Women in the Labor Market 9780231899796

Citation preview

Women in the Labor Market

Women in the Labor Market edited by CYNTHIA B. LLOYD, EMILY S. ANDREWS, and CURTIS L. GILROY

New York

C O L U M B I A U N I V E R S I T Y PRESS

1979

Library of Congress Cataloging in Publication Data Conference on Women in the Labor Market, Barnard College, 1977. Women in the labor market. Sponsored by Barnard College and the U. S. Dept. of Labor. Bibliography: p. 1. Women—Employment—United States—Congresses. I. Lloyd, Cynthia B., 1943- II. Andrews, Emily S. III. Gilroy, Curtis L. IV. Barnard College, New York. V. United States. Dept. of Labor. VI. Title. HD6095.C663 1977. 331.4'0973 79-15547 ISBN 0-231 -04638-3

Copyright ® 1979 Columbia University Press All rights reserved. Printed in the United States of America Columbia University Press New York Guildford, Surrey

Contents Preface Contributors Introduction Cynthia B. Lloyd, Emily S. Andrews, and Curtis L. Gilroy

vii ix xi

Part One. Household Decision-Making and Labor Supply 1. Bargaining Analyses of Household Decisions Marilyn Manser and Murray Brown 2. Comment Nancy M. Gordon 3. Comment Orley Ashenfelter

3 27 37

Part Two. Labor Supply Projections 4. Projecting the Size of the Female Labor Force: What Makes a Difference? Ralph E. Smith 45 5. New Evidence on the Dynamics of Female Labor Supply James J. Heckman 66 6. Comment Glen G. Cain 98 7. Comment Nancy Smith Barrett 111 Part Three. Career Decisions 8. Career Decisions and Labor Force Participation of Married Women Paula E. Stephan and Larry D. Schroeder 9. Occupational Segregation Among Women: Theory, Evidence, and a Prognosis Soloman William Polachek 10. Comment Janice Fanning Madden 11. Comment Finis Welch

119 137 158 168 v

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CONTENTS

Part Four. W a g e Differentials 12. The Convergence to Racial Equality in Women's Wages James P. Smith 13. Work Experience, Labor Force Withdrawals, and Women's Wages: Empirical Results Using the 1976 Panel of Income Dynamics Mary E. Corcoran 14. An Evaluation of Sex Discrimination: Some Problems and a Suggested Reorientation Brian Chiplin 15. Comment Myra H. Strober 16. Comment Jacob Mincer

173 216 246 271 278

Part Five. E E O : Training and Affirmative Action 17. Training Programs and the Employment and Earnings of Black Women Nicholas M. Kiefer 18. The Impact of Equal Employment Opportunity Laws on the Male-Female Earnings Differential Andrea H. Beller 19. Male-Female Wage Differentials: Has the Government Had Any Effect? Edward Lazear 20. Comment Isabel V. Sawhill 21. Comment Phyllis A. Wallace 22. Comment Mark R. Killingsworth 23. Reply to Killingsworth Edward Lazear Bibliography

289 304 331 352 356 362 376 379

Preface

BARNARD COLLEGE and the U.S. Department of Labor sponsored a Conference on Women in the Labor Market which took place on the Barnard College campus, September 27-28, 1977. Within the Department of Labor, this Conference was co-funded by the office of the Assistant Secretary for Policy Evaluation and Research (ASPER) and the Women's Bureau. Since so much recent economic research had been done on women in the labor force, it seemed a felicitous time to gather leading academics and policy makers together to discuss research and policy issues. This collection is a direct outgrowth of that conference. The papers appearing in this collection were competitively selected from 60 that were submitted. We were looking not just for quality but also for breadth and policy relevance. The papers fell into 5 broad topics: (1) household decision-making and labor supply; (2) labor supply projections; (3) occupational choice; (4) wage differentials; and (5) equal employment opportunity policy. Each of these five areas represents central questions around which much recent research has revolved. In the discussion following each set of papers, many of the larger debates within the profession are raised. This book is organized exactly as the conference was, with the addition of an introduction by the editors which sets the papers into the context of ongoing research and policy development in this field. The enthusiastic support given by Mary Hilton of the Women's Bureau and Ernst Stromsdorfer, formerly of ASPER, was essential in making the initial idea a reality. The conference itself could not have been the success it was without the masterful help of my assistant, Liz Gewirtzman. Her truly exceptional abilities, her calm approach to all crises and her sensitive and supportive personality made the conference, through its planning stages and its aftermath, a pleasant and satisfying undertaking for all those who were involved. I gratefully acknowledge the generous support of Barnard College through the Spivack fund in financing the costs of editing and preparing this manuscript for publication. The Ford Foundation provided additional support in the book's final phase of preparation through its grant covering the initial vii

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three years of the Program in Sex Roles and Social Change of the Center for the Social Sciences at Columbia University. The completion of this book would not have been possible without the aid of three excellent assistants. Liz Gewirtzman continued to help out after the conference by transcribing the taped proceedings and handling correspondence. Angela M. Dambrie and Mary O'Neill Berry came in at the end of the project t o help with the final typing, editing, and the preparation of a bibliography. New York, August

1979

Cynthia B. Lloyd

Contributors

Emily S. Andrews

Pension and Welfare Benefit Programs U.S. Department of Labor

Orley Ashenfelter

Department of Economics Princeton University

Nancy Smith Barrett

Department of Economics American University

Andrea H. Belter

Institute for Independent Study The Bunting Institute of Radcliffe College

Murray Brown

Department of Economics State University of New York at Buffalo

Glen G. Cain

Department of Economics University of Wisconsin

Brian Chiplin

Department of Industrial Economics University of Nottingham Nottingham, England

Mary E. Corcoran

Department of Political Science Institute for Social Research University of Michigan

Curtis L. Gilroy

National Commission on Employment and Unemployment Statistics

Nancy M. Gordon

Interdepartmental Task Force on Women

James J. Heckman

Department of Economics University of Chicago

Nicholas M. Kiefer

Department of Economics University of Chicago

Mark R. Killingsworth

Department of Economics Rutgers University

Edward Lazear

Graduate School of Business University of Chicago and National Bureau of Economic Research

X

CONTRIBUTORS

Cynthia B. Lloyd

Department of Economics Barnard College, Columbia University

Janice Fanning Madden

Department of Regional Science University of Pennsylvania

Marilyn Manser

Mathematica Policy Research

Jacob Mincer

Department of Economics Columbia University and National Bureau of Economic Research

Solomon William Polachek

Department of Economics University of North Carolina

Isabel V. Sawhill

Director National Commission for Employment Policy

Larry D. Schroeder

The Maxwell School Syracuse University

James P. Smith

RAND Corporation

Ralph E. Smith

National Commission for Employment Policy

Paula E. Stephan

Department of Economics Georgia State University

Myra H. Strober

The Graduate School of Business Stanford University

Phyllis A. Wallace

Alfred Sloan School of Management Massachusetts Institute of Technology

Finis Welch

RAND Corporation and Department of Economics University of California, Los Angeles

Introduction CYNTHIA B. LLOYD, EMILY S. ANDREWS, and CURTIS L. GILROY

TVIE ARTICLES and comments presented in this volume demonstrate the common concern of policymakers in the federal government and scholars in the research community with real world events that have affected women in the labor market. Three primary areas of mutual concern are investigated: (1) labor supply, (2) wage differentials, and (3) program impacts. In all three areas, the increasing involvement of women in the world of work, as well as the growing strength of the women's movement, has led to a rekindling of both academic and governmental interest and action. In terms of labor supply, the labor force participation rate for women has risen sharply and steadily over the past twenty-five years. In a macroeconomic context, the increasing numbers of women entering the work force has alerted policymakers to the increasing need to expand job opportunities for a growing working population. Yet the greater labor force activity of women continues to confound both government and private forecasters. Indeed, the Bureau of Labor Statistics has consistently underestimated the growth of the female work force. Its 1976 projection for the female participation rate for the year 1980 has already been exceeded. Searching for the causes of this increase in participation, microeconomic researchers have looked to theories of household decision-making and the consequent choices between home production, market work, and leisure. Such choices, which determine labor supply, of course, also interact with forces of demand to set wage rates women receive in the marketplace. Scholars have been seeking to understand wage determination by investigating the impact of such factors as education and work experience on earnings growth. These concerns have led naturally to the investigation of the causes behind observed earnings differentials between men and women. At the same time,

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the growth in female employment has shaken many into a greater recognition o f the effects o f discrimination on women's pay and employment, which, in turn, has initiated efforts by the federal government to institute programs to mitigate the adverse effects o f discrimination. Within the Labor Department, a number o f agencies are deeply concerned about the differential treatment o f male and female workers. The primary mandate o f the Women's Bureau, for example, is to provide for the employment and employability o f women. The Employment Standards Administration enforces the Equal Pay Act and insures that federal contractors comply with equal employment opportunity guidelines through the Federal Contract Compliance Program. In addition, the Employment and Training Administration has the potential to enhance the employment o f women through job skills training. Evaluating the effectiveness o f such programs has been a high government priority. Academic interests and government

concern have merged most

directly in such evaluations as increasingly more sophisticated research tools are being used to scrutinize government action. The recent growth in program evaluation literature is an indication o f the way in which scholars can respond energetically to issues in the policy area.

R E S E A R C H A N D PUBLIC POLICY Despite increased reliance on program evaluation studies and the incorporation o f macroeconomic forecasting into the governmental decision-making process, the role of research, particularly the microeconomic variety, frequently continues to be misunderstood. T o the nonacademic community, research may appear far removed f r o m the primary concerns o f public policymakers. Scholars, on the other hand, are reluctant to provide government officials with quick answers which avoid dealing with difficult underlying issues. Y e t , the bond between government and researchers needs strengthening to deal with today's complex problems. Sound policy can only be founded on an accurate conception o f the operation o f the economy in general, and labor markets in particular. For these reasons, we begin with an overview o f the ways in which economic research may be used to meet the needs o f government in helping working women. Policy-related research can be categorized as " d i r e c t " and "indirect." Direct analysis is necessary to fully explore areas where there is a need for or a current program o f government intervention. Such research

Introduction

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may take a number of forms. The government may wish to ascertain the extent and investigate the nature of a particular labor market problem. The expected impact of suggested policy remedies can and ought to be estimated in advance. Finally, programs and policies already in place have to be evaluated. While evaluation is often regarded as the most direct link between programs and research, information that leads to policy formation is also vital to sound government processes. Studies of this kind, initiated inside and outside government, are frequently brought together at hearings on proposed legislation. The value of "indirect" research is less frequently appreciated, since such work deals with topics that underlie direct policy. In other words, information about seemingly unrelated topics is often essential for an accurate analysis of an issue at hand. Indirect research is perhaps best demonstrated by example and can be better appreciated through a discussion of the policy implications of research in the three areas of interest concerning women in the labor market. Both direct and indirect government research may be seen in the area of labor supply. Direct research stems from the need to develop, for example, forecasts of labor force growth to support long run macroeconomic policy. Indirect research is also needed to analyze the behavioral determinants of labor supply. Such research may not immediately produce new forecasts, but is likely to feed indirectly into improved forecasting equations in the future. Research on wage differentials is of "direct" policy interest to the extent that wage studies indicate the degree of discrimination faced by women in the labor market. Research which concentrates on the factors which lead to differences in male/female productivity may be considered "indirect." Yet it is essential for government to separate out the effects of both discrimination and other factors on wage differentials in order to plan effective programs to promote equal employment opportunity. Studies evaluating the effect of job training and contract compliance are obviously examples of "direct" research. In the analysis of program impacts, however, direct and indirect interests may merge. For instance, it may be necessary to sort out differences in women's occupational preferences from the effects of occupational discrimination against women. The first factor is not of particular interest for policy, while the latter is an essential measure of program failure or success. Data and methodology are not primary substantive concerns of policy-

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makers, but interest in these areas is real, since studies relying on inappropriate methodology will be both incorrect and difficult to defend. Thus, on subjects of "direct" and "indirect" policy interest, the government requires access to the best possible research. This requirement of excellence meshes with the interests of scholars, who often find methodological development a primary objective of research. METHODOLOGY AND DATA CONSIDERATIONS

Many of the most recent methodological breakthroughs in the analysis of labor market problems have been prompted by the challenge of unraveling the true facts about women's relative economic contributions and economic rewards. Whereas we usually think of economic theory and empirical methodology being designed to explain economic events, often the causation may actually work the other way, with changing events stimulating the development of applicable methodological tools. The latter sequence of events has certainly been true in the case of research on women in the labor market. In fact, the external economies to the field of labor in general generated by research on women have been substantial and have encouraged many with no particular ideological commitment to women's issues to move into this challenging research area. In addition to methodological advances, research on women can be said to have acted as a catalyst in the development and more widespread use of new longitudinal data bases. These data—often referred to as "panels"-are collected for different reasons than are the more traditional cross-sectional or time-series data sets. The interest is not so much in observing a variable at a point in time (statics) but in comparing this variable at different points in time (comparative statics), and in investigating change through time (dynamics) in order to uncover causal relationships. Panels reobserve the same individuals or families at different time intervals and provide a rich framework for tracing the movement of individuals over time among different demographic and economic states—such as marriage and divorce, or employment and unemployment. For policy purposes, the advantages of such microdata are obvious Labor market knowledge based purely on cross-sectional or time-series data analyses in the past have been strong on aggregate relationships but weak on individuals and their behavior. In this volume, seven of eleven papers base their empirical research on these micrcdata sets.

Introduction

xv

The papers in this collection can be seen as illustrations of the new directions being taken in the pursuit of answers to questions about women in the labor market. These new directions in theoretics, econometrics, and data development can be categorized according to three major areas of interest discussed above: (1) labor supply; (2) wage differentials; and (3) the analysis of program impacts.

LABOR SUPPLY Every paper in the book dealing with labor supply is concerned with the dynamics of the decision-making process, on either a theoretical or an empirical level. Manser and Brown, in their "Bargaining Analyses of Household Decisions," are concerned about the interpersonal dynamics of decisionmaking within the household—an issue glossed over in virtually all traditional labor supply theory. They reject the "neoclassical household utility f u n c t i o n , " which subsumes all the personal dynamics into an amorphous " f a m i l y " utility function and assumes that spouses are indifferent to the distribution of production and consumption within the household as long as "family" utility is maximized. The bargaining models Manser and Brown deal with allow for other outcomes by including variations in bargaining power between the spouses. Given the rapid increase in women's labor force participation concomitant with marital instability, it seems logical that such models when fully developed should be more realistic and more useful. In their empirical testing of the model, they used the 30 to 44-year-old female cohort of the National Longitudinal Surveys (NLS), a data base that also permits rich comparative static analysis. In contrast, Jim Heckman's article, "New Evidence on the Dynamics of Female Labor Supply" utilizes the Panel Study of Income Dynamics (PSID) t o explore the intertemporal dynamics of decision-making. He posits a theory called state dependence, in which past labor force participation is hypothesized to increase the probability of future labor force activity. The concept of state dependence adds a whole new dimension to the usual labor supply analysis. Typically, labor supply models assume optimization over a lifetime on the basis of fully anticipated labor market opportunities and home time demands. Heckman's model builds a sequential factor into the decision-making process, and therefore adds a more realistic ingredient to the determination of labor supply. Obviously, this theory is sex neutral, and also relates to other states

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such as unemployment; but it was developed with women's participation particularly in mind because changes in their labor force participation are the primary determinants of changes in the overall size of the labor force. Both Heckman and Ralph Smith, in his article "Projecting the Size of the Female Labor Force: What Makes a Difference?", are concerned about advancing the methodology of forecasting beyond the usual straight-line projections typically used by the Bureau of Labor Statistics and typically wrong in the case of women. In moving toward estimating equations based on behavioral relationships, it becomes crucial to pick the model most descriptive of actual behavior. Smith takes an eclectic approach, selecting cross-section wage elasticities and time-series unemployment elasticities from the existing literature rather than developing a fully consistent empirical model of his own. Heckman's results, on the other hand, suggest that probabilities estimated from a cross-section do not provide a reasonable guide to the dynamics of labor supply and would tend to overestimate labor force turnover. The evidence he finds of state dependence requires the kind of information now available in panel data for proper labor supply projection because of the longitudinal as well as retrospective data on work experience that are available. Heckman's dynamic model requires the full use of panels; his study of life-cycle processes demonstrates that nothing but longitudinal data could serve his purpose. Paula Stephan and Larry Schroeder, using the mature women cohort of the NLS, attempt to investigate the determinants and consequences of "career commitment" in the context of labor force participation in their article "Career

Decisions and Labor

Force Participation

of Married Women."

From a slightly different angle, they are asking the same question raised by Heckman; that is, is there something systematically different about women who usually work relative to those who usually do not? As one would expect, they find that "career" women's current labor force status is not affected by the traditional neoclassical variables found significant in conventional labor supply equations, whereas women who have experienced more turnover are affected by these variables. Their results also suggest that conventional crosssection regression results have overestimated labor turnover. Stephan and Schroeder and Heckman have recognized the heterogeneity of women with respect to work patterns and have reestimated conventional labor supply functions with that in mind. But in addition, Heckman has found that initial

Introduction

xvii

heterogeneity among women is reinforced over time by the accumulation of labor market experience. In his article, "Occupational Segregation Among Women: Theory, Evidence and a Prognosis," Solomon Polachek extends the dynamic analysis of labor supply by viewing the occupational distribution as an outcome of the same life-cycle decision-making process. Occupational differences are seen to be the key determinant of differential human capital accumulation over the life cycle, and therefore women are said to choose their occupations according to their expected lifetime labor force participation. Atrophy rates-defined as the rate of depreciation of skills occurring during periods of labor force intermittency-are derived and attached to five broad occupational categories. On the basis of this categorization of occupations, Polachek finds that those women with greater labor force intermittency are more likely to be found in occupations with low atrophy rates-primarily low skill and menial in nature.

