Gender Convergence in the Labor Market 9781784414559, 9781784414566

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GENDER CONVERGENCE IN THE LABOR MARKET

RESEARCH IN LABOR ECONOMICS Series Editor: Solomon W. Polachek IZA Co-Editor: Konstantinos Tatsiramos Recent Volumes: Volume 31: Child Labor and the Transition between School and Work Edited by Randall K. Q. Akee, Eric V. Edmonds and Konstantinos Tatsiramos Volume 32: Who Loses in the Downturn? Economic Crisis, Employment and Income Distribution Edited by Herwig Immervoll, Andreas Peichl and Konstantinos Tatsiramos Volume 33: Research in Labor Economics Edited by Solomon W. Polachek and Konstantinos Tatsiramos Volume 34: Informal Employment in Emerging and Transition Economies Edited by Hartmut Lehmann and Konstantinos Tatsiramos Volume 35: 35th Anniversary Retrospective Edited by Solomon W. Polachek and Konstantinos Tatsiramos Volume 36: Research in Labor Economics Edited by Solomon W. Polachek and Konstantinos Tatsiramos Volume 37: Labor Market Issues in China Edited by Corrado Giulietti, Konstantinos Tatsiramos and Klaus F. Zimmermann Volume 38: New Analyses of Worker Well-Being Edited by Solomon W. Polachek and Konstantinos Tatsiramos Volume 39: Safety Nets and Benefit Dependence Edited by Ste´phane Carcillo, Herwig Immervoll, Stephen P. Jenkins, Sebastian Ko¨nigs and Konstantinos Tatsiramos Volume 40: Factors Affecting Worker Well-Being: The Impact of Change in the Labor Market Edited by Solomon W. Polachek and Konstantinos Tatsiramos

RESEARCH IN LABOR ECONOMICS VOLUME 41

GENDER CONVERGENCE IN THE LABOR MARKET EDITED BY

SOLOMON W. POLACHEK State University of New York at Binghamton and IZA

KONSTANTINOS TATSIRAMOS University of Nottingham and IZA

KLAUS F. ZIMMERMANN IZA and University of Bonn

United Kingdom
North America
Japan India
Malaysia
China

Emerald Group Publishing Limited Howard House, Wagon Lane, Bingley BD16 1WA, UK First edition 2015 Copyright r 2015 Emerald Group Publishing Limited Reprints and permissions service Contact: [email protected] No part of this book may be reproduced, stored in a retrieval system, transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without either the prior written permission of the publisher or a licence permitting restricted copying issued in the UK by The Copyright Licensing Agency and in the USA by The Copyright Clearance Center. Any opinions expressed in the chapters are those of the authors. Whilst Emerald makes every effort to ensure the quality and accuracy of its content, Emerald makes no representation implied or otherwise, as to the chapters’ suitability and application and disclaims any warranties, express or implied, to their use. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN: 978-1-78441-456-6 ISSN: 0147-9121 (Series)

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CONTENTS EDITORIAL ADVISORY BOARD

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PREFACE

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CONVERGENCES IN MEN’S AND WOMEN’S LIFE PATTERNS: LIFETIME WORK, LIFETIME EARNINGS, AND HUMAN CAPITAL INVESTMENT Joyce Jacobsen, Melanie Khamis and Mutlu Yuksel A BIOLOGICAL BASIS FOR THE GENDER WAGE GAP: FECUNDITY AND AGE AND EDUCATIONAL HYPOGAMY Solomon W. Polachek, Xu Zhang and Xing Zhou PARENTAL LEAVE AND THE GLASS CEILING IN SWEDEN James Albrecht, Peter Skogman Thoursie and Susan Vroman

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THE FAMILY GAP IN CAREER PROGRESSION Astrid Kunze

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COMMON LAW MARRIAGE, LABOR SUPPLY, AND TIME USE: A PARTIAL EXPLANATION FOR GENDER CONVERGENCE IN LABOR SUPPLY Shoshana Grossbard and Victoria Vernon

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SKILL DISPARITIES AND UNEQUAL FAMILY OUTCOMES Shelly Lundberg

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CONTENTS

WHO CARES
AND DOES IT MATTER? MEASURING WAGE PENALTIES FOR CARING WORK Barry T. Hirsch and Julia Manzella GENDER COMPLEMENTARITIES IN THE LABOR MARKET Giacomo De Giorgi, Marco Paccagnella and Michele Pellizzari THE RIGHT TAIL AND THE RIGHT TALE: THE GENDER WAGE GAP IN MEXICO Sonia R. Bhalotra, Manuel Ferna´ndez and Atheendar S. Venkataramani THE EFFECT OF FEMALE LEADERSHIP ON ESTABLISHMENT AND EMPLOYEE OUTCOMES: EVIDENCE FROM LINKED EMPLOYER-EMPLOYEE DATA Stefano Gagliarducci and M. Daniele Paserman

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EDITORIAL ADVISORY BOARD Orley C. Ashenfelter Princeton University

Daniel S. Hamermesh University of Texas

Francine D. Blau Cornell University

James J. Heckman University of Chicago

Richard Blundell University College London

Alan B. Krueger Princeton University

David Card University of California

Edward P. Lazear Stanford University

Ronald G. Ehrenberg Cornell University

Christopher A. Pissarides London School of Economics

Richard B. Freeman Harvard University

Klaus F. Zimmermann IZA and University of Bonn

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PREFACE For most countries, women’s labor force participation has risen while men’s has fallen. Concomitantly, fertility rates declined, marriage rates decreased, and the average husband-wife age difference shrunk slowly but steadily. Further, the number of unwed mothers rose, and at least in the United States, women’s schooling levels surpassed men’s. Along with these trends, men’s and women’s wages and occupational structures have been converging. Are these trends related? This volume contains 10 articles on gender convergence. The first presents a general overview of the trends, including that over the last 50 years women workers’ quality increased more than men’s. The second offers a general biologically-based theory underlying the trends. The remaining eight articles deal with particular aspects of gender convergence, from family aspects of the pay gap, to government policy, to the role of skill-biased technological change, and finally to productivity differences at the establishment level. In the first article, Joyce Jacobsen, Melanie Khamis, and Mutlu Yuksel provide an overview of the trends. They outline the evolution of women’s relative to men’s work activity from 1964 to 2013. In doing so, they track the changing levels of and returns to human capital in terms of education and potential experience over the last 50 years in the United States. They show that the average number of years of education has been increasing for both males and females since 1964, but at a much higher rate for females. This gender convergence began in the mid-1980s and by the early 2000s women overtook men in the average years of education. Concurrently, Jacobsen et al. find that the returns to education also converged, but when accounting for selection women’s returns appear to be higher in the later years. Similarly, women experienced a convergence in hourly wages, but this convergence slowed down in the 2000s. Finally, the authors also document convergence in hours of work, but smaller convergence in expected lifetime earnings. To explain these trends, Jacobsen et al. examine worker selectivity. They find relatively more productive work-oriented women to be joining the labor market than men, especially since the late 1980s and 1990s. But questions remain both concerning why women are becoming

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more devoted to work and the mechanism through which this commitment is beginning to pay off. The predominant story to explain these trends relate to family constraints. Family constraints, proxied by marital status and the presence of children, manifest themselves through division of labor in the home. In turn, household division of labor often is explained by dissimilar husbandwife bargaining power, frequently related to disparities in male and female productivity at home and in the market. Solomon W. Polachek, Xu Zhang, and Xing Zhou propose a new explanation underlying the division of labor in the home and the resulting trends in the wage gap. The idea is based on inherently biological fecundity constraints facing women: Women cannot give birth to children past a certain age, whereas in contrast, men can impregnate women at almost any age, young or old. This fecundity imbalance makes older women less desirable to marry, and results in husbands being older and typically more educated than their wives at the onset of marriage. The extent of these age and education differences is related to the demand for children. A high demand for children strengthens men’s demand for younger less educated wives because women have limited years of fecundity and because education takes time. To support this hypothesis empirically, Polachek et al. examine the effect of China’s one-child law on fertility and on husband-wife education and age gaps. The decrease in demand for children induced by the one-child law reduced husband-wife age and education gaps, and it did so more in rural areas. Also, age and education gaps decreased even more in areas where there was a higher fine for violating the one-child policy. The authors’ approach is consistent with the simultaneous decrease in fertility over time, the narrowing of husbandwife age differences over time, the rise in female labor force participation, and the contraction of gender wage and occupational disparities. A number of studies validate the impact of family, particularly children, on the gender wage gap. Most of this “family pay gap” literature is centered on the United States and Western countries. Government policies may also affect lifetime work for those with children. One such policy is family leave legislation designed to subsidize parents to be home with new born or newly adopted children. The next article by James Albrecht, Peter Skogman Thoursie, and Susan Vroman examines the evolution of the glassceiling in Sweden over the period from 1985 to 2008. They concentrate on the extent the glass-ceiling is related both to having children, and to the way parental leave is taken. The authors find that the glass-ceiling in Sweden has persisted over time; it exists for natives; it is more pronounced among white-collar workers; and it increases with age. Although the

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glass-ceiling is present even before the first child is born, it increases after having children and it increases if parental leave taking is spread out. These findings suggest that the availability of very long parental leave in Sweden may be responsible for the glass-ceiling because of lower levels of human capital investment among women and employers’ responses by placing relatively few women in fast-track career positions. Although family constraints may be important for the career prospects of women, few studies examine the impact of marriage and children on promotion probabilities. In the next article, Astrid Kunze fills this void by analyzing the family gap in job promotions in Norway using 1987
1997 panel data. She finds that women with children are 22% less likely to be promoted, and that work experience, work tenure, and part-time work explain a considerable part of the gap. Further, she shows that women fall behind men especially during the early parts of their careers, which coincide with their fertile period. As mentioned above, one main mechanism for the family to be related to labor market outcome is the division of labor in the home and subsequent lifetime labor force participation. A number of past studies show marriage and family are associated with greater men’s but smaller women’s lifetime work. However, none examine more informal cohabitation type marriages. Common Law Marriage (CLM) is an informal marriage form considered valid by both partners, but not formally sanctioned through a formal ceremony
especially in the United States. In the next article, Shoshana Grossbard and Victoria Vernon use the 1995
2011 Current Population Survey (CPS) micro data as well as the 2003
2011 American Time Use Survey (ATUS) data to investigate effects of CML on labor, household production, and leisure. They identify CLM effects through cross-state variation, given that three states abolished CLM over the time period they examine. Consistent with theory, they find CLM reduces labor supply for married women by 1
2 hours per week, but raises men’s labor supply to a small extent. However, they find little evidence CLM affects leisure and household production. Secularly, marriage rates appear to be declining and nonmarital childbearing appears on the rise, especially for low-education low-income segments of the population. The strength and type of one’s relationship status, whether it be a formal marriage, a CLM, or simply cohabitation, may depend on one’s own personal traits. In the next article, Shelly Lundberg examines how personality is related to family union. Using Wave IV data from the National Longitudinal Study of Adolescent Health, she investigates whether disparities in cognitive ability and noncognitive skills

