, Chapter 2.

1 32

Chapter Four

curve for the output), the larger the cut in employment and the more elastic the industry's labor demand curve . •

Labor demand is more elastic the greater labor's share in total costs. Suppose labor is a relatively "important" input in the production process, in the sense that labor's share of total costs is large. This situation might occur, for example, when production is very labor intensive, as with a fIrm employing highly trained craftspeople to produce expensive handmade glass ornaments. In this case, even a small increase in the wage rate would substantially increase the marginal cost of production. This increase in marginal cost raises the output price and encourages consumers to cut back on their purchases of the glass ornaments. Firms, in tum, would cut back on employment substantially. In contrast, if labor is "unimportant," so that labor makes up only a small share of total costs, a wage increase has only a small impact on marginal cost, on the price of the output, and on consumer demand. There is little need for the fIrm's employment to shrink. 1 3

•

The demandfor labor is more elastic the greater the supply elasticity of other factors ofproduction, such as capital. We have assumed that fIrms can hire as much capital as they want at the constant price r. Suppose there is a wage increase and fIrms want to substitute from labor to capital. If the supply curve of capital is inelastic, so that the price of capital increases substantially as more and more capital is hired, the economic incentives for moving along an isoquant are greatly reduced. In other words, it is not quite as profItable to get rid of labor and hire capital instead. The demand curve for labor, therefore, is more elastic the easier it is to hire additional capital (that is, the more elastic the supply curve of capital).

An Application of Marshall s Rules: Union Behavior

The behavior of labor unions illustrates how Marshall's rules can help us understand various aspects of the labor market. Consider a competitive fIrm that is initially nonunion. The fIrm hires 1 ,000 workers at the going wage. A union wants to organize

13Actually, Marshall's third rule holds only when the absolute value of the elasticity of product demand exceeds the elasticity of substitution. The reason for this exception follows from the fact that we can arbi­ trarily make the labor input ever less important by redefining it in seemingly irrelevant ways. For example, we can subdivide the labor input of craftspeople producing glass ornaments into the various inputs of Irish craftspeople, Italian craftspeople, Mexican craftspeople, etc. Each of these new labor inputs would obvious­ ly make up a very small fraction of total costs, but it is incorrect to say that the demand curve for Irish craftspeople is less elastic than the demand curve for all craftspeople. As we redefine the labor input into ever smaller subpopulations, the elasticity of substitution among the various inputs rises (Is there any differ­ ence in productivity between the typical Irish and Italian craftsperson?). Marshall's third rule, therefore, holds only when the elasticity of substitution is sufficiently small (in effect, the various labor inputs used by the firm are not essentially the same input broken up into arbitrary categories). This clarification of the exception to Marshall's third rule is due to George J. Stigler, The Theory of Price, 3d ed. New York: Macmillan, 1 966, p. 244.

Labor Demand

1 33

the firm's workers, and promises the workers that collective bargaining will increase the wage substantially. Because the firm's labor demand curve is down­ ward sloping, the firm may respond to the higher wage by moving up its demand curve and cutting back employment.14 Therefore, the union organizing drive has a greater chance of being successful when the demand curve for labor is inelastic. After all, an inelastic demand curve ensures that employment is relatively stable even if the workers get a huge wage increase. In other words, the workers would not have to worry about employment cutbacks if they voted for the union. It is in the union's best interests, therefore, to take whatever actions are available to lower the firm's elasticity of demand. In view of this fact, it is not surprising that unions often resist technological advances that increase the possibilities of substituting between labor and capital. The typesetters' unions, for example, long objected to the introduction of computerized typesetting equipment. This type of behavior is an obvious attempt to reduce the value of the elasticity of substitution. A smaller elasticity of substitution reduces the size of the substitution effect and makes the demand curve for labor more inelastic. Similarly, unions want to limit the availability of goods that compete with the out­ put of unionized firms. For example, the United Auto Workers (UAW) has been a strong supporter of policies designed to prevent (or at least slow down) the entry of Japanese cars into the U.S. market. If the UAW obtained a huge wage increase for its workers, the price of American-made cars would rise substantially. This price increase would drive many potential buyers toward foreign imports. If the union could prevent the entry of Toyotas, Nissans, and Hondas into the American marketplace, consumers would have few alternatives to buying a high-priced American-made car. It is in the union's interests, therefore, to reduce the elasticity of product demand by limiting the variety of goods that are available to consumers. Marshall's rules also imply that unions are more likely to be successful when the share of labor costs is small. Unions can then make high wage demands without rais­ ing the marginal cost (and hence the price) of the output very much. In fact, there is evidence that unions that target small groups of workers such as electricians or carpen­ ters tend to be very successful in getting high wage increases. 15 Because these special­ ized occupations make up a small fraction of total labor costs, the demand curve for these workers is inelastic. Finally, unions often attempt to raise the price of other inputs, particularly nonunion labor. For example, the Davis-Bacon Act requires that contractors involved in publicly financed projects pay the "prevailing wage" to construction workers. 16 Not surprisingly, the prevailing wage is typically defined as the union wage, even if the

"Chapter 1 1 analyzes whether firms, in fact, move along the demand curve in response to a union wage demand, or whether fums might have incentives to move off the demand curve. 15These unions are typically called "craft unions," in contrast to the "industrial unions" that unionize all workers in a given industry (like the UAW). 16For a review of the economic impact of "prevailing wage" policies, see Robert Goldfarb and John Morrall, "The Davis-Bacon Act: An Appraisal of Recent Studies," Industrial and Labor Relations Review 34 (Janu­ ary 1981): 191-206; and A. J. Tieblot, "A New Evaluation of Impacts of Prevailing Wage Law Repeal," Journal of Labor Research 7 (Spring 1 996): 297 322 . -

1 34

Chapter Four contractor hires nonunion labor. This type of regulation raises the cost of switching from union labor to other inputs. Union support of prevailing wage laws, therefore, can be interpreted as an attempt to make the supply of other factors of production more inelastic, and hence reduce the elasticity of demand for union labor.

4-8 FACTOR DEMAND WITH MANY I N PUTS Although we have assumed that the production function only has two inputs-labor and capital-we can easily extend the theory to account for more realistic production processes. There are clearly many different types of workers (such as skilled and unskilled, young and old) and many different types of capital (such as old machines and new machines). The production technology is then best described by the produc­ tion function:

(4- 1 8) where Xi denotes the quantity of the ith input that is used in production. As before, the production function tells us how much output is produced by any combination of the inputs. We can define the marginal product of the ith input, or MPi, as the change in output resulting from a one-unit increase in that input, holding constant the quantities of all other inputs. We can use this production function to derive the short- and long-run demand curves for a particular input. It will still be true that a profit-maximizing firm hires the ith input up to the point where its price (or w) equals the value of marginal product of that input:

(4- 19) All of the key results derived in the simpler case of a two-factor production function continue to hold. The short-run and long-run demand curves for each input are down­ ward sloping; the long-run demand curve is more elastic than the short-run demand curve; and a wage change generates both a substitution effect and a scale effect. One common empirical finding is that the labor demand for unskilled workers is more elastic than for skilled workers. 17 In other words, for any given percentage increase in the wage, the cut in employment will be larger for unskilled workers than for skilled workers. An interesting interpretation of this result is that employment is inherently more unstable for unskilled workers than for skilled workers. As various economic shocks shift the wage of the two types of workers, the number of workers demanded will fluctuate significantly among unskilled workers, but much less so among skilled workers. The presence of many inputs in the production process raises the possibility that the demand for input i might increase when the price of input j increases, but might fall when the price of input k increases. To measure the sensitivity in the demand for a particular input to the prices of other inputs, we define the cross-elasticity of factor demand as: I7Daniel Hamermesh, Labor Demand. Princeton, NJ: Princeton University Press, 1 993, Chapter 3.

Labor Demand

1 35

Cross-elasticity of factor demand

percent change in Xi

=

percent change in Wj

(4-20)

The cross-elasticity of factor demand gives the percentage change in the demand for input i resulting from a 1 percent change in the wage of input). The sign of the cross-elasticity in equation (4-20) provides one definition of whether any two inputs are substitutes or complements in production. If the cross­ elasticity is positive, so that the demand for input i increases when the wage of input ) rises, the two inputs i and ) are said to be substitutes in production. After all, the increase in w. increases the demand for input i at the same time that it reduces the J demand for input j. The two inputs are substitutes because they respond in different ways to the change in the wage; the firm is getting rid of the more expensive input and replacing it with the relatively cheaper input. If the cross-elasticity of factor demand is negative, the demand for input i falls as a result of the increase in w., and inputs i and ) are said to be complements in produc­ J tion. The inputs are complements when they both respond in exactly the same way to a change in wr Put differently, the two inputs "go together." Figure 4- ] 6 illustrates this definition of substitutes and complements in terms of shifting demand curves. In Figure 4- 1 6a, the demand curve for input i shifted up when the price of input ) increased. In this case, the two inputs are substitutes . As input ) became more expensive, employers substituted toward input i. Hence the demand curve for input i shifted to the right. In Figure 4- 1 6b, the demand curve for input i shifted down when the price of input ) rose. In other words, the demand for both inputs fell when input ) became more expensive. The two inputs go together in production and are, therefore, complements. A number of empirical studies suggest that unskilled labor and capital are substi­ tutes and that skilled labor and capital are complements. 18 In other words, as the price of machines rises, employers substitute toward unskilled workers. In contrast, as the price of machines rises and employers cut down on their use of capital equipment, the demand for skilled workers falls because skilled workers and capital equipment "go together." It has been found that a 10 percent increase in the price of capital increases the employment of unskilled workers by 5 percent, and reduces the employment of skilled workers by 5 percent. 1 9 This result has come to b e known a s the capital-skill complementarity hypothe­ sis. This hypothesis has important policy implications. It suggests that subsidies to investments in physical capital (such as an investment tax credit) will have a differen­ tial impact on different groups of workers. Because an investment tax credit lowers the

18Zvi Griliches, "Capital-Skill Complementarity," Review of Economics and Statistics 5 1 (November 1 969): 465-468. See also Ann P. Bartel and Frank Lichtenberg, "The Comparative Advantage of Educated Workers in Implementing New Technology," Review of Economics and Statistics 69 (February 1987): I - I I ; and

Claudia Goldin and Lawrence F Katz, "The Origins of Technology-Skill Complementarity." Quarterly 1 13 (August 1 998): 693-732. Although there is some debate over the validity of this finding, the evidence makes a strong case that, at the very least, skilled workers and capital are much more complementary (or less substitutable) than unskilled workers and capital. 19Kim Clark and Richard B . Freeman, "How Elastic Is the Demand for Labor?" Review of Economics and Statistics 62 (November 1980): 509-520. Journal of Economics

i. ,

i

I

1 36

Chapter four

Figure 4- 1 6

The Demand Curve for a Factor of Production I s Affected b y the Prices of Other Inputs

The labor demand curve for input i shifts when the price ofanother input changes. (a) If the price of a substitutable input rises. the demand curve for input i shifts up. (b) If the price of a complement rises. the demand curve for input i shifts down. Price of Input i

Price of Input i

E

Employment of Input i

(al Demand Curve Shifts Up When the Price of a Substitute Increases

E

Employment of input i

(b) Demand Curve Shifts Down When the Price of a Complement Increases

price of capital to the finn, it increases the demand for capital, reduces the demand for . unskilled workers, and increases the demand for skilled workers. An investment tax credit, therefore, spurs investment in the economy, but also worsens economic conditions for less-skilled workers. The capital-skill complementarity hypothesis also suggests that technological progress-such as the substantial reduction in the price of computing power in the 1 980s and 1 990s- WHS • In a sense, the high wage paid to

232

Chapter Seven

workers with more schooling is a compensating differential that compensates workers for their training costs. If college graduates earned less than high school graduates, no one would get a college education because we are assuming that workers do not get any other benefits from attending college.

Present Value of Age-Earnings Profiles The present value of the earnings stream if the worker gets only a high school educa­ tion is:

PVHS

=

WHS

+

WHS W_ WHS H_ S_ + . .+ + + 46 2 ( 1 + r) (l ( l + r) r)

_

.

(7-4)

where r gives the worker's rate of discount. There are 47 terms in this sum, one term for each year that elapses between the ages of 1 8 and 64. The present value of the earnings stream if the worker gets a college diploma is:

PVCOL = - H .

+

( l + r)

-

H ( 1 + r)

2 -

H -...,( l + r)3

-

Direct Costs of Attending College

WCOL

+

( 1 + r)4

,

H

--

WCOL

( l + r)5

+

. . . +

WCOL

( 1 + r)46

(7-5)

Postcollege Earnings Stream

The first four terms in this sum give the present value of the direct costs of a college education, whereas the remaining 43 terms give the present value of lifetime earnings in the postcollege period. We assume that a person's schooling decision maximizes the present value of life­ time earnings. Therefore, the worker attends college if the present value of lifetime earnings when he gets a college education exceeds the present value of lifetime earn­ ings when he gets only a high school diploma, or:

(7-6) Let's illustrate the worker's decision with a simple numerical example. Suppose a worker lives only two periods and chooses from two schooling options. He can choose not to attend school at all, in which case he would earn $20,000 in each period. The present value of earnings is:

20,000 PV = 20,000 + a 1 + r

(7-7)

He can also choose to attend school in the first period, incur $5,000 worth of direct schooling costs, and enter the labor market in the second period earning $47,500. The present value of this earnings stream is:

- 5 000 +

47,500

(7-8) 1 + r Suppose that the rate of discount is 5 percent. It is easy to calculate that PV a $39,048 and that PV $40,238. The worker, therefore, chooses to attend school. j PV

1

=

'

=

=

Human Capital

233

Note, however, that if the rate of discount were 15 percent, PV $37,39 1 ; PV. = o $36,304; and the worker would not go to school. As this example shows, the rate of discount r plays a crucial role in determining whether he chooses to go to school. The worker goes to school if the rate of discount is 5 percent, but does not if the rate of discount is 15 percent. The higher the rate of dis­ count, therefore, the less likely a worker will invest in education. This conclusion should be easy to understand. A worker who has a high discount rate attaches a very low value to future earnings opportunities-in other words, he discounts the receipt of future income "too much." Because the returns to an investment in education are col­ lected in the far-off future, persons with high discount rates acquire less schooling. It is sometimes assumed that the person's rate of discount equals the market rate of interest, the rate at which funds deposited in financial institutions grow over time. After all, the discounting of future earnings in the present value calculations arises partly because a dollar received this year is not equivalent to a dollar received next year. The rate of discount, however, also depends on how we feel about giving up some of today's consumption in return for future rewards-or our "time preference." Casual observation (and a large number of psychological experiments) suggests that people differ in how they approach this trade-off. Some of us are "present oriented" and some of us are not. Persons who are present oriented have a high discount rate and would be less likely to invest in schooling. Although there is some evidence suggesting that poorer families have a higher rate of discount than wealthier families, we know little about how a person's "time orientation" is determined.3 =

The Wage-Schooling Locus The simple rule that a person should choose the level of schooling that maximizes the present value of earnings obviously generalizes to situations when there are more than two schooling options. The person would then calculate the present value associated with each schooling option (for example, 1 year of schooling, 2 years of schooling, and so on), and choose the amount of schooling that maximizes the present value of the earnings stream. There is, however, a different way of formulating this problem that provides an ,, intuitive "stopping rule. 4 This stopping rule tells the individual when it is optimal to

3Emily C. Lawrance, "Poverty and the Rate of Time Preference: Evidence from Panel Data," Journal of Political Economy 99 (February 1991): 54-77; see also Lawrence L. LeShan, "Time Orientation and Social Class," Journal of Abnormal and Social Psychology 47 (July 1952): 589-592; and Angela O'Rand and Robert A. Ellis, "Social Class and Social Time Preference," Social Forces 53 (September 1974): 53-62. A theoretical analysis of the determinants of the rate of time preference is given by Gary S. Becker and Casey B. Mulligan, "The Endogenous Determination of Time Preference:' Quarterly Journal of Economics 1 12 (August 1997): 729-758. 4Sherwin Rosen, "Human Capital: A Survey of Empirical Research," Research in Labor Economics 1 ( 1 977): 3-39; and David Card, "Earnings, Schooling, and Ability Revisited," Research in Labor Economics 14 ( 1 995): 23-48. An excellent (though more technical) exposition of the schooling model is contained in David Card, "The Causal Effect of Education on Earnings," in Orley Ashenfelter and David Card, editors, Handbook of Labor Economics, Volume 3A. Amsterdam: North-Holland, 1999.

234

Chapter Seven

Figure 7-2

The Wage-Schooling Locus The wage-schooling locus gives the salary that a particular worker would earn if he completed a particular level of schooling. If the worker graduates from high school, he earns $20, 000 annually. Ifhe goes to college for 1 year, he earns $23,000. Dollars

30,000

25,000 23,000

20,000

o

12

13

14

18

Years of Schooling

quit school and enter the labor market. This alternative approach is useful because it also suggests a way for estimating the rate of return to education. Figure 7-2 illustrates the wage-schooling locus, which gives the salary that employers are willing to pay a particular worker for every level of schooling. If the worker gets a high school diploma, his annual salary is $20,000; whereas if he gets 1 8 years of schooling, his annual salary rises to $30,000. The wage-schooling locus is market determined. In other words, the salary for each level of schooling is determined by the intersection of the supply of workers with that particular schooling and the demand for those workers. From the worker's point of view, the salary associated with each level of schooling is a constant.

Human Capital

235

The wage-schooling locus shown in Figure 7-2 has three important properties. I.

The wage-schooling locus is upward sloping. More educated workers must earn more as long as educational decisions are motivated only by financial gains. To attract more educated workers, employers must compensate those workers for the costs incurred in acquiring an education.

2. The slope of the wage-schooling locus tells us by how much a worker's

earnings would increase if he were to obtain one more year of schooling. The slope of the wage-schooling locus, therefore, will be closely related to any empirical measure of "the rate of return" to school.