WAGE DIFFERENTIALS Although in recent years there has been much literature analyzing the determinants of male-female wage differentials, none of it has unraveled the compounding effects of human capital variables and discrimination. In fact, there has even been much debate about the size of wage differentials and the direction of change. Several of the articles in this book deal with these questions in new ways both at a theoretical and at an empirical level. The dynamics of the process are an important focus of attention in Edward Lazear's article, "Male-Female Wage Differentials: Has the Government Had Any Effect?" and in James Smith's article, "The Convergence to Racial Equality in Women's Wages." Lazear makes a major contribution to our view of how wage differentials should be properly measured. Prior to his paper, wage differentials have always been based on current wages for a cross-section of men and women at a moment in time. This creates certain problems in the interpretation of changes in the wage ratio. First, labor force flows change the composition of the groups whose average wages are being measured each year, and therefore selectivity bias becomes a problem in interpreting changes over time. Second, current wages obscure life cycle changes in wage differentials that are related to differential investments in on-the-job training. By comparing changes in rates of wage growth for young men and women in

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1968-69 and 1973-74, he estimates the "true" change in the wage differential between men and women. Lazear uses the appropriate NLS cohorts for the earlier period and the National Longitudinal Study of the High School Class of 1972 for the latter period. Although there remains debate about assumptions and estimation techniques, there is no question that the life cycle approach provides a more appropriate framework for the analysis of wage differentials. James Smith uses decennial census data from 1960 and 1970 to analyse changes in the black-white female wage differential over time. He finds that one third of the convergence in wage differentials was due to convergence in the labor market characteristics of black and white working women. Because selectivity bias could possibly mean that this convergence of wages for working women was not representative of what had happened for all women. Smith uses Heckman's technique for correcting for selectivity bias using the richer data from the NLS, which includes crucial information on market experience. However, he had to manufacture a measure of the hourly wage from the NLS. Here he finds that black women moving into the labor market between 1960 and 1970 were those who received relatively higher wages on average than previously working black women, whereas the white women moving into the labor market in the same ten-year period were those who received relatively lower wages on average than previously working white women. Mary Corcoran's article "Work Experience, Labor Force Withdrawals, and Women's Wages" examines the life cycle dynamics of women's wage determination using retrospective data from the Ninth Wave of the PSID. She finds that women's wages in general do not suffer directly because of depreciation of skills during labor force absence. Women 30-44, however, do pay a financial penalty foi labor force interruption, possibly because of job search and information problems. This finding is consistent with the earlier work of Mincer and Polachek (1974). In this study, selectivity bias was not found to be a major problem, so the estimated effect on wages of work experience and labor force withdrawals can be assumed to be roughly applicable to all women. As can be seen from this article, the richness of panel data gives the analyst the level of detail, the disaggregated characteristics of individuals or families, that can be followed over time. In addition to conventional economic and demographic variables, direct questions on hard-to-measure factors such as work experience and even attitudes have beccmc an integral part of longi-

Introduction

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tudinal surveys. Together these data sources can help us more effectively bridge the gap between research and policy. Brian Chiplin, in his article "An Evaluation of Sex Discrimination: Some Problems and a Suggested Reorientation" moves tentatively toward a new methodology for estimating discrimination's impact on wages. He first surveys the methodology used to investigate sex discrimination and outlines the problems in current techniques. He points out the arbitrariness of discrimination measures derived as residuals from earnings functions and suggests that the proper method of estimating discrimination is not through measuring the effect of sex in a reduced form wage equation, but rather estimating directly a wage offer curve for men and women and testing for differences. This is easier said than done because of the lack of requisite data from which to measure discrimination. Specific information on particular subgroups of the population and firms in the business sector are needed in many cases, and these data, except in the aggregate, are unavailable. Although household data are generally more detailed and provide some information disaggregated by sex, detailed establishment data (broken down by occupation and by industry) are not currently available. In particular, firm-specific data on applicant pools for specific jobs are nonexistent. Chiplin's example of places in a British university gives no particular insight into the presence or absence of job discrimination but does provide a new methodology that could be used if proper data were available. Unfortunately, in the meantime empiricists and the courts rely on the so-called residual approach, which, given omitted variables and other data constraints, makes the interpretation of policy implications problematic.

PROGRAM IMPACTS One of the most difficult tasks of empirical research is the measurement of the impact of a program or policy on the particular population group targeted by - that policy. Program evaluation has become an increasingly sophisticated art as more and more policymakers have become aware of the inadequacies of the usual "before and after" analysis. The particular programs of concern in this book are equal employment opportunity and job training as complementary vehicles for increasing the employment and earnings of disadvantaged groups. The empirical methodologies discussed in this volume are applicable to the analysis of many other government programs; similarly,

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methodologies developed to analyze women's labor market situation may be generalized to deal with a wide range of issues. Andrea Beller uses variables measuring the differences in the number of investigations and settlements by the Equal Employment Opportunity Commission (EEOC) among states as a measure of the differential degree of enforcement of Title VII of the Civil Rights Act. Using annual Current Population Survey (CPS) data and a comparative static approach, she analyzes the factors determining relative male-female wages in three different years (1967, 1971, and 1974) and the changes between them. Despite the overall widening in the male-female wage gap over the 1967-74 period, Beller suggests that it would have widened even further without the enforcement efforts of the EEOC. Nicholas Kiefer, in his article "Training Programs and the Employment and Earnings of Women," finds positive post-training employment and wage effects for black women. Because training programs may be a logical route through which women enter or reenter the labor force, it is important to isolate the independent effect of training programs on employment and earnings. Kiefer builds a series of steps, first estimating the determinants of entering training and then using estimated individual training probabilities as a determinant of employment and wage differentials. His article is one of the first which has introduced the necessary econometric methodology to deal with the problem of selectivity bias in the proper analysis of policy impact. Kiefer uses the Office of Economic Opportunity-Department of Labor longitudinal study of four federally sponsored training programs, although he warns the reader that his results should be used with caution, since the data are not from a well-designed experiment. He points to a basic difficulty which pervades some of the present-day research—the fact that methodological advances in estimation techniques are often considerably beyond data capabilities. A researcher can massage the data base; but if it is not intrinsically rich enough, there is a danger in applying sophisticated econometric analyses; and conclusions drawn from these studies must therefore be accompanied by the appropriate caveats. Although it is not the main focus of his study, James Smith also looks at affirmative action as a possible determinant of the racial convergence of women's wages. He looks at wage premiums paid in sectors most succeptible to government pressure: (1) the government itself, (2) industries regulated by

Introduction

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federal or local government, and (3) industries with a high proportion of sales going to the government. Black women made relatively large employment gains in the government sector, suggesting the beneficial effect on job prospects of being both black and female. All these methodological and policy considerations are woven together and embellished through discussants' lengthy comments. The interaction of articles and discussions gives this book its special flavor. Usually, commentators are limited to a technical critique of an article. In this volume, however, they go well beyond the articles to include more general issues of methodological and policy interest. This volume also brings together a diverse group of economists with different perspectives. Often, authors in a compendium tend to come from a single mold and discussants' comments are merely refinements of an accepted viewpoint. Such a narrow scope seemed particularly inappropriate for the subject of women in the labor market. In this area, many economists have been producing thought-provoking studies with varied motives. Economists differ on the basis of political persuasion, on feminist grounds, and for purely methodological reasons. To ignore the importance of such differences would be naive indeed, and in compiling this book we have made no attempt to edit them out (to standardize pronoun use, for example) in the interests of homogeneity. But what is lost in consistency of viewpoint is gained in richness of discussion. The commentators here were free to center their attention on those components of the papers they felt needed the greatest amplification. In that way, the volume as a whole brings together an unusually broad range of economic thought on labor supply, wage differentials, and program evaluation regarding women. Most important is the interaction that results from the representation of different schools of thought. Perhaps in this way new approaches to some of the problems that women face in the labor market may emerge.

ONE Household Decision-Making and Labor Supply

ONE

Bargaining Analyses of Household Decisions M A R I L Y N M A N S E R and M U R R A Y BROWN

IN THIS article, we apply the bargaining models of household decision-making which were proposed and analyzed in Manser and Brown (1977). We begin by describing our bargaining approach, comparing our models to those in the existing literature, and setting out certain testable hypotheses for labor supplies of males and females. The estimates presented here support our bargaining approach and suggest that recent major changes in labor supplies can be explained by such models without reference to changing tastes of individuals or other sources of structural change. The motivation for a bargaining analysis of household decision-making arises from the recognition of two deficiencies of the existing literature on household decision-making. The first is that decisions concerning marriage, fertility, labor supply, and consumption have customarily been treated in a compartmentalized manner, ignoring the potential interactions among the various decisions. This can be remedied by means of a bargaining analysis. A second deficiency is that marriage and, of course, divorce are difficult to analyze without explicit recognition of the utility functions of the individuals comprising the household or those considering its formation. In a neoclassical household, a (strictly quasi-concave) household utility function, UH, is assumed to be maximized, subject to the budget, time, and in some cases production constraints of the household. As far as we can determine, the literature on this type of household contains no discussion of sex role differentiation; nor is there any indication of whether the neoclassical household utility function is an aggregate of the individual's utility functions or refers to the function of one member of the household. Finally, the proThe order of the authors' names resulted from a coin flip.

3

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M A R I L Y N M A N S E R and M U R R A Y

BROWN

cess by which the household preferences are derived is not spelled o u t - e . g . , is the utility function a result of a bargain or is it imposed? In short, in a neoclassical household a utility function whose theoretical properties apply to an individual is assumed to hold for the collection of individuals forming the household. T o our knowledge, only the pathbreaking work of Becker (1973, 1974) attempts to come to grips with this aspect of the household, but that work itself is based on several very special assumptions which render unacceptable the maintained hypotheses based on it. An initial difficulty we have with the Becker formulation is that the household is viewed as producing a single good which yields utility to all its members. This requires the satisfaction of stringent aggregation conditions upon which Gorman (1953) polar form utility functions are based. 1 An example of these conditions is that the proportion of the wife's time and clothing, say, in producing children's services must be equal to the ratio of the same factors in producing household meals. If one accepts that, then it is obvious that one can ignore differences among the utility functions of the members of the households. Aside from the requirement that utility functions be homothetic, we have argued (Manser and Brown, 1977) that given the sex role differentiation which exists in most societies, it is not appropriate to begin analysis of the household with the assumption that the utility functions of males and females are the same. Socialization patterns differ, and these differences may be reflected in utility functions. When utility functions do differ, they cannot possess the special Gorman properties; so it is then necessary to know something about the relationship among the utilities in order to determine the household's allocation of goods and the distribution of the goods among members of the household. This point has been raised by Ferber and Birnbaum (1977: 22) who argue that "it would be a rare couple that would share a single utility function. Not only is this intuitively obvious, but empirical studies have found that 'The empirical and para-economic behavior of the family is a multi-person decision process.' . . . (Ferber and Nicosia 1977)." In short, a rule must be explicitly considered, as is done in our bargaining approach. Becker (1974) does mention a solution for the situation where b o t h individuals possess different interdependent utility functions including more than one good. The solution there is determined not by interdependence, as Beckcr claims, but by a rule which is simply the male's maximization prob-

Bargaining Analyses of Household Decisions

5

lem, a male dictatorial solution to the household allocation and distribution problem. Clearly, other rules are admissible; as indicated below, these yield household objective functions, allocations, and distributions which differ significantly and operationally from the dictatorial solution. A not unrelated difficulty is that Becker's aggregate good is a private good. That is, the consumption of this good by one member of the household reduces the amount that can be consumed by the other, a characteristic that does not seem to apply to children's services and housing, for example. There are no shared goods in a Beckerian household. 2 T o rectify this difficulty requires that a bargaining rule be adopted, since clearly no price mechanism exists that will determine the outcome. There are many bargaining rules that could apply to households. In the next section we focus on two extreme types of bargaining rules. At one extreme is the dictatorial household, in which it is agreed that one individual determines the distribution of the gains from marriage to each member by maximizing his or her own utility, subject to providing the spouse with the minimally acceptible level of utility. Opposed to that is the symmetrical household, in which the solution to the distribution and allocation problems is based on the utility functions of both individuals but is independent of the labels assigned to the two individuals who are contemplating forming, or w h o actually form, the household. These bargaining models differ, in ways noted below, from the neoclassical model, in which a household utility function is maximized subject to the budget and time constraints of the household. It is possible to characterize all these households by means of a program, i.e., in terms of an objective function to be maximized subject to constraints. A characteristic o f all of these models is that they imply that it is not appropriate to include earned income of the spouse in an individual's labor supply function, as has been done in many single-equation estimates; instead, the wage rate of the spouse and unearned income should be included as explana t o r y variables. But the households differ in important respects. Since both the objective functions and the constraints are different for the various households, there are different implications for the household demand functions. Thus, for the neoclassical household it is well known that the demand functions possess three and only three empirically verifiable properties: Cournot aggregation, Engel aggregation, and a negative semidefinite symmetric Slutsky matrix.3 Similarly, the programs associated with dictatorial and symmetrical house-

6

M A R I L Y N M A N S E R and M U R R A Y

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holds also imply testable restrictions on their respective demand functions, and these differ not only with respect to each other but also with respect to those of the neoclassical program. In this article, we focus on several differences between the bargaining models and the neoclassical approach. Neither the dictatorial nor the symmetrical bargains generally imply symmetry of the Slutsky matrix even though each member of the household is assumed to possess a neoclassical utility function. Also, the nonwage incomes of the two individuals in the dictatorial and symmetrical households have different effects on demand, whereas in the neoclassical household they have the same effect. Finally, the bargaining approach implies that search costs and expectations relating to the marriage decision (see the next section) can influence the household demands. The empirical procedure, using NLS panel data (see the third section for a description of the variables), is straightforward: first we estimate a general model of husband-wife leisure demands which does not impose the restrictions from the various models, then estimate the model under the restrictions, and then test whether the restrictions can be rejected by means of the standard likelihood ratio statistic. We employ the Rotterdam specification of a complete system of demand equations, which was used to test neoclassical restrictions on household labor supply functions by Ashenfelter and Heckman (1974a); as we will demonstrate, this specification can be extended to estimate our bargaining models as well. We find that the hypothesis of separate effects for male and female incomes cannot be rejected and that the imposition of symmetry of the Slutsky matrix is unwarranted-both results supporting the bargaining rather than the neoclassical specification. The estimated coefficients of the leisure demand functions are discussed below in the section on functional form. Our last set of estimates bears on the question of whether the major changes in labor force participation rates between the two time points for which we have sufficient observations can be attributed to changes in tastes or to changes in wage rates and other economic variables. Using the NLS data for 1966 and 1971, we performed a test of structural change, revealing that the hypothesis of structural change between the two years can be rejected with respect to our general model of male and female leisure demands. Subject to several qualifications noted below, it appears that changes in economic variables were responsible for the variations in participation rates over the fiveyear period. Whether that result applies to a longei time interval or to pe-

Bargaining Analyses of Household

7

Decisions

n o d s of greater variation shall have to be determined with the aid of an expanded data set. Much needs t o be done to determine the interrelationships between types of marriage decision and household demands. We have attempted t o show that retaining the received theory does not facilitate this determination, while introducing bargaining theory to the problem appears to do just that. Whether this alternative to the existing theory is reasonable is a question that will be answered on the basis of empirical tests. Our preliminary empirical evidence suggest that it is. But, abstracting from that, we can claim that the bargaining models have served to identify new variables as well as offering new interpretations of already identified variables; they have made possible an expanded set of econometric specifications for marriage, labor supply, and other household decisions; and they offer the promise of uncovering important elements in an economy-principally, the predominant type of marriage arrangement, its changes over time, and its impact on outcomes of the household decision-making process. If we are correct, the approach certainly merits further consideration.

BARGAINING MODELS OF HOUSEHOLD DECISION-MAKING We begin our analysis with the assumption that each individual has a neoclassical utility function, the form of which is independent of marital status, m , where 0,

if single

I,

if married

The general Manser-Brown (1977) model allows for an arbitrary number of c o n s u m p t i o n goods, some of which are public goods to the household and s o m e of which are private goods. For our empirical work in this article, we assume that there are only two goods in the individual's utility function, own leisure [we let x4 stand for the female's (F"s) leisure and x2 stand for the male's (M's) leisure] and a composite consumption good, x3; here, the composite consumption good is taken to be a "public" good to the household. 4 We include caring in our analysis by specifying that the satisfaction received f r o m own leisure is changed as a result of the decision to marry; specifically, leisure services for F are taken to be a

M

,

a M = Amm + 1, where AM is an

8

M A R I L Y N M A N S E R and M U R R A Y

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index of M's characteristics and aF is defined analogously. We also include committed quantities of each good, which we denote by y k , where k = 1,2, 3. Thus, we write the utility functions of F and Af, respectively, as UF = UF[aM(xi M

U

M

= U [aF(xi

- 7 i ) , * 3 " 73]

(1.1)

-T2),*3-73]

(1.2)

Both individuals face the usual time constraint: T = xt + L F ,

for F

(1.3)

T = X2+LM,

forAi

(1.4)

where T is total time available to the individual and L is the individual's time devoted to market labor. Define Pk to be the price of xk(k =1, 2, 3), yM and yF to be nonwage incomes of M and F, respectively, and IH to be exogenous income received (lost) only if the household is formed. Clearly, a single individual, /, will maximize U1 subject to the time constraint and to the own-budget constraint; we denote utility received by i if single by U'0. Any two individuals who have formed or are contemplating forming a household must determine how much of each good to consume subject to the time constraints and the household budget constraint: £/>,*,-= / M + / F + / „ 1=1

(1.5)

where IF = PiT + yF equals "full income" of F, and IM is defined analogously. If their utility functions differ, the presence of public goods which enter both parties' utility functions in identical amounts and the assumption that incomes of both spouses are pooled would necessitate a bargaining solution. Before discussing alternative bargaining rules, it is necessary to consider the marriage decision for reasons that will be discussed below. T h e Marriage Decision An essential feature of the marriage decision is imperfect information. In most cases, information about potential spouses must be obtained sequentially by means of a search process that involves both time and .money costs. Furthermore, the individual does not have the possibility of undertaking a further search after the offer is made, since the offer will in general be withdrawn if it is not accepted within a relatively short period. Thus, it cannot be

Bargaining Analyses of Household

Decisions

9

assumed that individuals make marriage decisions only when all individuals reach a state of equilibrium. Each individual has some expectation regarding the satisfaction to be obtained from marriage, which we denote by U'E, where U'E is likely to depend on own characteristics. We assume that the individual acts as if he or she were certain that the next offer will yield exactly U(E. Thus, the individual expects that, if the present offer is rejected, he or she will receive average utility over the planning period equal to

where C 0 / C i is the fraction of the planning horizon during which the individual expects to remain single; this fraction depends on search costs, which are taken as exogenous in the analysis. A marriage offer will be accepted only if the individual receives utility from the bargaining process which exceeds Z ' . For this reason, Z' is taken to be /'s threat point in the bargaining process and, in general, any variable affecting Z ' will appear in the household demand functions.

Properties of Alternative Bargaining Models Obviously, because of the existence of public goods and caring, the marriage "bargain" can be viewed as a two-person, non-zero-sum game. Since the marriage decision involves to some extent a degree of cooperation that may be absent in other types of bargains, a cooperative game approach is not an inappropriate one. We limit the bargaining rules considered to those having certain desirable properties. First, we require that the solution be Pareto optimal. Pareto optimality would not obtain if, for example, the two people successfully hid their true preferences from each other. We rule that out in the present situation because it is not unreasonable to assume that even if the (potential) spouse does not state his or her true preferences, the other party will be able t o infer them with sufficient accuracy. A solution for the contract curve, the locus of Pareto optimal consumption points, can be obtained for this problem in the usual manner, i.e., by maximizing £/', say, subject to equations (1.3), (1.4), and (1.5) and assuming a fixed utility level for the potential marriage partner, j ( / /'). From the contract curve, the locus of alternative Pareto optimal utility levels for i and / , corresponding to given prices and incomes, can be traced out and plotted as the utility possibility curve ( U P F , ) in

10

M A R I L Y N M A N S E R and M U R R A Y

BROWN

figure 1.1. The curve UPFj forms the boundary of all the feasible pairs (UF, UM) ; we denote St as the (closed) set of these feasible outcomes for the household bargaining problem. The existence of a bargaining or trading area requires that the threat point, Zi = ( Z f , Zf*), be contained in the feasible set, i.e, Z, S 5 , . If Z, £ 5 , it is impossible that both individuals will agree to a solution. When there is a price change, the contract curve shifts and the bargaining area shifts also. If, for example, a wage rate rises, the loci of Pareto optimal points shift to UPF 2 , and the new set of feasible utility pairs for the household bargaining problem is S2, where S t C S2 • Also, a price change will cause a change in the threat point. A second property we will require for the solution to all the bargaining models we consider is invariance with respect to linear transformations of UF and UM. There is a third property, symmetry, which plays an important role in cooperative game theory. A bargain which satisfies this property is independent of the labels of the individuals involved. Of the set of bargaining rules which do not satisfy the symmetry property, we focus on an extreme rule within the set, namely the dictatorial marriage in which one partner determines the allocation. Of the set of rules which satisfy symmetry, we analyze two Nashtype models. One of the two symmetric models we consider is the well-known Nash (1953) solution, which has all three properties discussed above and, in addition, has the property of independence of irrelevant alternatives, which re-

Bargaining Analyses of Household

Decisions

11

quires that if new trading alternatives become available, and the threat point is unchanged, an old alternative which was a nonsolution shall not become the solution to the new problem (see Luce and Raiffa, 1957: 30). Many objections have been raised to this property (see Luce and Raiffa 1957; 126-27; Kalai and Smorodinsky 1975: 514-5). Kalai and Smorodinsky replaced the property of independence of irrelevant alternatives with the property of monotonicity, which states that "if, for every utility level that player 1 may demand, the maximum feasible utility level that player 2 can simultaneously reach is increased, then the utility level assigned to player 2 according to the solution should also be increased" (1975: 515). They demonstrated that there exists only one bargaining rule which has the first three properties plus monotonicity. We begin the bargaining analysis of the distribution of goods in the household with one of the extreme forms of marriage, the dictatorial household, and then proceed to the Nash and Kalai-Smorodinsky solutions in that order.