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such as self-control are related to relationship stability. She finds individual noncognitive traits, particularly the Big-Five personality traits (openness, conscientiousness, extraversion, agreeableness, and neuroticism), are significantly associated with relationship status and single motherhood. Indeed, measured skills can explain as much as 25% of differences in these outcomes, but this effect disappears when own education is included in the analysis. In short, both cognitive and noncognitive skills predict education, but conditional on education they explain little of the difference in family stability. Consistent with the division of labor and the gender wage gap is occupational segregation of women. For example, women are more likely to work in jobs involving helping and caring for others. These jobs are disproportionately in the public sector where wage penalties may be large. In the next article, Barry T. Hirsch and Julia Manzella perform cross-sectional and longitudinal analyses to examine the relationship between caring jobs and wages. Instead of simply depicting these jobs as the usual dichotomy of whether a job is in the care sector or not, Hirsch and Manzella consider the degree of caring tasks and attributes of all occupations in the United States. Their findings show that wage penalties are more notable for men than women, but that women are more likely to work in such jobs. Whereas marriage and children affect household division of labor and subsequent work patterns of women, it is likely that demand considerations also play a role. To a large extent, how demand plays a role depends on whether men and women are complements or substitutes. Giacomo De Giorgi, Marco Paccagnella, and Michele Pellizzari estimated the elasticity of substitution between men and women. Using data from Italy, De Giorgi et al. exploit two sources of variation in relative female labor supply. The first is the abolition of compulsory military service and the second consists of sex-ratios at birth. The authors find evidence of imperfect substitutability for a sample of 15
24 years old. These findings may have important implications in terms of evaluating policies aimed at increasing female participation in the labor market. Another consideration on the demand side is skill-biased technological change, which nowadays tends to favor women more than men. In the next article, Sonia R. Bhalotra, Manuel Ferna´ndez, and Atheendar S. Venkataramani investigate this hypothesis examining the evolution of the gender wage gap in Mexico from 1992 to 2012, before and after joining NAFTA, which has been associated with skill-biased technological change and differential growth across sectors. The relative share of collegeeducated women grew within the brain-intensive occupations largely

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eliminating the gender wage gap at the upper tail of the wage distribution, with no change in the gap for the median. This narrowing of the wage gap, mostly driven by increased gender-based occupational sorting and improvements in women’s relative to men’s returns to human capital is consistent with demand-side structural changes coupled with decreases in the reward for physical labor. Despite the increase in their labor force participation, women are still underrepresented in top leadership positions. Stefano Gagliarducci and M. Daniele Paserman investigate the effect of women in managerial positions on firm and employee outcomes. The focus of the analysis is based on the gender composition of the top and second layers of management using a linked employer-employee data set on a sample of German establishments in the last two decades. Gagliarducci and Paserman report a negative relationship between the share of women in top management and firm performance, wages, and employment outcomes. However, these effects at the firm level are mostly explained by women sorting into smaller firms, which are less productive, pay less, and have higher turnover. For employees, the authors find a negative effect of women in top management on employment and wages. These findings provide no evidence that a high fraction of women in top management improves relative women’s outcomes, although there is some evidence that having more women in top management is associated with more family-friendly policies at the firm level. These results are consistent with human capital wage and occupational choice models. As with past volumes, we aim to focus on important issues and to maintain the highest levels of scholarship. We encourage readers who have prepared manuscripts meeting these stringent standards to submit them to Research in Labor Economics (RLE) via the IZA website (http://rle.iza.org) for possible inclusion in future volumes. Solomon W. Polachek Konstantinos Tatsiramos Klaus F. Zimmermann Editors

CONVERGENCES IN MEN’S AND WOMEN’S LIFE PATTERNS: LIFETIME WORK, LIFETIME EARNINGS, AND HUMAN CAPITAL INVESTMENT$ Joyce Jacobsena, Melanie Khamisb and Mutlu Yukselc a

Wesleyan University Wesleyan University and IZA c Dalhousie University and IZA b

ABSTRACT The changes in women’s and men’s work lives have been considerable in recent decades. Yet much of the recent research on gender differences in $

The authors would like to thank the participants of the IZA Workshop on Gender Convergence in April 2014 and the seminar participants at Middlebury College, Wesleyan University and the IAFFE Annual Conference for helpful comments. The authors also would like to thank the editors Sol Polachek and Kostas Tatsiramos and two anonymous referees for their helpful suggestions on this paper.

Gender Convergence in the Labor Market Research in Labor Economics, Volume 41, 1
33 Copyright r 2015 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1108/S0147-912120140000041008

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employment and earnings has been of a more snapshot nature rather than taking a longer comparative look at evolving patterns. In this paper, we use 50 years (1964
2013) of US Census Annual Demographic Files (March Current Population Survey) to track the changing returns to human capital (measured as both educational attainment and potential work experience), estimating comparable earnings equations by gender at each point in time. We consider the effects of sample selection over time for both women and men and show the rising effect of selection for women in recent years. Returns to education diverge for women and men over this period in the selection-adjusted results but converge in the OLS results, while returns to potential experience converge in both sets of results. We also create annual calculations of synthetic lifetime labor force participation, hours, and earnings that indicate convergence by gender in worklife patterns, but less convergence in recent years in lifetime earnings. Thus, while some convergence has indeed occurred, the underlying mechanisms causing convergence differ for women and men, reflecting continued fundamental differences in women’s and men’s life experiences. Keywords: Gender earnings gap; lifetime work; lifetime earnings; human capital investment JEL classifications: J3; J16; J24; N3

1. INTRODUCTION The changes in women’s and men’s work lives since the mid-twentieth century have been considerable. The best known of such changes include women’s rising labor force participation, with some leveling off in more recent years; the narrowing of the gender wage gap, again with periods of leveling; and men’s falling labor force participation, exacerbated in part by the most recent economic downturn. These changes are true for most societies, although our specific statements in this paper will refer for the most part to the US experience. These changes have also made it harder for researchers to generalize about the experience of the typical woman or man. Workforce experiences, measured in terms of labor force attachment, hours worked, and returns per hour, have increasingly diverged for those with higher levels of human capital and lower levels of human capital. In addition, the current focus of much labor economics research on economic inequality within gender and

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within the labor force as a whole has reinforced this movement away from generalization regarding economy-wide patterns. In addition, much of the most recent research on gender differences in employment and earnings has been of a more snapshot nature rather than taking a longer comparative look at evolving patterns. In contrast, in this paper we use 50 years (1964
2013) of US Census Annual Demographic Files (March Current Population Survey) to track the changing levels of and returns to human capital (both education and potential work experience) by gender through estimation of comparable earnings equations at each point in time. We are also able to track changes in self-selection into the labor market for both women and men and the effects of selection on earnings. While our paper confirms many of the trends that papers examining subsets of the data also find, it also attempts to refocus on the general trends by gender rather than on divergence within gender. This has the effect in part of refocusing attention on the fact that women’s and men’s labor market experiences, while more similar now than in the past, are also still quite different in terms of both year to year and total lifetime outcomes. This time-series comparative methodology also allows us to see the very clear effects of both the longer upward trend in US workforce participation and returns to participation for women (and the slight downward trend for men in participation) along with the recent changes in the labor market driven by the long recession. These effects include a narrowing of the gender differentials in expected lifetime labor force attachment, lifetime hours worked, and lifetime earnings. These lifetime calculations provide another way of considering the full effect on women and men of the labor market changes over their work lifetime rather than focusing on yearly variations in earnings and participation. Furthermore, lifetime calculations, in particular with respect to labor force participation, are important when analyzing human capital investments (Polachek, 1975b). The paper is structured as follows: Section 2 contains discussion of previous related work. This is followed by a discussion of how we set up our analytical structure to be consistent across this 50-year time span (Section 3). Section 4 provides our graphical results and discussion of those results. Section 5 concludes and indicates directions for follow-up work.

2. LITERATURE REVIEW Recent research on male and female labor force participation, hours worked, and returns to human capital investment finds some clear trends

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over time (Goldin, 2014). Labor force participation rates of men and women have converged over time and there has been narrowing of the gender earnings gap. This convergence of labor force participation, earnings, and the educational attainment of men and women over time can probably be explained by a combination of structural changes in the economy, technology advances in the workplace, declines in fertility, in home production, child care provision and policies addressing discrimination, divorce, marriage, and labor markets (Ferna´ndez, 2013). Ferna´ndez (2013) argues that social transformation and a revolution in social attitudes toward married women in the labor market can also explain increases in the labor force participation of women. However, in explaining the gender gap in earnings, social changes in and of themselves may not be sufficient. Investment in human capital and time allocation toward the labor market, thus increasing the total work experience of women, are important determinants to understand female earnings (Mincer & Polachek, 1974). Without this human capital investment, social change would likely not have led to substantial measured effects on gender differences. Looking at the evolution of the gender earnings gap and human capital investments over the time period 1970
2010, Goldin (2014) indeed finds that underlying differences in human capital between men and women have decreased and the portion of the gender earnings gap attributed due to these differences has been reduced. These trends of convergence in hourly earnings for men and women have been documented and explained for particular recent time periods. For example, O’Neill and Polachek (1993) document earnings from 1890 to 1990 and find that since 1976 the gender earnings gap declined until 1990 by about 1 percent a year. They attribute much of this convergence in acquired characteristics such as education and work experience, while additional factors accounting for part of the narrowing include the returns to experience for women and declines in hourly earnings in blue-collar work, which is clearly a more male-dominated sector. However, for the 1990s, Blau and Kahn (2006) find that a slowing convergence in the gender pay gap cannot be explained by changes in human capital as continued improvements for women occurred through the 1980s and 1990s. Underlying mechanisms that might explain the slowdown could be changes in the selection into the labor force and changes in unobservable gender characteristics (Blau & Kahn, 2006). Blau and Kahn (2005) found over the time period of the 1980s a rapid growth of female labor supply. Polachek (2006) shows that the slowing convergence can be explained by changes in women’s relative to men’s labor force participation in the latter