3. The wage-schooling locus is concave. The monetary gains from each additional year of schooling decline as more schooling is acquired. In other words, the law of diminishing returns also applies to human capital accumulation.s Each additional year of schooling generates less knowledge and lower earnings than previous years.

The Marginal Rate of Return to Schooling The slope of the wage-schooling locus (or !:J..w/!:J..s ) teUs us by how much earnings increase if the person stays in school one more year. In Figure 7-2, for example, the first year of college increases annual earnings in the postschool period by $3,000. The percentage change in earnings from getting this additional year of schooling is 1 5 per­ cent, (or 3,00°/20,000 X 100). In other words, the worker gets a 1 5 percent wage increase from staying in school and attending that first year of coUege. We define this percent­ age change in earnings resulting from one more year of school to be the marginal rate of return to schooling. The marginal rate of return to schooling gives the percentage increase in earnings per dollar spent in educational investments. To see why, suppose that the only costs incurred in going to college are forgone earnings. The high school graduate who delays his entry into the labor market by 1 year is then giving up $20,000. This invest­ ment outlay increases his future earnings by $3,000 annually, thus yielding an annual 1 5 percent rate of return for the first year of college. Because the wage-schooling locus is concave, the marginal rate of return to schooling must decline as a person gets more schooling. For example, the marginal rate of return to the second year of college is only 8.7 percent (a $2,000 return on a $23,000 investment). Each additional year of schooling generates a smaller salary increase, and it costs more to stay in school. In effect, the wage increase generated by an additional year of college gets smaUer at the same time that the cost of continuing in school gets higher. The marginal rate of return schedule, therefore, is a declining 5See George Psacharapoulos, "Returns to Education: A Further International Update and Implications,"

Journal of Human Resources 20 (Fall 1985): 583-604, for evidence supporting the hypothesis that educa­ tional production functions exhibit diminishing marginal productivity,

236

Chapter Seven

function of the level of schooling, as illustrated by the curve labeled MRR in Figure 7-3. The MRR schedule gives the percentage change in annual earnings resulting from each additional year of school.

The Stopping Rule, or When Should I Quit School? Suppose that the worker has a rate of discount r that is constant; that is, it is indepen­ dent of how much schooling the worker gets. The rate of discount schedule, therefore, is perfectly elastic, as illustrated in Figure 7-3. Which level of schooling should a person choose? It turns out that the intersection of the MRR curve and the horizontal rate of discount schedule determines the optimal level of schooling for the worker, or s ' years in the figure. In other words, the stopping rule that tells the worker when he should quit school is given by: Stop schooling when the marginal rate of return to schooling

= r

(7 -9)

This stopping rule maximizes the worker's present value of earnings over the life cycle. To see why, suppose that the worker's rate of discount equals the market rate of interest offered by financial institutions. Would it be optimal for the worker to quit school after completing only s ' years in Figure 7-3? If the worker were to stay in

Figure 7·3

The Schooling Decision The MRR schedule gives the marginal rate ofreturn to schooling, or the percentage increase in earnings resulting from an additional year ofschool. A worker maximizes the present value of lifetime earnings by going to school until the marginal rate of return to schooling equals the rate of discount. A worker with discount rate r goes to school for s' years. Rate of Discount

MRR

L..--' --'_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

s'

s*

Years of Schooling

Human Capital

237

school for an additional year, he would forgo, say, W i dollars in earnings, and the rate of return to this investment equals r' . His alternative would be to quit school, work, and invest the W i dollars in a financial institution that offers a rate of return of only r. Because education yields a higher rate of return, the worker maximizes the present value of earnings by continuing in school. Conversely, suppose that the worker gets more than s' years of school. Figure 7-3 then shows that the marginal rate of return to this "excess" schooling is less than the market rate of interest, so that the extra years of schooling are not profitable. Equation (7-9)-the stopping rule for schooling investments-describes a general property of optimal investment decisions. The wealth-maximizing student who must d�cide if he should quit school faces the same economic trade-off as the owner of a forest who must decide whether to cut down a tree. The longer the tree is in the ground, the larger it gets and the more lumber and revenue it generates. But there are forgone earnings (as well as maintenance costs) associated with keeping the tree in the ground. The tree should be cut down when the rate of return on investing in the tree equals the rate of return on alternative investments. It is important to emphasize, however, that our decision of "what to be when we grow up" is not fully described by the simple schooling model presented in this section. The decision of whether or not to stay in school is obviously influenced by many factors (such as chance encounters with influential teachers and whether a "significant other" moves away to college) , not just the dollar value of the earnings stream. There is also a great deal of uncertainty in the rewards to particular types of education. The assumption that the stu­ dent knows the shape of the wage-schooling locus-and the marginal rate of return pro­ vided by each particular type of education-is clearly false. Economic and social condi­ tions change over time in unpredictable ways, and it is very difficult to forecast how these future shocks shift the rewards to particular types of skills and careers. This uncertainty will surely play a role in our human capital decisions-just like the uncertainty in finan­ cial markets affects the type of financial portfolio that maximizes our wealth.6

7-4 THE WAGE GAP AMONG WORKERS WHO DI FFER I N THEIR EDUCATION The schooling model summarized by Figure 7-3 tells us how a particular worker decides how much schooling to acquire, and as a result also tells us how a worker places in the income distribution in the postschool period. Workers who get more schooling earn more (although they also give up more). The model isolates two factors that lead different workers to obtain different levels of schooling and hence to have different earnings: Workers either have different rates of discount or they face different marginal rate of return schedules. 6Studies that incorporate uncertainty into the analysis of human capital include Josepb G. Altonji, "The Demand for and Return to Education When Outcomes Are Uncertain," Journal ofLabor Economics 1 1 (Jan­ uary 1993): 48-83; and Arthur Snow and Ronald S. Warren, Jr., "Human Capital Investment and Labor Sup­ ply Under Uncertainty," Inzernational Economic Review 31 (February 1990): 1 95-205.

, J; I

, I

!

. :1 I

' I

� '�1

238

Chapter Seven

Differences in the Rate of Discount Consider a labor market with two workers who differ only in their discount rates, as illus­ trated in Figure 7-4a. AI's discount rate is rAL' and Bo's lower discount rate is r80. The fig­ ure shows that Al (who has a higher discount rate) drops out of high school and gets only 1 1 years of education: Bo gets a high school diploma. As we saw earlier, workers who dis­ count future earnings heavily do not go to school because they are "present oriented." Figure 7-4b shows the implications of these choices for the observed earnings dis­ tribution in the postschool period. We have assumed that both workers face the same marginal rate of return schedule. Given our derivation of the marginal rate of return schedule, this assumption is equivalent to saying that both workers face the same wage-schooling locus. The different schooling decisions of the two workers, therefore, simply place them at different points of the common locus. Al ends up at point PAL' where he goes to school 1 1 years and earns wDROP dollars; Bo ends up at point P80' goes to school 1 2 years, and earns wHS dollars. Note that by connecting points PAL and P80 we can trace out the common wage-schooling locus faced by all workers. More­ over, note also that the wage differential between Al and Bo lets us estimate the rate of return to the 1 2th grade, the percentage change in earnings that a worker would experi­ ence in going from the 1 1 th to the 1 2th grade. Schooling and Earnings When Workers Have Different Rates of Discount

Figure 7-4

Al has a higher rate of discount (rAJ than Bo (rBO)' so that Bo graduates from high school but Al drops out. Al chooses point PAL on the wage-schooling locus and Bo chooses point PBO. The observed data on wages and schooling in the labor market traces out the common wage schooling locus of the workers. Rate of Interest

Dollars

MRR

12

11

(a)

Years of Schooling

II

12 (b)

Years of Schooling

,1

II'

Human Capital

239

As we shall see, empirical estimates of the returns to schooling play a crucial role in many discussions of public policy. It is often argued that the government can improve the economic fortunes of the poor by subsidizing their schooling or by man­ dating that all persons attain a particular level of schooling. Consider, for example, the impact of a proposed law requiring all students to complete their high school educa­ tion. By how much would this proposed policy increase the earnings of workers who are now high school dropouts? In effect, this policy "injects" Al (the high school dropout) with one more year of schooling. The wage-schooling locus in Figure 7-4 shows that a high school graduate earns wHS dollars. In other words, AI's earnings would increase to wHS if the law went into effect. A compulsory high school diploma legislation moves the worker along the observed wage-schooling locus. Therefore, as long as workers differ only in their discount rates, we can calculate the marginal rate of return to schooling from the wage differential between two work­ ers who differ in their educational attainment. We can then correctly predict by how much earnings would increase if we pursued particular policies that injected targeted workers with more education.

Differences in Ability It is much more difficult to estimate the rate of return to schooling when all workers have the same rate of discount, but each worker faces a different wage-schooling locus (which, in turn, implies that each worker has a different marginal rate of return sched­ ule). It is often assumed that higher ability levels shift the marginal rate of return schedule to the right, so that the earnings gain resulting from an additional year of

schooling outweighs the increase in forgone earnings. In other words, a more able per­ son gets more from an additional year of schooling. As illustrated in Figure 7-5a,

Bob's MRR schedule lies to the right of Ace's. Because both Bob and Ace have the same rate of discount and because Bob gets more from an additional year of schooling, Bob gets more schooling ( 1 2 years versus 1 1 years). Figure 7-5b illustrates the impact of this ability differential on the earnings distri­ bution. Bob chooses point P O on his wage-schooling locus; Bob gets 1 2 years of B B schooling and earns wHS dollars. Ace chooses point PACE on his wage-schooling locus; Ace goes to school 1 1 years and earns WDROP dollars. Note that Bob's wage-schooling locus lies above Ace's because Bob is more able. The data at our disposal include the education and earnings of the two workers, but do not include their ability levels. Innate ability, after all, is seldom observed. The observed data, therefore, connect the points PACE and P O in the figure and trace out B B the line labeled R. It is important to note that this line does not coincide with either Ace's or Bob's wage-schooling locus. As a result, the observed data on earnings and schooling do not allow us to estimate the returns to schooling. Suppose that the government proposes a law requiring all persons to complete high school. To determine the economic impact of the proposed legislation, we wish to know by how much Ace's earnings would increase if he is injected with one more year of schooling. The available data tell us that a person who graduates from high school (Bob)

Chapter Seven

240

Schooling and Earnings When Workers Have Different Abilities

Figure 7-5

Ace and Bob have the same discount rate (r) but each workerfaces a different wage-schooling locus. Ace drops out of high school and Bob gets a high school diploma. The wage differential arises both because Bob goes to school for one more between Bob and Ace (or WHS W DROP) year and because Bob is more able. As a result, this wage differential does not tells us by how much Ace 's earnings would increase if he were to complete high school (or WACE )' W -

-

Rate of Interest

Dollars

DROP

R Bob

WACE

I ····· ··· "

...........................�'.. .. ............. �...-

_ _ -

Ace

WOROP

r

II

12

Years of Schooling

11

12

Years of Schooling

(b)

(a)

earns wHS dollars and that a high school dropout (Ace) earns WOROP' Note, however, that the wage differential between these two workers does not give the wage gain that Ace would receive if the proposed legislation were enacted. Line R in Figure 7-5b connects points on different wage-schooling curves and provides no information whatsoever about the wage increase that a particular worker would get if he or she were to obtain additional schooling. If the law goes into effect, Ace's earnings would only increase from WOROP to W CE' which is much less than what a high school graduate like Bob now earns (wHs). A Put differently, the wage gap between Ace and Bob arises for two reasons. Bob has more schooling than Ace and, hence, is getting the returns to additional schooling. Bob, however, also earns more than Ace because Bob is more able (and his wage locus lies above Ace's). The wage differential between these two workers, therefore, incor­ porates the impact of both education and ability on earnings.

Ability Bias If there are unobserved ability differences in the population, earnings differentials across workers do not estimate the returns to schooling. This fact is called the ability

24 1

Human Capital

bias in the estimation of the rate of return to schooling. As we have seen, the corre­ lation between schooling and earnings across workers is contaminated by ability differentials, and hence does not provide an answer to the question that motivated our analysis: By how much would the earnings of a particular worker increase if he were to obtain more schooling? Why should one care about ability bias? Suppose that a well-meaning government bureaucrat observes that high school graduates earn $ 1 5 ,000 more per year than high school dropouts. He uses these data to convince policymakers that funding programs that encourage students to complete high school would increase the average wage of high school dropouts by $ 1 5,000. In the bureaucrat's calculations, this earnings gain implies that the program "funds itself' (presumably from higher tax revenues, lower expenditures on social assistance programs, and so forth). We now know that the bureaucrat's argument is fatally flawed. He is assuming that high school graduates and high school dropouts lie on the same wage-schooling locus, so that the low earnings of high school dropouts could be "fixed" if they just could just be injected with more schooling. It might be the case, however, that high school graduates lie on a higher wage-schooling locus. Encouraging high school dropouts to complete their high school education would not lead to a $ 1 5,000 increase in their earnings upon gradua­ tion, and it might be much more difficult to argue that the program "pays its way."

7-5 ESTIMATI NG THE RATE OF RETU RN TO SCHOOLI NG As suggested by the discussion in the previous section, the typical method for estimat­ ing the rate of return to schooling uses data on the earnings and schooling of different workers and estimates the percentage wage differential associated with one more year of schooling-after adjusting the data for differences in other worker characteristics, such as age, sex, and race. The "consensus" estimate of the rate of return to schooling in the United States was probably around 9 percent in the 1 990s, so that schooling seems to be a good investment.? The typical study estimates a regression of the form: log w =

as

+

(7- 1 0)

other variables

where w gives the worker's wage, and s gives the number of years of schooling acquired by this worker. The coefficient a gives the percent wage differential between two workers who differ by 1 year of schooling (holding other variables constant), and is typically interpreted as the rate of return to schooling. 7Hundreds of studies estimate the rate of return to schooling in this fashion. The classic references include Gary S. Becker and Barry R. Chis wick, "Education and the Distribution of Earnings,"

American Economic

Review 56 (May 1966): 358-369; Jacob Mincer, Schooling, Experience. and Earnings.

New York: Columbia

University, 1974; and Giora Hanoch, "An Economic Analysis of Earning and Schooling,"

Resources 2

Journal of Human

(Summer 1967): 3 1 0-329. The "consensus" estimate of the rate of return to schooling rose

between the 1970s and 1990s, from about 7 to 9 percent. Chapter 8 provides a detailed discussion of this rise in the returns to schooling.

242

Chapter Seven

Although most of the empirical studies use this type of regression model to estimate the rate of return to schooling, one must not forget the central point made in the previous section. The percentage wage differential between two workers who differ in their educational attainment estimates the rate of return to schooling only if the workers lie on the same wage-schooling locus so that there is no ability bias. Workers do differ in their ability, however, so a great deal of effort has been de­ voted to ensuring that the other variables included in the regression control for these ability differences. Some studies, for example, include measures of the worker's IQ.8 It is doubtful, however, that these test scores are good measures of a worker's innate productive capacity. After all, there is still an unsettled debate on what IQ measures, even in the context of scholastic achievement. Theory at Work

Can We Afford to Improve the Skills of H igh School Dropouts? Education is clearly a good inyestment if the rate of return to education is on the order of 9 percent. Nevertheless, it would be extremely expensive to pursue a policy that injects less-educated workers with additional schooling. There are over 30 million persons over the age of 25 who do not have a high school diploma in the United States. High school . . . . dropouts, on average, earn about $6,000 less than the typical high school graduate. Sup­ pose the governrtlent injects high school dropouts with enough schooling so as to reduce their wage disadvantage by, say, $4,000 a year. Let's even assume that the rate of return to schooling is high, on the order of 10 percent. How much would this policy cost the taxpayers? In order to increase annual earnings by $4,000 for a · worker, the governrtlent has to invest $40,000 on each high school dropout. Because there are 30 rnillion high school dropouts, the policy would . cost $ 1 .2 trillion. It is instructive to compare these projected costs with current expenditures on pro­ grams that sUbsidize hurnan capital investments. The Clinton administration's highly . touted (and ill-fated) 1993 proposal to stimulate the economy by "investing in workers" . .•.• was budgeted at $ 165 billion annually. Not even an annual appropriation on the order •. .• ••.• $ 100 billion would come close to narrowing the wage gap between high school dropouts .• • . . ••• .. and high school graduates. . ·····

.

Note: Based on James J. Heckman, "Is Job Training Oversold?" Public Intetest 1 l5 (Spring 1 �94): 9 1 - 1 1 5 .

8Good reviews o f the econometric issues involved are given b y Zvi Griliches, "Estimating the Returns to Schooling: Some Econometric Problems,"

Econometrica

45 (January 1977): 1-22; and David Card, "The

Causal Effect of Education on Earnings," in Orley Ashenfelter and David Card, editors,

Economics,

Bias in Panel Data: Estimating the Returns to Schooling,"

Data)

Handbook of Labor

Volume 3A. Amsterdam: North-Holland, 1 999. See also Gary Chamberlain, "Omitted Variable

Annales de I'INSEE (The Econometrics of Panel

3 1-32 ( 1 978): 49-82; John Hause, "Ability and Schooling as Determinants of Lifetime Earnings, or If

You're So Smart, Why Aren't You Rich?" in F. Thomas Juster, editor,

Behavi01:

Education, Income, and Human

New York: McGraw-Hill, 1975; McKinley L. Blackburn and David Neumark, "Omitted-Ability

Bias and the Increase in the Return to Schooling," Journal of Labor Economics 1 1 (July 1993): 5 2 1 -544. An interesting study that estimates the returns to particular types of courses is given by Joseph G. Altonji, "The Effects of High School Curriculum on Education and Labor Market Outcomes,"

Resources

(Surruner 1995): 409-438.