The Dictatorial Model If the marriage is such that individual /', say, has dictatorial power to determine the gains each partner obtains from the union, then /'s strategy is to offer individual / just sufficient gain to induce / to accept. The problem for i is t o maximize {/', subject to equations (1.3), (1.4), and (1.5), and to: U'-Z'>

0

(1.7)

and X>0

(1.8)

where X = (jc, , x2, x3). Here, i is maximizing his or her own utility function subject to the usual budget and inequality constraints and also to a constraint which guarantees a minimally acceptable level of satisfaction to / . For given values of the exogenous variables, Z' is determined, and thus there exists a unique X° which maximizes U'. Note that Z1 includes 7 ; but does not include /,-. Consequently, 7, will have a different effect on the solution than will /,, which enters only through the budget constraint. We now consider the household demand equations for the situation when equation (1.7) is binding. Clearly, this solution is Pareto optimal, since the dictatorial program has the same structure as that program from which the LTPF is derived. Moreover, the conditions for the application of the implicit

12

M A R I L Y N M A N S E R and M U R R A Y

BROWN

f u n c t i o n theorem are satisfied, and hence the quantities d e m a n d e d can be expressed as c o n t i n u o u s , differentiable functions of the exogenous variables: X=fD(P,IhIhlH,ahah

7 , U'E,C'0IC[)

where P = (Pi ,Pi,P3),

(1.9)

and 7 = ( 7 i , 7 : , 7 3 ) ; the f u n c t i o n s fD

are c o n t i n u o u s

and differentiable at every point where the Jacobian is nonvanishing. Note that fD

in equation ( 1 . 9 ) does not depend o n /'s search costs and expecta-

tions, and that /,• and

have separate effects o n the demands.

U n d e r m o r e special assumptions, namely that the utility f u n c t i o n s are concave rather than strictly quasi-concave and, f u r t h e r , that / ' s threat p o i n t is held fixed as prices and incomes change, it can be shown that the Slutsky m a t r i x of the demand equations is symmetric (see Manser and Brown 1977). However, in general, the household d e m a n d equations will not posses a symmetric generalized Slutsky matrix. Up t o this point, we have not considered explicitly the possibility that the utility f u n c t i o n s m a y be i n t e r d e p e n d e n t . It would be straightforward t o ext e n d the dictatorial m o d e l to allow for the case where i's utility d e p e n d s on U1 and U1 does not depend on U1, or vice versa. Even if the utility f u n c t i o n s are i n t e r d e p e n d e n t , the necessity for a household bargaining rule remains. This situation is akin to the type of interdependence allowed for by Becker ( 1 9 7 4 ) , whose specification implicitly assumes that the bargaining rule is " d i c t a t o r i a l . " Obviously, in this situation, / would prefer more than his or her allowed share of goods, but the conflict is nevertheless resolved, since ; did agree t o the rule. If j did n o t agree to some bargain, then even were / ' s utility f u n c t i o n to include / ' s utility, n o solution would be possible. We c o n c l u d e that the conflict is not resolved as a result of t h e presence of i n t e r d e p e n d e n t utilities, as Becker claims. At the other extreme f r o m dictatorial marriages are organizations in which the t w o individuals are treated in a symmetric manner. We begin by applying the well-known Nash bargain t o the household decision-making p r o b l e m .

The Nash Model The Nash solution t o the bargaining problem of the h o u s e h o l d is obtained b y solving the following optimization problem: m a x N = m a x [UF(a„(x, M

X [U (aF(x2

- 7 , ) , * 3 - 7 3 ) - ZF(P, - 7ilx3

M

' 7 3 ) - Z (P2,P3Jm,

,P3JF,

CFRCF,

t/#)]

C^/Cf,

U%)\

Bargaining Analyses of Household

Decisions

13

subject to the time and budget constraints in equations (1.3), (1.4), and (1.5), and t o * > 0 . Rewriting the maximization problem in logarithmic form, our problem is max TV = max l n ^ - ZF) + I n ( U M -

ZM)

subject to the same three equations and to X > 0 . Quasi-concavity of the Nash function itself, or concavity of the individual utility functions, is sufficient to guarantee a unique solution yielding the demands as functions of all the exogenous variables, X = hN(P,IF,IM,IH,aM,aF,7,

Ug, t / ^ . C f / C f . C ^ / C f )

(1.10)

N

where the functions h are continuously differentiate at every point where the Jacobian is nonvanishing. Notice that the exogenous variables, Ug and Co'/Ct1, as well as U§ and CF/Cf, enter these demand equations as arguments, which is not the case in the dictatorial marriage. If the threat points vary, it can be proved that there may not be a symmetric Slutsky matrix (see Manser and Brown, 1977; Homey and McElroy, 1977). An additional implication is that changes in IF and Im have different effects on the household demands, just as in the dictatorial model. Clearly, these conclusions will not change in the more general case when N is strictly quasi-concave. Again, one might argue that the utility functions of M and F are interdependent. As we noted earlier, introduction of interdependent utilities in no way solves the household bargaining problem, but if the Nash solution were adopted for the case, say, where u' = (/'(..., U1) (/' i= /; /', / = M, F), we would have to take the Nash objective function as strictly quasi-concave or as strictly concave in order to proceed to demand analysis, and the qualitative results derived above without interdependent utilities would hold. T h e K a l a i - S m o r o d i n s k y Model It is possible to represent the Kalai-Smorodinsky (K-S) solution to the household bargaining problem graphically for given exogenous variables, as in figure 1.2. The UPF in the figure is assumed to be concave and the point Z = (ZF, ZM) is simply the threat point discussed above. Let VF* be F's indirect utility function evaluated by inserting the household demand functions obtained from the dictatorial solution into UF, with F a s the dominant member of the household; similarly define VM* as Ai's dictatorial indirect

14

M A R I L Y N M A N S E R and M U R R A Y

BROWN

Figure 1.2 The Kalai-Smorodinsky Solution to the Marriage Bargain utility function. Consider the line joining Z to the point B = (VF*, which can be expressed as (UF - ZF) = [(Kf*

- ZF)I(VM'

- ZM)] (UM - ZM)

VM'), (1.11)

The K-S solution is the maximal element v on this line in the feasible set. It is the only solution satisfying the axiom of monotonicity as well as having the other three properties. Since the K-S solution clearly lies on the UPF, and since any point on the UPF maps into a unique X, the K-S solution yields a unique solution for the household demands. The K-S solution to the bargaining problem implies a set of household demand functions with the same general form and properties as the Nash demand equations (1.10).

Summary of Implications for, and Tests of, Household Demand Functions The household demand functions corresponding to the alternative bargaining models discussed above differ somewhat from one another, and, more importantly for the present study, they differ from the neoclassical demand equations. First, we test for equal effects of IM and IF on the demands; failure of the test supports our bargaining models, because the separate income effects arise because of the effect of the threat points on the distribution of gains. Further, we perform a joint test of equal income effects and of symmetry of the Slutsky matrix; rejection of this test means that the neoclassical model is inappropriate for our data because symmetry of the Sluisky

Bargaining Analyses of Household Decisions

15

matrix is one of the three so-called empirical implications of neoclassical demand theory. Another novel feature of the model is the inclusion of individual characteristics, because of caring and because of the influence of expectations on the threat point; we test whether these variables significantly improve the explanation of household demands. THE DATA We are concerned with estimating a system of three household demand equations arising from the bargaining models: one for female leisure (total time minus hours worked), another for male leisure, and the third for a composite consumption good. The expenditure on the latter is assumed to exhaust the budget. Our data are drawn from the NLS survey of women who were between 30 and 44 years of age in 1967, the initial year of the survey. The model is tested upon those data which refer to the calendar years 1971 and 1966. Only residents of standard metropolitan statistical areas (SMSAs) are included in the study, since labor market characteristics may differ considerably between SMSAs and non-SMSAs. Further this choice was necessitated by a lack of the information required to construct the population variables (see below) for non-SMSA residents. The following variables are employed in the study. s Dependent Variables x, = Female leisure (total hours minus hours worked per year). x2 = Male leisure (total hours minus hours worked per year). Price and Income Variables P* = Female hourly wage rate, obtained by dividing the wage and salary income of the respondent by the hours worked. P* = Male hourly wage rate, obtained by dividing the husband's wage and salary income by the hours worked. This is the only method of obtaining wage rate data for husbands from this data set. The female wage rate was computed in the same manner for consistency. P3 = Price of the composite consumption good ; P3 is taken to be constant across the sample of observations within any time period. >'* = y% + y * + ¡ h = nonwage and nonsalary income of households. y* = Female income excluding wages and salaries. Since some sources of household exogenous income are not broken down into male or

16

MARILYN

M A N S E R and M U R R A Y

BROWN

female components on the NLS tape, this variable is a proxy constructed by utilizing information for single women. Unfortunately, the NLS data do not include information on taxes paid, while our labor supply theory requires wage rates and exogenous income to be measured net of taxes. We have constructed a total tax variable, TAX, which includes estimated federal personal income taxes, state taxes, and payroll taxes; and a total tax variable, TAXF, applicable to female income. We have also estimated the marginal tax rates for M and F, TM and TF (which differ because of payroll taxes). The net wage and income variables employed in this study are defined as follows: Px P2 1 lp

= Net female wage rate;/», = 1 - TF) = Net male wage rate; P2 =P*{\ - TM) = y* +PtT + PiT-TAX = yp + P}T - TAXF

Characteristics The following characteristics variables are included in the analysis. a 1 F = Highest grade completed by female. c*2f ~ Female health status, a zero-one dummy variable indicating whether health limits the amount or type of work the respondent can do. a 3 p = A summary measure of married female's attitude toward women working. a 1 M = Highest grade completed by male. a 2M = Male health status, defined analogously to a2p. a 3M = Attitude of husband toward wife's working. Committed

Quantities

n t = Number of children less than 6 years of age. n2 = Number of children, 6-13 years of age. n 3 = Number of children, 14 years and older, living at home. «4 = If homeowner, market value of house or apartment (in thousands of dollars); zero otherwise. Search Costs and Expectations One set of variables which affect an individual's search costs and expectations (in the marriage market) is "own characteristics." Search costs may also be affected by the population characteristics of the individual's area of

Bargaining Analyses of Household Decisions

17

residence. We include two variables in our study to capture population effects:

Sformo

S = total population in area of residence ~ the ratio of single females to single males ( 1 5 - 6 4 ) in SMSA.

Labor Market Disequilibrium Although our theory requires data on desired labor supplies (or leisure demands) of the household members, actual labor supplies may differ from the desired amounts if there is disequilibrium in the market. To account for this, we include: UN = local area unemploymenkrate, measured as a fraction.

FUNCTIONAL FORM AND STOCHASTIC SPECIFICATION To estimate the household demand functions, we employ a form based on the Rotterdam approach of Barten ( 1 9 7 7 ) and Theil ( 1 9 7 5 - 7 6 ) , and utilized to explain household labor supply decisions by Ashenfelter and Heckman (1974a). Following this approach, in equation (1.12) we reformulate the unrestricted demand equations in terms o f infinitesimal changes in natural logarithms and choose the parametrization which yields leisure demand equations of the form:

_

4

p.

Wjd log Xj = £ fjj y diij + On d log Pi + ei2d log P2 + ti,d log I + UiM ( j j

+

i

&wTda>™

/ =( U 1 N) +M where the 7 I ; , 0,y, i i i M , 6/¡f, 1

+

d lo E

hi 7

1

h +E V

+ 1

J

daiF

\^M0/ 0 = 1,2,3)

(1.12) Py, and ft are constants to estimate and

Wj is the sample average of PjXjll. Notice that writing the model in terms of I and lp is equivalent to writing it in terms of Ip and IM, since for our sample / = Ip + IM. We call this form the unrestricted model, for it corresponds to the most general household demand function (1.10) arising from the bargain-

18

M A R I L Y N M A N S E R and M U R R A Y B R O W N

ing models. We adopt the following discrete approximation to the differentials of log/*,-: J log P, = log Pj-

log Pj

where Pj is the average of P,- across the sample. The other differentials are constructed similarly. The restrictions detailed in the previous section enable us to distinguish between the neoclassical and the bargaining models. Because there is no variation in P3, the price of the aggregate consumption good, across our sample within any time period, we are unable to test for homogeneity or for the generalized Engel aggregation conditions that are associated with the bargaining models. One of the major differences between the bargaining approach and the neoclassical model is whether changes in ¡ F affect the demands in the same way that changes in I\f (or /) do. Thus, we test the two restrictions Mim=^2M

=

0

(1.13)

In order to test the validity of symmetry of the Slutsky matrix, define d l o g / * , the log differential of "real" full income, to equal 2

dlogl-

_

£ wkd log Pk k-\

where w, is the sample average of P,•*,•// and w 2 is the sample average of P i X i \ I , and reparameterize the model as follows:

_

4 P Wjd l o g x , = £ y,y y drij + Knd log Px +Ki2d 1 /=l

logP2

3 3 p. + Hid log /* + ] T hijF J dajF + X 1 /=> /= i

+

+ 1

p. 7 d afM ' (/=1,2,3)

1

(1.14)

W M 0/

Thus, the Slutsky parameters k^ are defined as k,-, =

+

Estimation of

the model parametrized as equation (1.14) will yield the same parameter estimates as the model parametrized as equation (1.12) with equation (1.13) imposed. For our problem, there is one symmetry condition to test, namely that Kiî = k 2 i . The model described above is obviously a seemingly unrelated regression ( S U R ) system. As is well known, it is necessary to drop one equa-

Bargaining Analyses of Household

Decisions

19

tion because of the singularity of the variance-covariance matrix; we have chosen to omit the demand equation for the composite good. We apply a maximum likelihood estimating technique to the model, and the estimates refer to households in which the wife works. There is a nontrivial problem with our procedure which should be mentioned at the outset. We omit observations on nonworking women so that no household in our restricted sample attains a corner; this has been done in previous studies of joint husband-wife labor supply systems (see Wales and Woodland, 1976). The inclusion of corner observations requires the application of bivariate tobit estimation techniques within the context of the SUR system, a problem we will address in future research. In the meantime, we present these estimates for the purpose of comparison with those in the existing literature on labor supply.

ESTIMATES OF HOUSEHOLD LEISURE DEMANDS Estimates of the unrestricted leisure demand functions for M and F for 1971 are presented in the first and fourth columns, respectively, of table 1.1. Values of the likelihood ratio test statistics for tests of the hypotheses of equal income effects and of symmetry are presented in table 1.2, together with critical values of Xq for two significance levels.6 We discuss these first and then return to an examination of the parameter estimates themselves. Conditional on the unrestricted form, the joint test of the restrictions for equal effects of Im and IF on the household demands is decisively rejected. The joint test of equal income effects and symmetry is also decisively rejected. Hence, there is no question that symmetry can be rejected conditional on our general specification, which allows for unequal income terms. Previous tests for symmetry of the Slutsky terms have been based on the neoclassical specification which requires equal income terms (see Ashenfelter and Heckman, 1974a; Wales and Woodland, 1976). The likelihood ratio value for a test of symmetry conditional on our estimates with equality of income terms imposed, presented on line c of table 1.2, indicates that the hypothesis cannot be rejected. Thus, for these data, the neoclassical model can be rejected on the basis of our bargaining model but not on the bases of the usual approach. The importance of the separate income effects in these estimates illuminates a definite need for better data, data on asset holdings and/or exogenous income of each spouse in a household, since such factors are

20

M A R I L Y N M A N S E R »nd M U R R A Y

oomr-^j-iNsor^wi NflO(»)OOi/)WM v-> — rs o rN O O ö o ö o o o ö ö

voooc-i — — so fN ö o

o m

BROWN

—

o M m o r- — m i n r^ \0 ^ O — — 00 ~ ö o ö ö o d c o d o

•o e r ^ T t - o o ^ f m - ^ O m r ^ T f ^ o - H f S a O v f - ^ f ì O O - i O i N O I

r- cm 1— 00 vo oo cm —^ CTv d w .

0 0 O S o o o

o CO o w

w w

1 a .

tt oo —>

0 0 o o « w t -H o O O F ~ 5»/Af ~ 0

( / = 1 , 2 ; / = 1.2, 3)

The test statistic presented cn line d of table 1.2 indicates that the characteristics variables taken together do contribute significantly to the fit of the demand equations. V/e can now discuss the parameter estimates themselves, focusing on the

Bargaining Analyses of Household

Decisions

23

preferred specification allowing for differing income effects, nonsymmetric Slutsky terms, and the effect of individual characteristics. From table 1.1, it is clear that the committed variables help determine leisure demands of husbands and wives in the households under consideration. Specifically, female leisure demand varies directly with the presence of children between the ages of 6 and 13 and indirectly with the presence of children 14 and older, while these committed variables are not significant for males. However, the market value of house or apartment does have an effect on male leisure demand. Female leisure demand is positively related to the husband's education, while male leisure demand is significantly and inversely related both to his own educational level and that of his wife. The other characteristics variables contribute less to the explanation of leisure demands. For the age range in our sample, the male and female health dummies have essentially no impact on male leisure demand. Our results contrast sharply with Parsons' (1977) result, which found a large and significant impact of male health status on the labor supply of males 45-59 years of age in 1966; those results are unconvincing because his model omits wage and income variables, variables which are included in virtually all labor supply studies in some form or other, and which are found to be highly significant in our specification. The population variables, which reflect expectations and search costs but may also capture labor market disequilibrium effects, are not significant. It is important to note that the unemployment variable affects only female leisure demand. This is consistent with results in the labor supply literature which show that actual female labor supply is more likely to be reduced as the overall unemployment rate rises (see, for example, Finegan, 1975). Our results indicate that both male and female wage rates as well as IF are significant determinants of female leisure demand, while both IM and lp and the female wage rate are significant determinants of male leisure demand. In order to compare the implications of our estimates with the labor supply estimates in the received literature, we compute the elasticity (at the mean) of the labor supplies implied by our estimates. The total effect of a change in own wage rate on individual /'s labor supply curve involves the 0„ parameter and the coefficients of the exogenous full income variables (since IF = P\T + and similarly for IM). The elasticity of the estimated labor supply curve for F with respect to the female wage rate (evaluated at the mean) is +.091, while the elasticity of the estimated labor supply curve for M (at the mean) is -.087. 8 The result that the male labor supply curve is highly wage

24

MARILYN

M A N S E R and M U R R A Y

BROWN

inelastic but backward bending is in accord with single-equation estimates of male labor supply: see, for example, Ashenfelter and Heckman's (1973) results and results of other studies cited therein. The result that the slope of the female labor supply curve (with respect to own wage) is positive is in accord with prior results, but our estimate that it is highly inelastic differs from other estimates. For example, Ashenfelter and Heckman (1974a) estimate an elasticity of .870, but that is based on aggregate data for SMSAs. Some difference is not unexpected, since the data used in the two studies involve different degrees of aggregation. Also, our data refer only to women who worked, and hence we may obtain an underestimate. Further analysis of our model including nonworking women is clearly required. The evidence provided here indicates that for our sample the explanation of leisure demand (or labor supply) is significantly improved when equal income effects and symmetry are not required, and when characteristics variables are included. Further research may indicate that although estimates of the effect of the female wage on female labor supply are not large enough to explain fully the large increase in aggregate female labor supply during the past twenty years or so, the other economic effects included in our model may allow us to conclude that this major labor market change can be explained by economic models without reference to taste changes. We turn now to some preliminary evidence on this issue.