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1990s. For the period 1979 to 2001, O’Neill (2003) finds a narrowing of the returns to potential experience for men and women, which is consistent with the earlier studies (Blau & Kahn, 2006; O’Neill & Polachek, 1993). Overall, a convergence of earnings for men and women has been documented for the period from the 1970s to the early late 1990s (Blau & Kahn, 2000). Polachek and Robst (2001) find for the 1970s a rapid increase in female labor force participation that is not observed in the 1980s. However, in the 1980s, they find that the earnings gap narrowed more quickly than in the 1970s, which they explain by the higher labor force entry rate of women with relatively less human capital in the 1970s. At the same time, rising inequality and increases in the returns to skill might account for a potential opposing trend of widening the gap in turn. Autor, Katz, and Kearney (2008) analyze US wage inequality over the 1980s and 1990s and attribute this to skill-biased technological change. The effect on the gender earnings gap is not entirely clear: on one hand Blau and Kahn (2000) argue that the trend in wage inequality is similar for men and women over this period and on the other hand Bacolod and Blum (2010) find that a narrowing gender gap and increases in wage inequality are consistent with differential returns to skills, which favor women. In explaining potential candidates for the residual gender wage gap, while observable attributes such as educational attainment cannot account for this, Goldin (2014) argues that increases in the earnings gap by age, and the increases in the earnings gaps and hours worked within and across occupations and sectors can explain large parts of the remaining earnings gap. Occupational characteristics as an explanation of the gender wage gap were already found to be an important determinant for the period up to 2001 (O’Neill, 2003). This widening gender gap within occupations over the life cycle is also consistent with the problem of life-cycle division of labor within the family where husband and wife have differential human capital investments that in turn have effects on female wage gap. The male-female earnings gap for singles does not appear to widen the same way (Polachek, 1975a). To understand gender convergence patterns over time, a number of factors, including the selection into the labor force, earnings, composition effects of the labor force, returns to education and experience, and hours worked need to be analyzed in further detail. This paper is most closely related to research by Mulligan and Rubinstein (2008), who investigate selection into the labor force and hourly earnings for women over time. In particular, they find that over time women’s selection into labor force participation changed from negative selection in the 1970s to positive selection

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in the 1990s.1 Our finding and Mulligan and Rubinstein’s finding are consistent with the human capital approach: women with less human capital may drop out of the labor force and women with more human capital may have entered in greater numbers, which in turn implies increased selectivity due to human capital and not necessarily due to ability. This indicates that the selection rule was changing over time for women and a different composition of women was selecting into the labor force. This can explain the narrowing of the gender wage gap at the same time that there are increases in within-gender wage gaps. We also account for self-selection into the labor force for men and women over the entire period. Thus we extend earlier basic research into the patterns of both returns to human capital investment and levels of human capital investment over this 50-year time period to see whether our results, which utilize a consistent estimation methodology over the full time period, are both consistent with other researchers’ results and internally consistent in terms of tracking both investments in human capital and returns to human capital from year to year. Building on the previous research in the area, we are able to extend the analysis over a longer timespan than most other studies, considering returns to education and potential experience as well as calculating additional descriptive measures of synthetic lifetime labor force attachment, lifetime earnings, and lifetime hours worked. Our synthetic worklife estimates are similar in spirit to those calculated by the Census Bureau (U.S. Dept. of Commerce, 2011). Closely related work by Polachek (1975a) and Goldin and Polachek (1987) also use work probabilities at each age in a given US census year in their work to understand earnings differentials; Joshi and Davies (2002) take a related approach to study women’s lifetime earnings using British data.

3. DATA AND REGRESSION SPECIFICATION For this paper, we employ 50 years (1964
2013) of the US Census Annual Demographic Files (March Current Population Survey). We run two 1. Negative selection into the labor force means that the unobservables driving selection into work participation are negatively correlated with factors leading to higher earnings; positive selection means there is a positive correlation. Thus the apparently relatively less productive women were more likely to work in the earlier time period, while the apparently relatively more productive women were more likely to work in the later time period.

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regressions per year (one for males and one for females). This amounts to 100 regressions over the 50-year time span. The data for our paper were downloaded from the Integrated Public Use Microdata Series (IPUMS) CPS webpage at the University of Minnesota (http://cps.imps.org/cps/) (King et al., 2010). We restrict our sample to individuals aged 25
65 and obtain individual characteristics such as gender, age, race, marital status, years of education, educational attainment, urban-rural location, and regions. These variables are all measured as consistently as possible over the full sample period, although changes in CPS sampling procedure and definitions can show up as jumps in the data. We run all regressions separately by gender. From the data we create dummy variables for race that cover whites, black, and other races.2 The marital status is a dummy variable that takes the value 1 for married with spouse present or absent and 0 for any other status. To account for geographic effects of rural-urban location, we include a dummy that takes the value 1 for location in the central city or outside the central city and 0 for not in the metropolitan area. For location within the United States, we use the regional codes from the CPS for the Northeast, Midwest, South, and West region. For educational attainment, we create three categories: high school attendance without high school diploma, high school diploma or equivalent and some college attendance but no degree, and bachelor degree and above.3 For years of education, we code 0
22 years of education from the CPS, which we employ to obtain potential experience. Potential experience for males and females is calculated by subtracting years of education minus 6 from individual age. In our OLS regressions and the two-step selectioncorrected Heckman model, we include potential experience as a quartic function.4,5

2. The Hispanic category is only available after 1971. For a consistent definition, the Hispanic/ Latino population is classified as “other races.” 3. We coded the category “high school diploma” from the CPS data category of “High School Diploma or equivalent.” The GED is therefore counted as high school diploma or equivalent. 4. See Mincer (1974) for the original specification for the inclusion of experience as a quartic function and the review article on the Mincer equation by Lemieux (2006). 5. Potential experience can lead to biases as women have roughly the same potential experience but less actual experience than men. Over time the actual experience of women is rising relative to men’s actual experience while potential experience remains probably relatively constant.

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For our main left-hand side, variables in the hourly earnings regressions, for our calculation of the wage we use the log hourly earnings in real terms and log annual earnings in real terms. To obtain this, we use the wage and salary income variable from the CPS that records individuals’ total pre-tax wage and salary income from the previous calendar year (thus the latest year for the earnings data is 2012, and the earliest 1963, but we will refer to earnings by the year of the sampling). We then convert this wage and salary income variable to real terms, with the base year 2013. We obtain log annual earnings taking the logarithm from this. For the hourly numbers, we divide the annual wage and salary income variable by the annual hours worked before converting it into the logarithm of hourly earnings.6 Annual hours worked are calculated from weeks worked last year multiplied by usual hours worked per week in the last year after 1976. Before 1976, annual hours worked are calculated from hours worked last week multiplied by weeks worked in the last year, available in intervals. This particular change causes a one-time jump in the data series at 1976.7 To analyze convergence and divergence of earnings over time, we estimate separate hourly earnings regressions for each year t and for each gender j: wijt = αjt þ βjt Xijt þ ɛ ijt

for t = 1964; 1965; … 2013; and j = 1 and 2

ð1Þ

Thus we estimate the hourly earnings (Eq. (1)) as a yearly cross-sectional regression with individual data, where data are available for a sample of individuals i of gender j (men or women) in year t. This yields, for our sample, 100 different equations (50 years times two genders). X is a vector that includes educational attainment dummies, potential work experience as a quartic, race dummies, a rural-urban dummy, and regional dummies. The base categories for our regressions are high school dropout, race other than white or black, rural and the West region. We estimate Eq. (1) as an OLS regression, without selection correction and then also estimate a two-step Heckman selection model (Heckman, 1979). We mainly discuss the Heckman results in the following sections but ran OLS for comparison and show those results in the appendix. 6. We code the observations that have less than 1 and greater than 1,000 US$ hourly earnings as missing. Annual earnings greater than 9,999,997 US$ we also code as missing. 7. We choose to let this variable definition change causes a one-time level reset in the data rather than include a dummy in the hourly earnings equation for this so as to keep the regression specification identical across the years.

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In the first stage, we estimate the participation (Eq. (2)) that includes an exclusion restriction. As a determinant for selection into labor force participation, the vector Z includes marital status in addition to the variables included in X. Contrary to Mulligan and Rubinstein (2008), who assume no selection bias on the part of men, we include the marital status, hence being married, into the selection equation for both men and women. Mulligan and Rubinstein (2008) also interact the marital status with the number of children aged 0
6. However, the number of own children under age 5 in the household is only available from 1968 onwards, thereby this would limit our sample by a few years. For this reason, we only use marital status in our selection equation as an exclusion restriction in the results we present here.8 However, we have also estimated the Heckman selection models with marital status interacted with the number of children and found similar results over the period (1968 onwards) where both variables are available.9 Pijt ðLFP = 1jZ = 1Þ = ΦðZδÞ

ð2Þ

  b From Eq. (2), we compute the inverse Mills ratio λc ijt = λ Zijt δjt . Then we estimate the 100 hourly earnings regressions with the selection correction term included: wijt = αjt þ βjt Xijt þ ρjt λc ijt þ ɛ ijt

ð3Þ

The inverse Mills ratio obtained from a probit regression then corrects our hourly earnings regressions for the selection into labor force participation. It measures the degree of selection bias of persons in our sample. In addition to degree of selection over time and earnings over time based on the Heckman regression models, we calculate the synthetic worklife measures of years in the labor force, total hours worked, and total earnings

8. Heckman (1980) in his original paper includes linear and squared terms for children less than six, 1967 assets, husband’s age, husband’s education, husband’s hourly earnings, wife’s education, and interactions of all linear terms (p. 226, Table 5.1). He uses the cross-section data of the 1967 National Longitudinal Survey of Work Experience of Women Aged 30
44 and has other variables available that the CPS does not include for our project over a 50 year horizon. 9. Full regression results, including all coefficients, as well as results from these alternative specifications, are available upon request from the authors.