Journal of Human

r 243

Human Capital

Using Natural Experiments to Compare Workers of the Same Ability A number of recent studies have chosen a very clever way out of the fundamental problem raised by unobserved ability differences among workers. Our discussion sug­ gests that the ability bias would disappear if we could compare the earnings of two workers who we know have the same ability, but who have different levels of school­ ing. These two persons would necessarily lie on the same wage-schooling locus, and the wage gap between the two workers would provide a valid estimate of the rate of return to schooling. The comparison of the earnings of identical twins provides a nat­ ural experiment that satisfies these restrictions. Suppose that we have a sample of identical twins in which each twin reports both earnings and years of schooling. We can calculate the percentage wage differential per year of schooling with each pair of twins and average this number across the twin pairs. The average percentage wage differential is a valid estimate of the rate of return to schooling because ability differences have been completely controlled for. Although the idea makes a lot of sense, the evidence is mixed. Some studies report that the rate of return to schooling in a sample of identical twins is roughly on the order of 3 percent, which is much lower than the rate of return typically estimated in studies that do not control for a worker's ability. These studies conclude that ability differences account for much of the earnings gap between highly educated and less-educated work­ ers.9 Other studies, however, find that using data on twins raises the rate of return to schooling to about 1 5 percent, far higher than conventional estimates. 10 Even if these studies agreed on the direction of the ability bias, the study of data drawn from samples of identical twins raises an important question: Why do identical twins have different levels of schooling in the first place? Our theoretical model of the schooling decision isolated two variables that deter­ mine how much schooling a person acquires: ability and the rate of discount. Since iden­ tical twins who differ in their schooling do not differ in their innate ability, it must be the case that they must have differed in their rate of discount. The identical twins, in other words, differ in important and unobservable ways. In short, the identical twins do not seem to be completely identical. Unless we can understand why identical twins have dif­ ferent rates of discount, therefore, it is not clear that we should interpret the earnings dif­ ferential between identical twins as a measure of the "true" rate of return to schooling. A number of researchers have found other natural experiments that permit the com­ parison of workers who have the same ability. The U.S. government carried out a lottery during the final phase of the Vietnam War to establish draft priority among potential drafteesY The lottery randomly assigned a number (from 1 to 365) to the birth dates of a

9Paul Taubman, "Earnings, Education, Genetics, and Environment,"

Jou171al of Human Resources 1 1

(Fall

1 976): 447-461 .

"I :

I

!

WOrley C . Ashenfelter and Alan B . Krueger, "Estimates of the Economic Return to Schooling from a New Sample of Twins,"

American Economic Review 84 (December 1994): 1 157-1 173; and Orley Ashenfelter and Quarter­ ly Journal ofEconomics 1 13 (February 1998): 253-284. Cecilia Rouse, "Income, Schooling, and Ability: Evidence from a New Sample of ldentical Twins,"

I!

IlJoshua Angrist and Alan B. Krueger, "Estimating the Payoff to Schooling Using the Vietnam-era Draft Lottery," National Bureau of Economic Research Working Paper No.

4067,

May

1 992;

and Joshua Angrist

and Alan B. Krueger, "Split-Sample Instrumental Variable Estimates of the Returns to Schooling,"

ofBusiness and Economic Statistics 1 3 (April 1995): 225-235.

Journal

'I I

244

Chapter Seven

particular cohort (for example, men born in 1 95 1 ), and this lottery number "lined up" the men for military service. Men with low lottery numbers were the first to be drafted, whereas men with higher numbers completely escaped the draft. Young men eligible to be drafted could avoid the draft for a number of technical reasons, including "student deferments." Therefore, men with low lottery numbers who wanted to avoid a trip to Vietnam courtesy of the U.S. government had an obvious alternative: Go to college. Suppose that men born on the days assigned a low lottery number have the same average ability as men born on days assigned high lottery numbers. This seems like a sensible assumption because there is no reason to expect that men born on July 9, 1 95 1 (who happened to be first in the draft line) differ from men born on July 7, 1 95 1 (who were last on line). The wage-schooling locus for the two groups, therefore, is the same. The draft lottery "encouraged" men with low lottery numbers to stay in school so that these workers were nudged along the wage-schooling locus. In contrast, men with high lottery numbers did not have to stay in school a few extra years to avoid the draft. The wage gap between workers with low lottery numbers and high schooling levels and workers with high lottery numbers and low schooling levels, therefore, measures the true rate of return to schooling because there are no ability differences between the two groups. If one controls for ability bias in this fashion, the estimated rate of return to schooling is on the order of 7 percent. 1 2

The Quality 0/ Education Conventional wisdom has it that today' s high school graduates are not as good as yesterday' s graduates. The media often reports that a large fraction of high school graduates are "functionally" illiterate despite the fact that expenditures on primary and secondary education rose dramatically in the past three decades (per-student real expenditures in public schools increased from $4, 1 00 in 1 980 to $5 ,600 in 1 996). 1 3 Does "throwing money" at the public school system raise the rate of return to schooling?

1 2An additional natural experiment is created by compulsory schooling laws that force workers to remain in school until they reach some predetermined age, such as

16 or 17;

see Joshua Angrist and Alan B . Krueger,

"Does Compulsory Schooling Affect Schooling and Earnings?" (November

Quarterly Journal of Economics 106 1 991): 979-1014. A critical appraisal of these studies is given by John Bound, David A. Jaeger,

and Regina Baker, "Problems with Instrumental Variables Estimation When the Correlation Between the Instruments and the Endogenous Explanatory Variable Is Weak," Journal of the American Statistical Associ­ ation. 90 (June 1995): 443- 450. 1 3U.S. Bureau of the Census, Statistical Abstract of the United States, 1997. Washington, DC: Government Printing Office, 1997, p. 163. A detailed survey of the trends in expenditures and "quality" of the public schools is given by Eric A. Hanushek, "The Economics of Schooling: Production and Efficiency in the Pub­ lic Schools," Journal of Economic Literature 24 (September

1986): 1 141-1 177.

Human Capital

24S

A recent influential study suggests that the rate of return to schooling is indeed affected by the level of expenditures on public education. 14 In general, the rate of return to schooling is higher for workers who were born in states with a well-funded education system. For example, decreasing the pupiVteacher ratio by 10 students increases the rate of return by 1 percentage point, whereas increasing the relative wage of teachers by 30 percent (which presumably attracts better teachers) increases the rate of return to schooling by 0.3 percentage points. The evidence, therefore, suggests that expenditures on public education generate higher postschool earnings because they increase the payoff to an additional year of schooling. We do not yet know, however, if the increase in worker productivity is sufficiently high to justify the increased expendi­ tures on public education.

7-6 DO WORKERS MAXIMIZE LI FETI M E EARN I NGS? The schooling model provides the conceptual framework that allows us to estimate the rate of return to schooling. We have seen that-under certain conditions-percent wage differentials among workers who differ in their education can be interpreted as a rate of return to schooling. This calculation of the rate of return to schooling, however, does not test the theory. Rather, the calculations use the theory to interpret the earnings differences among workers in a particular way. Therefore, we want to determine if the schooling model provides a useful "story" of how persons actually go about the business of deciding whether to stay in school. The schooling model assumes that workers choose the level of schooling that maxi­ mizes the present value of lifetime earnings. The person goes to college if the present value of the earnings stream associated with going to college exceeds the present value of the earnings stream associated with a high school diploma. Otherwise, he will quit school after getting a high school diploma. If we could observe the age-earnings profile of a particular worker both if he were to go to college and if he were to stop after high school, it would be easy to test the key hypothesis of the schooling model. We could use these annual earnings to cal­ culate the present value of each option, compare the two numbers, and check to see if the worker chose the one with the largest present value. This simple test, however, can never be conducted. The reason is both trivial (because it is painfully obvious) and profound (because it raises a number of concep­ tual questions that have yet to be adequately resolved). Once a worker makes a par­

ticular choice, we can only observe the earnings stream associated with that choice. Consider the group of workers who go to college. For these ,

:;;2 " "

College Graduates

800 Some College High School Graduates

600

:::

High School Dropouts

400 200 18

25

32

46

39

53

60

Age

Women

900

'" OIl

§

os IJJ ;>,

:;;2

College Graduates

700

500

Some College

" "

:::

High School Graduates High School Dropouts

300

100 18

25

32

39 Age

Source: Current Population Survey, 1 997.

46

53

60

Human Capital

257

7-9 ON-TH E-JOB TRA I N I NG Until now, we have focused on one particular aspect of human capital investments, the schooling decision. Most workers augment their human capital stock after completing their education, particularly through on-the-job training (OJT) programs. The diversity of OJT investments is striking: Secretaries learn word processing skills, lawyers get courtroom experience, investment bankers concoct new financial instruments, and politicians learn from failed policies. It is evident, therefore, that OJT is an important component of a worker's human capital stock, making up at least half a worker' s human capital.21 There are two types of OJT: general training and specific training.22 General training is the type of training that, once acquired, is equally useful (that is, it enhances productivity) in all other firms. These general skills, which include such things as typ­ ing, learning how to drive, and learning how to use a calculator, are found frequently in the labor market. Specific training is the type of training that enhances productivity only in the firm where it is acquired, and the value of the training is lost once the worker leaves the firm. Examples of specific training also abound in the labor market: learning how to drive a tank in the Army or memorizing the hierarchical nature of a particular organization. In reality, much OJT is a mixture of general and specific train­ ing, but the conceptual separation into purely general and purely specific training is extremely useful. Consider a simple framework where the employment relationship between the firm and the worker lasts two periods. Suppose that in the first period (when the worker is hired) the total labor costs equal TCI dollars, and in the second period the costs equal TC2 dollars. Similarly, the values of marginal product in each of the two periods are VMP I and VMP2 , respectively. Finally, let r be the rate of discount. The profit-maximizing con­ dition giving the optimal level of employment for the firm over the two periods is: TC2 TCI + 1 + r

=

VMP2 VMPI + 1 + r

(7-2 1 )

The left-hand side of the equation gives the present value of the costs associated with hiring a worker over the two-period "life cycle." The right-hand side gives the present value of the worker' s contribution to the firm. It is easy to see that this equa­ tion en�raliZeS the condition that the wage ��ual the value of marginal product. In a mu Ipenod framework, the analogous condItIOn IS that the present value of employ­ m t costs equals the present value of the value of marginal product. / Suppose OJT takes place only in the first period. It costs the firm H dollars to put <J/ worker through the training. These costs include teacher salaries and the purchase of raining equipment. The total cost of hiring a worker during the first period can be

�

�

�

1

l

�lJaCOb Mincer, "On-the-Job Training:

"!flY 70 (October 1962, Part 2): 50-79,

Costs, Returns, and Some Implications,"

Journal of Political Econo­

22The definitions of general and specific training are due to Gary S. Becker, Human

University of Chicago Press,

Capital, 3d ed. Chicago: 1993, Becker's framework continues to be the cornerstone of the human capital

literature and has become an essential component in the tool kit of modem labor economics.

. .; i

, ',

258

Chapter Seuen

written as the sum of training costs H and the wage paid to the worker during the train­ ing period, or W I ' This implies that TC I = W I + H. Because no training occurs in the second period, the total cost of hiring the worker in the second period simply equals the wage. We can then rewrite equation (7-2 1 ) as:

WI

+H+

w2

-- =

l + r

VMP I

+

VMPz

--

l + r

(7-22)

Who Pays for General Training? Consider the case where all training is general. In the posttraining period, the worker's value of marginal product increases to VMP2 in all firms. As a result, many firms are willing to pay the worker a wage equal to VMP2• The firm that provided the training must either follow suit and increase the wage to VMP2, or lose the worker. Therefore, the second period wage, w2 will equal VMP2• As a result, equation (7-22) simplifies to: '

(7-23 ) Therefore, the first-period wage equals the value of the worker's initial marginal prod­ uct minus training costs. In other words, workers pay for general training by accepting a lower "trainee wage" during the training period. In the second period, workers get the returns from the training by receiving a wage that equals the value of their post­ training marginal product. Firms provide general training, therefore, only if they do not

pay any of the costs. There are many examples of workers paying for general training through lower wages. It is common for trainees in formal apprenticeship programs to receive low wages during the training period and to receive higher wages after the training is com­ pleted. Similarly, medical interns (even though they already have a medical degree) earn low wages and work long hours during their residency, but their investment is well rewarded once they complete their training. If a firm were to pay for general training, as some firms claim to do when they pay for the tuition of workers who enroll in an MBA program, the firm would surely attract a large number of job applicants. After all, many workers would quickly realize that this firm was offering free general training. Because the firm cannot legally enslave its employees after they receive their degree, the workers would take advan­ tage of the free training opportunities and then run to a firm that offers them a wage commensurate with their newly acquired skills. Therefore, a firm that paid for general training and did not raise the posttraining wage would get an oversupply of trainees and the workers would quit in the posttraining period. This firm faces the worst of all possible outcomes : It pays for the training and gets none of the benefits. A profit­ maximizing firm would quickly learn that it can lower the wage because there is an 2 oversupply of trainees, passing on the training costs to the workers. 3 23Recent studies have shown that noncompetitive firms may be willing to pay for general training under some circumstances; see Daron Acemoglu and J6rn-Steffen Pischke, "The Structure of Wages and Invest­ ment in General Training,"

Journal of Political Economy, 107 (June 1999): 539-572; and Daron Acemoglu Economic Journal 1 09

and Iiirn-Steffen Pischke, "Beyond Becker: Training in Imperfect Labor Markets,"

(February 1 999): F I 1 2-FI42. A rare empirical study of who pays for training is given by John M. Barron, Mark C. Berger, and Dan A. Black, "Do Workers Pay for On-the-Job Training?"

Resources 34 (Spring 1999): 235-252.

Journal of Human

Human Capital

259

Who Pays for Specific Training? The productivity gains resulting from specific training vanish once the worker leaves the firm. As a result, the worker's alternative wage (that is, the wage that other firms are willing to pay) is independent of the training and equals his pretraining productivi­ 2 ty. Who then pays for specific training and who collects the returns? 4 Consider what would happen if the firm paid for specific training. The firm could incur the cost and collect the returns by not changing the wage in the posttraining pe­ riod, even though the worker's value of marginal product in this firm has increased. Because VMP2 would then exceed w2, there are gains to providing the training. If the worker were to quit in the second period, however, the firm would suffer a capital loss. The firm, therefore, would hesitate paying for specific training unless it has some assurance that the trained worker will not quit. Suppose in�at the worker pays for the specific training. Workers would then receiv� lowwage during the training period and higher wages in the posttraining p�ri6d. The worker, however, does not have an ironclad assurance that the firm will �mploy him in the second period. If the worker were to get laid off, he would lose his /' .. investment because specific training is not portable. The worker, therefore, is not will­ ing to invest in specific training unless he is very confident that he will not be laid off. Both the firm and the worker, therefore, are reluctant to invest in specific training. The problem arises because there does not exist a legally binding contract that ties together workers and firms "until death do them part." Neither party wishes to take the initiative and pay for the training. The way out of this dilemma is to note that fine-tuning the posttraining wage can reduce the probabilities of both quits and layoffs. Consider a labor contract in which the worker's posttraining wage, w2 , is set such that:

(7 -24) where w is the alternative wage. This contract implies that the worker and the firm share the returns from specific training. The worker's posttraining wage w2 is higher than his productivity elsewhere, but less than his productivity at the current firm. Note that because the worker is better off in this firm than elsewhere, he has no incentive to quit. Similarly, because the firm is better off by employing the worker than by laying his off (that is, the worker gets paid less than his value of marginal product), the firm does not want to let the worker go. If both the firm and the worker share the returns of the specific training, therefore, the possibility of job separation in the posttraining period is eliminated. If firms and workers do share the returns of specific training, they will also have to share the costs. After all, if firms paid all the costs of providing specific training and got only part of the returns, they would attract an oversupply of trainees. There­ fore, if firms pay, say, 30 percent of the costs of specific training, they will also get 30 percent of the returns. Otherwise the firm would attract either too few or too many job applicants.

24A more detailed discussion of these issues is given by Masanori Hashimoto, "Firm-Specific Human Capi­ tal as a Shared Investment," American Economic Review 7 1 (June

1981): 475-482.

260

Chapter Seven

Theory at Work

Formal Training Programs Many workers enroll in formal training programs: 1 5 percent of workers under the age

30 have acquired skills in formal "off-the-job"

by computer schools and beautician trainmg. An addliticmal mal on-the-job training, · and These formal

2

such as those DrC)v1._��es _9nly in earn more than th� less_U!l�!:l!��, I��_ su.R�.1.!tar . some professions. The superstar phenomenon requires that sellers are not perfect SUb h·tutes aniTthat the technology of mass .Q!illluction all()ws the ��ry tal�!l!� -i.12� l1!� _ r, ccupations to reach very large markets.,Barbra Streisand, for example, need only sing . . a articular song a few hmes in a stii(ii(; until a perfect take is recorded. Modem technology translates this performance into digital code and permits the pristine recording to be heard in millions of homes around the world. The fact that Barbra Streisand can come "live" into a very large number of homes expands the size of her market and rewards her with an astronomically high salary. In contrast, a talented heart surgeon must have personal contact with each of her patients, thus constraining the size of the market for her services. In some occupations, therefore, the .� of distributing a particular output to the consumers do not rise in proportion to the size of the market. The superstar phenome-

Is

�

P�!!Q.l!'_

p

23Sherwin Rosen, "The Economics of Superstars,"

]

American Economic Review 7 1 (December 1 98 1 ): 845-858; see also William A. Hamlen, Jr., "Superstardom in Popular Music," Review of Economics and Sta­ tistics 73 (November 1991): 729-733.