Increasing Female Labor Supply: Evidence of Structural Change? During the period 1966-71, a continuing increase in labor market participation and hours worked of married women appears to have occurred. The NLS data permitted us to construct our data set for calendar year 1966 as well as for 1971. We find that average hours worked in our sample (for which both spouses worked in both 1966 and 1971) increased by 3.61 percent for women and declined by 3.91 percent for men over this period. These data can be used to test whether the coefficients of the labor supply functions have changed over the period, i.e., whether a structural change occurred. The procedure is as follows. We obtain two sets of estimates of our model, one for 1966 and the other for 1971, obtaining a likelihood value of L66 for 1966 and L n \ for 1971. The test of structural change can be accomplished by a test based on the likelihood ratio X = where L ^ is the value of the likelihood function with the restrictions that the coefficients and the

Bargaining A nalyses of Household

Decisions

25

variance-covariance matrix do not change between the two years (obtained by estimating the model with pooled data) and L n = L66 • Z,71 is the value of the likelihood when the coefficients and the variance-covariance matrix are allowed to differ in the two periods. 9 Note that if we reject the hypothesis that the estimates are identical for 1966 and for 1971, then the differences can be attributed to any of the following sources: (1) changes in tastes of males, (2) changes in tastes of females, (3) changes in the omitted variables, or (4) changes in the types of marriage. If we accept the hypothesis of no structural change, we conclude that changes in wage rates, exogenous income, and the other exogenous variables in our model, rather than the above four factors, explain the observed changes in labor supply behavior of the households in our sample over the period. Our test statistic, - 2 log X = 45.989, distributed as chi-square with 39 degrees of freedom, indicates that the hypothesis of structural change between the two years 1966 and 1971 can be rejected for our data at the .01 level. In view of this, as well as the more casual observation that most of the parameter estimates, including all those that were statistically significant, were very close in the two periods, there is no necessity to examine the 1966 estimates further.

NOTES 1. The Gorman (1953) conditions require that the expansion paths of the two utility functions be parallel straight lines through their respective origins. In other words, the utility functions must be identical honiothetic forms except for a scalar difference; in effect, this means that ratios of each pair of arguments in the two utility functions be identical. 2. "Shared" or "public" goods to the household are goods which are nonrival in consumption and must be consumed in the same amount by both spouses. 3. See Intriligator (1971: 159-63). Though there are only three properties of, or restrictions on, demand fuctions, they are often given different names from those in the text. Thus, "homogeneity of degree zero in prices and income of the demand functions" is an implication of the three properties in the text and can replace one of them. Ashenfelter and Heckman (1974a) formulate the theoretical restrictions in terms of labor supply functions. 4. Various goods demanded by households, most obviously children's

26

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BROWN

services which form a public good to the household, are produced by the members of the household. We have not specified an explicit household production function because we are not interested in separating those parameters in the marriage, goods, and leisure demand functions which are associated with tastes from those associated with the production technology. Also, we feel that the results that may be obtained by making the additional assumptions required for a household production function analysis are not rich enough to justify their cost. Furthermore, even if we were interested in a decomposition of technology and tastes, we would require more information than is needed for our traditional demand analysis (this new information may be very difficult to obtain). Finally, even accepting the burden of the extra assumptions and assuming we have access t o new information, Pollak and Wachter (1975) have shown that the household production function approach is inapplicable (unless one has direct estimates of the production functions, one for each commodity) under conditions of joint production, which certainly apply to the household's allocation problem. 5. A more detailed description of our data set is provided in an appendix which is available upon request from the authors. 6. The likelihood-ratio test for tests of sets of linear restrictions is explained in Anderson (1958: 187 ff.) and in many econometrics texts. 7. Wales and Woodland (1976) stratified their data on the basis of children present and education, arguing that neoclassical models did not permit their inclusion. Clearly, such is not the case; committed quantities and/or a characteristics index can be included in a neoclassical family utility function as well as in an individual's utility function. 8. The separate "price" and " i n c o m e " effects of a change in the own wage rate are offsetting, resulting in this small net effect. In order to allow the reader to break up the total wage effect into these components or to compute any wage or income elasticity desired, we report the sample means for the relevant variables Jiere. They are w, = .1877, w 2 = .3334, ( i , / L F ) = 4.111, (x2/Lm)= 3.072, Pi = 1.80, P7 = 3.42, IF = 28,410, I M = 40,088. 9. See Anderson (1958: 247 ff.) for further discussion of this type of test.

TWO

Comment NANCY

M.

GORDON

MOST DISCUSSIONS regarding public policy and women emphasize differences in the labor market behavior of men and women, usually said to result from a greater c o m m i t m e n t by women to home and family life. This greater commitment t o h o m e and family life is used t o explain the fact that women invest less in h u m a n capital than do men (whether through formal education, training programs, or on-the-job training) and the fact that women often exhibit less stable attachment to the work force.

These characteristics, in

turn, lead to lower earnings for women, who often obtain "dead-end" jobs with little chance for advancement, few fringe benefits, and eventually low retirement benefits. Policymakers are interested in understanding the factors influencing the extent to which women participate in the work force and, more specifically, in explaining the long-term increase in women's labor force participation. To do this, they require a general model that not only considers work decisions but also explains choices regarding marriage, fertility, and consumption. Manser and Brown argue effectively that past research has analyzed these decisions separately and therefore has not adequately explained any of them. As a result, empirical estimates of the determinants of women's labor force participation that are based on previous models may lead policymakers astray. In the present article, Manser and Brown have developed a theoretical model

that considers simultaneously decisions associated with marriage,

fertility, consumption, leisure, and labor force participation. In doing so they have made a significant contribution. However, their model simplifies certain important aspects of these decisions in ways that may also affect the validity of empirical estimates derived from it. This comment will focus on the theoretical model. First, the model will be summarized, then some difficulties 27

28

N A N C Y M. G O R D O N

with their analysis will be discussed, and finally, some concluding remarks will be made. 1

THE MODEL The authors start by concentrating on the marriage decision. Specifically, they examine the question of whether marriage to a prospective spouse is superior to both living alone and continuing to search for alternative marriage candidates. They use bargaining theory to explain h o w two individuals contemplating marriage might resolve differences of opinion about their future lives. 2 The bargaining approach would be reasonable for examining one particular decision, since the opportunity for both individuals lo benefit from a cooperatively reached agreement (which is assumed to be the case when two people are considering marriage) fits the assumptions of a twoperson, non-zero-sum cooperative game in bargaining theory. However, the assumption that individuals bargain with each other before marriage to negotiate the entire future course of their lives together is rather far-fetched. In particular, Manser and Brown assume that decisions about (a) (b) (c) (d)

the number of children the couple will have, how much each will participate in the work force, how they will allocate their resulting money income, and how much leisure time each will have

are made before marriage for all future periods in which the two people expect to remain married to each other. A more realistic description of marital decision-making might be a model based on a sequential bargaining process. Putting this issue aside, the model in the paper then uses these negotiated values for fertility, labor force participation, consumption, and leisure to evaluate the utility that is expected to result from accepting a current marriage offer. In addition, each individual is assumed to have estimated the utility (s)he expects to receive from a random offer of marriage. This estimate is called the expected utility f r o m marriage offers. If the utility f r o m marriage with the current candidate is thought to be greater than, the expected utility f r o m marriage offers, marriage to the current candidate is assumed to occur; if it is less than the utility derived from remaining single, marriage will not occur.

Comment

29

One possibility remains: the utility from remaining single may be less than the utility from marriage with the current candidate but utility from marriage with the current candidate may also be less than the expected utility from marriage offers. In this case, the decision about marrying the current candidate will depend upon the individual's views about when future marriage offers will occur and about what level of utility will be received from them. The authors assume that each individual holds expectations about the future with certainty. That is, individuals behave as though they know exactly when the next marriage offer will occur (when the expected waiting time has elapsed) and exactly how much utility will be derived from accepting it (the expected utility from marriage offers). Manser and Brown then proceed by postulating that the marriage decision is made by comparing the present values of the two streams of utilities that are expected in the future: one if marriage occurs and one if it does not. 3 Suppose marriage is chosen. The utility stream expected in this case is based on marriage to the prospective spouse, followed by divorce and remarriage to another person. That is, the decision to marry is based on the assumption that when the next marriage offer occurs (recall, it is anticipated at a known time in the future with a known level of utility), the married individual will divorce in order to accept the better offer. (This is the only cause for divorce considered by Manser and Brown's model in this paper. 4 ) These assumptions imply that the stream of utility from marriage need only be evaluated up until the time the better marriage offer is expected, since the first marriage is assumed to terminate then. (See figure 2.1.) Now suppose remaining single is chosen. This option is also evaluated under the certain expectation that a marriage offer yielding the expected utility from marriage offers will become available at a known time in the future. In particular, the next marriage offer is anticipated to occur sooner than the first marriage would be projected to end if the individual had decided to marry. This follows from the assumption that single people are more likely to receive marriage offers than are married people. For evaluation purposes, the two utility streams (from marrying and from remaining single) are expected to be identical (and equal to the expected utility from marriage offers) after the projected termination date of the marriage being evaluated. Hence, the latter portions of the two streams may both be ignored in the comparison. As a result, marriage occurs if the present value of the utility stream expected after marriage (up until the expected termination date)

30

NANCY

M.

GORDON

Utility

expected utility from marriage offers

utility of current offer

utility of remaining single

f 0 : time of decision about current marriage offer r, : expected time of next marriage offer if current offer is refused t2 : expected termination of marriage, if current offer is accepted utility path if marriage occurs • • • • utility path if marriage does n o t occur

Figure 2.1 Comparison of Utility Streams (Utility When Single < Utility of Current Marriage Offer < Expected Utility from Marriage Offers) exceeds the present value of the utility stream expected if the individual remains single, evaluated over the same length of time. If the individual and the prospective spouse decide to marry it is assumed that the agreements negotiated before marriage regarding fertility, labor force participation, consumption, and leisure will be followed. If the decision is made not t o marry, the individual will decide on time and money allocations alone until such time in the f u t u r e when marriage does occur (if at all). D I F F I C U L T I E S WITH THE MODEL Our interest in the model is primarily related to labor force participation decisions, and they, in turn, are intricately related to choices about marriage, divorce, and childbearing. In practice, all these decisions are made over a lifetime. Hence, any model that attempts to explain them must consider more than one period of time. Thus the authors' simplifying assumptions regarding the stability of these decisions in f u t u r e time periods is questionable. First, the utility anticipated f r o m marrying the current candidate is assumed to be exactly the same throughout the couple's life together. This follows f r o m the fact that the utility function is always evaluated at the same, negotiated set of values for the variables that are the arguments of the f i n e -

Comment

31

tion. 5 Second, the conditions under which divorce can occur are too restrictive. Third, the authors ignore the possibility that psychic or monetary costs might be associated with the divorce process. Finally, the availability and quality of future marriage offers to married individuals are assumed to be independent of the characteristics of the current marriage. For example, future marriage offers do not depend upon the number of children from the present marriage that would be included in the new household. Let us discuss the implications of each of these difficulties in turn. Even if the individuals did negotiate agreements before marriage covering the rest of their lives together on such factors as number of children, participation in the work force, allocation of money income, and amount of leisure, these variables would be expected to take on different values over time. For example, time is required to "produce" or adopt children. Further, there is considerable evidence in the literature that family size decisions are made sequentially and usually result in fewer children in actuality than were planned before marriage. Assuming that these decisions (and the resulting utility derived from marriage) will be the same in each future period is an unrealistic simplification. Similarly, the assumption that labor force participation is constant over the life cycle is a critical one. The difficult policy issues arise precisely from the fact that women only allocate most of their time to the home during part of their lives. Subsequently, they often return, voluntarily or involuntarily, to paid employment. To capture the effects of this change in time allocation requires a model that allows different allocations of time between home work and market work in different periods. A related problem surrounds the assumption that wage rates for both men and women are exogenous and remain constant over time. Yet, one current and important policy issue concerns the flat age-earnings profiles of women compared with the increasing age-earnings profiles of men. This difference is attributed to women's intermittent attachment to the work force. At a minimum, in the real world having more children is likely to be related to having a less skilled job and a lower wage rate and to spending more time working in the home. All these factors lead one to conclude that a model concerned with childbearing, paid employment, and work in the home should allow for interactions among these factors. If these variables are not allowed to vary over time and if the tradeoffs between different life cycle patterns are not taken into account explicitly, the model cannot help to address some of our most important policy issues.

32

NANCY M. G O R D O N

Let us turn now t o the second major difficulty with respect to the current model, how divorce is handled. The authors discuss the marriage decision f r o m the point of view of only one of the prospective spouses and assume that, should divorce occur, it would be the result of that spouse's receiving a better marriage offer. The model would be more realistic if it included the possibility that divorce would occur because the individual's spouse received a better offer and initiated a divorce or because one or both spouses decided after marriage that living alone would be preferable. The first possibility could be incorporated into the model easily by changing the method by which the individual calculates the expected utility f r o m marrying. For example, the individual could include an estimate of the time at which the prospective spouse would receive a better marriage offer that would then cause the spouse to initiate Jivorce. The individual might assume that the more desirable the prospective spouse appeared, the sooner the prospective spouse would receive a better marriage offer and terminate the marriage with the individual. The second possibility requires a different " s t o r y " about marriage. One could argue that agreements negotiated before marriage are likely to be renegotiated after marriage, in some cases fairly quickly and in other cases as the years pass. In fact, a "rational" person contemplating marriage might do well to assume that both people were behaving in a more agreeable fashion before marriage than they might be willing, or able, to continue in the long run. Thus, if one could anticipate the renegotiated agreements, one should include them in the decision-making process rather than relying solely on the agreements negotiated before marriage. Although conceptually this change would not be difficult t o implement, it would not improve the model's ability t o yield empirical results, since expected values of unobserved variables (the renegotiated agreements) are no more useful than the unobserved variables (the negotiated agreements) themselves. A more serious aspect of the treatment of divorce concerns the real life implications for a married person (especially a woman) if divorce occurs for reasons other than to marry a " s u p e r i o r " spouse. For example, if divorce is initiated by the other spouse or if it is sought because other factors change (i.e., "renegotiated" agreements are unsatisfactory), this is likely to have ramifications for past decisions. For instance, a rational person might have invested in market work rather than in home production, since the former contributes to increased future earning potential while the latter does n o t .

Comment

33

In the past, women have generally behaved as if divorce were unlikely or as if, should it occur, support would be continued by their ex-husbands. Consequently, they have not been averse to devoting much of their time to home activities. Unfortunately, upon divorce they have often suffered a considerable decline in their standards of living and have often been unable to earn enough to support themselves (or their children) at anywhere near their previous standards of living. Alimony and child support, if paid at ail, have been paid at extremely low levels. Some specific statistics may be illuminating. An International Women's Year study reported that alimony was awarded in only 14 percent of recent divorces, and often when awarded, it was to be paid for only a few years (Bryant, Evans, and Powell, 1975). The determinants of child support and alimony payments have recently been studied at the Urban Institute (Jones, Gordon and Sawhill, 1976). The analysis used a nationally representative sample of the U.S. population covering the years 1968 to 1973 and found that both the probability of a mother's ever receiving a payment from her ex-husband and the amount of the payment increased with the ex-husband's income. Nevertheless, by 1973, 39 percent of the women who were eligible to receive child support payments had never received anything. Among those who received at least one payment, the average amount received per year was less than $1,400 in 1973 dollars. 6 It should be noted that the data were based only on the first few years following divorce or separation. Since payments generally tend to drop rapidly as time passes, our results actually overstate the frequency and amount of payments. Furthermore, it was found that payments were not low because of the poverty of ex-husbands. Men with incomes over $7,000 per year allocated only about 16 percent of their aftertax incomes to their former families. These statistics make one question the basic postulate that marriage or, more precisely, women's reduced participation in paid employment, is the result of rational decision-making. Why would a rational woman decide to allocate, or agree to allocate, her time in such a personally disadvantageous fashion? One possible answer is lack of information. However, there has been considerable public discussion about rising divorce rates and about the difficulties encountered by displaced homemakers reentering the job market, as well as lack of financial support from ex-husbands and lack of benefits from the civil service retirement system and the social security system. Another possible explanation is selective perception. Women may believe that al-

34

N A N C Y M. G O R D O N

though many marriages will end in divorce and that divorced women will bear substantial costs, they, themselves, will not be in that group. A third possibility is that the problems enumerated above may be faced primarily by older women whose decisions to invest in home production were made at a time of greater marital stability. Younger women whose decisions are being made with access to information about the current instability of marriage may be responding appropriately by working more in paid employment. The increasing labor force participation of young women, including those with young children, is consistent with this hypothesis. The third difficulty with the Manser and Brown model is that no costs are associated with divorce. Alternative assumptions could be introduced into the model easily. As long as individuals believe that they know the costs of divorce and that these costs are limited in size, incorporating them into the model would then imply that for divorce to occur, the utility derived from a subsequent marriage offer must be at least a specified amount (the costs of divorce) greater than that derived from the current marriage. The last assumption of the model that I questioned concerns the fact that the probability and/or desirability of other marriage offers does not depend upon the negotiated agreements reached with the first spouse, especially those regarding number of children or, more specifically, the number of children that would form part of the new family. To elaborate, the individual's marriage decision is based upon the utility that is expected in future periods, which, in turn, is based upon a negotiated agreement that includes, among other factors, the number of children the couple will have if they marry. Explicit in the evaluation of a marriage offer is the possibility of divorce and remarriage. The difficulty arises in that remarriage opportunities in the model are not dependent upon the number of children that would be in the individual's custody after divorce. Incorporating an interdependence in the model would be a significant improvement; however, it presents serious theoretical problems. Its importance and its difficulty are analagous to the problem of allowing the arguments of the utility function to vary over time. In both cases, interactions among the various decisions that may occur currently or in future periods must be specified explicitly. The most important implication of this discussion is the necessity to develop a model that deals with more of the interactions among these interrelated decisions: marriage, childbearing, labor force participation, consump-

Comment

35

tion, and leisure. Especially important are the interactions that occur over time. To summarize, the Manser-Brown paper has highlighted the need to analyze several life cycle decisions simultaneously. It has improved considerably on the neoclassical model of the household in wliich decisions are based upon maximizing one utility function that is assumed to represent the preferences of the household. However, because of the conceptual difficulties described above, empirical estimates of the determinants of women's labor force participation based on the Manser-Brown model must be treated cautiously. Before such estimates are incorporated in public policy formation, one must explicitly consider whether the simplifying assumptions are inconsistent with the policy under examination. In particular, the treatment of divorce in the model is weak. Yet divorce, or its possibility, is probably a major factor in some women's decisions to work in paid employment. Further theoretical research might focus on model development to incorporate more fully interactions among the five decisions: marriage, family size, labor force participation, consumption, and leisure. Especially important are those interactions that occur over time. If this is done, more of the complex life cycle decisions affecting women would be included. This would, in turn, lead to the quality of empirical estimates regarding women's labor force participation that is necessary for sound public decision-making.