10

JOYCE JACOBSEN ET AL.

based on average outcomes by age group by gender in a given year. We calculate this for a person just entering the age range on which we are focusing, namely someone age 25 in the given year, and consider what their worklife experience would be if they experience the same average experience in the future as those persons now older than them in the workforce are experiencing in the given year. This could be viewed as a steady state calculation wherein a static economic system would yield the same outcomes for each person on average indefinitely into the future. Thus we calculate the 100 expectations: EðLTYÞjt =

65 X

pijt

ð4Þ

i = 25

where E(LTY)jt is the expected lifetime years in work for a person aged 25 of gender j in year t, i is an age group of gender j in year t and pijt is the probability of employment for age group i of gender j in year t, which is the same as the proportion of the gender-age group that is employed in the given year t. In addition to Eq. (4), we can calculate the expected lifetime hours worked as in Eq. (5) below, and the expected lifetime earnings as in Eq. (6): EðLTHWÞjt =

65 X

pijt hijt wijt

ð5Þ

i = 25

where E(LTHW)jt is the expected lifetime hours worked for a person aged 25 of gender j in year t, hijt is the average hours worked per week for employed individuals in age group i of gender j in year t, and wijt is the number of weeks worked for employed individuals in age group i of gender j in year t. EðLTEÞjt =

65 X

pijt eijt

ð6Þ

i = 25

where E(LTE)jt is the expected lifetime earnings for a person aged 25 of gender j in year t, and eijt the annual earnings for employed individuals in age group i of gender j in year t. Thus, for our sample, there are 100 estimations each of synthetic lifetime years of work, total hours worked, and total earnings for someone of age 25, based on gender and a particular year of the CPS and calculation over

Convergences in Men’s and Women’s Life Patterns

11

the 41 age-gender cohorts for that person and ahead of that person. This concept of “expected lifetime outcome” should be thought of as the mean value of each variable in a steady state where the current experience of each cohort is mirrored by all the cohorts that come after it. We will then discuss what the evolving patterns are in these expected outcomes, which of course then makes clear that the states are indeed not steady but rather changing from year to year.

4. RESULTS 4.1. Descriptive Results Looking at general trends over the 50-year period under consideration, we plot graphs for both men and women that display the developments in terms of average demographics, individual and labor market patterns over time.10 We highlight the results for the sample selection model in the body of the paper with accompanying graphs and also discuss the OLS results, but the OLS graphs are relegated to the appendix. In Fig. 1, average education, measured in terms of years of schooling completed, exhibits an increasing trend over time for both men and women, rising from a little over 10 years in 1964 to 14 years of schooling in 2013. While both men and women saw increases in the average years of schooling over the entire time, women had lower levels until the early 2000s, changing after 2001. From that point onwards, women have obtained on average more years of schooling than men. In terms of average potential experience, while both genders exhibit a U-shaped pattern over this time frame, women had more average potential experience than men over the entire period (Fig. 2). This is driven by the age component as potential experience is derived from age and years of education as outlined in the previous section. Thus women in the workforce 10. The descriptive graphs are weighted by the person-level weights provided by the CPS data. The graphs based on the regression coefficients are not weighted due the Heckman selection correction estimation not allowing weights in Stata if the two-step command is specified. In practice the weights make little difference and the unweighted descriptive graphs are quite similar to the weighted ones. Also, while we plot these graphs for the entire sample, when we instead restrict them to either labor market participants, non-zero hourly earners, or nonzero annual earners, the general patterns remain the same. These alternative graphs are available upon request from the authors.

JOYCE JACOBSEN ET AL.

12 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

10

11

Years

13

14

12

Male

Fig. 1.

Female

Descriptive Results: Average Education by Gender, 1964
2013.

are slightly older than men (partly related to their longer average lifespan) and over this time period, the demographics change to favor relatively younger members in the labor force over the middle years, bottoming out in the early 1980s, and subsequently displaying a rising average age (and thus potential years of experience) subsequent to the 1980s. However, labor market outcomes
real hourly earnings, real annual earnings, and annual hours worked
do not exhibit any cases where women rise above men, or any case of gender reversal as seen in educational attainment. Over the entire time period, men receive higher average real hourly earnings (Fig. 3), higher average real annual earnings (Fig. 4) and display higher average annual hours worked (Fig. 5). Men also display significantly more year-to-year variation in earnings and hours worked, while women show a significantly smoother pattern from year to year. This is likely caused in large part by the fact that men have a much higher labor force participation rate (and an employment rate), so they are less likely to adjust their labor supply in response to the business cycle and thus are more subject to fluctuations in labor demand affecting their hours worked and pay.

13

1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

22

23

24

Years

25

26

27

Convergences in Men’s and Women’s Life Patterns

Male

Fig. 2.

Female

Descriptive Results: Average Potential Experience by Gender, 1964
2013.

For women over time, increases in terms of real hourly earnings and real annual earnings are visible and show some narrowing of the gender earnings gap, but it is still a persistent gap (Figs. 3 and 4). In terms of annual hours worked, women saw increases in their hours worked, in particular from late 1970s and early 1980s onwards, converging toward the male average hours worked. However, still women work fewer hours than men in 2013 by a substantial margin of over 200 hours per year on average (Fig. 5).

4.2. Heckman and OLS Regression Results In our analysis over the 50-year time period, we analyze log real hourly earnings and log annual earnings. We find that selection bias plays a large role in our data: for male negative, almost stable, selection is found for these two measures; in other words, men who are in the labor force have unobservable characteristics that are negatively correlated with earnings

JOYCE JACOBSEN ET AL.

1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

15

20

Dollars

25

30

14

Male

Fig. 3.

Female

Descriptive Results: Average Real Hourly Earnings by Gender, 1964
2013.

potential. For women the finding is more striking, but also consistent with the finding of Mulligan and Rubinstein (2008) for the real hourly earnings. Women initially have negative selection until about the late 1980s, thereafter the selection is positive. These results are not echoed identically in annual earnings where women also have negative selection into employment, albeit reducing over time, but only display positive selection at the very end of the period under investigation. For the experience results, we find convergence in returns for increasing potential experience levels for both hourly earnings and annual earnings. For education, the results differ for hourly earnings and annual earnings: returns to High School and College are higher for women than for men for hourly earnings. For annual earnings, male and female returns to either education level tracked each other and only a higher return for females is found in the later years, after 2008. Looking at the selection effects over time, Fig. 6 displays the degree of selection bias as percentage of log real hourly earnings. The coefficient

15

40,000 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

20,000

30,000

Dollars

50,000

60,000

Convergences in Men’s and Women’s Life Patterns

Male

Fig. 4.

Female

Descriptive Results: Average Real Annual Earnings by Gender, 1964
2013.

of the Mills ratio from the hourly earnings regression multiplied by the    average sample Mills ratio is calculated, exp ρbjt λbjt − 1 100. The Mills ratio coefficient is always significant at the 1 percent level, indicating that selection is an important factor in our data. For both genders, we plot this number over time: For men, we find negative selection bias over the entire period and the effect remains relatively stable in the 15
25 percent. This indicates that males in the labor force are negatively selected and they will receive lower hourly earnings than a randomly selected sample. This could potentially be driven both by younger men who work due to not continuing with higher education, and by men who do not stop working at later ages, potentially due to lower retirement savings than their more productive peers. For women the trend is very different, but always above the male levels of negative selection in any given year. In the few early years in the 1960s, up to 1968, there is slightly positive selection for women, then negative

JOYCE JACOBSEN ET AL.

1,800 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

1,400

1,600

Hours

2,000

2,200

16

Male

Fig. 5.

Female

Descriptive Results: Average Annual Hours Worked by Gender, 1964
2013.

selection until the late 1980s and then positive selection which is increasing over time. These trends for women are similar to the results found by Mulligan and Rubinstein (2008), who use the selection correction with marital status interacted with children under the age of 6. We also find similar results when we mirror these results.11 In our case, only using marital status as exclusion restriction, we are able to extend our analysis to the early 1960s and up to 2013. Contrary to Mulligan and Rubinstein (2008), we find a positive selection in the early years of 1960s, where they do not have the data, and a strong increase in positive selection after 1999, which is their cut-off in their analysis. For women in the beginning of the 1990s, 5 to 10 percent of their hourly earnings can be accounted for by positive selection. In the late 2000s, particular around the economic recession, 20
60 percent of hourly earnings can be accounted for by positive

11. Results are available upon request from the authors.

17

Convergences in Men’s and Women’s Life Patterns

60 55 50 45 40 35 30 25 20 15 10 5 0 –5 –10 –15 –20 –25 –30 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

Percent

Selection: Mills Effect

Male

Fig. 6.

Female

Heckman Selection Corrected Graphs: Selection: Mills Effect in Percentage, Log Real Hourly Earnings.

selection. However, this peak declines about 40 percent in 2013. Demographic changes and the composition of women selecting into the labor force could partially account for these trends and changes in the selection. This is one of the most interesting findings from our research and is consistent with an increasing trend toward potential high earners among women being more likely to both marry and continue working. We wanted also to see whether our models fit relatively better or worse over time. In particular, we were concerned that a regression specification that is fit to data available in 1964 might no longer be relevant by 2013. While a simple measure of fit would be the R-squared, this is not calculable for selection models (we do show the R-squared measure for our OLS models in Fig. A1 of the appendix). Hence in Fig. 7, to try to ascertain goodness of fit, we instead plot the year-to-year correlation of individual predictions from our Heckman model and the actual observed levels of outcomes for hourly earnings. We find a positive correlation that is slightly increasing over time, implying that our models fit no more poorly over time even though they are based on a stable specification, and if anything,

18

JOYCE JACOBSEN ET AL.

Hourly Earnings: Actual and Predicted 0.6 0.55

Correlation

0.5 0.45 0.4 0.35 0.3 0.25

1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

0.2

Male

Fig. 7.

Female

Heckman Selection Corrected Graphs: Correlation: Actual and Predicted, Log Real Hourly Earnings. Note: Only observed earnings, Heckman.

actually work better for the more recent period (a similar pattern obtains for the OLS results as measured by the R-squared, as shown in Fig. A1). For men the correlation between predicted and observed outcomes is always higher than it is for women. We now turn to taking a closer look at the underlying trends in the returns to potential experience and education for men and women over the entire time period. Given the nonlinear specification for returns to potential experience, we show the marginal returns to an additional year of potential experience at different points in the function and compare these across time and by gender. Fig. 8 shows the marginal returns at different levels of experience, 5, 10, 15, and 20 years respectively, for both genders.12 These are based on the

12. We also estimated returns to 25 years of experience, but these graphs look quite similar to those for 20 years’ experience and thus we have dropped them from the paper for brevity; they are available from the authors upon request.