Chapter Eight

296

{I

non thus arises in occupations that allow extraordinarily talented persons to reach very large markets at a very low price. A recent study of television ratings for games in the National Basketball Associa­ tion shows that more fans watch the games when certain players-the superstars­ play. This larger television audience increases revenues from advertisers and raises the value of particular players to the NBA teams. In the mid- 1 990s, it was estimated that the value of "owning the rights" to Michael Jordan, the Chicago Bulls player who many consider to be the finest basketball player in history, was worth at least $50 million. 24

8-5 I N EQUALITY ACROSS GENERATIONS Up t o this point, w e have analyzed how human capital investments can generate a great deal of income inequality within a particular population and how changes in the structure of the economy can change the wage distribution in significant ways within a very short time period. We now address the question of whether wage inequality in a particular genera­ tion is transmitted to the next generation. The link between the skills of parents and children-or, more generally, the rate of social mobility-is at the heart of many of the most hotly discussed policy questions. Consider, for instance, the debate over whether the lack of social mobility in particular segments of society contributes to the creation of an "underclass"; or the debate over whether government policies help strengthen the link in poverty and welfare dependency across generations. Throughout our discussion, we have assumed that workers invest in their own human capital. In fact, a large part of our human capital was chosen and funded by our parents, so it is useful to think of the human capital accumulation process in an intergenerational context. Parents care both about their own well-being and about the well-being of their children. As a result, parents will invest in their children's human capital. The investments that parents make in their children's human capital help create the link between the skills of parents and the skills of their children. High-income par­ ents will typically invest more in their children, creating a positive correlation between the socioeconomic outcomes experienced by the parents and the outcomes experienced by the children. Many empirical studies have attempted to estimate the relationship between the income of the children and the income of the parents. Figure 8-8 illustrates various possibilities for the regression line that connects the earnings of fathers and children. The slope of this line is often called an intergenerational correlation. An intergener­ ational correlation equal to 1 (as in line A in the figure) implies that if the earnings gap between any two parents is $ 1 ,000, their children's income will also differ by $ 1 ,000. If the correlation were equal to .5, a $ 1 ,000 earnings gap between the two parents translates to a $500 earnings gap between their children. Most empirical studies find 24Jerry A. Hausman and Gregory K. Leonard, "Superstars in the National Basketball Association: Economic Value and Policy," Journal of Labor Economics 1 5 (October

1997): 586- 624.

The Wage Structure

Figure 8-8

297

The Intergenerational Link in Skills The slope of the regression line linking the earnings of the children and the earnings of the parents is called an intergenerational correlation. If the slope is equal to I, the wage gap between any two parents persists entirely into the next generation and there is no regression toward the mean. If the slope is equal to 0, the wage of the children is independent of the wage of the parents, and there is complete regression toward the mean. Earnings of Children

A, Slope

C,

=

I

Slope is between 0 and I

1------::::;;o."Ml!::.....�-- B, Slope

=

0

45 Earnings of Parents

that the intergenerational correlation is less than 1 so that earnings differences among any two parental households will typically exceed the earnings differences found among the children of these two households. The possible attenuation of the differences in skills or incomes across generations is known as regression toward the mean-a tendency for income differences across families to get smaller and smaller over time as the various families move toward the mean income in the population. The phenomenon of regression toward the mean may arise because parents do not devote their entire wealth to investing in their children's human capital-but rather consume some of it themselves. Regression toward the mean may also occur if the parents encounter diminishing returns when they try to invest in their children's human capital-the marginal cost of education would then rise very rapidly as parents try to "inject" more schooling in their children. Finally, regression toward the mean in income may also arise because there is probably some regression toward the mean in ability-it is unlikely that the children of exceptionally bright parents will be even brighter. Note that the closer the intergenerational correla­ tion gets to 0, the faster the regression toward the mean across generations. In fact, if the intergenerational correlation were equal to ° (as in line B in Figure 8-8), there would be complete regression toward the mean because none of the differences in parental skills are transmitted to their children.

298

Chapter Eight

Until recently, it was generally believed that the intergenerational correlation between the earnings of fathers and children was in the order of .2.25 Put differently, if the wage differential between any two parents is in the order of 30 percent, the wage differential between their children would be in the order of only 6 percent (or 30 per­ cent X .2). If the rate of regression toward the mean were constant over time, the wage differential among the grandchildren would then be only 1 .2 percent (or 30 percent X .2 X .2). An intergenerational correlation of .2, therefore, implies that there is a great deal of social mobility in the population because the economic status of workers in the parental generation would not be a good predictor of the economic status of the grand­ children. A number of recent studies, however, raise serious doubts about the validity of this conclusion.26 These "revisionist" studies argue convincingly that the intergenera­ tional correlation is probably much higher, perhaps in the order of .3 to .4. The prob­ lem with the earlier results is that there is a great deal of error in observed measures of parental skills. When workers are asked about the socioeconomic status of their par­ ents, the responses regarding parental education and earnings are probably not very precise. This measurement error weakens the estimated correlation between the skills of parents and children. It turns out that if we net out the impact of measurement error in the estimation of the intergenerational correlation, the estimated correlation often doubles. If the intergenerational correlation were indeed on the order of .4, it would imply that a 30 percent wage gap between two parents translates into a 1 2 percent wage gap between the children and a 5 percent wage gap between the grandchildren. Skill and income differentials among workers, therefore, would be much more persis­ tent across generations.

Human Capital Externalities A number of recent studies have argued that social capital the set of variables that characterizes the "quality" of the environment where a person grows up or lives-also helps determine the worker's human capitaJ.27 For a given level of parental skills, chil-

25Anthony B. Atkinson, A. K. Maynard, and C. G. Trinder,

tions.

Parents and Children: Incomes in Two Genera­

London: Heinemann Educational Books, 1983; Jere R. Behrman and Paul Taubman, "Intergenera­

tiona! Earnings Mobility in the United States: Some Estimates and a Test of Becker's Intergenerational Endowments Model," Review of Economics and Robert M. Hauser,

and Statistics 67 (February 1985): 144- 1 5 1 ; William H. Sewell Education, Occupation, and Earnings: Achievement in the Early Career. New York:

Academic Press, 1975. A survey of the evidence is given by Gary S. Becker and Nigel Tomes, "Human Cap­ ital and the Rise and Fall of Families," Journal ofLabor Economics 4 (July 1986 Supplement): S I-S39. 26Gary R. Solon, "Intergenerational Income Mobility in the United States," American Economic Review 82 (June 1992): 393-408; David J. Zimmerman, "Regression Toward Mediocrity in Economic Stature," Ameri­

can Economic Review

82 (June 1992): 409-429; Joseph G. Altonji and Thomas A. Dunn, "Relationship

Among the Family Incomes and Labor Market Outcomes of Relatives," Research

in Labor Economics

12

( 1 99 1 ) : 269-310; and Kenneth A . Couch and Tomas A. Dunn, "Intergenerational Correlations i n Labor Mar­ ket Status,"

Journal of Human Resources 32 (Winter

1997): 2 1 0-232. A good summary of the literature is

given by Gary Solon, "Intergenerationa! Mobility in the Labor Market," in Orley Ashenfelter and David Card, editors, Handbook of Labor Economics, Volume 3A. Amsterdam: North-Holland, 1999. 27James S . Coleman, "Social Capital in the Creation of Human Capital," American Journal ( 1 988 Supplement): S95-S120; and William Julius Wilson,

of Sociology 94 The Truly Disadvantaged: The Inner City, the

Underclass, and Public Policy. Chicago: University of Chicago Press,

1987.

The Wage Structure

299

dren exposed to "role models" and "peer groups" that are highly educated, have steady employment, and are economically successful will tum out differently than children exposed to role models who are predominantly unemployed or receive public assis­ tance. In effect, the quality of the environment where the child grows up acts as a human capital externality in the production of the children's human capital. In other words, the environment is an external factor-beyond the control of the parents-that affects the human capital accumulation process.28 Human capital externalities attenuate the regression toward the mean across gen­ erations. The children's human capital will depend both on parental skills as well as on the social capital to which he or she is exposed. Children raised in disadvantaged envi­ ronments will be "pulled down" by the human capital externality, whereas children raised in high-skill neighborhoods will be "pushed up" by the externality. In effect, the human capital externality acts as a double-sided magnet-preventing the children of the particular demographic group from deviating too far from the group mean. Human capital externalities can also help explain why racial and ethnic differ­ ences in labor market outcomes seem to persist across generations.29 Some racial or ethnic groups do particularly well generation after generation, whereas other ethnic groups do poorly for a very long time. The evidence, in fact, suggests that 50 percent of the gap in the average wage between any two ethnic groups persists from one gener­ ation to the next.30 Part of this may be attributable to the fact that children who are raised in disadvantaged ethnic environments will tend to have less human capital, even after adjusting for differences in the human capital of the parents. Of course, race and ethnicity are not the only environmental factors that influence the humari capital accumulation process. There is evidence that such variables as the overall quality of the neighborhood, the importance of religious organizations, and the socioeconomic background of a child's classmates influence a child's human capitat.3' For instance, residing in a neighborhood that has relatively high levels of criminal activ280f course, parents may be abLe to attenuate the impact of the environment by moving to areas where the child is exposed to different characteristics. 29Glenn C. Loury, "A Dynamic Theory of RaciaL Income Differences," in Phyllis A. Wallace and A. LaM­ ond, editors,

WcJmen, Minorities, and Employment Discrimination. Lexington, MA: Lexington Books, 1977;

Shelly Lundberg and Richard Startz, "On the Persistence of Racial Inequality," Journal of Labor Economics

16 (ApriL 1 998): 292-323; and George J. Borjas, "Ethnic Capital and Intergenerational Mobility," Quarterly Journal of Economics 1 07 (February 1992): 1 23- L50. JOGeorge J. BOIjas, "Long-Run Convergence of Ethnic Skill Differentials: The ChiLdren and Grandchildren of the Great Migration,"

Industrial and Labor Relations Review 47

(July

1994): 553-573:

David Card, John

DiNardo, and Eugena Estes, "The More Things Change: Immigrants and the Children of Immigrants in the

1 940s,

the

1 970s,

and the

1 990s,"

in George J. Borjas, editor,

Chicago: University of Chicago Press,

Issues in the Economics of Immigration.

2000.

3 1 Anne C. Case and Lawrence F. Katz, "The Company You Keep: The Effects of FamiLy and Neighborhood on Disadvantaged Youths," National Bureau of Economic Research Working Paper No.

3705,

May

1 99 1 ;

Mary Corcoran, Robert Gordon, Deborah Laren, and Gary Solon, "The Association Between Men's Eco­ nomic Status and Their FamiLy and Community Origins," Journal of Human Resources 27 (Fall 1992): 575-601 ; William N. Evans, Wallace E. Oates, and Robert M. Schwab, "Measuring Peer Group Effects," Journal of Political Economy 1 00 (October . 1992): 966-991 ; and Jonathan Crane, "The Epidemic Theory of Ghettos and Neighborhood Effects on Dropping Out and Teenage ChiLdbearing," American Journal of Soci­ ology 96 (March 1991): 1 226-1 259. For a review of the literature, see Christopher Jencks and Susan E. Meyer, "The Social Consequences of Growing Up in a Poor Neighborhood," in L Lynn and M. McGeary,

editors, Inner City Poverty

in the United States, Washington, DC:

National Academy Press,

1990.

300

,

Chapter Eight

ity greatly increases the probability that an individual will enter that profession, even holding parental background constant. Many studies document strong "neigh­ borhood effects" not only on the accumulation of skills, but also on other aspects of human behavior including welfare dependency, substance abuse, and teenage pregnancy.

Summary •

The positive correlation between human capital investments and ability implies that the wage distribution is positively skewed so that workers in the upper tail of the wage distribution get a disproportionately large share of national income .

•

Wage inequality rose rapidly in the 1 980s and 1 990s. Wage dispersion increased between education and experience groups, as well as within narrowly defined skill groups.

•

Some of the changes in the wage structure can be explained in terms of shifts in supply (such as immigration), the increasing globalization of the U.S. economy, institutional changes in the labor market (including the deunionization of the labor force and the decline in the real minimum wage in the 1 980s), and skill-biased technological change. No single variable, however, is the "smoking gun" that explains the bulk of the changes in the wage structure.

•

Superstars receive a large share of the rewards in some occupations. The output produced by very talented workers is not perfectly substitutable with the output produced by less-talented workers. Superstars arise when the highly talented can reach very large markets at a very low price.

•

Wage dispersion among workers is transmitted from one generation to the next because parents care about the well-being of their children and invest in their children's human capital. The typical intergenerational correlation exhibits some regression toward the mean, with the wage gap between any two families narrowing across generations.

Key Concepts human capital externality intergenerational correlation positively skewed wage distribution regression toward the mean

skill-biased technological change social capital social mobility superstar phenomenon

The Wage Structure

30 1

Review Questions l . Why is the wage distribution positively skewed?

2. Describe the key changes that occurred in the U.S. wage distribution during the 1 980s. 3. Why did the U.S. wage distribution change so much in the 1 980s? 4. What is the superstar phenomenon? What factors create superstars in certain occupations and not in others? 5. What factors determine how much parents invest in their children's human capital? 6. Discuss why there is regression toward the mean in the correlation between the earnings of parents and children.

7. Discuss the implications of regressions toward the mean for the changing shape of the wage distribution across generations.

Problems 1 . Evaluate the validity of the following claim: The increasing wage gap between highly educated and less-educated workers will itself generate shifts in the U.S. labor market over the next decade. As a result of these responses, much of the "excess" gain accruing to highly educated workers will soon disappear. 2. Suppose the U.S. government is considering changes in economic and social policy to reduce the extent of wage inequality-or at least to slow down its very rapid rise. What will be the impact of these proposed changes on wage inequality? a. Indexing the minimum wage to inflation. b. A decrease in the benefit level paid to welfare recipients. c. An increase in the benefit level paid to welfare recipients. d. An increase in wage subsidies paid to firms that hire less-advantaged workers. e. An increase in border enforcement, reducing the number of illegal aliens entering the country. 3. Suppose that the United States were a closed economy (meaning there is no immigration from foreign countries and no international trade). The current labor force has 50 million skilled workers and 50 million unskilled workers-and both types of labor have perfectly inelastic supply curves. In the next year, there is a net increase in the U.S. labor force because of the growth of the native population. In addition, the country opens its borders to international trade and immigration. At the same time, however, there is no change in demand for final goods or in production technology. Calculate the impact of each of the following developments on the relative wage of skilled and unskilled workers: a. Of the new domestic entrants in the U.S. labor force, 360,000 are skilled and 220,000 are unskilled. At the same time, 60,000 skilled workers and 1 20,000 unskilled workers retire. b. One million immigrants enter the country, of which 800,000 are unskilled and 200,000 are skilled.

302

Chapter fight c.

4

a.

U.S. exports require the services of I million skilled workers and 500,000 unskilled workers . At the same time, U.S. imports "embody" the services of 800,000 skilled workers and 1 ,500,000 unskilled workers (in the sense that this combination of workers would have been required to produce these imports in the United States). What would happen if the labor demand elasticities equal -0. 1 for each type of labor? What if they equal - I ?

Ms. Aura is a psychic. She is not like other psychics in her approach to her clients' problems, so her service is different from that of other psychics. In economic terms, she is a monopolist. The demand for her services can be described by the formula Q = 2,000 - l OP, where Q is the number of I -hour sessions per year and P is the price of one session in dollars. The marginal revenue is MR = 200 - 0 . 2 Q Ms. Aura's operation has no fixed costs, but she incurs a cost of $ 1 50 per session (going to the client's house or renting a room for the meeting, finding out about the client; the 0ppOltunity cost of her time, and so on). What is Ms. Aura's yearly profit? b. Now suppose Ms. Aura becomes famous after appearing on the Psychic Network. The new demand for her services is Q = 2,500 - 5P. Her new marginal revenue is MR 500 - O.4Q. Note that not only does the demand curve shift to the right as more people want to consult with Ms. Aura, but also it becomes steeper-that is, less elastic-as Ms. Aura sets herself apart from other psychics. What is her profit now? c. Finally, advances in telecommunications and information technology revolutionize the way Ms. Aura does business. First, she uses the Internet to find all relevant information. Second, she now meets with the clients through teleconferencing. Maintaining this technology involves a fixed cost of $ 1 ,000 a year, but the marginal cost is only $20 per session. What is Ms. Aura's profit? d. Could you summarize the lesson of this problem for the superstar phenomenon? .

