Labor economics

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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

Vice presidentlEditor-in-chief: Michael W. Junior Publisher: Gary Burke Executive editor: Lucille Sutton Senior marketing manager: Nelson W. Black Project manager: Beatrice Wikander Senior production supervisor: Richard DeVitto Senior designer: Amy Feldman Cover illustrator: Boris Lyubner © SIS Editorial assistant: Joanna Honikman Compositor: Black Dot Group Typeface: limes Roman Printer: RR Donnelley & Sons, Crawfordsville Library of Congress Cataloging-in-Publication Data

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.

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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- 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

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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 . -

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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

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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-