NOTES 1. Ashenfelter's comment, which follows, will address their empirical estimation. 2. Several specific bargaining models varying from dictatorship by one prospective spouse to symmetric bargaining between the two prospective spouses are examined. 3. Note that the decision to marry is based on what is expected to occur in the future. However, if the individuals do marry, other marriage offers (if any) that occur in the future are likely to be associated with different levels of utility from that "expected" before marriage. As a result, individuals are likely to behave in the future in different ways from those anticipated when the original decision regarding marriage was being made.

36

N A N C Y M. G O R D O N

4 . If the values of exogenous variables (such as wage rates) change, the amount of utility received from a particular marriage or from being single may also change. Hence, divorce occurring because the utility received from marriage changed (as the result of changes in exogenous variables) is consistent with the Manser-Brown model. Their analysis, however, assumes that the values of exogenous variables do not change. 5. These negotiated values depend upon the particular levels of the exogenous variables. 6. If we include only years in which payments were received, the average increases to $ 2 , 0 9 8 .

THREE

Comment ORLEY

ASHENFELTER

MANSER AND Brown have opened up a useful avenue for a more general discussion of family decision-making. In the most widely used empirical models of labor supply, it has been taken as a maintained hypothesis that family formation results in a straightforward but sophisticated form of decision-making. In particular, it is assumed that the family can be described as doing the best it can to satisfy a consistent set of preferences regarding market goods and the nonmarket time of the various family members in the face of the constraints the family faces. How the family's preferences are aggregated from those of the individuals comprising it and the details of how decisions are made have usually not been considered in much detail. Indeed, the primary motivation for the standard assumptions has been the strong empirical predictions they generate. Although the conventional model has had some success, not all its predictions have been subjected to serious testing. Moreover, the household's formation has been taken as a predetermined act, so that the effect of changes in the constraints the family faces on the family's continued existence has been ignored. All these limitations can be serious, depending on the use to which such empirical models are to be put. For example, in determining the effects of a negative income tax on labor supply it has often been assumed that the analysis should be restricted to continuously existing husband-wife families. The conventional family labor supply model might be a satisfactory tool conditional on the family's remaining intact, but recent evidence from the Seattle and Denver Income Maintenance Experiments suggests that the effects of a negative income tax on the constraints the family faces may affect family status. If this is the case, the labor supply response to a negative income tax computed conditionally on the basis of intact families may give a misleading picture of the ultimate labor supply response and cost of various welfare reforms. Developing a model of 37

38

ORLEY

ASHENFELTER

family labor supply where the continued existence of the family and the labor supply of the family members are determined jointly may then be of considerable practical significance. Developing a more complete model of family labor supply and its full empirical implementation is a tall order, however. On the one h a n d , it would not be very surprising if, in a more elaborate model, the strong predictions of conventional models of family labor supply were lost. Indeed, it is precisely their loss that should keep us from rejecting the simple models too quickly. Likewise, we should have a clear indication of just what predictions a more complete model will offer to compensate us for this loss. On the other hand, the empirical analysis of labor supply has already become complicated by the desire to account for the noncxperimental data with which most analyses are undertaken. Only a careful analysis of replicated data sets should be sufficient grounds for abandoning the useful prior knowledge now available to us. In what follows I elaborate on these two issues with respect to Manser and Brown's analysis.

THEORETICAL ISSUES Analyses of labor supply based on the assumption of a well-defined set of family preferences between nonmarket time and commodities are silent about the social structure that leads to so well-defined an objective for the family. Although there is no presumption that this represents internal family harm o n y or, alternatively, a dictatorial decision-making system, neither is ruled o u t . Manser and Brown suggest that an alternative view might be based on the classical bilateral monopoly models that lead to bargaining solutions. In such a model there would always exist a gain to trade for each party compared to alternative arrangements so long as the parties remained a family unit, and when there was no longer a gain t o remaining intact the family would be expected to break up. By itself this is an economist's view of the theory of marriage, but there is more involved here than the "all or nothing" decision associated with the formation or destruction of a cooperative family unit. For the intact family must agree on the amount of labor to be supplied to the market by each family member in order to support the collective consumption of commodities. The key point here is that a change in any variable, such as a wage rate that increases the bargaining power of one of the family members, may be expected to have effects on the labor supply and the consumption of

Comment

39

all family members. Moreover, these effects will not result only from the change in income associated with the wage rate change, or merely from the fact that the nonmarket time of one family member has changed in price compared to that of other family members, but also from the fact that relative bargaining powers within the family have changed. These issues may be made clearer if we follow the effect of wage and unearned income changes on the various decisions a family makes under each decision-making regime. Given that the family remains intact, in conventional models an increase in the unearned income received by one family member is indistinguishable in its effects on the labor supply of all family members from an increase in unearned income received by any other family member. In effect, unearned income is treated as if it were owned by the family as a group, no matter who received title to it. Thus, to the extent that the nonmarket time of each family member is a normal good, we should expect an increase in any family member's unearned income to decrease the labor supply of all family members. Moreover, changes in unearned income, regardless of its source, should affect the labor supply of each family member in the same way. Now consider the effect of an unearned income change on the labor supply of family members when decisions are reached within a bargaining framework. Of course, some unearned income is the result entirely of the existence of the family relationship, but consider the effect of unearned income that is received explicitly by one family member. It still remains true that in the face of such an increase in unearned income the family can enjoy more of the nonmarket time of all family members as well as a higher consumption of commodities than before, but the relative bargaining strengths of the family members have also changed. The result is that even though the effect of an increase in each family member's own unearned income would be to induce less market work by that family member, the market work of other family members may not be similarly affected. Thus, the source and the size of any unearned income increase affects the resulting pattern of changes in family labor supply. The effect of a wage rate change for any family member may be analyzed similarly. In a conventional model a wage increase leads to greater income for the family at the old level of hours at work and a corresponding decrease in labor supply for each family member. In addition, a wage increase is an increase in the relative price of the nonmarket time of the family member whose wage has increased, and this will cause the family to substitute away

40

ORLEY

ASHENFELTER

f r o m the consumption of the nonmarket time of this family member. In a bargaining framework there will be these effects and a change in the bargaining power of the family member whose wage has changed. 1 The result is that in a bargaining framework some of the strongest implications of the conventional models are lost. The main difficulty, of course, is that it is unclear whether there are any positive predictions whatever from a bargaining framework. This causes two serious difficulties for empirical testing. First, one may reject the conventional model because of its empirical failures, but this hardly constitutes evidence that a bargaining framework offers any serious alternative explanation for the data. It is precisely because the conventional models have such strong predictions that they are useful, but it is also for this reason that they may be rejected as inconsistent with the data. Naturally, t h e n , the question must arise as t o just what would constitute a test of a bargaining model. On this important issue Manser and Brown remain silent, and further work clearly remains to be done. A second empirical difficulty is that one must be careful to insure that the conventional model has received a fair test, in the sense that n o serious specification

errors are present to make rejection of the conventional models

probable on improper grounds. I now turn to a more complete discussion of these empirical issues. EMPIRICAL ISSUES The most novel feature of the empirical work reported by Manser and Brown is the e f f o r t t o test the hypothesis that unearned income has the same effect on the labor supply of each family member regardless of its source. In principle this seems a simple enough proposition to test, but in practice testing is hard to perform satisfactorily. The difficulty, of course, is in measuring the unearned income that each spouse has under some form of legal control. In most families there exists joint ownership of many assets, and so it is not surprising that most survey questionnaires do not satisfactorily untangle actual control of assets as between husband and wife. Given the critical nature of the problem of separating out the flow of unearned income attributable to h u s b a n d , wife, and joint ownership in the data, it is surprising that Manser and Brown devote so little discussion to their methods for doing this. Indeed, the only discussion of the measurement of the female's exogenous income that I can find says merely that "since some sources of household exogenous income are not broken down into male or female components on the

Comment

41

NLS tape, this variable is a proxy constructed by utilizing information for single women." In a more detailed version of their paper (1977), Manser and Brown explain that the data on married female exogenous income is constructed by first classifying married and single females into five groups according to their own and their parents educational attainment, and then assigning to married females the mean unearned income that single females have in the same educational group. There are two obvious and severe biases that this measurement procedure can cause. The first is simply the host of difficulties caused by measurement error in an independent variable. Second, in practice Manser and Brown's testing of the "equal income effects" hypothesis is equivalent to testing whether a set of variables measuring the educational class of the woman and her parents affects the labor supply of either the husband or the wife. Finding that this is the case can hardly be taken as strong evidence that the unearned income of different family members has different effects on labor supply. As things stand, Manser and Brown simply do not have an appropriate data set to provide a plausible test of the equal income effects hypothesis, however desirable it would be to obtain such a test. Manser and Brown also report tests of the equality of the effect of a change in the husband's wage rate on the wife's labor supply with the effect of a change in the wife's wage rate on the husband's labor supply. This symmetry of the male and female labor supply equations is a basic but sophisticated prediction of the conventional family labor supply models. Manser and Brown find that when the effects on labor supply of the various sources of unearned income are required to be the same, the data are consistent with this symmetry prediction. When the income effects are not required to be the same, however, it is not clear what logical character the symmetry restriction has. 1 therefore find the fact that the symmetry restriction is consistent with the data when the income effects are constrained to equality to be evidence for and not against the usefulness of the conventional framework. Clearly, the crux of the Manser and Brown testing procedure revolves on the acceptance of their unconvincing finding regarding the equality of income effects. Although I find other problems with their empirical procedures—for example, why perform all income compensation at the mean hours rather than at some intermediate point, as Barten (1967) and Theil (1967) suggest?—it seems more appropriate here to simply spell out what is required for the development of a more convincing testing procedure for the research agenda

42

ORLEY

ASHENFELTER

that Manser and Brown have suggested. First, it would be useful to work through the Nash bargaining model for the labor supply functions of husband and wife and to work with the specific form of utility functions used in previous work. This might lead directly toward implementing the resulting scheme empirically. Second, it would be necessary to test the resulting framework using data where unambiguous meaning can be attached to the ownership of the various flows of unearned income available to the family, as in, say, the various income maintenance experiments. This is the research agenda that Manser and Brown have usefully opened up, and will hopefully continue.

NOTES 1 . In the formal setup used by Manser and Brown one might think of a change in a threat point as a change in bargaining power as I have used this term, and substitute this terminology f o r what they use. This is, however, somewhat misleading, for one element in the outcome of the bargain is the shape of the utility possibility frontier, and this may also change as the wage rate changes.

TWO Labor Supply Projections

FOUR

Projecting the Size of the Female Labor Force: What Makes a Difference? R A L P H E. S M I T H

STANDARD LABOR force projections are made by extrapolating time-series observations of age-sex specific participation rates, without consideration of the determinants of these trends. These have often seriously underestimated the growth in the participation rate of women in recent years, producing errors in the assumptions used in the setting of macroeconomic and labor market policies, in measuring the success or failure of women in the labor market, and in predicting the costs of employment-conditioned programs. This article provides the initial results of an extensive analysis of the determinants of female labor force growth. In the complete study on which this article is based, a series of conditional forecasts of female labor force growth through 1990 will be provided, each forecast based on alternative assumptions about the marital and family characteristics of the future female population and about the future values of a wide range of variables that influence each group's participation. In this article, attention will be focused on the sensitivity of the female labor force to real wage rates and job availability. I am particularly interested in the potential impacts on women's participation of a strong and sustained economic recovery and of a future narrowing of the gap between the wage rates of men and women. The article presents a brief analysis of the projection methods used by the The material in this article was prepared under Grant No. 21-11-77-09 from the Employment and Training Administration, U.S. Department of Labor, under the authority of Title III, Part B, of the Comprehensive Employment and Training Act of 1973. Researchers undertaking such projects under government sponsorship are encouraged to express freely their professional judgment. The opinions expressed are those of the author and do not necessarily reflect the views of the Urban Institute or its sponsors.

45

46

R A L P H E. S M I T H

Bureau of Labor Statistics (BLS). A projection model that integrates information from various studies of the determinants of labor force participation is provided and applied to the projection of the growth in the labor force of prime-age (25-54) women through 1990. Finally, some lessons are presented from this analysis for assessing the latest BLS projection and for directing future labor supply research toward the improvement of labor force projections. T R E N D EXTRAPOLATIONS Between 1960 and 1975 the labor participation rate of prime-age women increased by 13.4 points to 55.0 percent. Will this rate of growth of almost a percentage point a year continue over the next fifteen years? The latest set of projections from the Bureau of Labor Statistics indicates that it will not. The BLS projects a 7.6 point increase to 62.6 percent in 1990. The difference between directly extrapolating the growth in participation rates from the past 15 years and using the BLS procedure is about 3 million female labor force participants. Virtually all of the participation rate increase during the 1960-75 period is associated with the increased participation of wives. The participation rate of married women, husbands present, in this age group increased by 15.5 points, while that of the smaller number of other ever-married women (divorced, separated, widowed) increased by 3.7 points and that of never-married women declined by 1.6 points. 1 Some of the increase in wives' participation is attributable to the decline in the birthrate during this period. But most of it results from increases in participation rates within age and family status categories. (For example, the participation rate of wives, aged 25-34, with children under 6, doubled to 36.8 percent in this period.) The BLS projections of the growth of the prime-age female labor force between 1975 and 1990 are shown in table 4.1. These aie based on a procedure which begins with the estimation of linear time trends for each of two dozen age-sex population groups covering the period 1955 through 1975. No variables other than time are used in the Bureau's trend estimates. The absence of even a cyclical variable makes their current short-run projections especially doubtful. Assuming that their trends will continue, the slope of their time coefficient is used to project the participation rate of each group for each year from 1975 through 1990. Recognizing that linear trends cannot go on into the indefinite future, they next introduce a tapering procedure by which

47

Size of the Female Labor Force Table 4.1 B L S Female Labor Force Projection«, 1975-1990

(Number in thousands)

Ages 25-54 25-34 25-29 30-34 35-44 35-39 40-44 45-54 45-49 50-54

¡975 (Actual)

¡990 (Projected)

Labor Participation Population Force Rate (percent)

Labor Participation Population Force Rate (percent)

39,361 15,531 8,480 7,051 11,621 5,929 5,691 12,207 6,028 6,179

21,635 8,473 4,838 3,635 6,495 3,256 3,239 6,667 3,372 3,295

55.0 54.6 57.1 51.6 55.9 54.9 56.9 54.6 55.9 53.3

52,020 20,605 10,097 10,508 18,530 9,755 8,775 12,885 7,059 5,826

32,578 13,100 6,822 6,278 11,683 6,170 5,513 7,795 4,282 3,513

62.6 63.6 67.6 59.7 63.0 63.2 62.8 60.5 60.7 60.3

Source: Fullerton and Flaim (1976: A-2). I am grateful to the authors for providing unpublished worksheets used in the preparation of their projections.

the rate of change is gradually reduced to zero by 1995, which has the effect of reducing the predicted change in each group's participation rate by about 20 percent between 1975 and 1990. The final step is to multiply the projected participation rate of each age-sex group in each year by the corresponding population projection provided by the Census Bureau and to adjust that to a civilian, noninstitutional population. To make a fifteen-year participation rate projection, it is not clear how far back they should have gone to estimate their trend, but it is clear that this decision is critical. Most of the time-series analyses of the discouraged worker effect, which typically use a cyclical term and a trend variable, are subject to the same criticism if used for long-term projections. The size of the trend term is quite sensitive to the selection of the estimation period and functional form. In this regard, the advantages of these studies are in reducing one source of error in the trend estimate and in permitting the user of the projection to examine the implications of alternative assumptions about the state of the labor market in the projection period. In a period of accelerating participation rates, the effects of tapering and using a long linear trend combine to produce piojected growth considerably below the growth rates of recent years. Had BLS chosen not to taper, their projected increase for prime-age females would have been 1.6 million higher

48

R A L P H E. SMITH

than their 10.9 million estimate. If they had simply assumed that during the next fifteen years age-sex specific participation rates would increase by the same amount as in the preceding fifteen years, their projection would have been 2.7 million higher. Similar projection procedures in previous years resulted in serious underpredictions of female labor force growth. 2 The main point here is that extrapolation techniques of this sort are inherently arbitrary. It is at least as reasonable to base a fifteen-year projection on the preceding fifteen years as on the preceding twenty. If there is no basis for choice, then the producer of the projections should indicate this. Projections could be provided which are explicitly based on an extrapolation of a twenty-year trend, a fifteen-year trend, etc. Properly interpreted, such projections will mean that, if things continue as they did in the base period, these will be the participation rates in the projection year. The tapering procedure used by BLS clouds the picture because it is based on the arbitrary assumption that the rate of change in each group's participation rate will decline to zero by the year 1995. Again, there is really no basis for selecting an asymptotic year. There may be a basis for choosing an asymptote for each group's participation rate, but this is not what they have done. A solution to the trend extrapolation problem would be to develop a projection model which incorporated the behavioral relationships that underlie the year-to-year changes in each group's participation. Short of the complete estimation of such a model, the results of analyses of various determinants of participation could be used at least to supplement extrapolations in two ways. First, they could be useful in selecting from among alternative projections. Second, they could guide the user of trend extrapolations in making alternative projections that took into account new information about the paths of variables that influence participation. The remainder of this article is a first step in that direction.