19

Convergences in Men’s and Women’s Life Patterns

Fig. 8.

1999

2004

2009

2014

2004

2009

2014

1994

1989

1984

1999

1994

1989

1984

1979

1974

1969

2014

2009

2004

1999

1994

1989

1984

1979

1974

1969

Male

1964

20 Years Experience

2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4 1964

Percent

15 Years Experience

1979

1974

1964

1969

Percent

2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4

2014

2009

2004

1999

1994

1989

1984

1979

1974

1969

2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4

Percent

10 Years Experience

2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4

1964

Percent

5 Years Experience

Female

Heckman Selection Corrected Graphs: Heckman, Experience, Log Real Hourly Earnings.

Heckman selection-corrected hourly earnings regression with the dependent variable in log real hourly earnings. The lines display the average marginal effect of the years of potential experience in percent of (level) hourly earnings. In addition, we show with bars around each line the 95 percent confidence intervals for the estimates. Across all the years of experience, it is possible to see that the male average marginal effects are usually above the female marginal effects, indicating higher returns for men than women. However, for the different years of experience, different degrees of convergence, and even coincidence at the same level for both male and female returns are visible. In Fig. 8 the average marginal returns to 5 years of experience for males are above the ones for females and no convergence is apparent. Also the variances of the results for both men and women, as shown by the 95 percent confidence interval bars, are large. But a large decrease in the variance occurs between 5 and 10 years of experience. This variance continues to decrease with higher levels of years of experience. For 10 years

20

JOYCE JACOBSEN ET AL.

of experience, one can see already a narrowing of the returns for men and women over time, the lines converging toward each other but with a gender gap remaining in the returns. Men in 2013 increased their earnings by 0.8 percent of hourly earnings if they increased their experience from 9 to 10 years while average marginal return for women was only 0.4 percent of hourly earnings. The average marginal returns to 15 years of experience show a convergence of male and female return at the end of the period and in the 2000s coinciding even. Men and women have almost the same returns of 0.5 percent of hourly earnings from moving from 14 to 15 years of potential experience. The returns for 20 years of experience are almost identical in terms of patterns to the 15 years of experience figure and also show a convergence and coincidence at the end of the period. The marginal returns for men and women are 0.2 percent of hourly earnings.13 Comparing the above Heckman selection-corrected results for returns to experience with the OLS results (Fig. A2 of the appendix), it is possible to see that the two main general patterns remain: male returns being higher than female returns in general and the decreasing variance. However, the figures showing higher than 5 years of experience and up to 20 years of experience exhibit convergence in the marginal returns for men and women. And, contrary to the Heckman selection-corrected graphs, the OLS graphs of the returns do not converge to close the gender gap entirely for 15 and 20 years of potential experience. We turn now to the Heckman results for the returns to education of high school completion and college completion (Bachelor’s degree and above). As shown in Fig. 9, the female marginal return to high school graduation and some college education is above that of the male return and increasing since the late 1980s. The male returns are almost flat at about 20
25 percent higher hourly earnings for moving from no high school diploma to high school completion. For women, these returns have

13. In Fig. 7, the use of potential experience overstates actual experience, and more so for women than for men. The coefficients do not only represent returns to experience but a combination of returns to experience and other forms of human capital investment. Following Mincer (1974) lower rates of investment might be the reason for the narrowing in gender differences with higher experience levels. Given that over time actual experience of women relative to men has risen while potential experience has remained relatively constant, one concern is that the potential experience coefficients might be biased if earnings are based on actual experience instead of potential experience.

21

Convergences in Men’s and Women’s Life Patterns

College Graduate

Fig. 9.

2014

2009

2004

1999

1994

1989

1984

1979

1974

1969

150 145 140 135 130 125 120 115 110 105 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 1964

Percent Male

2014

2009

2004

1999

1994

1989

1984

1979

1974

1969

1964

Percent

High School Graduate 150 145 140 135 130 125 120 115 110 105 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0

Female

Heckman Selection Corrected Graphs: Heckman, Education, Log Real Hourly Earnings. Note: Marginal effect, Heckman.

increased from 25 percent to 55 to 60 percent higher hourly earnings in 2012 and 2013. For college graduate, women always have a higher marginal effect of college completion than men, and from the late 1980s, the gender gap in favor of women widens (of course this is still relative to a lower base earnings for less educated women relative to men). While in 1964, women were able to increase their hourly earnings by 60
70 percent with the additional educational attainment of a bachelor degree or above, women at the end of the period during the years 2010
2013 almost increased their hourly earnings by 115
125 percent. For men, college completion compared to high school completion increased their hourly earnings by 30 percent in 1964 and by 75 percent in 2013. While the OLS and Heckman selection-corrected graphs are very similar in general trends for the various levels of experience, the returns to education results differ substantially. The OLS graphs (Fig. A3 of the appendix) for the returns to high school and college do not exhibit the same diverging pattern of men and women as the Heckman results. In fact it seems that

22

JOYCE JACOBSEN ET AL.

the marginal effects for both seem to coincide and evolve fairly similarly, and generating the different result that men’s relative returns to college education rise above women’s returns by the end of the period. This in turn points to the fact that selection seems to be an important element in the hourly earnings regression for log real hourly earnings, changing the calculated returns to education significantly when accounting for selection into the labor force. Without accounting for selection, the returns to education are actually understated, particularly for women. We also consider total earnings in our analyses to allow for the effects of changing hours as well as changing hourly earnings. Using the log real annual earnings as the dependent variable in our total earnings analysis (but again converting all our results to show effects on levels), we find results that are different for the selection effects estimations over time than when using log hourly earnings (Fig. 10). For women, in particular, a negative selection effect is present over almost the entire time period until 2009, with decreases starting in the late 1980s. From 2009 onwards, a sharp

Selection: Mills Effect 15 10 5 0 –5 –10

Percent

–15 –20 –25 –30 –35 –40 –45 –50 –55 –60

1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

–65

Male

Fig. 10.

Female

Heckman Selection Corrected Graphs: Selection: Mills Effect in Percentage, Log Real Annual Earnings.

Convergences in Men’s and Women’s Life Patterns

23

increase occurred and the selection effect turns positive, coinciding with the economic crisis period. The selection effect for men is still negative as with the log hourly earnings but decreases since the late 1980s and becoming less negative. The reduction in negative selection effect eventually turning to positive indicates that the women with lower earnings potential were both more likely to work and much more likely to work more hours, but that this effect was eradicated on both fronts over time as women with higher earnings potential increasingly became more likely both to work at all and also to work more hours. For men, the hours effect is apparently minimal in terms of change over the period, but again implies that negative selection occurs both in terms of likelihood of working and in terms of likelihood of working more hours (but that the hours selection effect is dominated by the participation selection effect, as the graph is not that different from Fig. 6 for men). In terms of correlation between actual and predicted annual earnings from the Heckman model, men have a higher correlation than women over the entire period. However, over time these correlations for both genders decline slightly and then increase again (Fig. 11) with a higher correlation in the earlier years, perhaps due to less hours variation in the population in the earlier part of the sample period. The average marginal effect for returns to experience for the various years of experience, 5 to 20 (in intervals of 5 years), exhibits almost an identical pattern to the hourly earnings results: the variance decreases over time, male returns are above female returns in general but convergence and almost full coincidence in returns as a percent of earnings occurs for the 15
20 years of experience (Fig. 12). The magnitudes in terms of percentages tend to be somewhat smaller than for the hourly earnings. For the log annual earnings, we also estimated these OLS returns to experience for different years and found that albeit male returns are above female returns a convergence over time.14 The results for 5
20 years of experience show a convergence. For 20 years of experience, the returns for male and females in the later years of our time period coincide. An anomalistic result in the OLS results were negative returns for women at the 5 years of potential experience level, which indicate the need for correcting for selection into the labor force to obtain believable returns to work

14. These OLS graphs and results for annual earnings are available upon request from the authors.

Annual Earnings: Actual and Predicted 0.6 0.55

Correlation

0.5 0.45 0.4 0.35 0.3 0.25

1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

0.2

Male

Female

Fig. 11. Heckman Selection Corrected Graphs: Correlation: Actual and Predicted, Log Real Annual Earnings. Note: Only observed earnings, Heckman.

2004

2009

2014

2009

2014

1999

1994

1989

1984

20 Years Experience

1999

1994

1989

1984

1979

1974

1969

1964

2014

2009

2004

1999

1994

1989

1984

1979

1974

1969

1964

Percent

1.2 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4

Male

Fig. 12.

2004

15 Years of Experience

1979

1974

1969

1964

Percent 2014

2009

2004

1999

1994

1989

1984

1979

1974

1969

1.2 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4

10 Years Experience 1.2 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4

1964

Percent Percent

5 Years Experience 1.2 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4

Female

Heckman Selection Corrected Graphs: Heckman, Experience, Log Real Annual Earnings.

25

Convergences in Men’s and Women’s Life Patterns

experience (and thus another grounds for preferring the selection-corrected estimates over the OLS estimates). Comparing the returns to high school and college for the Heckman selection-corrected estimates of annual earnings, we find that the patterns for annual earnings are consistent with the hourly earnings in later years (Fig. 13). Women achieve higher returns to high school and college than men starting from 2001. In the hourly earnings, they started to achieve this earlier in time and a larger gap between the genders was visible. For annual earnings, the returns for men and women closely track each other and then diverge after the economic crisis in 2008, with women then receiving higher returns to high school and college completion. Thus partly the difference in these patterns is likely due to differential changes in the hours worked over time, with women steadily increasing their hours worked from the mid1980s onward. The OLS results for annual earnings follow the OLS patterns observed for the hourly earnings and are dissimilar to the Heckman results. This

College Graduate

Fig. 13.

2014

2009

2004

1999

1994

1989

1984

1979

1974

1969

150 145 140 135 130 125 120 115 110 105 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 1964

Percent Male

2014

2009

2004

1999

1994

1989

1984

1979

1974

1969

1964

Percent

High School Graduate 150 145 140 135 130 125 120 115 110 105 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0

Female

Heckman Selection Corrected Graphs: Heckman, Education, Log Real Annual Earnings. Note: Marginal effect, Heckman.

26

JOYCE JACOBSEN ET AL.

again points toward the issue that selection is an important component of the picture in order to understand the actual returns to educational attainment for men and women over time.