=

Labor Mobility

C H A P T E R

9

Comes ouer one an absolute necessity to moue. And what is more, to moue in some particular direction. A double necessity then: To get on the moue, and to know whither. D . H . Lawrence

A competitive labor market equilibrium allocates workers to firms so as to maximize the total value of labor's product. Workers are continually searching for better jobs (that is, jobs where they are more productive and earn higher wages), and firms are searching for better workers. As a result of these search activities, the value of mar­ ginal product of labor is equated across firms and across labor markets (for workers of given skills). The equilibrium allocation of workers and firms, therefore, is efficient. No other allocation can increase the value of labor's contribution to national income. Needless to say, actual labor markets are not quite as neat. Workers often do not know their own skills and abilities, and are ill informed about the opportunities avail­ able in other jobs or in other labor markets. Firms do not know the true productivity of the workers they hire. As in a marriage, information about the value of the match between the worker and the firm is revealed slowly as both parties learn about each other. Therefore, the existing allocation of workers and firms is not efficient, and other allocations are possible that would increase national income. This chapter describes the mechanism that labor markets use to improve the allo­ cation of workers to firms, namely labor mobility. There is a great deal of mobility in the labor market. In fact, it seems as if the U.S. labor market is in constant flux: Nearly 4 percent of workers in their early twenties switch jobs in any given month, 3 percent of the population moves across state lines in a year, and about I million legal and ille­ gal immigrants enter the country annually. This chapter argues that all these "flavors" of labor mobility are driven by the same fundamental factors: Workers want to improve their economic situation, and firms want to hire more productive workers. The analysis of labor mobility helps us address a number of key questions in labor economics. What are the determinants of migration? How do the migrants differ from the persons who choose to stay? What factors determine how migrants are self­ selected? What are the consequences of migration, both for the migrants themselves and for the localities that they move to? In particular, do the migrants gain substan­ tially from their decision? And how large are the efficiency gains from migration? 303

304

Chapter Nine

9- 1 GEOGRAPHIC MIGRATION AS A H U M AN CAPITAL I NVESTM ENT In 1 932, Nobel Laureate John Hicks argued that "differences in net economic advan­ tages, chiefly differences in wages, are the main causes of migration."! Practically all modem analysis of migration decisions uses this hypothesis as the point of departure, and views the migration of workers as a form of human capital investment. Workers calculate the value of the employment opportunities available in each of the alternative labor markets, net out the costs of making the move, and choose whichever option maximizes the net present value of lifetime earnings. The study of the migration decision, therefore, is a simple application of the human capital framework set out in Chapter 7. Suppose there are two specific labor markets where the worker can be employed. These labor markets might be in different cities, in different states, or perhaps even in different countries. Suppose that the worker is currently employed in New York and is considering the possibility of mov­ ing to California. The worker, who is 20 years old, now earns w oY dollars. If he were to move, he would earn w dollars. It costs M dollars to move to California. These migration costs include the actual expenditures incurred in transporting the worker and his family (such as airfare and the costs of moving household goods), as well as the dollar value of the "psychic cost"-the pain and suffering that inevitably occurs when one moves away from family, neighbors, and social networks. Like all other human capital investments, mobility decisions are guided by the comparison of the present value of lifetime earnings in the alternative employment opportunities. Let py-, 0

Q. E " c

;:J

,

.

10

European Community

�. .. ..

.,#�"

,.'. - - - . _ - - - _

:

..,.. ... ,.,,, ... .. - ... ' .

8

6

4

2

0 1965

1 970

1975

1980

1985

1 990

1 995

2000

Year Source: GECD, Labour Force Statistics. Paris: GECD, various issues. The European Community includes Belgium, Denmark, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal. Spain, and the United Kingdom.

The Unemployment Problem in Europe Until about 1 980, the United States had substantially higher unemployment rates than most western European countries (see Figure 1 3 - 1 8). In 1 970, the unemploy­ ment rate in the United States was 4.8 percent, as compared to 2.5 percent in France, 0.6 percent in Germany, and 2.2 percent in the United Kingdom. By 1 993, however, the unemployment rate in the United States was 6.7 percent, whereas France had an unemployment rate of 1 1 .6 percent, Germany 5 . 8 percent, and the United Kingdom 10.3 percent. Some economists have argued that the natural rate of unemployment in Europe exhibited "hysteresis"-the faster the unemployment rate rose during the 1 980s, the higher the natural rate of unemployment became. In other words, deviations from the natural rate of unemployment themselves changed the natural rate.42 Discussions of the European unemployment problem and the possible existence of hysteresis typically isolate three factors. First, employment policies in many western European countries penalize employers who want to lay off workers. For instance, employers may have to pay sizable severance pay to workers at the time of the layoff. Because firms know that it is expensive to lay off workers, they do not want to hire

42Sources: Olivier J. Blanchard and Lawrence H. Summers, "Hysteresis and the European Unemployment Problem," NBER Macroeconomics AnnuaL 1986. Cambridge, MA: MIT Press, 1986, pp. 1 5-78; Assar Lind­ beck and Dennis Snower, "Wage Setting, Unemployment, and Insider-Outsider Relations," American Eco­ nomic Review 76 (May 1986): 235-239.

Unemployment

sos

new workers or recall their previously laid-off workers unless they expect favorable economic conditions to persist for a long time. The firm's reluctance to expand gen­ erates long spells of unemployment. European countries also offer much more gen­ erous UI benefits than the United States. In the United Kingdom, an unemployed worker can receive some type of benefit indefinitely. Finally, European countries have much higher rates of unionization than the United States. The unionized work­ ers who hold a job, the "insiders," may be only concerned about keeping their above-market wages without suffering any additional unemployment. The unem­ ployed workers, the "outsiders," have no power to bring down the wages because unions prevent employers from hiring nonunion workers (or perhaps because of the presence of specific training or turnover costs). As a result, wages remain at above­ market levels and unemployment persists.

Summary •

Although the unemployment rate in the United States drifted upward between 1 960 and 1 990, the economic expansion of the 1 990s reduced the unemployment rates substantially.

•

Even a well-functioning competitive economy experiences frictional unemployment because some workers will unavoidably be "in between" jobs. Structural unemployment arises when there is an imbalance between the supply of workers and the demand for workers.

•

The steady-state rate of unemployment depends on the transition probabilities among employment, unemployment, and the nonmarket sector.

•

Although most spells of unemployment do not last very long, most weeks of unemployment can be attributed to workers who are in very long spells.

•

The asking wage makes the worker indifferent between continuing his search activities and accepting the job offer at hand. An increase in the benefits from search raises the asking wage and lengthens the duration of the unemployment spell; an increase in search costs reduces the asking wage and shortens the duration of the unemployment spell.

•

Unemployment insurance lengthens the duration of unemployment spells and increases the probability that workers are laid off temporarily.

•

The intertemporal substitution hypothesis argues that the huge shifts in labor supply observed over the business cycle may be the result of workers reallocating their time so as to purchase leisure when it is cheap (that is, during recessions).

•

The sectoral shifts hypothesis argues that structural unemployment arises because the skills of workers cannot be easily transferred across sectors. The skills of workers laid off from declining industries have to be retooled before they can find jobs in growing industries.

•

Efficiency wages arise when it is difficult to monitor workers' output. The above­ market efficiency wage generates involuntary unemployment.

'I

506

Chapter Thirteen

•

Implicit contract theory argues that workers prefer employment contracts where incomes are relatively stable over the business cycle, even if such contracts imply reductions in hours of work during recessions .

•

A downward-sloping Phillips curve can exist only in the short run. In the long run, there is no trade-off between inflation and unemployment.

Key Concepts asking wage frictional unemployment imperfect experience rating implicit contracts intertemporal substitution hypothesis natural rate of unemployment no-shirking supply curve nonsequential search Phillips curve

replacement ratio seasonal unemployment sectoral shifts hypothesis sequential search structural unemployment wage curve wage offer distribution temporary layoffs

Review Questions 1 . Discuss some of the basic patterns of unemployment in the Vnited States since 1 960. 2. What are the differences between frictional and structural unemployment? Should we be equally concerned with all types of unemployment? Do the same policies help alleviate both frictional and structural unemployment?

3 . Derive the steady-state rate of unemployment. Show how it depends on the transition probabilities between employment and unemployment.

4. Discuss how it is simultaneously possible for "most" unemployment to be due to short spells and for "most" unemployment to be accounted for by persons in very long spells. 5. Should a job seeker pursue a nonsequential or a sequential search strategy? Derive a job-seeker's asking wage. Discuss why the asking wage makes a worker indifferent between searching and not searching.

6. Discuss the impact of the VI system on a job seeker's search behavior. Discuss the impact of the VI system on the firm's layoff behavior. 7. What is the intertemporal substitution hypothesis? Does this argument provide a convincing account of the cyclical trend in the unemployment rate?

8. What is the sectoral shifts hypothesis? 9. Why do implicit contracts generate unemployment? 10. Why do efficiency wages generate involuntary unemployment? What factors prevent the market from clearing in efficiency wage models?

1 1 . Why is the Phillips curve vertical in the long run?

Unemployment

S0 7

Problems 1 . Suppose there are 100 unemployed persons in the economy. You are given the following data about the length of unemployment spells:

Duration of Spell (in Months)

Exit Rate 0.6 0.2 0.2 0.2 0.2 1 .0

1

2 3 4 5 6

where the exit rate for month t gives the fraction of unemployed persons who have been unemployed t months and who "escape" unemployment at the end of the month. a. How many unemployment months will the 1 00 unemployed workers experience? b. What fraction of persons who are unemployed are "long-term unemployed" (that is, are in unemployment spells that last 5 or more months)? c. What fraction of unemployment months can be attributed to persons who are long-term unemployed? d. What is the nature of the unemployment problem in this example: too many workers losing their jobs or too many long spells? 2. Suppose that the marginal revenue from search is given by: MR = 50 - 1 . 5 w

where w is the wage offer at hand. The marginal cost of search is given by: MC = 5 a.

+

w

Why is the marginal revenue from search a negative function of the wage offer at hand? b. Why is the marginal cost of search a positive function of the wage offer at hand? Can you give an economic interpretation of the intercept in the marginal cost equation; in other words, what does it mean to say that the intercept equals $5? Similarly, what does it mean to say that the slope in the marginal cost equation equals $ l ? c. What i s the worker's asking wage? Will a worker accept a job offer o f $ 1 5? d. Suppose UI benefits are reduced, and the marginal cost of search increases to MC = 20 + w. What is the new asking wage? Will the worker accept a job offer of $ 1 5?

S08

Chapter Thirteen

3 . Compare two unemployed workers; the first worker is 25 years old and the second worker is 55 years old. Both workers have similar skills and face the same wage offer distribution. Suppose also that both workers incur similar search costs. Which worker will have a larger reservation wage? Why? Does search theory help you understand why the unemployment rate of young workers differs from the unemployment rate of older workers? 4. Suppose the government proposes to increase the level of UI benefits for unemployed workers. Firms now pay efficiency wages to its workers in order to discourage them from shirking. What is the impact of the proposed legislation on the wage and on the unemployment rate for workers in this economy? 5. It is well known that more-educated workers are less likely to be unemployed and have shorter unemployment spells than less-educated workers. Which theory-the job search model, the sectoral shifts hypothesis, implicit contracts, or the efficiency wage model-best explains this empirical correlation? 6. Suppose a country has 100 million inhabitants. The population can be divided into the employed, the unemployed, and the persons who are out of the labor force (OLF). In any given year, the transition probabilities among the various categories are given by:

Moving into Moving from

Employed

Employed Unemployed

OLF

0.20 0.05

Unemployed

OLF

0.02

0.04 0. 1 5

0.03

(These transition probabilities are interpreted as follows. In any given year, 2 percent of the workers who are employed become unemployed, 20 percent of the workers who are unemployed find jobs, and so on). What will be the steady-state unemployment rate?

Name Index

Note: All citations in the Name Index

Azariadis, Costas, 497

italicized. Abowd, John M . , 175, 223, 399, 4 1 1 , 445, 447 Abraham, Katherine G., 152, 337, 492 Acemoglu, Daron, 258 Adams, James, 223 Addison, John T., 1 52, 153, 388, 389, 424 Aigner, Dennis J., 357 Aizcorbe, Ana, 1 52 Akerlof, George A., 455 Ali, Muhammad, 201 Allen, Steven G., 408, 42 1 , 424, 450, 457 Altonji, Joseph G., 75, 175, 237, 242, 253, 298, 337, 344, 361, 367, 376 Andersen, Torben, 357 Anderson, Patricia M., 484 Angrist, Joshua D., 53, 161, 1 77, 178, 243, 244 Anstie, R, 382 Antos, Joseph, 220 Arrow, Kenneth J., 249, 348 Asch, Beth J., 439 Ashenfelter, Orley c., 23, 55, 140, 1 77, 178, 202, 214, 223, 233, 242, 243, 266, 269, 278, 280, 281-283, 285, 298, 333, 344, 348, 367, 397, 400, 410-41 2, 4 1 8 , 426, 427, 478 Atkinson, Anthony B., 276, 298, 485 Auerbach, Alan J., 47 AUtor, David H., 278, 280, 28 1-283, 285, 286, 290

Betts, Julian R, 185, 245 Biddle, Jeff E., 40, 213, 353

appear in footnotes except those that

Bils, Mark J., 490

are

H., 172

Baily, Martin N., 497

Bishop, John

Baker, Michael, 147, 325

Black, Dan A., 258

Baker, Regina, 244

Blackburn, McKinley L., 1 53, 242, 276,

Balfour, Frederick, 170

284

Banerjee, Biswajit, 344

Blakemore, Arthur E., 379, 438

Bank, Roy J., 347

Blanchard, Olivier Jean, 1 64, 165, 496,

504

Bamow, Burt, 269 Barro, Robert J., 164

Blanchflower, David G., 223, 390

Barron, John M., 258, 422

Blank, Rebecca M . , 344, 367, 376

Barsky, Robert, 490

Blau, Francine D., 89, 293, 344, 358, 368,

Bartel, Ann P., 135, 219, 289, 330

373-375, 3 8 1 Bloch, Farrell E . , 422

Bassi, Laurie, 269 Beach, Charles, 170

Bloom, David E., 276, 284, 426, 427

Bean, Frank, 176

Blum, James, 141

Beaudry, Paul, 499

Bodie, Zvi, 83, 450

Becker, Brian, 416

Bognanno, Michael L.,

Becker, Gary S . , 72, 88, 95, 98-100, 233,

444

BOIjas, George 1., 49, 59, 148, 175, 180,

24 1 , 257, 298, 344, 344-345,

1 8 1 , 181, 1 82, 287, 288, 299, 3 1 2,

348-350, 448

3 1 4, 3 1 8, 318, 3 1 9, 319, 320, 321, 323, 325, 328, 330

Behrman, Jere R, 298 Bell, Brian, 293

Boskin, Michael J., 83

Bell, Linda, 144

Boudett, Kathryn Parker, 254

H., 269 Beller, Andrea H., 377

Boyer, George R., 99

Bell, Stephen

Bound, John, 48, 84, 244, 289, 29 1 , 373

Bellman, Dale, 196

Bradford, David, 170

Benjamin, Dwayne, 147, 325

Brainard, S . Lael, 492

Ben-Porath, Yoram, 26 1 , 264

Berger, Mark c., 258, 397 Bergmann, Barbara Berman, Eli, 289

E, 377

Bronars, Stephen G., 399, 425 Brown, Charles, 48, 143, 144, 1 9 1 , 220,

22 1 , 372, 424, 433 Brown, James N., 410, 452, 499

509

BIUCk, Connie, 433 Buckley, John E., 477 Bull, Clive, 441 Bulow, Jeremy I., 460 Burkhauser, Richard v., 8 1 , 1 47, 148 Burtless, Gary, 79, 82, 83, 85, 87, 269, 284, 485 Butler, Richard J., 3 7 1 Byers, James F. , 485, 489

Cain, Glen G., 357, 460 Cameron, Stephen v., 254 Campbell, Carl M., III, 456 Canto, Victor, 5 1 Cappelli, Peter, 456 Card, David, 75, 1 44, 145, 146, 1 47, 175, 1 76, 1 77, 1 78, 1 80, 233, 242, 245, 269, 278, 280, 28 1-283, 285, 286, 291, 293, 298, 299, 325, 333, 344, 363, 367, 368, 373, 398, 401 , 410, 4 1 6, 418, 422, 489, 496 Carliner, Geoffrey, 3 14 Carlson, Leonard A., 363, 383 Carlyle, Thomas, 275, 465 Carmichael, H. Lome, 455, 460 Carrington, William J., 5, 7, 177, 348 Carter, William H., 419 Case, Anne c., 299 Castillo-Freeman, Alida, 148 Castro, Fidel, 1 76 Chamberlain, Gary, 242 Chauvin, Keith, 456 Chay, Kenneth Y, 369 Chiswick, Barry R., 241 , 3 14, 315, 355, 384, 489 Christ, Carl F., 88, 99 Christofides, Louis N., 41 1 Clark, Kim B., 1 35, 424, 477 Clark, Robert L., 450 Classen, Kathleen P., 485 Clinton, Bill, 22, 55, 1 54, 1 73 Clotfelter, Charles T., 43 Coase, Ronald H., 193 Cobb-Clark, Deborah, 323 Cogan, John F. , 53 Cohen, Roger, 443 Coleman, Mary T., 47 Collier, Irwin L., 473 Connolly, Robert A., 424 Cook, Philip J., 43 Corcoran, Mary, 299, 376 Costa, Dora L., 79, 3 1 1 Couch, Kenneth A., 147, 148, 298 Courant, Paul N., 376 Cox, Donald, 376

Cramton, Peter c., 4 1 6 Crane, Jonathan, 299 Crawford, Vincent P, 426 Cross, Harry, 347 Cunningham, James, 143 Currie, Janet, 425, 426 Cutler, David M., 354, 471, 492

Daly, Anne, 382 Danziger, Sheldon, 291 Darby, Michael, 503 Da VarlZo, Julie, 47, 308, 309 Davis, Joe c., 398 Davis, Stephen J., 1 54, 289, 293 Deere, Donald R., 399, 425 DeFreitas, Gregory, 77, 382 de Jong, Philip, 84 de Lima, Pedro, 177 Denton, Nancy, 470 Deolalikar, Anil, 452 Dertouzos, James, 153 DeTray, Dennis N., 47, 99 Devine, Theresa J., 269 Dickens, William T., 398, 399, 448, 460 Diebold, Francis X., 330 DiNardo, John, 290, 291 , 299, 499 Disney, Richard, 154 Doeringer, Peter, 460 Dominitz, Jeff, 1 85 Donohue, John J., 369 Dou, Thomas, 378 Duncan, Greg J., 48, 94, 221 , 376, 420, 422 Dunn, Thomas A., 298 Dunne, Timothy, 155

Easterlin, Richard A., 99 Eatwell, John, 475 Eberts, Randall w., 220, 410 Echikson, William, 1 00 Edmonston, Barry, 328 Ehrenberg, Ronald G., 152, 154, 1 96, 220, 444, 486 Eissa, Nada, 64 Elgar, Edward, 289 Ellis, Robert A., 233 Ellwood, David T., 55, 398 England, Paula T., 378, 379 Estes, Eugena, 299 Evans, William N., 53, 299