PROJECTION MODEL Between 1975 and 1990 the size of the female labor force will change because of growth in the size of the aggregate female population (age 16 and over), changes in the age, marital status, family status mix of the female population, and changes in group-specific labor participation rates. In my model, changes in the total size and age distribution of the population are exogenous and are taken from Census Bureau projections. For sim-

Size of the Female Labor Force

49

plicity, I will begin by assuming that, within each age group, the distribution by marital status and presence of children is constant. In fact, however, exogenous increases in the proportion of the female population within each age group that never marries or that is childless, for example, would probably increase the size of the female labor force, since never-married and childless women have higher participation rates than women in the same age group who are married or who have young children. The determinants of changes in the group-specific participation rates, particularly the rate among married women, have been the subject of many analyses by economists and sociologists, and their results are reflected in my model specification. As an introduction to the model, I will briefly review the main explanations of past female labor force growth. The long-term growth in real wages has been the principal explanation offered by economists for the rise in the labor participation rate of women in this century. As the monetary rewards for working outside the home have increased, more women have opted to enter and remain in the paid labor market. The absolute value of the positive substitution effect from increases in women's own potential wages has exceeded the negative income effect from these increases and from other family income. An extensive literature is devoted to the estimation of these substitution and income effects. A second—not totally independent—explanation has been the growth in the educational attainment of the female population. In addition to its impact on potential wages, increased education, some have argued, improves the nonmonetary returns from work outside the home. A direct relationship between job satisfaction and educational attainment is posited. A third source of labor force growth, suggested by many of the sociological analyses, is the changes in attitudes and expectations of both men and women about women's life role. Particularly in the last decade or two, there has been a decline in the "a woman's place is in the home" attitude which had inhibited participation. Finally, labor economists have generated a voluminous literature on shortrun fluctuations in group participation rates. Most of it has focused on the impact of unemployment (or other demand-oriented variables). For women, the "discouraged worker" effect has usually been found to dominate the "added worker" effect, generating estimates of procyclical labor force fluctuations. 3 The following projection model takes these factors into account. Define AL as the change in the female labor force between the base year (o) and the

50

R A L P H E. S M I T H

projection year (f), Lit as the labor force size of group i in year t, Pit as its population size, and (L/F) i t as its participation rate. Then, AL = £

(Lit - Lio) = £

[PiAiL/P),

+ {LIP)ioAPi\

(4.1)

where the groups are delineated by age, marital status, and family status, and are mutually exclusive. 4 Each group's projected labor force growth or decline is associated with changes in its participation rate and in its population size. If each group's participation rate and its share of the total female population were constant, then labor force growth would be proportionate to population growth and the female participation rate would be constant. If groups with above-average participation rates grew more rapidly, then this population shift would generate further labor force growth. The change in each group's population is exogenous and the change in its participation rate is given by: A (LIP)i = buAW, + buAH, + + bAiAEt

+ bsiAAt

b^Aty + fc7lAi/ +

b8iAT

(4.2)

The first three variables on the right-hand side of equation (4.2) are measures of the expected growth in potential sources of income to the women in that group: own real wages (A Wt), wages of husband or other members of the income-sharing unit (A//,), and noneamed income (AN f ). These are the variables that standard neoclassical theory suggest. The coefficient on AWt can be positive or negative, depending on whether the substitution or income effect dominates; most studies of women's participation behavior have found that the positive substitution effect dominates. The coefficients on other sources of income, b1{ and b3i, should be negative. The next two variables measure changes in the group's average educational attainment (E) and work-related attitudes (.4); the coefficients on each should be positive. The next variable, U, is a cyclical variable which may reflect variations in job market conditions either for the group or for the entire labor force. If it is measured by unemployment, the sign on its coefficient should be negative. The final variable, a time trend (T), is included to depict the net effect of omitted variables which, themselves, are expected to increase or decrease systematically over time. The major purpose of the trend term in this model is to provide an alternate means of projecting the participation rates of groups

Size of the Female Labor Force

51

for which there is insufficient behavioral information on which to base a projection. In this event, the trend extrapolation method is the recourse. With this model, three kinds of information are needed to project labor force growth: estimates of the parameters of each group's participation rate equation, projections of the values of the right-hand variables, and projections of the changes in size and distribution of the female population. By accepting the Census Bureau projections of the size and age distribution of the population and temporarily assuming no change in the marital and family distributions, I can focus on the parameter and variable values of equation (4.2). This equation could not be directly estimated from historic time-series data, even if the data existed. Several of the variables are hopelessly collinear. Also, causality flows in both directions, suggesting the need for simultaneous equation methods. Estimation from cross-sectional data could not provide accurate estimates of the impacts of cyclical variations. The solution used here is to piece together the parameters of equation (4.2) from several sets of estimates, derived from both the time-series and the cross-sectional literature. This approach is not very elegant, but should provide, at a minimum, a good indication of which factors are likely to make a difference in projecting labor force growth and whether the standard labor force projections are likely once again to be too low. Equation (4.2) should be viewed as a convenient framework for integrating the available information on the determinants of participation rate change. It is not set forth as a rigorous forecasting model but rather a first stage in identifying the elements that such a model should include and in determining whether the official labor force projections are reasonable. In this article I will present estimates of the effects of wage and unemployment changes only. Thus, my projections will be partial ones. The complete study will examine the potential impacts of changes in the other variables.5

WAGES

The conceptual and empirical bases for anticipating that growth in the female participation rate would be directly related to real wage growth are well established. Mincer (1962) and Cain (1966) each demonstrated that most of the growth in the participation rate of married women in the first half of the century was associated with wage growth. However, less confidence can be placed on the precise parameters of this relationship. Single-equation esti-

52

R A L P H E. S M I T H

mates are no longer in fashion, and the more sophisticated techniques are still in the experimental stage. This section reviews the state of the art as it relates to the projection issue. Three types of data are available for estimating the relation: time-series, micro, and grouped cross-sectional. For inferring the labor force response to permanent or long-run differences in wages, cross-sectional data grouped by geographic unit are generally preferred. This type of data avoids the biases associated with contemporaneous changes in tastes, technology, etc. inherent in the time-series observations, as well as the problem of distinguishing between a short-term timing response and a response to long-run changes in reward structure. Grouping is preferred over direct use of individual observations because it avoids the need to infer potential wages for nonparticipants and probably reduces biases resulting from a positive relation between one's potential wages and one's tastes for work. In Mincer's original (1962) analysis, 1950 census tabulations for the 57 largest northern metropolitan areas were used to estimate an equation in which the participation rate of married females, spouse present, was related to the median income of females who worked year-round and the median income of married males, spouse present. Mincer argued that the differences in average wages among areas primarily reflected differences in long-run potential earning power. Hence, the coefficients could be interpreted as the estimated impacts of differences in "permanent" earnings in the Friedman sense. This equation, together with data on changes in real earnings, was then used to project backward decennial changes in the participation rate of married women from 1890 to 1960. He found that about three-fourths of the 25-point increase in their participation rate could be accounted for by this relationship, but with considerable variation from one decade to the next. Cain (1966) further developed this framework and estimated participation equations with additional data sets. He, too, found that the majority of the secular growth in the participation rate of married women could be accounted for by growth in real wages. However, his estimates were sensitive to the choice of data sets. He concluded that Mincer's finding that the absolute value of the elasticity with respect to wive's earnings exceeded that with respect to other income "was weakened by my research but not overturned" (Cain, 1966: 117). 6 The experiences of Mincer and Cain in using cross-sectional wage coefficients to account for past increases in female participation are precedents for

Size of the Female Labor Force

53

the projection method examined here. As far as I know, no one has used this approach to project the course of future participation, but it is a straightforward extension of their work. The empirical problems, however, are formidable. First, this method requires information about the future paths of wages for men and women. These may be as hard to project as participation itself. Second, it requires wage coefficient estimates, which are also subject to considerable error. Because of these uncertainties, I have chosen to present a range of projections corresponding to alternative patterns of real wage growth and to alternative estimates of the underlying participation-wage relationships.

Future Wage Growth Three alternative wage scenarios will be used, reflecting the uncertainty about the long-term productivity growth of the economy, its translation into real wage growth, and whether the gap between women's and men's wages will begin to narrow by 1990. My main projection will be based on the assumption that between 1975 and 1990, hourly real wages of women and men will each grow at a compound rate of 2 percent per year, so that by 1990, wages will be about 35 percent above their 1975 levels. Two alternative scenarios are intended to illustrate the sensitivity of the labor force projection to aggregate wage growth and to changes in the female-male wage ratio. For the former, a 3 percent annual growth rate in female and male wages will be assumed. For the latter, the 2 percent aggregate growth will be maintained, but with the aggregate female-male wage ratio increasing from about .59 to .65. From these projections, readers can readily examine the implications of their own guesses or forecasts. The 1990 wage patterns under each of the three assumptions are shown in table 4.2. The 2 percent annual growth rate in real wages is based on the assumption that the slowdown in private productivity growth between 1966 and 1973 will continue through 1990. During that period output per hour grew by only 2.1 percent per year, substantially below the 3.3 percent annual growth between 1948 and 1966. The Ford administration's Council of Economic Advisers, in their revision of potential GNP estimates, assumed that this slowdown would continue at least through 1981 (see U.S. Office of the President, 1977: 45-56; Clark 1977). George Perry (1977) has argued that this assumption is unwarranted. In either case, my baseline main projection is probably conservative in that the recovery from the recession should, itself, provide

54

R A L P H E. SMITH

is I L

¿3 5 J; »3 * t s o> ,c o> i

•s; ~ «j 00 w ^

£

J»


00 NO, 00 r i oh OH oH w

fN O -ni- 00 r- co NO r-i on OH 00 © o" o"

On l ÌS >o 00 OH_ NO r i CO co CN CN CN

OS «o CO rn rN

rOO n o OH >o

M

on

fi

oó

TjI

«5 I

ON

O

vo

OO

«O so

rf

fO f ) IO ^

y

ON "t © SO O H H V)

«O I- g

o

io

On

t'

t = 1,..., T

(5.1)

Note that 0 ( 0 is the intercept in the regression. If this regression were fit on data for a single individual, a statistically significant value for 6 would indicate that the fourth urn scheme is more appropriate than the third, i.e., that there is evidence for true state dependence at the individual level. If 5 were estimated to be zero, the third urn model would fit the data better. If regression (5.1) is computed across people and time periods, and no allowance is made for individual differences in intercepts, the regression model for the pooled sample could be written as

d(i, t) = 0(0 + 5 X d{i, t') + U(i, t) + 4>{.i) -Hi) *>*'

t=

i=l,...,/ .. . ,T

(5.2)

where #(/) is the average intercept in the population. The composite disturbance in the regression is U(i, t) + 4>(i) - 4>(i). Because of equation (5.1), the term

E t>t'

d(i,t')

would be correlated with the composite disturbance. Regression estimates of 6 would be upward biased because past work experience is positively coirelated with the composite disturbance. This bias could be avoided by permitting each individual t o have his own intercept. 2

Dynamics of Female Labor

Supply

73

The empirical work reported below presents evidence on the question of whether there is genuine state dependence in individual probabilities of participation. This issue is of particular importance in developing female participation equations to be used in dynamic simulation models. Since these models attempt to estimate the lifetime participation patterns of individuals, the distribution of participation patterns in the population, and the change in these patterns in response to policy stimuli, it is desirable that the input to these models be a genuine microdynamic model. Quite apart from the technical requirements of simulation models, there is considerable interest in knowing whether there is state dependence at the individual level. Such dependence could arise for several reasons. First, human capital (both market and nonmarket) can give rise to such state dependence. As a consequence of schooling, on-the-job training, and manpower investment programs, individual probabilities of participation in the work-force can be altered. Second, state dependence can arise as a consequence of fixed costs of entry into the work force. Given such costs, a woman who is in the work force is less likely to drop out as a consequence of a transitory random shock than if there are no fixed costs of entry and exit. Moreover, fixed costs of this sort make it optimal for a woman to plan to spend consecutive spells of time in the work force, even if in the absence of such costs optimal supply behavior would imply a more intermittent form of labor force activity. The evidence reported below lends support to the notion that there is genuine state dependence in individual probabilities. This evidence is consistent with human capital theory and a model with fixed costs of labor force entry. The data also display considerable evidence of heterogeneity in the population.

A D Y N A M I C M O D E L OF LABOR FORCE PARTICIPATION In this section of the paper, a simple dynamic model of labor force participation is presented. Following Lucas and Rapping (1970), participation is defined as work and excludes unemployment. Unemployment is viewed as one of many forms of nonmarket activity. Women are assumed to have choice in their participation decisions at each point in time. Each woman has two options at each period in her life cycle: to work or not to work. Let u ( l , i, t) be the expected lifetime utility that arises if woman / works at age t. This utility is a function of all relevant

74

J A M E S J. H E C K M A N

decision variables including her expectations about demographic events, such as the birth of children and divorce, and state variables such as her stock of human capital. The highest level of lifetime utility that the woman can attain given that she works today is i>(l, i, t). The highest level of lifetime utility that the woman can attain given that she does not work today is u(0, i, t). Implicit in both value functions is the notion that subsequent participation decisions are optimally chosen given the current choice, and given any new information, unknown to the agent as f, that becomes known in future periods when future participation decisions are being made. Participation occurs at age t for woman i if i>(1 , i, t) > u(0, i, t), i.e., if the expected lifetime utility of participation at age t exceeds the expected lifetime utility that arises from nonparticipation. This view of the participation process is consistent with a wide variety of models commonly employed in economics. In particular, under special assumptions it is consistent with McFadden's (1976) random utility model applied to an intertemporal context or models of lifetime decision-making under perfect certainty developed by Ghez and Becker (1975), Heckman (1976a) and others. For the purpose of the present analysis, the difference in utilities V(i, t) = v(l, i, t) - u(0, j, f) is the relevant quantity. If V(i, t) is positive a woman works at time f; otherwise she does not. The difference in utilities, V(i, t), may be decomposed into two components. One component is a function of variables that can be observed, V(i, t), while the other component is a function of variables that cannot be observed e(z\ t). Thus, the difference in utilities can be written as V(i, t)=V(i,t)

+ e(i, t)

It is convenient for the analysis to record whether or not woman i works at time t by introducing a dummy variable d(i, t) that assumes the value of one when a woman works and is zero otherwise. Thus, d(i, t) = 1 if V(i, t) > 0, while d(i, t) = 0 if V{i, t) < 0. In order to make the model empirically tractable, it is convenient to assume that the difference in expected utilities, V(i, t), can be approximated in linear form by V(i, t) = Z(i, f)0 + 6 £ d(i, t') + e(i, t) t>t'

(5.3)

where Z(i, t) is a vector of exogenous variables that determine choices in period t. 0 is a vector of coefficients that multiplies the Z(i, t) variables.

Dynamics of Female Labor Supply

75

Included in the vector Z(/, t) are variables such as education, income of the husband, number of children, and the like, as well as expectations about future values of these variables. The effect of previous labor force experience on current choices is represented in the model by the term 6 L t>t'

d{i,t')

This variable is important for the analysis and is to be viewed as a proxy for unmeasured human capital and transactions capital associated with entry into the work force. There are several restrictive features of this variable that should be explicitly noted. First, it is assumed that participation has the same impact on current decisions no matter when it occurred. That is, the model assumes no depreciation of "experience capital." This restriction is inessential, and in fact is relaxed to some degree in the empirical work reported below. Second, the model assumes that the impact of past participation on the current difference in utility V(i, t) is the same for everyone. This restriction is consistent with the current practice of introducing past work experience into human capital models that assume that current earnings are a function of past experience (measured by age minus schooling years minus s i x e.g., Mincer, 1974), with a common regression coefficient for the experience variable assumed for everyone in the sample. A better procedure would be to assume that the coefficient 6 is a function of variables that determine future work experience, or in the absence of such data, to assume that 5 is a random coefficient. A standard result in human capital theory (e.g., Ben-Porath, 1967) demonstrates that current investment in human capital is a function of expectations of future work activity, and empirical work by Polachek (1976) demonstrates that this point is empirically important for women. This improvement in the model of equation (5.3) is not pursued in this paper. There is an unmeasured disturbance, e(i, / ) , that arises from essential randomness (as perceived by the consumer) as well as from factors unknown to the observing economist but known to the consumer. The full set of T values of these disturbances is generated from a multivariate distribution. Letting E denote mathematical expectation taken with respect to this distribution, it is assumed that 0] =0 £[€(«, f ) e ( « \ r ' ) ] = a ^ E[e(i,t)e(i',t")]

=0

i

76

J A M E S J.

HECKMAN

The first assumption is innocuous. The second assumption permits intertemporal covariance in the unmeasured variables. The third assumption, that disturbances across consumers are u n c o r r e c t e d , is an implication of the random sampling scheme used to generate the data analyzed below. It is plausible that on: ^ 0 for t ¥= t', i.e., that unmeasured variables like ability are correlated over time for a consumer. Even if the only source of randomness in the model arose f r o m variables that operate on the consumer at a point in time, and are themselves uncorrelated over time (e.g., the incidence of minor illness), it is likely that the disturbances e(i, f ) are serially correlated. This is so because the w o r k - n o work differences in utilities at ages t and t' depend on some of the same set of unmeasured expected future variables that determine remaining lifetime

utility. In the empirical work

presented below, considerable evidence is found in support of a model of serial correlation in the unobservables that obeys a first-order stationary Markov process. The model of equation (5.3) can be used to characterize all the urn models previously considered. The first urn scheme, in which all women face identical urns, and successive drawings are independent, is given by a specialization of equation (5.3) in which Z(i, t) = 1, 8 = 0, and e(i, t) is distributed independently of all other disturbances. This is so because under these assumptions the probability that V(i, t) is positive is the same for all women at all time, and is independent of any past events. The second urn scheme in which a woman's work status is perfectly correlated over time is a special case of equation (5.3) in which Z(i, t) = 1,6 = 0, and e(/, t) is perfectly correlated over time. 3 The third urn scheme in which each woman in a population makes independent drawings from her own (distinctive) urn is a special case of equation (5.3) in which Z(i, t) = Z(i) (regressors are constant over time for a given person but may vary among people), 6 = 0 , and e(/, t) has a components of variance structure, i.e., e(i, t) = 0, and e(i, t) is an independently, identically distributed random variable with zero mean. The general model that is estimated below contains all these schemes as special cases of a more general model in which the exogenous variables, Z(i, /), are permitted to change over time, 5 is permitted to be non-zero, and e(i, t) is permitted to have an arbitrary serial correlation pattern. The information that woman i works in period t reveals that V(i, t ) > 0. The direction of the inequality is not reversed by division through by the standard deviation of the unobservables, o}/ 2 . This implies that from sample information about a sequence of participation patterns it is not possible to estimate the coefficients f} and 5 in equation (5.3) except up to a factor of proportionality. However, if there are regressors in equation (5.3), it is possible to estimate the ratios among variances, anlat-t• (Heckman, 1978, Heckman 1979a). If it is arbitrarily assumed that a n = 1, one can estimate o 2 2 , . . . , aTT. If the latent variables e(i, t) are covariance stationary (see, e.g., Koopmans, 1974), = ot*k,t'*k for all t, t\and k. Since it is possible to estimate these parameters up to a common factor of proportionality, it is possible to test for stationarity in the disturbances of equation (5.3). This test is performed below. If 6 is not zero, past work experience Z t>t'

d(i,t')

creates a nonstationarity in the evolution of life cycle participation probabilities. It is of interest to determine whether the unobserved factors in the disturbances operate on life cycle participation probabilities in a fashion similar to their operation on past work experience. EMPIRICAL RESULTS A N D THEIR IMPLICATIONS This section presents evidence from an extensive empirical analysis of the dynamics of female labor supply. To focus the discussion, empirical results are presented only for white women aged 45-64 in 1968 who were married to the same spouse in the seven years of panel data drawn from the probability sample of the Michigan Panel Study of Income Dynamics. 4