4.3. Lifetime Results We turn now to our synthetic worklife calculations to see if convergence occurs in these calculations. Overall, synthetic, or expected, work lives for women, in terms of years in work, their earnings and hours worked over their lifetime, have converged toward men’s work lives. In Fig. 14, female expected lifetime years in work (as defined in Section 3) are increasing over the 50-year period of our data while male expected lifetime years in work are slightly decreasing from above 35 years in work lifetime expectation in 1964 to 30 years in lifetime work in 2013. Contrary to this, female expectations rose steadily from 15 years of lifetime

Expected Lifetime Years in Work 45 40 35 30

Years

25 20 15 10 5

1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

0

Male

Fig. 14.

Female

Lifetime Graphs: Expected Lifetime Years in Work by Gender, 1964
2013.

27

Convergences in Men’s and Women’s Life Patterns

work expectation in 1964 to over 25 years of expected lifetime work in 2013, thereby narrowing the gap between genders. In addition to increased expectations of lifetime years in work, women expect to accumulate more hours worked over their lifetime while men have not seen a comparable increase, maybe even a slight decrease, in their expected lifetime hours worked. This leads to a narrowing of the gender gap in expected lifetime hours worked for men and women (Fig. 15). Not only have expectations of lifetime years in work and expected life hours worked increased, but women have also increased over time their lifetime expectation regarding total earnings, almost doubling from 1964 to 2013. Men over the same time period have also increased their expected lifetime earnings, but across the entire period have consistently had much higher expected lifetime earnings. While there is some convergence of the female and male expected lifetime earnings, the gap does not seem to have narrowed much (Fig. 16). This last pattern reflects the continued gap in hourly earnings as well as a continued difference in hours worked; thus notably the increased attachment of women to the labor force in terms of both participation and

Expected Lifetime Hours Worked 80,000 70,000 60,000

Hours

50,000 40,000 30,000 20,000 10,000

1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

0

Male

Fig. 15.

Female

Lifetime Graphs: Expected Lifetime Hours Worked by Gender, 1964
2013.

28

JOYCE JACOBSEN ET AL.

Expected Lifetime Earnings 2,600,000 2,400,000 2,200,000 2,000,000 1,800,000

Dollars

1,600,000 1,400,000 1,200,000 1,000,000 800,000 600,000 400,000 200,000

1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

0

Male

Fig. 16.

Female

Lifetime Graphs: Expected Lifetime Earnings by Gender, 1964
2013.

hours worked does not appear to have paid off fully in terms of closing the lifetime earnings gap. These synthetic calculations thus underscore both the convergence in male and female patterns and the continued inequalities underlying those patterns as full convergence is yet to be achieved.

5. CONCLUSION The patterns that we show and discuss in this paper indicate that there has been significant convergence over this 50-year period in the work lives of women and men, but that differences continue. We have emphasized the commonality of women’s (and men’s experiences) by focusing on average returns. But perhaps the most notable change over this period is the rising effect and switch from negative to positive selection into work in the case of women, which implies that those women who profit most from paid work participation are increasingly likely to be found in it. This is also

Convergences in Men’s and Women’s Life Patterns

29

reflected in the differences between the OLS and sample selection-corrected results for returns to education. Interestingly, returns to potential work experience do converge for women and men in both OLS and sample-selection-corrected results for those with more years of potential experience. This convergence is thus not observed for all workers but does affect those with longer potential labor market attachment. And again, given that women still make less than men at the lowest levels of experience (and education), this also still implies lower absolute returns to working for pay for women than for men. In our year-by-year calculations of expected lifetime labor attachment and earnings for young persons starting out on their work lives, these indicate again convergence by gender in worklife patterns but less convergence in recent years in lifetime earnings. The interesting question here in part is what causes the evolution of expected values of lifetime labor attachment and earnings. This is clearly not a steady state situation, and thus, particularly given the relatively smooth evolution of the expected values, one might look for causes of this evolution that have also evolved relatively smoothly. Possibilities include demographic changes of a smooth but changing nature, including rises in the age at first marriage, drops in lifetime fertility, and increasing lifespans for both women and men. These changes could have effects on human capital investment decisions (both education and work experience) both directly on cohorts and indirectly through their effects on prior cohorts (and thus affect younger cohorts through changing their expectations of what will happen over their lifespan). We expect our future research agenda will explore the determinants of this evolution of expected values and also how expected values differ from the actual values that the cohorts experience. This line of research is meant to complement rather than supplant the more recent research focus on divergence in outcomes within women and within men taken as groups. Our research focuses more on commonality of outcomes for women and for men to consider how larger trends in gender differences can also be seen in these average results and to remind us of the primacy of gender as a factor of interest and in determining life’s outcomes.

REFERENCES Autor, D. H., Katz, L. F., & Kearney, M. S. (2008). Trends in U.S. wage inequality: Revising the revisionists. The Review of Economics and Statistics, 90(2), 300
323.

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Bacolod, M. P., & Blum, B. S. (2010). Two sides of the same coin: U.S. “residual” inequality and the gender gap. The Journal of Human Resources, 45(1), 197
242. Blau, F. D., & Kahn, L. M. (2000). Gender differences in pay. Journal of Economic Perspectives, 14(4), 75
99. Blau, F. D., & Kahn, L. M. (2005). Changes in the labor supply behavior of married women 1980
2000. NBER Working Paper 11230. Blau, F. D., & Kahn, L. M. (2006). The U.S. gender pay gap in the 1990s: Slowing convergence. Industrial and Labor Relations Review, 60(1), 45
66. Ferna´ndez, R. (2013). Cultural change as learning: The evolution of female labor force participation over a century. The American Economic Review, 103(1), 472
500. Goldin, C. (2014). A grand gender convergence: Its last chapter. The American Economic Review, 104(4), 1
30. Goldin, C., & Polachek, S. W. (1987). Residual differences by sex: Perspectives on the gender gap in earnings. The American Economic Review, 77(2), 143
151. Heckman, J. J. (1979). Sample selection bias as a specification error. Econometrica, 47(1), 153
161. Heckman, J. J. (1980). Sample selection bias as a specification error with an application to the estimation of labor supply functions. In J. Smith (Ed.), Female labor supply: Theory and estimation (pp. 206
248). Princeton, NJ: Princeton University Press. Joshi, H., & Davies, H. (2002). Women’s income over a synthetic lifetime. In E. Ruspini & A. Dale (Eds.), The gender dimension of social change: The contribution of dynamic research to the study of women’s life courses (pp. 111
131). Bristol, UK: The Policy Press. King, M., Ruggles, S., Alexander, J. T., Flood, S., Genadek, K., Schroeder, M. B., … Vick, R. (2010). Integrated Public Use Microdata Series. Current Population Survey: Version 3.0. (Machine-readable database). Minneapolis, MN: University of Minnesota. Lemieux, T. (2006). The “Mincer equation” Thirty years after Schooling, Experience and Earnings. In S. Grossbard-Shechtman (Ed.), Jacob Mincer, A Pioneer of Modern Labor Economics (pp. 125
145). United States: Springer. Mincer, J. (1974). Schooling, experience and earnings. In National Bureau of Economic Research. New York, NY: Columbia University Press. Mincer, J., & Polachek, S. W. (1974). Family investments in human capital: Earnings of women. Journal of Political Economy, 82(2), 76
108. Mulligan, C. B., & Rubinstein, Y. (2008). Selection, investment and women’s relative wages over time. The Quarterly Journal of Economics, 123(3), 1061
1110. O’Neill, J. (2003). The gender gap in wages, circa 2000. The American Economic Review, 93(2), 309
314. O’Neill, J., & Polachek, S. W. (1993). Why the gender gap in wages narrowed in the 1980s. Journal of Labor Economics, 11(1), 205
228. Polachek, S. W. (1975a). Potential biases in measuring male-female discrimination. The Journal of Human Resources, 10(2), 205
229. Polachek, S. W. (1975b). Differences in expected post-school investment as a determinant of market wage differentials. International Economic Review, 16(2), 451
470. Polachek, S. W. (2006). How the life-cycle human-capital model explains why the gender wage gap narrowed. In F. D. Blau, M. C. Brinton, & D. B. Grusky (Eds.), The declining significance of gender? (pp. 102
124). New York, NY: Russel Sage Foundation. Polachek, S. W., & Robst, J. (2001). Trends in the male-female wage gap: The 1980s compared with the 1970s. Southern Economic Journal, 67(4), 869
888. U.S. Dept. of Commerce. (2011). Education and synthetic work-life earnings estimates. American Community Survey Reports, AC-14.

1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

Percent

Convergences in Men’s and Women’s Life Patterns

APPENDIX: OLS RESULTS, LOG REAL HOURLY EARNINGS

30

R-Squared

27

24

21

18

15

12

9

6

3

0

Male Female

Fig. A1. OLS Goodness of Fit, Log Real Hourly Earnings. 31

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JOYCE JACOBSEN ET AL.

1999

2004

2009

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2004

2009

2014

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1989

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1999

15 Years experience

1979

1974

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1969

Percent 2014

2009

1999

2004

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20 Years experience

Male

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1989

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2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4

1979

2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4

10 Years Experience 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4

1964

Percent Percent

5 Years Experience 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4

Female

Fig. A2. OLS, Experience, Log Real Hourly Earnings. Note: Average marginal effect with confidence interval.

33

Convergences in Men’s and Women’s Life Patterns

College Graduate

Male

Fig. A3.

Female

OLS, Education, Log Real Hourly Earnings. Note: Marginal effect.

2014

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100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0

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High School Graduate 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0

A BIOLOGICAL BASIS FOR THE GENDER WAGE GAP: FECUNDITY AND AGE AND EDUCATIONAL HYPOGAMY$ Solomon W. Polacheka, Xu Zhangb and Xing Zhouc a

State University of New York at Binghamton and IZA State University of New York at Farmingdale c Nankai University b

ABSTRACT This paper shows how a shorter fecundity horizon for females (a biological constraint) leads to age and educational disparities between husbands and wives. Empirical support is based on data from a natural experiment $

Part of this paper was written while Solomon W. Polachek was a visiting scholar at the NBER in Cambridge, MA. We thank Vikesh Amin, Talia Bar, Erling Barth, Fran Blau, Richard Burkhauser, Henry Farber, Dan Feenberg, Richard Freeman, Claudia Goldin, David Hacker, Larry Kahn, Subal Kumbhakar, Shelly Lundberg, Haim Ofek, Thomas Rawski, Susan Wolcott, Dennis Yang, Xi Yang, seminar participants at Cornell University, IZA, Kasetsart University (Thailand), Rutgers University, SUNY-Albany, and SUNY-Buffalo, as well as Kostas Tatsiramos and two anonymous referees for valuable comments and suggestions.