Fair, Ray, 152 Fama, Eugene F., 433

Farber, Henry S., 268, 330, 331, 333-335, 337, 394, 398-400, 416, 426 Farkas, George, 378 Farrell, John, 421 Fay, John, 1 5 2 Feldstein, Martin S . , 47, 153, 261, 486, 488 Feliciano, Zadia M., 144 Ferber, Marianne A., 89 Fields, Gary S., 79, 8 1 Filer, Randall K., 1 80, 378 Fine, Glenn, 398 Fischer, Stanley, 455 Fishelson, G, 459 Flaim, Paul, 78 Fortin, Nicole, 291 Fraker, Thomas, 269 Fraundorf, Martha, 421 Freeman, Richard B., 3 1 , 1 34, 1 35, 148, 1 7 1 , 175, 1 80, 1 8 1 , 181, 1 82, 1 83, 1 97, 284, 286-288, 291, 293, 3 18, 3 19, 325, 369, 370, 373, 388, 390, 392, 399, 401 , 420-425, 434 Frey, William H., 1 80 Friedberg, Leora, 85 Friedman, Milton, 230, 500 Fuess, Scott, 422

Garen, John, 2 1 3 , 248 Gary, Wayne B . , 2 1 9 Ghez, Gilbert R . , 7 2 Gibbons, Robert, 268, 335, 433, 445, 447 Gilroy, Curtis, 143, 144 Glaeser, Edward L., 354, 471 Glenn, Andrew J., 147 Goddeeris, John H., 208 Goldberg, Matthew S., 348 Goldfarb, Robert, 1 33 Goldin, Claudia, 5 1 , 54, 1 35, 366, 379 Gompers, Samuel, 400 Gordon, M.S., 77 Gordon, R.A., 77 Gordon, Robert, 299 Gottschalk, Peter, 1 7 1 , 291 Graham, John w., 94 Gramm, Cynthia, 4 1 3 Grant, Kenneth E . , 307 Green, Carole A., 94 Green, David, 47 Greenberg, David H., 47 Greenwood, Michael, 305 Gregory, Paul R., 473 Gregory, Robert, 382 Griffin, Peter, 1 3 1 , 370 Griliches, Zvi, 1 34, 242, 289 Grogger, Jeffrey, 245

Kleiner, Morris M., 399, 434

Gronau, Reuben, 89, 377

Hunt, Jennifer, 177

Groshen, Erica L., 457

Hunt, Joseph w., 193

Grossman, Jean B., 1 75

Hurd, Michael, 83

Grosso, Jean-Luc, 152

Huston, John H., 398

Gruber, Jonathan, 170, 22 1 , 332

Hutchens, Robert M., 223, 448, 450, 45 1

Kohen, Andrew, 143, 144

Gustman, Alan L., 79, 83, 87

Hutchinson, Bill, 356

Kosters, Marvin, 287, 363, 373

Gwartney, James D., 363, 370

Hackett, Edward 1., 196

Kroch. Eugene A., 253

Ihlanfeldt, Keith R., 356

Kropp, David, 253

Imbens, Guido w., 43

Krueger, Alan B., 83, 85, 144, 145, 146,

Ito, Takatoshi, 439

Jasso, Guillermina, 320

147, 148, 1 53, 170, 1 73, 1 77, 178, 194, 198, 243-245, 286, 288, 290, 368, 456, 457, 458, 459 Kruse, Douglas L., 439 Kuskin. Mark S., 422 Kuznets, Simon, 230

Jencks, Christopher, 299

Kydland, Kinn, 75

Haltinwanger, John, 154, 155, 289, 475,

503 1 3 1 , 134, 1 52, 170, 176, 213, 353, 485 Hamilton, James, 1 9 1 Hamlin, William A., Jr., 295 Handy, Ferrnida, 193

Kostiuk, P. E, 220

lchniowski, Casey, 194, 392, 421

Hall, Robert E., 223, 260, 328

Hamermesh, Daniel S . , 40, 8 1 , 1 24, 126,

Knoeber, Charles R., 441

Kramarz, Francis, 293

Gyourko, Joseph, 194

Hall, Brian J., 447

Kneisner, Thomas J., 47, 2 1 3

Knight. J. B . . 344

Jaeger, David A, 244, 249, 330 Jakubson, George, 152, 420

Jensen, Michael c., 445, 447

Jevons, W. Stanley, 388

Johnson, George E., 1 8 1, 289, 29 1 , 382,

Hanoch, Giora, 241

408, 4 1 2

LaCroix, Summer, 357

Laffer. Arthur, 50-5 f , 5 1

Lalonde, Robert J . , 175, 269, 270, 3 1 8.

Hansen, w. Lee, 264, 485, 489

Johnson, William R . , 374

Hanushek, Eric A., 244

Joines, Douglas, 51

Hart, Robert, 1 52, 154, 170

Jones, Carol Adaire, 2 1 9

Hartmann, Heidi I., 378, 382

Jones, Ethel, 25

Hartsog, Catherine E., 4 1 8, 419

Jones, Stephen R. G., 483

Laren, Deborah, 299

Hashimoto, Masanori, 259, 328

Jovanovic, Boyan, 329, 334, 337

Lauer. Harrison, 421

Juhn, Chinhui, 278, 363, 372, 373, 503

Lawrence, D. H., 303

Hause, John, 242 Hauser, Robert M., 298 Hausman, Jerry A., 47, 296

Juster, E Thomas, 88, 94, 242

Haveman, Robel1, 84

319

LaMond, A, 299

Lang, Kevin, 155, 253, 448, 460

Lawrence, Robert Z., 287 Layard, Richard, 20, 202, 266, 400, 41 1 ,

478 Lazear, Edward P., 82, 83, 152, 432,

Haworth, Charles, 370

Kaestner, Robert, 266

Haworth, Joan Gustafson, 370

Kahn, Lawrence M., 193, 293, 344, 355,

Hayes, Beth, 413

358, 358, 368, 373-375, 3 8 1 , 42 1 Kahn, Matthew, 3 1 1 Kalleberg, Arne, 344 Kang, Kyoungsik, 439

Lee, Lung-Fei, 248

Heckman, James J., 23, 42, 49, 55, 59, 72,

433, 441, 445, 448, 450, 460, 496 Lebergot, Stanley, 466 Lee, David, 29 1

99, 172, 242, 248, 254, 26 1 , 264, 269, 27 1 , 369-371, 420 Herrnstein, Richard, 373 Hersch, Jom, 2 14, 423

Kaplan, H . Roy, 43

Leeth, John, 2 1 3

Karoly, Lynn, 153

Leibowitz. Arleen S . , 94

Heston, Alan, 15

Katz, Eliakim, 196

Heywood, John S., 1 96

Katz,

Hicks, D. H., 304 Hicks John R., 304, 4 1 2 Hill, Anne M . , 375, 377 Hill, C. R., 94 Hill, M. S . , 88

Hirsch, Barry T., 378, 378, 379, 389, 392,

397, 4 1 8, 419, 424 Holley, David, 100 Holmlund, Bertil, 221 Holzer, Harry J., 356,480, 483

Hotz, Joseph v., 75, 27 1

Houseman, Susan N., 152 Howland, Juliet, 344

Hoynes, Hilary Williamson, 59

H any C., 426

Katz, Lawrence E, 135, 144, 145, 1 64,

1 65, 1 7 1 , 1 8 1 , 181, 1 82, 197, 26 1 , 278, 280, 281-285, 286, 287, 288, 290. 293. 299. 448 , 455, 486, 48� 489, 492

Leigh, Duane, 420, 450 Lemann, Nicholas, 306 Lemieux, Thomas, 286, 29 1 , 293, 363,

373, 399, 4 1 1 Leonard, Gregory K . , 296 Leonard, Jonathan S., 1 55 , 1 85, 370, 398,

447, 477

Kawasaki, Seiichi, 1 70

Leontief, Wassily, 407

Keane, Michael, 490

LeShan, Lawrence L., 233

Kehrer, Kenneth, 60

Levine, David, 452

Kennen, John E, 144, 4 1 1 Kenny, Lawrence W., 248

Levine, Phillip B., 489 Levy. Frank, 276, 278

Kilbourne. Barbara Stanek, 378

Lewin, David, 368, 3 8 1 , 432, 460

Killingsworth, Mark R., 20, 25. 172, 377,

Lewis, H. Gregg, 42, 1 00, 4 1 7 , 419,

381 King, Sandra, 437

420

Lewis, Kenneth A, 193

Name Index

512

Li, Elizabeth, 223 Li, Jeanne, 154 Lichtenberg, Frank R., 135 Liebenstein, Harvey, 452 Liebman, Jeffrey B., 64, 447 Lilien, David M., 491 Lindbeck, Assar, 504 Link, Albert, 1 96 Linneman, Peter D., 143, 419 Lochner, Lance, 172 Loewenstein, Mark, 422 Long, Clarence D., 24 Long, James E., 196, 363 Loury, Glenn c., 299 Low, Stuart A., 379, 438 Lucas, Robert E. B., 77, 164, 220, 489 Lundberg, Shelly J., 3 1 , 55, 77, 299, 357, 359

Lynch, Lisa M., 260, 422 Lynn, L., 299

Machin, Stephen, 144 Macpherson, David A., 378, 378, 379, 389, 392, 399, 4 1 8 , 419

MaCurdy, Thomas E., 47, 75, 4 1 0 Maddala, G . S., 248 Madrian, Brigitte C., 332 Magat, W. A, 2 1 8 Main, Brian G. M., 440, 446 Malthus, Thomas, 95, 97-99 Mankiw, N. Gregory, 1 64 Manning, Alan, 144 Manski, Charles E, 1 85 , 248 Marshall, Robert C., 337 Marston, Stephen T., 476 Mason, Robert, 421 Massey, Douglas, 470 Maxwell, Nan, 374 Maynard, A. K., 298 Maynard, Rebecca, 269 McConnell, Sheena, 4 1 6, 425 McDermed, Ann A., 450 McDonald, Ian, 407 McGreary, M., 299 McGuire, Mark, 114 McLaughlin, Kenneth J., 490 Medoff. James L., 1 52, 1 9 1 , 388, 40 1 , 42 1 , 423, 424

Mellor, Earl, 143 Melville, Herman, 20 Mervis, Phillip H., 196 Meyer, Bruce D., 484, 486, 487, 489 Meyer, Laurence, 51 Meyer, Susan E., 299 Michael, Robert T., 230, 378, 382

Micklewright, John, 485 Milgate, Murray, 475 Milgrom, Paul, 432 Milken, Michael, 433 Mincer, Jacob, 42, 5 1 , 53, 77, 88, 99, 1 4 1 , 230, 257, 264, 264-266, 268, 289, 309, 329, 330, 334, 375, 452, 468 Mishel, Lawrence R., 424 Mitchell, Olivia S., 78, 79, 8 1 , 368. 373, 38 1 , 432, 460 Moffitt, Robert A, 55, 60, 79, 82, 83, 85, 87, 490 Montgomery, Edward, 220 Montgomery, Mark, 154, 172 Morrall, John, 133

Morrison, Peter A., 308 Mortensen, Dale T., 478, 501 Moulton, Brent R., 194 Mroz, Thomas, 54 Muhally, John, 266 Mulligan, Casey, 75, 233 Mumame, Richard J., 254, 278 Murphy, Kevin J., 445, 447 Murphy, Kevin M., 99, 264, 278, 284, 287, 363, 373, 459, 503

Murray, Charles, 55, 373

Nakamura, Alice, 54 Nakamura, Masao, 54 Nardinelli, Clark, 357 Naskoteen, Robert A, 305 Neal, Derek A., 374 Needels, Karen, 293 Neumann, George R., 416 Neumark, David, 145, 147, 242, 330, 347, 377

Newman, Peter, 475 Nickell, Stephen, 152, 293

Oates, Wallace E., 2 1 4, 299 Oaxaca, Ronald L., 363, 363-367, 3 73-374, 486

O'Farrell, Brigid, 378, 382 Olsen, Randall J., 99 Olson, Craig, 416 O'Neill, David, 172 O'Neill, June E., 374, 375, 380, 380, 381

O'Rand, Angela, 233 O'Reilly, Charles A., III, 440, 446 Ormiston, Michael, 438 Orr, Larry, 269 Ortega y Gasset, Jose, 159 Oswald, Andrew 1., 223, 4 1 1 , 496

Paarsch, Harry, 47 Page, Marianne E., 249 Paglin, Morton, 379 Parker, Jonathan A, 490 Parsons, Conal 0., 84 Payner, Brook S., 370 Peck, Jennifer Marks, 3 1 7 Pencavel, John H . , 23, 47, 388, 397, 410, 4 1 8, 419, 437

Perloff, Jeffrey, 1 72 Peterson, William, 4 1 8 Phelps, Edmund S., 357, 500 Phillips, A W H., 499, 499 Pickton, Todd S., 2 1 4 Pierce, Brooks, 278, 363, 373 Pierret, Charles R., 253, 361 Piore, Michael, 460 Pischke, Jom-Steffen, 83, 85, 258, 290 Plant, Mark, 503 Poincare, Jules Henri, 1 Polachek, Solomon W, 264, 375, 379, 380, 3 8 1

Polsky, David, 330 Preston, Anne E., 196 Proust, Marcel, 342 Psacharapoulos, George, 235

Quinn, Joseph J., 83, 2 1 4

Raff, Daniel M. G., 457 Raisian, John, 328 Ramey, Valerie A, 287, 288 Ransom, Michael R., 335, 363 Rapping, Leonard, 77, 489 Reagan, Ronald, 50-51, 216, 432 Reder, Melvin W, 416 Rees, Albert, 348, 390, 403 Register, Charles A, 266 Reimers, Cordelia W, 363, 383 Reskin, Barbara E , 377 Revenga, Ana L., 293 Reza, Ali M., 223 Riley, John G., 253 Ritter, Joseph A., 476 Roberts, John, 432 Roberts, Mark, 1 5 5 Robins, Phillip K., 60 Robinson, Chris, 420 Robinson, Robert, 344 Rogers, Willard, 48 Romer, David, 164 Rosen, Sherwin, 153, 172, 202, 2 1 3, 220, 223, 233, 248, 295, 308, 330, 334, 369, 42 1 , 44 1 , 445, 446, 497

Name Index

513

Rosenberg, Pamela, 154

Solow, Robert, 407, 453

Van Nort, Kyle D., 347

Rosenfeld, Rachel, 344

Sorenson, Elaine, 377, 3 8 1 , 382

Vered, Krauss, 344

Rosenzweig, Mark R, 98, 1 00, 305, 320

Spence, A. Michael, 249, 253

Viscusi, W. Kip, 213, 2 14, 2 16, 2 1 8, 358

Rouse, Cecilia, 243, 366

Spiegelman, Robert, 485

Voos, Paula, 424

Roy, Andrew D., 321

St. Luke, 103

Vroman, Susan B., 4 1 6

Ruback, Richard, 424

Stafford, Frank P., 88, 94

Rubin, Donald B., 43

Stanger, Suchita, 147

Ruhm, Christopher J., 377

Stark, Oded, 305

Runkle, David, 490

Startz, Richard, 299, 357, 359

Wade, James, 440, 446

Steinmeier, Thomas L., 79, 83, 87

Waidmann, Timothy, 84

Stem, Steven, 450

Waldfogel, Jane, 377

Stevens, Ann Huff, 330

Walker, James R., 99

Ruser, John w., 218, 219

Wachter, Michael L . , 172, 419

Sacerdote, Bruce, 43

Stewart, James, 399

Wallace, Phyllis A., 299

Saks, Daniel H., 394

Stewart, Mark, 344

Ward, Michael P., 5 1 , 54, 380, 381

Sala-i-Martin, Xavier, 164

Stigler, George J., 132, 1 38, 448, 477

Warren, Robert, 293, 3 17

Samuelson, Larry, 155

Stiglitz, Joseph E., 249, 455, 492

Warren, Ronald S., Jr., 237

Sandell, Steven H., 284, 287, 309, 3 1 1 , 375

Stock, James H., 83

Wascher, David, 145, 147

Schnell, John, 4 1 3

Stone, Joseph, 220, 410, 423

Weigelt, Keith, 441 Wei!, David N., 164

Scholz, John Karl, 64

Stone, FUchard, 4 1 8

Schotter, Andrew, 441

Stratton, Leslie S., 468

Weisbrod, Burton A., 208

Schuh, Scott, 154

Strauss, John, 452

Weiss, Andrew, 253, 453, 455

Schwab, Robert M., 299

Stuart, Charles E., 51

Schwarz, Aba, 305

Sullivan, Daniel, 1 9 1

Scully, Gerald w., 192 Sedlacek, Guilherme, 75

Summers, Lawrence H . , 288, 448, 457, 457, 458, 459, 460, 477, 504

Weiss, Y., 459 Welch, Finis R, 48, 1 4 1 , 143, 264, 278, 284, 287, 368, 368, 369, 372, 485 Wellington, Alison, 143

Seiler, Eric, 433, 437

Summers, Robert, 15

Sewell, William H., 298

Svejnar, Jan, 407, 4 1 1

Wessels, Walter J., 424

Swartz, Caroline, 363, 383

Willett, John B., 254

Szyszczak, Erica M., 154

Williams, Donald R, 266

Shakespeare, William, 69 Shakotko, Robert A., 337

Williams, Nicolas, 337

Shapiro, Carl, 455, 492 Shapiro, David, 375 Shapiro, Matthew, 152 Shaw, Kathryn, 220 Sherer, Peter D., 358, 368, 373, 3 8 1 , 432, 460 Shoven, John B., 83, 450 Sicherman, Nachum, 289, 358 Simon, Curtis, 357 Sims, Christopher A., 75 Sindelar, Jody L., 266

Sjaastad, Larry A., 304 Sjoblom, Kriss, 253 Slade, Frederic B., 84 Slaughter, Matthew J., 287 Slottje, Daniel J., 276