78

J A M E S J. H E C K M A N

The major finding reported here is that there is some evidence for genuine state dependence in individual probabilities, so that the micro Bernoulli model of Heckman and Willis (1977) is called into question. There is also some question about the validity of the simple "permanent-transitory" scheme utilized by Heckman and Willis (1977) to characterize the distribution of the unobserved variables generating participation probabilities. A firstorder Markov process for the disturbances appears to fit the data better. Tests for nonstationarity in the unobservables reject the hypothesis that the unobservables are nonstationary. The set of regressors used to estimate the model is confined to a conventional list of variables, so as to make the results reported here comparable to previous cross-sectional work on labor force participation (e.g., Mincer, 1962; Cain, 1966; Bowen and Finegan, 1969). In a companion paper (Heckman and MaCurdy, 1979), the set of variables used here is augmented to permit estimation of the effect of future variables on current behavior. That work demonstrates that future births raise the probability of current participation—a result consistent with a life cycle model of labor supply in which children raise the value of time in the home, and in which there is intertemporal substitution of time. The variables used to explain participation are (1) the woman's education, (2) family income excluding wife's earnings, (3) number of children under six, (4) number of children at home, (5) presample work experience, (6) sample work experience, (7) unemployment rate in the county in which the woman resides, (8) the wage of unskilled labor in the county—a measure of the availability of substitutes for the woman's time in the home—and (9) the national unemployment rate for prime age males—a measure of aggregate labor market tightness. The mean values for each of these variables are displayed in table 5.1. Table 5.2 records the distribution of participation patterns in the sample. A woman is defined to be a market participant if she worked for money any time in the sample year. This definition departs from the standard census definition in two respects. First, as noted earlier, participation is defined as work, and excludes unemployment. This view is consistent with the recent analysis of Lucas and Rapping (1970) that views unemployment as one of many forms of nonmarket activity. Second, the time unit of definition of the event is the year and not the usual census week. The most noteworthy feature of table 5.2 is that roughly 80 percent of the women in the sample either work all the time or do not work at all. The sample is roughly evenly divided between full-time workers and full-time

Dynamics

of Female Labor

Supply

79

Tabi* 5.1 M u n V a l u « of Variablas

1968 No. of children under 6 County unemployment rate (%) County wage rate ($/hr.) ChUdren (total) Presample work experience (yrs.) a Wife's education Family income ($) (excluding wife's earnings) Cumulated sample b experience National unemployment rate prime age males 35-44 Participation rate Num ber of observations

1969

.035

1970

.020

.040

4.01 1.90 2.68

3.61 1.99 2.68

4.92 2.05 2.74

11.22 11.71

11.22 11.71

11.22 11.71

12,600

13,000

0

13,400 .459

1.4 .46 198

1.4 .51

.969 2.3 .47

Source: University of Michigan Panel on Income Dynamics 1968-74. "Defined as the number of years since age 18 that a woman worked prior to 1968. kDefined as the number of years the woman has worked in the sample years. nonworkers. There is little evidence of frequent turnover in these data, nor is there much evidence of turnover in the full seven years of data. s

The Econometric Specification The model of equation (5.3) is estimated by the method o f maximum likelihood. The errors e(/\ t) are assumed to be jointly normally distributed so that the statistical model is a "multivariate probit model with structural Table 5.2 Run« Pattern* in the Data (1 corresponds to work in the year, 0 corresponds to no work)

Runs Pattern (1968, 1969, 1970) 0 0 0 1 1 0 1 1

0 0 1 0 1 1 0 1

0 1 0 0 0 1 1 1

Number of Observations 87 5 5 4 8 10 1 78

80

J A M E S J. H E C K M A N

shift"; a formal analysis of this model is presented elsewhere (Heckman 1979a). In estimating the model, special care must be taken to avoid a simultaneous equation bias that arises from the correlation of e(i, t) with previous work experience. Such bias would arise in estimating the coefficients of the model if values of e(/, t) are serially correlated, as is plausibly the case. In the presence of such serial correlation, the work experience variable is correlated with the disturbance term for period t, e(i, t), since previous work experience is determined by previous values of the disturbances, and previous disturbances are correlated with the current disturbance. The statistical model utilized in this paper avoids simultaneous equation bias in the estimated coefficients by using the structural equations of the model to correct the distribution of e(i, t) for the effect of previous work experience. The distribution of e(i, t) conditional on previous work experience is g[e(i,t)\d(i,t-

l),d(i, r - 2), • • •]

The probability that d(i, t) is unity (i.e., that woman i works in period t) is the probability that V(i, t) is positive. This probability is computed with respect to the conditional distribution of e(i, t). Defining p as the probability of participation in period t, p[V(i,t)>0\d(i,t= p[e(i,t)>Z(i,t)ii-8

= Jf l-ZV,t)P-6Zd(i,t'))

1 ),t' g[e(i,t)\d(i,t

1), - ]

- 1 ),•••]&(!,

f)

Conditioning the distribution of e(i, t) on previous experience by using the structural equations of the model avoids simultaneous equation bias in estimated coefficients, at least in large samples (see Heckman 1979a for a more complete discussion). In the empirical analysis, two types of prior work experience are considered, presample experience and experience over the duration of the sample. It is likely that presample experience exerts a weaker measured effect on participation than more recent experience because of the operation of depreciation and also because presample experience, which is based on a retrospective question, is more likely to be measured with error. Moreover, as discussed elsewhere

Dynamics of Female Labor Supply

81

(Heckman 1978), the data source utilized in the empirical analysis is not rich enough to allow the conditional distribution of e(i, t) to be adequately adjusted for the effect of presample experience. 6 As an expedient, presample experience is predicted by a set of regressors and entered in the analysis on the same footing with other regressors in the Z(i, t) vector. 7 Recent work experience is treated in the manner described in the preceding paragraph. Distributions of e(i, t) are explicitly conditioned on realizations of work experience within the sample period. There is one final technical detail. To facilitate computations, it is assumed that the disturbances in the equations can be "one factor" analyzed. This means that it is possible to represent the correlation matrix among the three disturbances in the following fashion. Define the correlation coefficient between disturbance e(i, t) and disturbance e(z, t') as rtt\ If the disturbances can be one-factor analyzed, r

tt'

= a a

t r'> t

t', t', t = 1, • • ,T

Since the number of panel observations per person (T) is three in the analysis of this article, this restriction is innocuous (Heckman, 1977d). For a discussion of one-factor probit models, see Heckman (1979a), especially Appendix A. To illustrate this point, consider the following examples. Suppose the disturbances follow a first-order Markov process which is assumed to have been operating for a long time, i.e., e(i,t)

= pe(i,t-

1) +

U(i,t)

where U(i, t) is a mean zero, independently and identically distributed random variable. For three years of panel data, this scheme can be one factor analyzed with the coefficients a 3 = a , = p, and a2 = 1. If e(i, t) follows a permanent-transitory scheme e(i,t)

=

(i)+V(i,t)

where ,227(.4)

-3.53(4.6)

-.814(2.1)

-1.42(2.3)

-.018057)

-.059(1.3)

.099093)

.139(1.5)

• 105(.68)

.004(02)

-.124(4.9)

-.116(2.2)

-.160(6.1)

-.090(2.4)

-.203(3.9)

.152(7.3)

.095(2.5)

.105(3.3)

.104(3.7)

.196(4.8)

.031 X

10"*(5.2)

-.003038) -

.062(6.2)

-.020 X 10"3(2.3) -.021026) -

.062(3.5)

.920(35)

-

.997(196)

-

.949(42)

-

1 1 -

-.038 X

10"'(20)

-.71(0) -

.095(11.0) -

-.032 X

10"3(3.6)

-1.30(6)

.27(1.1)

-.06 X 10"'(3 1.03014)

1.46(12.2)

-

.045(3.4)

.101(5.4)

-

-

-

-

-

-

-

1

1

1

1

1

1

1

1

.942(50)

-

-

-239.81

-243.11

-

.941(4.1) -242.37

-

-

-

-

-263.65

'

-367.3

84

J A M E S J. H E C K M A N

THE

EMPIRICAL

RESULTS

The empirical results for the most general model estimated in this paper are presented in column 1 of table 5.3. Coefficients of the variables that influence participation are displayed in this table. A positive value for a coefficient means that an increase in the associated variable increases the probability of participation, while a negative value of a coefficient means that an increase in the associated variable decreases the probability of participation. Inspection of the coefficients arrayed in column 1 reveals that more children and a higher family income (excluding wife's earnings) depress the probability of female participation. These results are consistent with previous findings based on analyses of cross-sectional data. Higher rates of unemployment (both local and national) tend to depress the probability of female participation. While the coefficient associated with each unemployment variable is not statistically significant at conventional levels, the joint set is statistically significant. This finding suggests that the net impact of labor market unemployment is to discourage female employment. The estimated effect of the wage of unskilled labor in the county on participation is statistically insignificant. The measured effect of previous work experience on current participation is broken into two components: (a) the effect of work experience acquired prior t o the first year of the sample (1968), and (è) the effect of more recent experience measured in the sample. This division is made because if there is depreciation in experience capital it is anticipated that presample experience has a weaker effect on current decisions than more recent experience. Moreover, it is likely that there is considerable response error in answers to a question about presample experience, so that it is likely that this variable will have a weaker measured effect on current participation than more recent experience even if there is no depreciation. The coefficient of recent experience is roughly twice the size of the coefficient of previous experience. Both coefficients are positive, as expected, but only the coefficient of predicted presample experience is statistically significant according to "conventional" test statistics. This finding will be examined in greater detail below. The estimated values of the ratios of the second-and third-period variances in the disturbances to the first-period disturbance variance (i.e., o 2 2 and a 3 3 , respectively) are close to one. Utilizing conventional test criteria, one cannot reject the hypothesis that both of these estimated coefficients equal one. Thus the variance in the unobserved variables does not change over the sample

Dynamics of Female Labor Supply

85

period. When the model is recomputed constraining a 2 2 and 033 to unity (these results are reported in column 2 of the table), the decrease in log likelihood for the model is trivial (.82), and well below the variation that would arise solely from chance fluctuations. Moreover, the remaining coefficients in the model are unaffected by the imposition of this restriction, further suggesting that the assumption of constant variance in the unmeasured variables is concordant with the data. The coefficients a j , a 2 , and a 3 are "factor loading" coefficients which, when multiplied, yield estimates of the correlation coefficients among the unobservable variables, e(i, t). For example, from the empirical results reported in column 1 of table 5.3, the estimated correlation between disturbances in year 1 and year 2 is (.922) X (.992) = .915, while the estimated correlation between disturbances in year 2 and year 3 is (.992) X (.926) = .918. The estimated two-year correlation is (.922) X (.926) = .854. Note that the product of the one-year correlation coefficients (.840) is very close to the estimated two-year correlation coefficient, a result that strongly suggests that the disturbances obey a first-order stationary Markov process, i.e., that e(í, i ) = pe(i, t - l)+U(i,t)

i = I, • • • ,1

where U(i, t) is independently and identically distributed across people and time. Column 3 of table 5.3 reports estimates of a model that constrains the disturbances to follow a first-order Markov scheme. As noted earlier, the Markov model is a special case of the general model in which a i = 03 and a 2 = 1. The empirical results in either column 1 or column 2 would appear to support the Markov assumption. Comparing the value of the likelihood function presented in column 2 with the value presented in column 3, one cannot reject the null hypothesis that the Markov model describes the distribution of disturbances. Twice the difference in log likelihood (5.25) is to be compared with a value of the chi-square statistic with two degrees of freedom, 8 5.99, for a 5 percent significance level. Most of the estimated coefficients presented in column 3 are essentially the same as the corresponding coefficients presented in the two preceding columns of the table; so the Markov restriction appears to be innocuous. However, the coefficient on retrospective work experience drops slightly, while the coefficient on recent experience almost doubles, and almost becomes statistically significant according to conventional test statistics.

86

J A M E S J. H E C K M A N

Testing the null hypothesis that market experience does not affect the probability of participation is an issue of central importance to this article. Thus it is important to proceed cautiously before any final conclusions are reached on this matter. The numbers reported in columns 1 through 3 strongly suggest that presample experience is an important determinant of current participation, even after corrections are made for potential endogeneity in this variable that could plausibly arise from serial correlation in tastes or unmeasured variables. However, the estimated effect of recent experience on participation, while numerically greater than that of presample experience, is estimated with less precision, and conventional test statistics lead to acceptance of the null hypothesis that recent experience is not a determinant of current participation. This raises a technical issue that cannot be evaded. It is well known (Rao, 1973) that there are a variety of asymptotically equivalent test statistics available to test the same hypothesis. These alternative tests lead to the same inference in large samples but may lead to conflicting inferences in small samples. There is no theoretical basis for preferring one statistic over another. However, a recent Monte Carlo study of a model, somewhat similar to the one estimated in this article, that compares the "normal test statistics" of the sort presented in table S.3 with the likelihood ratio statistic obtained from likelihood functions evaluated at restricted and unrestricted values concludes with the advice, "use the likelihood ratio test when the hypothesis is an important aspect of the study" (Gallant, 1975). Following this advice, I have reestimated the statistical models, deleting the recent work experience variable from each model. The empirical results from this procedure are reported in columns 4 , 5 , and 6, which correspond,respectively, to the models associated with the estimates reported in columns 1,2, and 3. For the reader's convenience, the differences in log likelihoods between restricted and unrestricted models are recorded in table 5.4. At a 10 percent significance level, one would reject the hypothesis that recent work experience does not affect the probability of participation in all of the models. Maintaining the assumption of stationarity in the unobserved variables leads to rejection of the hypothesis at 5 percent significance levels. From these tests it seems appropriate to conclude that recent experience determines the probability of participation, although in the most general model, with the fewest a priori restrictions imposed, this inference is far from sharp. From this sequence of tests, it appears that the most appropriate model is

Dynamics of Female Labor Supply

87

T*>la 5.4 Twk* tha Diffaranca in Log Likaiihood in Modab With and Without Racant Work Exparianca as an Explanatory Variable

General Model (Columns 4 and 1)

Mode! with Stationary Disturbances (Columns 5 and 2)

Model -with First Order Serial Correlation in Disturbances (Columns 6 and 3)

4.14 2.96 chi-square statistic, one degree of freedom, 10% significance level, chi-square statistic, one degree of freedom, 5% significance level,

5.58 2.70 3.84

one with both recent and presample experience as determinants of labor force participation and with the disturbances in the equations generated by a stationary first-order Markov process. Having selected this model, I will discuss its implications for labor force dynamics and contrast it with other models, including the model of Heckman and Willis (1977) and models that neglect heterogeneity. It is important to note that all the estimated coefficients are of the "right" sign, and do not contradict previous cross-sectional findings from the literature on female labor force participation. This is not to say that there are no new empirical findings in this article. The evidence clearly suggests that participation in one period alters the probability of participation in future periods. This evidence is consistent with the notion that human capital acquired through work experience raises the future probability of participation. It is also consistent with the hypothesis that fixed costs of entry and exit from the labor force lead t o "runs" of participation or nonparticipation. Initial differences in participation probabilities grow with labor market experience, at least for a while. The effect of fixed costs of labor force entry and exit, and the impact of human capital accumulation on future participation probabilities, is to widen initial differences in probabilities of labor force participation within a group of women as they age. Because of a fundamental nonstationarity in the participation process—which has a good economic foundation-the population distribution of probabilities of participation changes over time for a group of women who are at first observationally identical. In addition to this finding, evidence is presented that labor market variables such as the local and national unemployment rates affect participation probabilities.

88

J A M E S J. H E C K M A N

In contrast to the model just selected, the Heckman and Willis (1977) model is a special case of the general model of equation (5.3) in which (a) the impact of past participation on the current probability of participation is ignored, (b) the disturbances obey a "permanent-transitory" model, so that e(z, 0 = 0(0+£/(" uS ì*3- i

H

•o

S

•c

CO tO

«

8:

«

a z S WD « « S < Q S; Ot S

h- ç -a

3 o. S O c •H "3 12 G 'S o l-S-0 •Sfc/ï 2 t« •
a>J (0 V C u cd a> a: cd a!

206

JAMES P. S M I T H

0

H I 1 e

c 5

—i (s NO v> rn m O «s O oo

c

o

— so — f

e

o ri

í o às ^- ì a ¿

t>c

o o •f o oò

CTv 00

I

vO — •«to O vO O f l"

C — 00

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¡ti

>o rJ ri O

•Q C c

o n

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o 1 — ' 1 »o

•Si r) vO — & fi o -o Ov O fS (N "t o 00 o O o — O o o r~ rñ l' (N i

•o

\D — — M J (N ^ - i O vC O O O r — r i

a

I

I

2 Tj »1 C I

B .O 5«

Ì 8 •g c

«X c

a

3

o ON fN O O Os O

•oO rj o O f>

O rO O

3

sC

oo a C4 O

00

»0

3

O 0«

0 . 3

X

u2-

(ui + yu3)

The expected wage among working women is: E(wm ) = aX+ yE (exp h > 0) + E(u, | h > 0) or

The regressors for the imputation of experience for workers included a quadratic in education of wife, income of husband, and X, and the following variables entered linearly: region of residence, cumulative years with children less than 3 and 3 - 6 , labor market exposure, children born, years in current residence, and labor market exposure education. 32. Note that these comparisons are conditional on the same level of attributes for nonworking and working females. Since nonworking women have less education, for example, than workers, nonworkers would have a lower predicted wage on the deterministic component of the regression.

THIRTEEN

Work Experience, Labor Force Withdrawals, and Women's Wages: Empirical Results Using the 1976 Panel of Income Dynamics MARY

E.

CORCORAN

women balance family and work demands. Even women who are currently childless may make career choices on the assumption that they will eventually raise a family. Consequently, decisions about work participation often are shaped by the conflicting demands of market versus home work. These work participation decisions, in turn, have implications for labor market earnings. MANY

WORKING

Mincer and Polachek (1974) argue that withdrawal from the labor market for child-rearing influences wages in two ways. First, women's human capital should actually depreciate (through lack of use) during periods of labor force withdrawal. And second, women who expect to leave the labor force have an incentive to defer investments in on-the-job training until they reenter the labor market after child-rearing and will invest less overall in on-the-job training than will women who plan to work continuously. Using the National Longitudinal Survey of Mature Women, Mincer and Polachek reported that 1967 wages for married employed women aged 30-44 years varied positively with work experience and negatively with spells of nonparticipation. They also found that wage returns to experience were lower for experience acquired prior to spells of nonparticipation than for experience acquired after labor market reentry, that white, college-educated females incurred larger wage losses for interruptions than did other groups, and that life cycle differences in patterns of work participation accounted for almost half of the observed wage gap between married men and women aged 30-44. The Mincer-Polachek analysis is seriously limited in three important re216

Work Experience,

Withdrawals,

Wages

217

spects. First, their analysis is restricted to women aged 3 0 - 4 4 years. Women in this age range are more likely than women in general to have recently reentered the labor market after a prolonged spell of nonparticipation. If wages are temporarily depressed upon reentry because of misinformation about job opportunities, analyses of women aged 3 0 - 4 4 years will overestimate the depreciation of work skills during labor market withdrawals. Second, Mincer and Polachek did not directly test how the frequency and timing of labor force withdrawals affects wages. This is a particularly interesting policy question. One might argue, for instance, that wage penalties should be least costly early in the work career, before a worker has invested extensively in on-the-job training. Or, perhaps several short withdrawals at different points in the career cycle result in less depreciation than does one prolonged withdrawal. Third, Sandell and Shapiro (1978) claim that Mincer and Polachek's experience variables were derived from incorrectly coded data. When they replicated the Mincer and Polachek analysis using the presumably "correct" recoded data on a slightly different subsample of NLS women, they concluded that women's wages were only slightly affected by spells of nonparticipation. This paper extends Mincer's and Polachek's investigation of the relationship between patterns of work participation and the 1976 wave of the Panel Study of Income Dynamics (PSID). The PSID is an ongoing, nationally representative, longitudinal survey of 5,000 families which began in 1968. In 1976, male heads of households, female heads of households, and wives were asked about their schooling, training, earnings, and work history. The PSID has three obvious advantages over the NLS. The age range is not restricted; men and women were asked comparable work history questions; and the PSID provides more precise measures of the timing, frequency, and duration of labor force withdrawals. This article begins by reviewing the Mincer-Polachek model of investment in on-the-job traning. The next section describes the PSID work history measures and women's patterns of labor supply. Here results confirm the popular stereotypes. The majority of women, white and black, have experienced a spell of nonwork since leaving school, and more than 20 percent of white women and 10 percent of black women experienced two or more such spells. But a large minority of women have worked continuously since school completion, and women time their labor force withdrawals quite differently. Some delay beginning work after school completion; others work for a while

218

MARY

E.