Gender Convergence in the Labor Market Research in Labor Economics, Volume 41, 35
88 Copyright r 2015 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1108/S0147-912120140000041009

35

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SOLOMON W. POLACHEK ET AL.

commencing before and ending after China’s 1980 one-child law. The results indicate that fertility in China declined by about 1.2
1.4 births per woman as a result of China’s anti-natalist policies. Concomitantly spousal age and educational differences narrowed by approximately 0.5
1.0 and 1.0
1.6 years, respectively. These decreases in the typical husband’s age and educational advantages are important in explaining the division of labor in the home, often given as a cause for the gender wage gap. Indeed, as fertility declined, which has been the historical trend in most developed countries, husband-wife age and educational differences diminished leading to less division of labor in the home and a smaller gender wage disparity. Unlike other models of division of labor in the home which rely on innately endogenous factors, this paper’s theory is based on an exogenous biological constraint. Keywords: Gender wage gap; marriage; husband-wife age; and educational gaps; homogamy; division of labor in the home; household economics JEL classifications: J1; J2; J3; J43; J7; J8; N3; N9; O5; Y8; Z13

Then Abraham … asked rhetorically … shall a child be born to me, a one-hundred year old man, and to Sarah a ninety year old women? (Genesis 17:17)

1. INTRODUCTION One explanation given for the gender wage gap is the division of labor in the home. According to this argument husbands specialize in market work whereas their wives specialize more in home activities. As a result, husbands work a greater portion of their lives, invest more in human capital, and attain higher wages. The relatively larger wage gap found between married men and married women (especially those with children) compared to the almost nonexistent wage gap found for single (especially never-beenmarried) men and women is consistent with this household division of labor hypothesis. Also consistent with this division of labor is the secularly declining wage gap coming about as fertility rates fell, divorce rates rose, and female labor force participation rates increased over the last century. These same patterns are generally observed in all countries for which there are data. However, the phenomenon social scientists still do not understand

A Biological Basis for the Gender Wage Gap

37

is why household division of labor occurs in the first place. This is the question addressed in this paper. The standard reason for division of labor is comparative advantage. Comparative advantage can come about at the outset of marriage if husbands have higher wages than wives. While discrimination is one explanation why husbands earn more than their wives, another explanation might very well be the mating process
how men and women meet and marry
and the resulting differences in demographic characteristics each spouse brings to the marriage. One of these demographic differences between spouses is age. As the biblical quote above indicates, husbands are typically older than their wives. Another is educational background. Again, at least in the past, husbands’ years of schooling exceeded their wives’. These husbands’ age and educational advantages translates to husbandwife wage disparities which could lead to division of labor, even in the absence of discrimination. Thus the study of husband-wife age and educational differences is important. Social scientists use the singulate mean age at marriage (SMAM) to compute the average age individuals marry. The SMAM data reported in the United Nations World Marriage Patterns (2000) based on 236 countries indicate husbands are older than their wives in all but one country.1 This husband-wife age gap tends to be larger in developing countries especially African nations, while in developed countries it tends to be smaller. In the United States, husbands are just over 2 years older than their wives and at least in the 1960s were almost ½ year more educated (Polachek, 1975). As a result of these age and educational advantages, husbands potentially earn more than their wives from the outset of their marriages. These earnings differences widen throughout the marriage as comparative advantage causes husbands to specialize in market activities, whereas wives tend to specialize more in home production (Becker, 1985; Polachek, 1975). Further, these husband-wife wage differences are exacerbated with increased family size (Bertrand, Goldin, & Katz, 2009; Harkness & Waldfogel, 2003).2 Understanding why most men marry younger less educated women than themselves, and correspondingly why women often marry older more educated men, should shed light on the division of labor,

1. www.un.org/esa/population/publications/worldmarriage/worldmarriage.htm 2. Bertrand et al. (2009) find that MBA mothers, especially those with well-off spouses slow down following their first birth, with concomitant deleterious effects on their subsequent wages.

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SOLOMON W. POLACHEK ET AL.

and hence help explain the gender (and family) wage gap so prevalent in the United States and other countries. In a series of papers beginning in 1973, Gary Becker developed an economics approach to the mating process. Given the usual principles of families maximizing household utility, he showed how couples positively sort based on complementary traits and negatively sort based on substitutes. Using this approach and taking into account the biological constraint that women are fecund for shorter time durations than men, Vella and Collins (1990) as well as Siow (1998) argued that fecund women are relatively scarce. As a result, they demonstrated that the average age at first marriage is lower for women than men. By employing a two-sided search model, Giolito (2003) proved that the husband-wife age gap is larger, the larger the difference in fecundity horizons. Our paper builds on this literature. We adopt a two-sided matching model along with the biological fact that men have a longer fecundity horizon than women. In addition, we assume that schooling is so time and effort intensive that those in school put off having children. Our model shows (1) that husband-wife age gaps are smaller, the lower the demand for children, and (2) that husband-wife schooling differences are smaller, the lower the demand for children. We test our model using data from a natural experiment occurring in China. Before 1970, China had an explicit pro-natalist policy. Between 1970 and 1980 government sentiment abruptly changed to anti-natalist, but the change was not mandated by law. The well-known “one-child law” followed in 1980. Chinese data indicate fertility decreased by over 1.4 children per family, husband-wife age differences declined by as much as 1.2 years, and the husband-wife education gap decreased by about 1.4 years from before to after China instigated its one-child policy. Further, the Chinese policy affected rural areas more than urban areas. Whereas urban fertility declined by 1.16 children, rural fertility declined by 1.5 children. Similarly the spousal age and educational gap narrowed more in rural than urban areas. This paper differs from others in at least several ways. First, it models age and educational differences between spouses, whereas others do not. Second, it is based on exogenous biological constraints whereas others (Chiappori, Iyigun, & Weiss, 2009) rely on higher female rates of return to schooling (a debatable assumption)3 and a technology where women are

3. For example, see Devereux and Hart (2008), DiPrete and Buchmann (2006), Munich, Svejnar, and Terrell (2005), and Hubbard (2011).

A Biological Basis for the Gender Wage Gap

39

more productive in the home than men (an unverified assumption). Third, it makes use of a natural experiment based on China’s one-child policy.4 In addition, our results reinforce important work on the demographic transition by Soares and Falca˜o (2008) by getting at the underlying biological mechanism which motivates the demographic transition causing the sexual division of labor. At this point, it might be worth mentioning that our results are consistent with long-term secular declines in the husband-wife marital age gap which we explain by the more or less consistent decline in fertility. On the other hand, current theories of marriage that explain the 1970
2000 increases in marriage age based on declining fertility are hard pressed to show how overall long-term declines in fertility explain cyclical changes in the age at first marriage exhibited over the last several centuries. The rest of the paper is organized as follows. Section 2 is a brief literature review about the theory of marriage. A two-period model in which males and females search for potential partners based on women having shorter fecundity horizons than men is introduced in Section 3. Section 4 presents some stylized facts. Section 5 empirically tests the predictions using changes in husband and wife age and educational differences resulting from China’s policy changes as a natural experiment. Section 6 concludes.

2. LITERATURE REVIEW An equilibrium search model is a useful tool to analyze how a union between two entities forms. Search models can apply to the job market where potential employers and perspective job applicants are looking for particular job matches, and it can apply to consumer markets where buyers and sellers try to match with each other to exchange specific commodities. In the marriage market, search can be used to determine who marries

4. Though not explored analytically in this paper, we should note that worldwide countries with higher infant mortality rates and higher fertility, such as the African nations, have husband-wife age gaps about five years bigger than in Western countries (United Nations World Marriage Patterns, 2000). Similarly, wives in African countries have about a year less schooling than husbands compared to wives in Western countries (http://earthtrends.wri.org/ searchable_db/results.php?years=all&variable_ID=1117&theme=4&country_ID=all&country_ classification_ID=all).

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SOLOMON W. POLACHEK ET AL.

whom. The development of the equilibrium search model started with onesided search. One-sided search examines how one participant determines whether to form a union from a pool of available potential partners. In these one-sided search models, one party was considered to be a passive receiver in the decision regarding who matches with whom. Gary Becker’s theory is usually taken to consider a woman who tries to select a partner from a pool of marriageable men by comparing the potential utility gained from matching compared to one’s current utility. The one-sided search model ignores the bilateral nature of matching, therefore now two-sided search models are more prevalent (i.e., Burdett & Wright, 1998; Gale & Shapley, 1962; Mortensen, 1988). Marriage is a process where women and men simultaneously search for partners and make a decision by comparing gains from marriage with their current utility. The theory of marriage as developed by Becker (1973, 1991) implies several sources of gains from marriage. First, it is assumed that men have a comparative advantage in the labor market while women have a comparative advantage in home production or childcare. Therefore, by forming a partnership, both men and women are better off from specialization. Second, Becker views the family as an entity which produces and raises children. In this case, a large part of gains from marriage arises from having children. Third, by combining a couple’s resources, gains from marriage also come about from economies of scale. Vella and Collins (1990) as well as Siow (1998) use Becker’s notions of marital selection to derive additional results. Utilizing the fact that men remain fertile longer than women, Vella and Collins (1990) argue that older men become relatively more valuable. This leads to “a positive age differential in favor of husbands” (p. 363). Siow (1998) puts it another way: Young fecund women become relatively scarce by being fertile a longer period of their lives. As such, young fertile women become more costly. This leads to an age disparity whereby husbands are older than their wives because high wage fertile men can better afford these young women. Giolito (2003) investigates the impact of different male and female fecundity horizons in the context of a two-period two-sided search model. He finds fecundity by itself can explain the age gap at first marriage.5

5. This contrasts with Bergstrom and Bagnoli (1993) who reach the same conclusion about the husband-wife age gap via a waiting game in which “males who regard their prospects as unusually good choose to wait until their economic success is revealed before choosing a bride.” Sociologists’ explanations of the husband-wife age gap are more descriptive. For example,