Smith, Adam, 159, 201, 202, 222 Smith, James P. , 49-5 1 , 53, 54, 328, 368, 368, 369, 372, 380, 3 8 1 Smith, Jeffrey, 27 1

Taber, Christopher, 172 Tamura, Robert F., 99

Taubman, Paul, 243, 298 Terleckyj, Nestor, 2 1 3 Thaler, FUchard, 2 1 3 Thomas, L . G . , 2 1 9 Thurman, Walter N . , 441 Thurston, Lawrence, 307 Tieblot, A. J., 133 Tomes, Nigel, 298, 420 Topel, Robert H., 175, 223, 287, 3 1 8, 3 1 9, 337, 458, 459, 485, 486, 488, 489, 503

Smith, Shirley, 375

Willis, Robert J., 99, 248, 266 Wilson, Nicolas, 154 Wilson, William Julius, 298, 470 Wise, David, 83, 143 Wittenburg, David C, 148 Wolfe, Barbara, 84 Wolfe, John R, 2 1 3 Wolpin, Kenneth I . , 99, 1 00, 253 Wood, Adrian, 293 Wood, Robert G., 376 Woodbury, Stephen, 485 Woods, Tiger, 114

Tracy, Joseph S., 194, 4 1 6

Trejo, Stephen J . , 126, 220, 383 Triest, Robert, 47 Trinder, C. G., 298 Troske, Kenneth R, 348

Yamada, Tadashi, 94 Yamada, Tetsuji, 94 Yezer, Anthony M. J., 307

Trost, R P., 248 Zabel, Jeffrey E., 54, 55

Smith, Robert S., 140, 214, 2 1 9 Smith, Sharon P., 1 94

Werin, Lars, 445

Ureta, Manuelita, 260, 328

Zarkin, Gary A., 2 1 3, 337 Zax, Jeffrey, 392

Ziliak, James P., 47

Smooha, Sammy, 344 Snow, Arthur, 237

Valletta, Robert G., 425

Zimmer, Michael, 305

Snower, Dennis, 504

Van Audenrode, Marc A., 152

Zimmerman, David J., 298

Solon, Gary R, 298, 299, 382, 490

Vanderkamp, John, 307

Zimmerman, Martin B., 424

Subject Index

internal migration and, 306-307

selection, 246-248, 269, 4 1 8-419

education and, 239-241

job turnover and, 335-337

self-selection, 49

immigrant flows by nation, 3 1 9-320

labor market contracts and, 447-45 1 ,

Ability:

piece rate versus time rate workers, 436-439 superstar phenomenon and, 293-296 wage structure and, 276-277

460-461 on-the-job training and, 261-268

Binding arbitration, 425-426 Bonding critique of efficiency wage model, 460-461 , 496

present value of, 232-233

Bonuses, 438-439

trade unions and, 422

Britain, 343-344

Airline deregulation, 401

Budget constraints, 3 1-33, 95-96

draft lottery, 243-244

Alcoholism, 265-266

Budget line, 32, 34-35

identical twin studies, 243

American Federation of Labor--Congress

Bureau of Labor Statistics (BLS), 2 1-23,

Ability bias, 240-24 1

Added worker effect, 76

of Industrial Organizations (AFL­

Adjustment costs, 149-145

CIO), 392-394

fixed, 150-152

Americans with Disabilities Act ( 1 990),

job creation, 154-155, 170-172

Apprenticeship programs, 260

job security legislation and, 152-153

Arbitration involving public sector

variable, 149-152

unions, 425-428 Asian Americans, labor market

African Americans:

discrimination and, 383-384

immigration and, 176- 1 78

Asking wage, 479-484

internal migration by, 306

Assimilation of immigrants and market

labor market discrimination and, 343-357, 366-374

perlormance, 3 1 5-319 Asymmetric information and strikes,

trade union membership of, 396 unemployment of, 468-469 Age and retirement, 78-82, 449-450

4 1 2-417 Austria, female-male wage ratio in, 344 Average product of labor, 1 05-106

Age Discrimination in Employment Act,

described, 23 1-232

5 14

internal migration, 306 minimum wage law, 145 overtime regulation, 1 25 population trends, 1 80-1 8 1 Canada: immigration policy, 325 race in the labor market, 343 retirement age, 78 Capital-skill complementarity hypothesis, 135-136 labor supply and, 56-57

Baby boom, 503 Beauty as basis for labor market

examples of, 255-256 immigrants and native, 3 14-3 19

California:

Cash grants:

82 Age-earnings profiles:

Business unionism, 390

353

job destruction, 154-155, 22 1-223

Affirmative action, 1 28-130, 369-370

77, 78 Business cycle and labor supply, 76-78

discrimination, 353 Bias:

unemployment compensation, 485 Certification elections, 3 9 1 , 399 Chief executive officers (CEOs): compensation of, 440, 445-447

Subject Index firm performance and, 447 principal-agent problem and, 445-446 tournaments in promotion of, 440, 445-446 China, fertility policy of People's Republic of, 100 Civil Rights Act (1964), 369-370 Coase theorem, 193 Cobweb model, 182-185 Cohort effect on immigrants' age-earnings profile, 315-319 Comparable worth, 381-382 Comparative advantage among workers, 248 Compensating wage differentials, 201-224 defined, 201-202 efficiency wages, 452-462, 492-497 gender discrimination and, 362-366 hedonic wage function and, 209-213 job amenities and, 219-223 layoffs and, 221-223 market equilibrium and, 206-208 negative reservation price, 207-208 race discrimination and, 353-355, 367-374 safety and health regulations and, 216-217 workers' supply to risky jobs and, 202-208 "wrong" direction of, 207-208, . 220-221 Complements: capital-skill complementarity hypothesis and, 135-136 perfect complements, 127-128 Comprehensive Employment and Training Act (CETA, 1973), 268 Computers and skill-biased technological change, 289-290 Consumer discrimination, 345, 355-357 Contract curve, 406-408, 410-411 Contracts: delayed-compensation contracts, 447-452, 460-461 efficient contracts, 405-411 fixed employment versus fixed wage, 498--499 implicit, 497-499 labor market, 432-452 yellow-dog contracts, 391 Conventional arbitration, 425-428 Convergence of regional wages, 164-166

SIS Cross-elasticity of factor demand, 134-135 Cuban immigration, 176-178 Current Population Survey (CPS), 21

Davis-Bacon Act (1932), 133, 134, 421 Decertification elections, 391, 399 Defined-benefit pension plans, 450 Delayed-compensation contracts, 447-452, 460-461 Demand curve for labor, 4 elasticity of, 112, 124-125 individual firm, 109-110 industry, 110-112 long-run, 119-125 risky jobs and, 205-206 short-run, 109-112 Demand-deficient unemployment, 474 Department of Labor, 140 Dependent variables, 13 Deregulation, 399--400 Derived demand, 103 Marshall's rules of, 13 1-134, 401 Difference-in-differences estimate, 65 Disability: benefits, 83-84 labor market discrimination based on, 353 Discouraged worker effect, 76-78 Discrimination. (see Labor market discrimination) Discrimination coefficient, 344-345 Drug use, 265-266 Dual labor markets, 459-460

Earned Income Tax Credit: labor supply and, 62-65 opportunity set, 60-62 work incentives, 62-65

Earnings test for Social Security, 85-87 Econometrics, 12

Economics ofDiscrimination, The (Becker), 344 Education, 226-255 ability and, 239-241 age-earnings profiles and, 255-256 funding and quality, 244-245 marginal rate of return to schooling and, 235-236 maximization of lifetime earnings and, 230, 245-248

on-the-job-training. (see On-the-job training) productivity and, 249-254 rate of return to schooling and, 235-236, 241-245 schooling model of, 230-237 signal of productivity, 250-254 stopping rule for, 233-234, 236-237 workforce distribution by, 286 Educational attainment, 24 gender differences, 227-229 immigration and, 318 labor mobility and, 306-309 raciaJ/ethnic differences, 227-229 statistics concerning, 227-228 unemployment and, 467-468 wage gap based on, 227, 237-241, 363-366, 368-369 Efficiency units, 262 Efficiency wages, 452--462 bonding critique of, 460-461, 496 determination of, 453-455 dual labor markets and, 459--460 fast-food restaurants, 456 market conditions and, 461 unemployment and, 492--497 Efficient allocation, 163 Efficient contracts, 405-411 Efficient turnover hypothesis, 332 Elasticity of labor demand, 112, 124-125 Elasticity oflabor supply, 45-51, 54-55, 59-60 Employee discrimination, 345, 354-355 Employer discrimination, 345-354, 357-362, 367-384 Employment discrimination, 129-130 Employment and minimum wage, 138-147 Employment population ratio, 21-22 Employment Standards Administration, 140 Enclave economies, 354 Endowment point, 32, 42 Environmental Protection Agency (EPA), 216 Equal Employment Opportunity Commission (EEOC), 369-370 Equilibrium, 4 hedonic wage function, 211-213 internal migration and, 307 labor market, 136-138, 351-354 risky-job market, 206-208 unemployment, 465

Subject Index

516

(See also Labor market equalization) Evolutionary wage change, 70-71

job training programs of, 268-27 1 public interest lawyers, 208 public sector employment and, 196-198, 392, 425-428

Fair Labor Standards Act (FLSA), 1 38, 147 Family migration, 309-3 1 2 Featherbedding practices, 408 Fertility, 94-100 China, People's Republic of, 100 poor relief and, 98-99 Final-offer arbitration, 426-428 Firms, 3-4 decision to offer risky working

Social Security system, 82-87, 166-167 Trans-Alaska Oil Pipeline, 5-7 unemployment compensation system, 484-488

environment, 205-206 employer discrimination and, 345-354, 357-362, 367-384 reputation of, 45 1 safety and health regulations, 2 1 6-2 1 7 Ford Motor Company, 457 France and immigrant flows, 177 Free-riding problem, 437-439 Free trade, 165-166 Frictional unemployment, 472 Fringe benefits, 332, 422-423

Gender comparable worth and, 3 8 1 -382 human capital and wage gap, 375-377 labor market discrimination based on, 343-344, 362-366, 374-382 labor supply and, 23-24, 5 1-55 Oaxaca decomposition and, 375-376 occupational crowding hypothesis and, 377-380 orchestra auditions, 366 trade union membership and, 396 unemployment and, 468-469 ' wage rate and, 362-366, 374-382 Gender norming, 361-362 General training defined, 257 payment for, 258 Globalization of economy, 287-288, 399-400 Government: Earned Income Tax Credit, 60-65 education policy of, 239-240, 244-245 employment subsidies of, 170-172 fertility behavior and, 98-99 health and safety regulations of, 2 1 6-2 1 9 immigration policies, 1 72-182, 325 job security legislation and, 152-153

welfare programs, 55-60, 98-99 Great Depression: union movement in relation to, 390 women in the marketplace, 23, 54 Gross domestic product (GDP), per capita, 12-19

Health care: job-lock and, 332 proposed reform of, 1 73 Hedonic wage function, 209-2 1 3

social capital, 298-300 social mobility, 296-298 substance abuse and, 265-266 Hungary: female-male wage ratio, 344 fertility policy, 100 Hysteresis, 504

Immigration, 3 1 2-327 African Americans, effect on, 176-178 base income levels and, 323-324 California population trends, 1 80-1 8 1 cohort effect on age-earnings profile, 3 1 5-3 1 9 complements of natives and immigrants, 1 74-175 Cubans, 1 76-178 economic benefits from, 3 1 5, 325-327 educational attainment and, 3 1 8

defined, 2 1 3 equilibrium, 2 1 1 -2 1 3 impact o f health and safety

France and Algeria, 177 history of, 3 1 2-3 1 3 impact on natives, 176-178

regulations on, 2 1 6-2 1 7 statistical value o f a life and, 2 1 3-21 6 Hicks paradox, 41 1-4 1 2

increase in, 3 1 2 Los Angeles labor market, 1 78-179 Mariel boatlift of Cubans, 176-178

Hidden unemployed, 22-23. 77-78 High school: dropouts from, 227, 242

Miami labor markets, 176-178 migration costs, 323-324 national income and, 326-327

equivalency diploma, 254 Hiring audits, 347 Hispanics: labor market discrimination and, 343, 382-384

perfect substitutes of natives and immigrants, 173- 1 74

trade union membership of, 396 unemployment of, 468-469 Household consumption, 95 Household division of labor, 9 1-94 Household opportunity frontier, 90-94 Household production function, 89-91 Human capital: acquisition over life cycle. 261-268 age-earnings profiles and, 23 1-233, 255-256 defined, 226 delayed compensation in relation to, 45 1 externalities, 298-300 gender and wage gap, 375-377 geographic migration as investment in, 304-305, 308-309, 3 14-3 1 5 job turnover and. 328 on-the-job training and, 257-268 postschool investments, 257-272 schooling and, 226-255

performance of immigrants in U.S. labor markets, 3 1 3-319 Pittsburgh labor market, 178-179 Portugal and African colonies, 1 77 response of native labor markets to, 178-182 surplus, 326-327 United States as destination, 3 1 2-327 wage dispersion by national origin, 3 1 9-320 wage gap and, 1 82 Immigration and Naturalization Act, 3 1 2 Immigration surplus, 326-327 Imperfect experience rating, 488-489 Implicit contracts, 497-499 Income effects, 36, 72 fertility, 97-98 Laffer curve and, 50-5 1 Independent variables, 1 3 India, wage differentials in, 344 Indifference curves: derivation of, 27-29 slope of, 29 tangency condition, 34-35

517

Subject Index

workers' supply to risky jobs and, 203-204, 209-210 Industry: interindustry wage structure, 457--459 unemployment and, 469 Inferior goods, 36 Injury rates by industry, 2 1 4 Internal migration. (see Migration, internal) Internationalization of U.S. economy, 287-288, 399--400 Interpersonal differences in worker preferences, 30--3 1 Intertemporal substitution hypothesis, 73-76, 489--49 1 Invisible hand theorem, 159

demand curve, 4, 109- 1 12, 1 1 9-125, 205-206, 4 10--4 1 1 elasticity of substitution and, 125-128

statistical, 357-362 taste discrimination, 344--345 Labor market equalization, 159-198

labor market equilibrium and, 136-- 1 38

across labor markets, 161-166

long-run employment decision,

cobweb model and, 182-185

1 14-- 1 1 9 Marshall's rules of derived demand, 1 3 1- 1 34, 401 , 425 number of workers to hire, 108-109

discrimination and, 349-354 employment subsidies and, 1 70-- 172 monopoly and, 193-196 monopsony and, 185-193

production function, 104-107

oligopoly and, 196

short-run employment decision,

payroll taxes and, 168-169

107-1 1 4 substitutes and, 125-128, 133, 135-136 union firms, demand curve for, 410--41 1 workers versus hours, 154--154

public sector, 1 96-- 1 98 single competitive labor market, 160--161 wage and employment levels, 1 36-- 1 38 Labor mobility, 303-338

Isocost lines, 1 1 6-1 17

Labor economics, 1-2

defined, 303

Isoprofit curves, 2 1 0-2 1 1 , 405--406, 414

Labor force participation rate, 2 1

educational attainment and, 306--309

Isoquants, 1 14-- 1 1 6

age and, 70--76

Israel:

disability benefits and, 83-84

demand elasticity for Palestinian commuters, 1 6 1 wage differentials, 344 Italy, retirement age in, 78

older workers, 78-82

internal migration and, 305-309

race and, 369-372

job turnover, 328-337, 456, 457

Social Security benefits and, 82-87 women, 23-24, 5 1-55, 72-73

Job-lock, 332 Job match, 330-332 Job search, 477--484 asking wage and, 479--484

304--305, 308-309, 3 14--3 1 5 immigration and. (see Immigration)

over time, 70--7 6

trends in, 23-25 Japan, 164

as human capital investment,

Labor-Management Relations Act (Taft­ Hartley Act, 1947), 39 1 , 4 1 6 Labor-Management Reporting and Disclosure Act ( 1 959), 391 Labor market:

Labor supply, 3-5 allocation of hours of work by gender, 87--89 Earned Income Tax Credit, 62-65 fertility and, 94-- 1 ()() hours of work decision, 33--40, 48, 7 1 -76, 85-87 impact of welfare programs on, 56--60

nonsequential, 479

actors in, 3-5

labor-leisure trade-off, 20

referrals, 480

dual labor market, 460

measuring, 2 1 -23

sequential, 479

economic story of, 2-3

neoclassical model of labor-leisure

wage offer distribution and, 477--479

participants in, 3-5

Jobs Training Partnership Act (JTPA, 1982), 268 Job turnover, 328-337 earnings and, 335-337

choice, 25-60, 87-94

spot. (see Spot labor market)

nonmarket sector and, 375-377

substance abuse and, 265-266

over the business cycle, 76-78

Labor market contracts, 432--452

over the life cycle, 70--76, 78-82

Labor market discrimination, 342-384

over time, 69-1 ()()

efficiency wages and, 456, 457

consumer discrimination, 345, 355-357

retirement and, 78-82

efficient turnover hypothesis, 332

defined, 342

in single time period, 20-68

job-lock and lack of, 332

discrimination coefficient and,

job match and, 330-332 movers, 333-337 stayers, 333-337 through layoffs, 328-330 unionized firms, 424 Junk bonds, 433

344--345 employee discrimination, 345, 354--3 55 employer discrimination, 345-354, 357-362, 367-384 gender-based, 343-344, 362-366, 374-382

Labor demand, 3--4, 103-156 adjustment costs and, 149-155 California's overtime regulation, 125 complements and, 127-128, 135-136

cost minimization, 1 17- J 1 9

supply curve for, 3--4, 44--46 trends in, 23-25 wage rates and, 54 women, 23-24, 5 1-55 Labor supply elasticity, 45-5 1 , 54--5 5, 59-60 Labor unions. (see Trade unions) Laffer curve, 50--5 1

measuring, 362-366

Landrum-Griffin Act ( 1 959), 391

nondiscriminatory firm's employment

Law of diminishing returns, 105-106,

decision, 346 profit maximization and, 349-354, 361-362 race-based, 343-374, 382-384