CORCORAN

and then drop o u t ; and still others combine these two patterns. Then, I investigate how work experience, job tenure, and work continuity affect women's wages. Surprisingly, women's work skills do not always become less valuable during periods of labor force withdrawal—even for white women. Finally, I estimate the extent to which average differences in patterns of work history account for differences in average wages between white men and women. Average differences in work history patterns account for about 36 percent of the wage gap between white men and white women and about 20 percent of the wage gap between white men and black women, almost entirely because women had accumulated less tenure and were less likely to have worked full time than were white men.

W O R K H I S T O R Y A N D WAGES: T H E MINCER-POLACHEK M O D E L In the human capital model, investments in on-the-job training are considered to be critical determinants of wages (see Mincer, 1974). On-the-job training has a cost, since time spent training is assumed to be time diverted from production and production presumably determines earnings. And on-the-job training has a return in the form of higher later earnings. Mincer and Polachek (1974) extend this model to account for the possible depreciation of human capital which may result from the discontinuity of married women's work experience. They argue that during periods of labor force withdrawal for child-rearing and child care, prolonged nonparticipation in the paid labor market may cause the skills acquired at school and work to become less valuable. The following function describes this hypothetical model: £ , = £ , + £ (rC, - 5,-£,) = Yt + C, ¿=1

(13.1)

where £", = earnings capability in year /, Es l e a r n i n g s which would be received in the absence of any postschool training, r = rate of return to on-the-job investments in human capital, C, = the dollar cost of investments in human capital in the I t h year, 8,- = the depreciation rate of human capital in the z',h year, Yt - earnings in the r t h year.

Work Experience, Withdrawals, Wages

219

The marginal benefits of investments in on-the-job training increase with the length of the payoff period but decline with the length of periods of nonparticipation which follow investments. This suggests that optimal investment patterns will differ, depending on the continuity of market activities. Continuously employed workers should concentrate investments early in their careers. Workers who interrupt their work careers for nonmarket activities will defer investments in on-the-job training until they reenter the labor market after completing these activities so as to minimize the loss from depreciation. And, since such workers have a shorter payoff period, their overall volume of investment should be lower than that of workers who remain continuously in the labor force. Equation 13.2 should capture the investment patterns of continuously employed workers and of workers who withdraw from the labor market for nonmarket activities. 1 y =

+ £ (ft«, + 7 / « ? ) + £ i=l /'=1

Z X*z* k=1

(13.2)

where Y = In (earnings), zk = variables other than experience (such as education) which belong in the wage equation, el,. .. , eN = distinct periods of work experience for those who interrupt, et,. . . , i = 0 for those who never interrupt, eN = total work experience for those who never interrupt, 2 hi,.. . , hM = distinct periods of labor force withdrawal (in years), for those who interrupt and 0 for those who do not interrupt, , 0 N is expected to be positive and greater than 0 | , . . . , y N should be negative, all values of 0/ are expected to be negative. The experience coefficients in these models ( f t ) measure the net rate of return, r, times the ratio of investment (C,/£",) in a given time period (see Mincer and Polachek, 1974: 79-80). The coefficients ( 0 ; ) in these models measure the net depreciation rate of human capital during the / t h period of labor force withdrawal. This model makes several assumptions which have been questioned by other researchers. First, it assumes the employee decides how much training she gets. Others argue that employers play a major role in this decision. Sec-

220

M A R Y E. C O R C O R A N

ond, work and training are treated as mutually exclusive; that is, time spent in on-the-job training necessarily reduces productivity. Yet there is no direct evidence that this is the case. Third, this model assumes that the intent to drop out is not itself influenced by training and opportunities for investment. But others have argued that women tend to be confined to female-dominated jobs which provide few incentives for continuous employment (Bergmann and Adelman, 1973).

WORK HISTORY P A T T E R N S - A DESCRIPTION The ninth wave questionnaire of the PSID asked heads and wives the eight work history questions and the two future work plans questions listed in figure 13.1. In addition, all wives under SO were asked whether or not they expected to have more children. These work history questions are, of course, retrospective, and ask about interruptions of only a year or more. To the extent that women misreport past work interruptions, estimated effects of labor withdrawals may be underestimated. To the extent that women workers stop work for periods lasting less than 12 months, the continuity of worker careers may be overestimated. The work history patterns of employed women fall into one of five basic categories pictured in figure 13.2. Workers in the first category (pattern A) worked continuously since school completion. Workers in the next category experienced a spell of nonwork between school completion and their first job and then worked continuously. For instance, women may have married after finishing school, raised a family, and begun their work career at age 30. Workers who followed pattern C began work immediately after school completion, dropped out for a period, and returned to work. Workers in the fourth category delayed the start of work and later interrupted their careers. Workers in the last category, pattern E, experienced five or more distinct periods of work and nonwork. Figure 13.3 reports the distribution of white and black women across the various patterns. Less than 36 percent of white women and less than 43 percent of black women had worked continuously since school completion. Spells of nonwork, particularly for white women, were quite long, and many white women (20 percent) experienced at least two periods of nonwork. As expected, black and white women differed considerably in their work history patterns. Black women were much more likely to have worked continuously

Work Experience,

Withdrawals, Wages

221

1. How many years altogether have you worked (or money since you were 18? (YEARS) I 00. N O N E [ ( G O T O 11) 2. How many of these years did y o u work full time for most or all of the year? (YEARS) |ALL | 3. Some people have stopped their regular work for a time for such things as family responsibilities or to go back to school. Have you ever stopped working for a year or more for any of these reasons and then gone back to work? |1. Y E S |

15. N O |

(GO T O 91

4. Was that only one period, or were you were not working?

several periods of a year or more when

1. O N E P E R I O D

3. S E V E R A L P E R I O D S

5. When was the period you were not working, from when to when?

6. When was the most recent

to

(MONTH. Y E A R !

period that you were not working, from when to when? (MONTH. YEARI

(MONTH, YEARI

to

(MONTH. Y E A R I

IF B E F O R E 1955, G O T O 9 7. For what reasons did you stop working the last time? 8. Did you get any training or skills during the time you were not working that you could use in a job? |l. Y E S |

| 5. N O |

9. D o you think you will keep on working for the next few years, or do you plan to quit? 1. K E E P O N W O R K I N G

5. P L A N T O Q U I T

10. Why might you stop working? 11. Do you expect to have any (more) children? (asked only of wives under 50). 1. Y E S

5. N O

8. D O N ' T K N O W

Figure 13.1 Work History Questions

222

M A R Y E. C O R C O R A N

Pattern A - C o n t i n u o u s Work :

S 3 S 2 S O U a

i .2 a -C ßH

E 3 ei « ä

S i l 5 .2 ° i a ? c „ .e o !jP "O o C

Work Experience,

Withdrawals, Wages

229

These data also provide little evidence that expectations about work continuity affect the extent to which women invest in on-the-job training. White women always had lower coefficients on preinterruption experience than postinterruption experience, and the effect of an additional year of preinterruption experience declined faster than that of an additional year of post-interruption experience. We would expect such a result if workers had invested less prior to work interruptions, but the difference between preinterruption and postinterruption coefficients was not significant in either equation (13.1) or equation (13.2), and is indeed quite small in the latter. For black women, preinterruption and postinterruption experience appeared to be equally valuable. Women who planned to stop work in the near future did earn less than otherwise similar women, but this was only significant for black women and the causality is unclear. Low wages may discourage workers and encourage plans to leave. Surprisingly, women who expected more children earned no less than other women. Indeed, fertility expectations had a significant positive effect on the wages of black women; blacks who expected more children earned 12-13 percent more than other blacks. This could result from reverse causation; higher-income blacks may be more likely to plan more children than other blacks. Or perhaps this variable differentiates between those blacks who are well organized and plan ahead both for children and careers and those who experience haphazard work and life patterns. These results provide little evidence that work skills grow less valuable during labor force withdrawals. Labor force withdrawals lowered wages for only a few persons-with the exception of white women. White women's wages were lowered only by labor force withdrawals which followed school completion and preceded one's first job. Interruptions after a work career had started affected expected wages only negligibly. 6 If human capital depreciates during prolonged periods of nonwork, it is unclear why such capital should depreciate at one time and not another. In fact, one would expect that the rate of depreciation of human capital would be greater the greater one's accumulated stock of human capital (see Mincer and Polachek, 1974: 94-95). Therefore, penalties would be greater for work interruptions than for delays in beginning work, since workers who interrupt may have invested in on-thejob training prior to interrupting and hence have more skills to become obsolete. An alternate explanation of these results is that the decision of whether to work after school completion either reflects basic motivational differences between women or affects women's motivations. For instance,

230

M A R Y E. C O R C O R A N

women who view themselves primarily as wives and mothers may be most likely to delay starting work, and perhaps these motivational differences persist over time. On the other h a n d , entering the labor market directly after school completion may itself alter w o m e n ' s perceptions and motivations. That is, women who work for a while after school completion may come to see themselves as potentially attached to the labor force throughout their lives, while women who delay work may not develop such perceptions until they begin work.

Estimated Effects of Experience and Labor Force Withdrawals by Education, Occupation, and Lifetime Work Experience A possible explanation for these results is that the depreciation rate of human capital varies with the amount and kinds of human capital one has acquired. The human capital of highly educated women, professional women, or women with a great deal of work experience may decline more during periods of nonwork than does the capital of nonprofessional w o m e n , less well-educated w o m e n , or women with very little work experience. Table 13-2 presents estimated wage equations by education, occupation, and lifetime work experience. Returns to work experience variables are remarkably similar across education and occupation groups—with one notable exception; women in professional occupations experienced

unusually

high returns to pre-

employer experience. This suggests that studies should not a t t e m p t to make generalizations about female wages f r o m a sample of professional women (see Johnson and Stafford, 1974a). The expected penalties of labor force withdrawals increase slightly with schooling ( f r o m 0.2 percent/year for women with less than 12 years of school t o 0 . 8 percent/year for college graduates), but effects in all groups are small and usually not significant. The wage penalties associated with labor force withdrawals were no higher for workers who have worked at least half the time since school completion than for similar workers who worked less than half the time since school completion. These results provide little evidence that work skills depreciate at a higher rate the more human capital a worker has.

A Replication of the Mincer-Polachek Analysis These empirical results are not necessarily incompatible with Mincer and Polachek's finding that for a 1967 national sample of white, married women aged 3 0 - 4 4 with children, expected wages appeared to depreciate at a net

Work Experience,

Withdrawals,

Wages

231

rate o f about 1.2 percent per year. These analyses d i f f e r f r o m those o f Mincer and Polachek in at least four important respects, however, any one o f which might account f o r this apparent discrepancy. First, these analyses include all e m p l o y e d w o m e n . A s table 13.3 indicates, unmarried and/or childless w o m e n have spent a great deal less time out of the labor force than have other w o m e n . Combining unmarried, childless women with ever-married w o m e n w h o have raised children may attenuate the observed e f f e c t s o f labor force withdrawals. A second possibility is that the difference in age ranges across the t w o analyses affects results. Many o f the married w o m e n aged 3 0 - 4 4 in Mincer's sample may have only recently reentered the labor force after a prolonged absence f o r child-rearing. If initial wages after a prolonged labor force withdrawal are l o w relative to a worker's skills because o f misinformation about available j o b opportunities, this might show up as a depreciation e f f e c t in a restricted age sample. A f t e r workers have been working awhile, they may easily acquire such information and obtain wages more appropriate to their skill levels. Third, the P S I D asked a very different and in some w a y s less detailed set o f work history questions than did the N L S . The N L S questions, f o r instance, focused on w o r k experience at different points in the marriage Table 13.3 Work Experi«nca and Years O u t of the Labor Fore« tinea School Completion for Employed White Women

N Ever-Married Women (PSID) with Children 18-64 Unmarried and/or (PSID) Childless Women 18-64 AU (PSID) Women 18-64 Married Women 30-44 (PSID) with Children3 Married Women 30-44 with Children"-1' (1967 NLS) a The

Weighted Percent

Years Out of the Labor Force since School Completion

Years of Work Experience

878

69.3

8.1

15.3

448 1,326

30.0 100.0

.6 5.8

10.1 13.7

270

20.8

6.1

11.7

11.0

10.1

-

895

-

sum of work experience and years of the labor force is 17.8 for PSID married women aged 30-44 and 21.1 for NLS married women aged 30-44-a difference of 3.3 years. On the average PSID women completed 1.1 more years of schooling than did NLS women; this accounts for part of this 3.3 year difference. And in the PSID, work experience prior to age 18 is not included. b These figures are taken from Sandell and Shapiro (1978).

232

M A R Y E. C O R C O R A N

and child-rearing cycle. The PSID ignored interruptions that lasted less than one year. Differences either in data quality or in model specification (because of differences in the wording of questions) may explain some of the differences between my results and those of Mincer and Polachek. Finally, women's work participation patterns are changing over time, and women's labor force withdrawals are likely to be decreasing both in frequency and in duration. This, in itself, may weaken the link between labor force withdrawals and wages for women. Mincer and Polachek described a married woman's work history using five segments, three periods of work and two periods of nonwork. These segments were based on a woman's activities during different points of the life cycle. These segments included length of work experience prior to one's first child (e/), time worked after first child and prior to current job (ei), current job tenure (e 3 ), time not working after the birth of the first child (/ij), and other nonwork time (h 2 ). The closest I could come to this specification was to separate women's work histories into years worked prior to current employer, years out of the labor force, and employer tenure. This first variable is in the and h2. Since the coefficients sum of e , and e2; the second is the sum of of e 2 and h 2 were insignificant in the Mincer and Polachek analysis, this may attenuate variable coefficients in the PSID replication. Table 13.4 reproduces results from Mincer and Polachek's analysis, and reports the results when In (hourly earnings) is estimated for married, white women 3 0 - 4 4 with children using PSID data. The effects of labor force withdrawals are remarkably comparable. In Mincer and Polachek's analysis, annual wages drop 1.2 percent for each year not worked, While in the PSID, hourly wages drop 1.4 percent for each year out of the labor force. Neither differences of data quality nor changes in women's labor supply between 1966 and 1975 appear to affect estimated effects of labor force withdrawals across samples. For both evermarried employed women 18-64 with children and for all employed women 18-64, effects of labor force withdrawals were much smaller, about 0.5 to 0.6 percent per year. Effects were quite comparable across these two groups, suggesting that combining unmarried and childless women with ever-married women with children did not alter effects of labor force withdrawals on wages. Women aged 30-44 appear to be much more strongly affected by labor force withdrawals than are otherwise similar women in a wider age range. This is not inconsistent with an argument that women's wages upon

Work Experience,

233

Withdrawals, Wages

.C e O m

O ~ £{ © >o © l"

i

13 06 °°

r» r© o ^ o ^ O aid less than their marginal product. Hence, removal of discrimination would imply that females would be paid according to the male function, and the first method outlined above is appropriate. If nepotism exists in favor of men, the composite function after removal of discrimination would lie somewhere between the male and female functions. Given the numerical superiority of males in the working population, it seems most likely that this would be closer to the male rather than the female function, and the first method would again be preferred. As Masters (1977) has noted, there is a crucial asymmetry in the context of discrimination.

THE E A R N I N G S FUNCTION APPROACH Aside from this index number problem there are two fundamental requirements for such an earnings function approach: (1) that the earnings function be correctly specified; and (2) that differences between earnings functions can rightly be regarded as evidence of discrimination. On the second of these points, analysis of decision-making within the family has suggested that differences in some coefficients within the earnings functions are perfectly consistent with nondiscriminatory behavior (Mincer and Polachek, 1974; Polachek, 1975c). In some data sets it may be argued that this source of bias is effectively minimized (Chiplin and Sloane, 1976b; Malkiel and Malkiel, 1973), but in general, and particularly with census data, this issue raises serious problems of interpretation. Indeed, the importance of analyzing decision-making within a household context perhaps marks a crucial distinction between sex and race discrimination. The issue is, therefore, an aspect of a more fundamental problem which will be returned to below. Specification error seems to have attracted much less attention in the discrimination literature, although debate within the human capital literature continues (Griliches. 1977; Chamberlin, 1977). Any specification problems such as omitted variable bias, errors in variables, or simultaneous equation bias are vitally important for the application of earnings functions to the question of discrimation. Thus, as Griliches points out, "studies which identify the 'residual' with something particular such as discrimination, are much

An Evaluation of Sex

Discrimination

251

more dependent on the original equation having accounted for 'everything else'" (Griliches, 1977:2). In order to improve the quality of data and minimize at least some of the sources of error, there have been a number of studies relating to earnings differentials by sex within particular occupations or individual firms (Johnson and Stafford, 1974b; Gordon, Morton, and Braden, 1974; Malkiel and Malkiel, 1973; and Chiplin and Sloane, 1976b). It is perhaps particularly important, therefore, to adopt some commonly agreed specification in order to preserve some comparability across samples. To date, one of the Mincerian earnings functions (also suggested as empirically the most appropriate by Heckman and Polachek) has seemed to provide such a basis. Distinguishing between education and on-the-job training and assuming that the investment ratio in the latter declines linearly over time.it is well known that the human capital earnings function can be written (Mincer, 1974):

where k0 is the investment ratio at the start of work experience; T is the span of the investment period in on-the-job training; S is years of schooling; / is years of work experience; rs is the rate of return to schooling; r, the rate of return to training; W, is the wage in period r ; a n d W0 is the wage that would be received in the absence of any human capital investment. Specified to a quadratic approximation in a Taylor expansion, this yields an estimating equation of the form In Wt = a + bS + cj + dj2 +u

(14.8)

Ideally, Wt should measure hourly wage rates (Blinder, 1976) but in the absence of such data the log of hours worked (In H ) can be added to eq. 14.8 to standardize for hours worked. In Wt = ax + f t , S + c , / + flf,/2 +