108-109 Lawyers: arbitration and, 427 public interest, 208

Subject Index

SI8

Layoffs: compensating wage differentials and, 221-223

Miami's labor markets and immigrants, 176-178 Migration, internal, 305-307

Netherlands, retirement age in the, 78 New Deal, union movement and, 3 9 1 New Jersey's minimum wage law,

perfectly predictable layoffs, 222-223

family, 309-3 1 2

quits vs., 328-330

region-specific variables in, 305-306

specific training and, 260-261

repeat, 308-309

Nonlabor income, 3 1-36, 49-50

temporary, 26 1 , 487-489

return, 308-309

Nonmarket sector:

Legal Services Corporation, 208

worker characteristics and, 306-307

Leisure over the life cycle, 70-73

Mincer earnings function, 264-266

Life cycle:

Minimum wage

hours of work by gender, 75 labor supply over, 70-76, 78-82

antipoverty program, effectiveness as, 1 47-149

leisure over, 70-73

California law, 145

maximization of earnings over, 230,

case studies of impact, 143-147

245-248 participation rates by gender, 74 Liquidity constraint in job search, 483-484

Loewe v. Low/or, 390-391 Long run, employment decision in, 1 14-1 1 9 Los Angeles' labor market and immigrants, 1 7 8-179 Lotteries: draft, 243-244 winners of, 43

Manpower Development and Training Act (MDTA, 1962), 268

family migration and, 309-3 1 2 fertility and, 94-100 household production function and, 87-91 labor supply and, 87-89 technological changes in, 53-54 Nonsequential search, 479

covered and uncovered sectors,

Normal goods, 36

1 4 1 -143 empirical evidence of effects, 143-147 monopsony and, 1 89-190 New Jersey law, 1 45-147 ' Puerto Rico law, 1 48

Normative economics, 9 Norris-LaGuardia Act ( 1923), 391 North American Free Trade Agreement (NAFTA), 1 65-166 Notch babies, 84-85

standard economic model of, 1 38-140 uncovered sectors, 141-143 unemployment and, 138-147, 474 Models, 7-1 1 unionism, 400-402

98-99

allocation of hours by gender, 87-89

compliance with, 1 40-14 1

Monopoly, 1 93-196 Malthusian model of fertility, 94-95,

145-147 New Jobs Tax Credit (NJTC), 1 7 1 - 1 72

Monopsony, 1 85-193 Coase theorem and, 193

Oaxaca decomposition, 363-367, 373-376 Occupational crowding hypothesis, 377-380 Occupational Safety and Health Administration (OSHA), 2 1 6-21 7 , 219

defined, 1 85

Oligopoly, 1 9 6

minimum wage and, 1 89-190

On-the-job training:

Marginal cost, 1 12- 1 1 3

nondiscrimination in, 1 87-189

age-earnings profile and, 261-268

Marginal productivity condition, 1 1 2

one-company town, 190-191

apprenticeship programs, 260

Marginal product of capital, 104

perfect discrimination in, 1 86-187

formal training vs., 260, 268-27 1

Marginal product of household time, 54

professional sports and, 1 9 1 -193

general training, 257, 258

Marginal product of labor, 104-106

Moral hazard, 2 1 8

delayed compensation and, 447-449

Movers, 3 1 0-3 1 2, 333-337

on-the-job training and, 257-261

Multiple regression model, 1 8-19

government training programs, 268-27 1 job turnover and, 332-334

value of, 107-1 1 0, 257-26 1 , 447-449

"last hired, last fired" rules, 260-261

work incentives and, 447-452

layoffs and specific training, 260-261

Marginal rate of substitution in consumption, 29, 34 Marginal rate of technical substitution, 1 1 5-1 1 6 Marginal revenue, 1 1 2-1 1 3 Marginal revenue product (MRP) of labor, 1 95 Marginal utility, 29 workers' supply to risky jobs and, 202-208

National Highway Traffic Safety Administration (NHTSA), 2 1 6 National Labor Relations Act (Wagner Act, 1935), 391 National Labor Relations Board (NLRB), 39 1 , 399 National Supported Work Demonstration (NSW), 269-270 Natural rate of employment, 500-504 Natural rate of unemployment, 475

marginal product of labor, 257-261 payment for, 258-259 specific training, 257, 332-334, 468 "tenure" from specific training, 260-261 trade unions and, 422 Opportunity set, 32-33, 60-62, 89-91 Optimal consumption/leisure bundle, 3335 Optimal sorting, 331

Marginal wage rate, 3 1

Negative selection, 322-323

Orchestra auditions and gender, 366

Mariel boatlift o f Cubans, 176-178

Neoclassical model of labor-leisure

Output decision, 1 1 2- 1 13

Marriage bars, 379 Marshall ' s rules of derived demand, 1 3 1- 1 34, 401, 425

choice, 25-60, 87-94

Overcompensation, 206-207

Nepotism, 345

Overtaking age, 267-268

Net gain to migration, 304-305

Overtime pay in California, 125

Subject Index

519

Palestinian commuters, 1 6 1

trade unions and, 424--425

Pareto optimality, 407

upward-sloping age-earnings profiles

Payroll taxes, 2 1 8

and, 447-449 wages affecting, 455-456

Payroll taxes:

Residential segregation and unemployment, 469-472 Retirement: age of, 80-82, 449--450

Social Security, 1 66-1 70

Professional Golf Association (PGA), 444

decline in age of, 78-79

unemployment insurance, 487-489

Profit maximization, 106-107

mandatory, 82

Pension plans, 450

discrimination and, 349-354

pensions and, 80-81

Per capita gross domestic product (GDP),

efficiency wages and, 453-455

Social Security benefits and, 82-87

isoprofit curves and, 2 10-2 1 1 ,

trade-off of leisure and consumption,

1 2- 1 9 Perfect complements, 127 Perfect substitutes, 1 25

405-406, 4 1 4 trade unions and, 424--425

78-79 wages and, 80-81

Phillips curve, 499-503

Profit sharing, 438-439

Return migration, 308-309

Piece rates, 433-439

Public sector:

Right-to-work laws, 39 1 , 398

Pittsburgh labor market and immigrants, 1 78-179 Pooling equilibrium, 250 Poor relief and fertility, 98-99 Population size in Current Population Survey, 2 1 Portugal and immigrant flows, 177

employment in, 1 96-198

Risk aversion, 203-207, 438

trade unions in, 392, 425-428

Risky jobs, 202-224

Puerto Ricans:

Roy model, 320-323

labor market discrimination and, 382-384 minimum wage law, 148 Quits, layoffs versus, 328-330

Scale effect, 122-124 Scatter diagrams, 1 3

(see Education)

Positive economics, 9

Schooling model

Positively skewed wage distribution,

Seasonal unemployment, 472, 489

276-277 Positive selection, 321-322 Present value:

Race, 24 labor market discrimination based on, 343-374, 3 82-384

age-earnings profiles, 232-233

statistical discrimination and, 357-362

investment returns of education,

taste discrimination and, 344--345

228-230

trade union membership and, 396

lifetime earnings, 245-248

unemployment and, 468-472

rate of discount, 229, 238

wage rates and, 35 1-354, 359-362,

retirement benefits, 450 Principal-agent problem, 445--446

367-374

(See also specific racial groups)

Sectoral shifts hypothesis, 49 1-492 Selection bias, 246-248 corrections to, 248 example of, 246-248 trade union membership and, 4 1 8--41 9 Self-selection, 49 immigration decision and, 3 1 4--3 1 5, 320-323 job training and, 269 Sequential search, 479

Prisoner's dilemma, 427

Race norming, 361-362

Sherman Antitrust Act, 390-39 1

Private gains in family unit to migration,

Rate of return to schooling:

Shirking behavior, 447--449, 455, 456,

309-3 1 2 Private rate o f return, 254--255 Production costs and affirmative action, 1 28-130 Production function, 1 04-107

estimations of, 241-245 marginal rate, 235-236 regression model, 241-242

Signal, education as, 250-254

Regression analysis, 1 9

Skill-biased technological change,

margin o f error in, 1 8

cross-elasticity of factor demand and,

multiple regression, 1 8- 1 9

134--135

107- 1 1 4

Rational expectations, 1 85

average product of labor in, 1 05-106

isocosts and, 1 16-1 1 7

461 , 492--494 Short run, employment decision in,

objective of, 1 3-14 statistical significance and, 1 8

289-290 Sleep time as response to economic environment, 40 Social capital, 298-300

isoquants and, 1 14-1 1 6

Regression coefficients, 1 3

Social experiments, 269-270

marginal product o f capital in, 104

Regression line, 1 4

Social mobility, 296-298

marginal product of labor in, 1 04-107

Repeat migration, 308-309

Social rate of return, 254--255

profit maximization and, 106-107

Replacement ratio, 484

Social Security system:

Productivity: delayed compensation contracts and, 447-452

Reservation wages, 4 1--44

disability benefits, 83-84

decision to work and, 42--44

earnings test, 85-87

defined, 203

payroll taxes for, 1 66-167 retirement benefits, 82-87

efficiency wages and, 452--462

labor force participation and, 72-73

on-the-job training and, 257-26 1

market wages versus, 52-53

piece rate vs. time rate workers,

negative reservation price, 207-208

defined, 257

nonlabor income and, 42

job turnover and, 332-334

433--439 schooling and, 249-254 tournaments and, 440-445

workers' supply to risky jobs and, 203-204

Specific training, 468

layoffs and, 260-26 1 payment for, 259

520

Subject Index

"tenure" from, 26Q.-26 I wages and, 335-336 Spillover effects, 4 1 8-42 1 Sports, professional: consumer discrimination and, 358 monopsony and, 1 91-193 superstar phenomenon, 293-296 tournaments in, 440, 442-444 Spot labor markets: compensation systems used in, 432-462 defined, 432 efficiency wages in, 452-462 work incentives in, 447-452 Statistical discrimination, 357-362 Statistical significance, 1 8 Statistical value of a life, 2 1 3-21 6 Stayers, 3 1 0-3 12, 333-337 Steady-state rate of unemployment, 474-476 "Stopping rule" for hiring workers, 1 1 2-1 1 3 Strikes, 41 1-417 unemployment insurance and, 484 Strongly efficient contracts, 408-410 Structural unemployment, 472-474, 495 Subsidies, employment, 17Q.-I72 Substitutes, 1 3 3 capital-skill complementarity hypothesis and, 135-136 intertemporal substitution hypothesis, 73-76, 489-491 perfect, 125 Substitution effects, 72, 124-128 fertility, 98 Superstar phenomenon, 293-296 Supply curve of labor, 3-5 no shirking, 493-494 risky jobs, 203-205 Supply-side economics, Laffer curve in, SQ.-51 Sweden, female-male wage ratio in, 344

Taft-Hartley Act ( 1 946), 391, 416 Targeted Jobs Tax Credit (TJTC), 172 Taste discrimination, 344-345 Tax credits as employment subsidies, 1 7Q.-17 1 Taxes, payroll, 2 1 8 Social Security, 166-170 unemployment insurance, 487-489 Team incentives, 438-439 Technological change, 53-54, 94, 289-290 Temporary layoffs, 260, 487-489

Threat effects, 418-421 Tied movers, 310-3 12 Tied stayers, 3 10-3 12 Time constraint, 31 Time rates, 433-439 Tournaments, 440-445, 445-446, 452 Trade unions, 388-429 asymmetric information and strikes, 412-417 compression of wages, 421-422 cooling off provisions, 416 costs of strikes, 416-417 deadweight loss from hiring policies, 404 decline of, 29Q.-291 , 389-390, 398-400 demand and supply for union jobs, 398-400 determinants of union membership, 394-400 dispersion of wages, 42 1-422 elections of, 39 I', 399 exit-voice hypothesis and, 423-425 labor market efficiency and, 402-404 Marshall's rules of derived demand and, 1 32-134 membership determinants, 394-400 monopoly, 400-402 national membership levels, 389-390 optimal length of strikes, 412-414 political activity and, 390, 392-393 public sector, 392, 425-428 resource allocation and, 402-404 strikes and, 41 1-417 wage effects and, 394-398, 417-423, 425 Training. (see Education; On-the-job training)

Unemployment, 465-506 age and, 468-469 asking wage and duration of, 479-484 cash bonuses and, 485 comparative, 465, 504-505 compensating wage differentials and, 221-223 duration of, 472-474, 476-477, 486-487 educational attainment and, 467-468 efficiency wages and, 492-497 equilibrium level of, 465 flows between employment and unemployment, 474-476 frictional, 472, 489-49 1 gender and, 468-469

general training and, 26Q.-261 industry and, 469 inflation and, 499-505 internal migration, 306 intertemporal substitution hypothesis and, 489-491 job search and, 477-484 job security legislation and, 152-153 minimum wage and, 138-147, 474 mismatch of supply and demand, 472-474 natural rate of, 475, 500-504 quits versus layoffs, 329-330 race and, 468-472 reasons for, 472-474 residential segregation ar,d, 469-472 seasonal, 489 sectoral shifts hypothesis and, 491-492 short spells and long spells, incidence of, 476-477 specific training and, 26Q.-261 , 468 steady-state rate of, 474-476 structural, 472-474, 495 trade-off between inflation and, 499-505 unemployment insurance's effects on, 482,-489 United States, 466-472 wage curve and, 496-497 Unemployment insurance, 482-489 Unemployment rate, 2 1-22 discouraged worker effect and, 76-78 hidden unemployed and, 22-23, 77-78 historically, in U.S., 466-467 Unfair labor practices, 391 Union resistance curve, 4 1 2-41 3 Unions. (see Trade unions) Union wage gap, 417-42 1 , 422-423, 425 United Auto Workers (UAW), 133 United Kingdom, retirement age in, 78 United States immigration in, 3 12-327 internal migration in, 305-307 internationalization of economy, 287-288, 399-400 retirement age in, 78 trade unions in, 39Q.-394 trends affecting income distribution in, 282-293 unemployment in, 466-472 U.S. Navy recruitment policy, 439 Utility, marginal. (see Marginal utility) Utility function, 26-27 indifference curves and, 26-27, 34-35

52 1

Subject Index

workers' supply to risky jobs and,

job search and, 477--484 job turnover and, 335-337, 456, 457

202-208

labor demand curve and, 1 1 1-1 12, 1 19-125, 205-206 Value of the average product, 107

labor supply curve and, 44--46

Value of the marginal product, 107- 1 1 0

labor supply elasticity and, 48-49

delayed compensation and, 447-449 on-the-job training and, 257-261 work incentives and, 447--452 Vietnam war and lottery selection,

life-cycle path of wages and hours,

(see Minimum

wage) monopsony and, 185-193

243-244

production levels and, 1 20-- 1 22 public-sector employment and, Wage curve and unemployment, 496-497

196-198 race and, 3 5 1 -354, 359-362,

Wage gap: between countries, 1 64-166 determinants of black-white wage ratio, 366-374 education and, 227, 237-241 , 363-366

supply) Work incentives: bonding critique of age-efficiency model, 460-461 , 496

367-374, 382-384 specialization and, 9 1 -94 trade unions and, 394-398, 4 1 7--423

chief executive officers, 440, 445--447 delayed compensation contracts, 447--452 Earned Income Tax Credit, 62-65 efficiency wages, 452--462, 492--494 profit sharing, 438-439 team, 438--439 tournaments, 440--445, 445--446, 452 upward-sloping age-earnings profiles, 447--452

women and, 54, 9 1-94 Wages:

experienced vs. new workers, 283 gender and, 374-382 human capital explanation, 375-377

dispersion among immigrants by national origin, 3 1 9-320 immigration and, 1 82

intergenerational correlation, 296-298

Wage-schooling locus, 233-235, 239

international trends, 283

Wage structure, 275-300

1980s wage structure, 372-373

ability and, 276-277

90th and 10th percentile worker, 283

changes during the 1 980s, 278-282

Oaxaca decomposition and, 363-367,

changes in income distribution during 1963-1995, 278-293

373-374 public interest lawyers, 208

earnings distribution and, 276-277

race and, 383-384

historical trends, 278-293

regression toward mean across families, 297 risky and safe jobs, 203-205 skill differences and, 373-374

intergenerational inequality, 296-300 interindustry, 457--459 international differences in income distribution, 278

trade upjons and, 417-421

reasons for inequality, 275, 282-293

trend in male-female ratio, 380--3 8 1

skilled and unskilled workers, supply

(See also Wage structure) Wage offer distribution, 477--479 Wage rates, 3 1 , 37-43

of, 284-285 superstar phenomenon and, 293-296 supply shifts, 286-287

age-earnings profiles, 70--7 1

Wagner Act ( 1 935), 391

chief executive officer compensation,

Welfare programs:

440, 445-447 cobweb model and, 182-185 education and, 233-235, 239-240, 255-256

actual vs. net wage rate, 57-58 fertility and, 98-99 hours of work and, 5 8-59 labor supply and, 56-60

efficiency wages, 452--462, 492-497

labor supply elasticity and, 59-60

employer discrimination and,

(See also Earned Income Tax Credit)

345-':354, 359-362, 367-384 equilibrium.

(See also Labor demand; Labor

bonuses, 438--43 9

70--7 1 minimum wages.

(See also Gender) Workers, 3--4

(see Labor market

equalization) gender and, 374-382 hours of work and, 37--43, 70-76 internal migration and, 307 intertemporal substitution hypotheses and, 73-76, 489-491

Women: family migration and, 309-3 1 2 fertility and labor supply, 94-100 labor force participation rate of, 23-24, 5 1-55, 72-73 in nonmarket sector, 87-89, 375-377 occupational segregation, 377-380 wage rates and, 54, 9 1 -94

Yellow-dog contracts, 3 9 1