A Biological Basis for the Gender Wage Gap

41

A marital characteristic economists do not readily consider is the educational gap, also prevalent between husbands and wives.6 Educational differences between husbands and wives, while narrowing and even reversing in a number of countries, continue to pervade (Quisumbing & Hallman, 2005; UN State of the World Population Report, 1997). Educational differences lead to specialization in the same way as age differences do. As such, it is important to model not only the husband-wife age gap, but also to model why men tend to be more educated than their wives. To do so, we also make use of the fact that females have shorter fecundity horizons than men. But, in addition, we make use of the fact that schooling takes time to acquire. In the extreme two-period case, one can assume education takes the full first time period, which means the educated put off children to the second period.7 For women, this means foregoing children entirely, given women’s fecundity limitation. Our model yields a number of predictions regarding the impact of changes in the demand for children. Most relevant is that husbands are older than their wives and husbands are more educated than their wives the more children they aspire to have. Further, changes in government policies that influence the demand for children, such as China’s one-child policy, can influence husband-wife age and educational gaps. Thus after 1980 when the Chinese government initiated a “one-child policy” in order to control its large population growth, we predict the husband-wife age gap at first marriage to decline and husband-wife educational differences to

Shorter (1975, pp. 337
339) presents an extensive table with cross-national historical data spanning 1655
1970 indicating that the percentage of husbands more than five years older than their wives averages about 50% whereas the percentage of wives five or more years older than husbands for the same countries and same dates averages only about 14%. Knodel (1988, p. 138) examines husband-wife age differences which vary between 3.1 and 4.8 across four regions of Germany between 1700 and 1899, and during this time period, from 2.0 for unskilled husbands to 6.8 for farmers. Van Poppel, Liefbroer, Vermunt, and Smeenk (2001, p. 12) looks at historical age homogamy in the Netherlands, finding that “age differences between spouses … have become much smaller … [in] the last century and a half.” 6. Sociologists have descriptively examined educational differences. For example, Rockwell (1976) attributes 1910
1970 declines in the US educational homogamy across marital cohorts to overall male and female educational distributions becoming more similar. Mare (1991) extends this analysis of the homogamy trends through the 1980s claiming homogamy increased … from the 1930s to the 1980s (p. 15). Kalmijn (1991) argues that this increased educational homogamy is at the expense of religious homogeneity. 7. Gustafsson and Kalwij (2006) serves as an example illustrating that education delays fertility.

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SOLOMON W. POLACHEK ET AL.

narrow. Similarly, any other policies that affect the demand for children will influence these marital demographics. Such policies might entail lumpsum taxes or subsidies which change the cost of having children, such as tax credits for daycare. Also, factors could include institutional considerations such as living environments. In this regard, farm families usually value children more than non-farm families. In contrast, urban areas often make children more costly. Thus we would predict smaller husband-wife age and educational disparities among urban families.

3. A TWO-PERIOD MODEL In this section we develop a two-sided search model. Similar to Vella and Collins (1990), Siow (1998) and Giolito (2003), we postulate male and female heterogeneity comes from different fecundity horizons. Further we expand Giolito’s (2003) model by introducing education along with the demand for children into the marriage search model. 3.1. Assumptions We assume a continuum of single women of measure F(t), and of single men, M(t). We focus on the steady state. In time t, there are F females and M males. Males and females of a given age and education are homogeneous except for their potential fecundity. Further, we assume individuals (males and females) are of either high or low ability. Ability affects the proclivity one goes to school, and going to school puts off marriage (Atkinson & Glass, 1985).8 For a woman, putting off marriage decreases her capacity to have children.9 All participants in the marriage market sort based on their age and education levels which are related to their fecundity

8. As a check, we tabulate number of children born against husband’s and wife’s age at marriage and husband’s and wife’s levels of school for the Chinese data we will use in the empirical section. We find an inverse correlation for each. More schooling is associated with few children and those getting married at a younger age have more children. These data are given in Appendix A. 9. We only consider the demand for children measured by number of children. As such, we neglect such issues as child spacing (i.e., having more children over fewer years) or quantityquality tradeoffs (i.e., having fewer children, but investing more heavily in each’s human capital).

A Biological Basis for the Gender Wage Gap

43

horizons. For simplicity, we assume both men and women live for two periods. Men are fertile for both periods (at all ages), but women are fertile only during the first period (when they are young). Since education directly affects a woman’s capability of having children, and since children affect the utility gained from marriage, we view education as another factor that affects marital decisions. We assume all young people are low educated but some of them are more intelligent (high ability) than their peers. We assume these highly intelligent young men and women can (but not necessarily) acquire schooling by the time they become old.10 We assume the young low intelligence men and women do not have the mental capacity for additional schooling, and thus remain less educated.

3.2. Payoffs As was indicated, both men and women can live two periods, but women are assumed to have shorter fecundity horizon than men, that is, only young women are fertile while both young and old men are fertile. A single man or woman will meet only one member of the opposite sex at each period. We assume meeting probabilities are independent of one’s ability or education level. They decide whether to propose or not by comparing current utility while being single with the possible utility obtained from matching. When a woman matches with a man and vice versa, the specific utility that the woman obtains from the man’ and the man from the woman’ are considered as an independent random draw from uniform distributions Gm(y) and Gf (x), respectively. Assume y ∼ [0,1] and x ∼ [0,1], where y and x refer to “type” or “quality” of men and women. Both x and y contain observed or unobserved characteristics. One sets a reservation value of one’s potential spouse based on the maximization of expected utility. We assume an individual’s potential marital payoff results from four aspects of the marriage: the marriage partner’s quality, the marriage duration, the utility of having children, and one’s own and one’s spouse’s education. Payoff matrices are given in Table 1 for women and Table 2 for men. We assume zero (marital) utility during the period the individual remains single. We assume marriage yields to women a level of

10. More specifically, in our two-period model, going to school precludes women from having children at all; but this rigid assumption could be relaxed by assuming school simply decreases the probability of getting pregnant.

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Table 1.

Women’s Payoff Matrix.

Husband

Wife High Low Intelligence Intelligence Young Women Young Women

High intelligence young men Low intelligence young men High-educated old men Low-educated old men

k(1 + β)y k(1 + β)y kyr ky

Table 2.

LowEducated Old Women

y y yr y

y y yr y

k(1 + β)y k(1 + β)y kyr ky

Men’s Payoff Matrix.

Wife

High intelligence young women Low intelligence young women High-educated old women Low-educated old women

HighEducated Old Women

Husband High Intelligence Young Men

Low Intelligence Young Men

HighEducated Old Men

LowEducated Old Men

k(1 + β)y k(1 + β)y xr x

k(1 + β)y k(1 + β)y xr x

k ex k ex

kx kx xr x

xr x

utility equal to y, and to men a level of utility equal to x; but that these levels of utility are augmented depending on own and partner quality, marriage duration, and demand for children. We define the parameter (k) to be the demand for children (nominated in number of kids). We assume the desire for more children raises the utility of marriage. For simplicity, we specify this by treating k as a multiplicative factor. Thus k is a parameter designated to raise utility multiplicatively by the desired number of children (k). We assume education to enter utility in either of two ways. First, education increases a person’s desirability because education is positively related to income, obviously an appealing marriage market characteristic. We denote the extra utility from a partner’s high education level to be the parameter r. Second, education raises opportunity costs of children and serves as a substitute to the benefits children bring. This latter effect is denoted as e (e > 1) in the denominator of the male payoff matrix in Table 2. The parameter β is the discount rate so that (0 < β < 1). One can easily justify the payoffs given in Tables 1 and 2 based on this notation and the assumptions regarding payoffs. Each table is divided into

A Biological Basis for the Gender Wage Gap

45

sixteen possible matches arising out of own and partner age (young and old), ability and schooling (low and high) levels. Thus an old woman’s utility from marrying a low educated young or old man is y, since the marriage lasts only one year and produces no children (columns 3 and 4, rows 1, 2, and 4 of Table 1). Should she marry a highly educated man, her utility would be yr, where r is the rate at which utility is augmented based on a highly educated spouse. Similarly, a young woman marrying an old man has a one-period marriage (old husbands die), but they can have children. The wife’s utility is ky if the husband is not educated, and kyr if the husband is educated. A young woman’s marriage to a young man lasts two periods and produces children. Thus, her utility is k(1 + β)y (column 1 and 2, row 1 and 2), independent of her spouses ability because we assume an intelligent person who gets married early in life gives up the opportunity to go to school in order to support children. Table 2 contains comparable payoffs for males except men’s utility from marriage is x instead of y. In addition, we assume education can serves as a substitute for children in that men can rely on own education to enhance wages in old age. As such, the utility of high-educated old men contains e (e > 1) in the denominator, partially offsetting the positive direct utility gain children provide.

3.3. Optimization Based on the payoff matrices, men and women respectively determine minimally acceptable quality characteristics for potential spouses based on maximizing expected utility over the two time periods. For young low and high ability women, this amounts to maximizing total discounted utility by choosing optimal male reservation characteristics (i.e., minimum male qualities) based on n   o Vf1;s = max γ f1;s Uf1;s þ 1 − γ f1;s βUf2;s s = l; h where γ f1;s is the probability young (low and high ability) women get married at period 1.11 Of course, this probability γ f1;s is a function of meeting 11. To be clear on notation, the subscript f denotes female, the further subscript 1 denotes young, and s denotes low (l) or high (h) ability. In the second period, the young woman becomes old; hence f2,s. High ability individuals go to school if they do not marry in the first period.

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SOLOMON W. POLACHEK ET AL.

 probabilities

m2s 1s Pm f1s ; Pf1s

 and reservation characteristics

  m2s 1s Rm for f1s ; Rf1s

young and old low and high ability men, so that γ f 1s = γ f 1s   m1s m2s m2s 1s Pm f1s ; Rf1s ; Pf1s ; Rf1s . Utility functions Uf1sk and Uf2;s are defined in Appendix B. They are functions of these reservation values as well as the payoff matrix parameters given in Tables 1 and 2. Similarly, young men maximize their total discounted utility by choosing the optimal female reservation characteristics for potential spouses based on maximizing expected utility over the two time periods. For young, low and high ability men, this amounts to maximizing total discounted utility by choosing optimal female reservation characteristics (i.e., minimum female qualities) based on n   o Vm1;s = max γ m1;s Um1;s þ 1 − γ m1;s βUm2;s s = l; h where γ m1;s is the probability young (low and high) ability men get married at of meeting probabilities  period 1.  This probability γ m1;s is a function   f1s f2s f1s f2s Pm1s ; Pm1s and reservation characteristics Rm1s ; Rm1s for young and old   low and high ability men, so that γ m1s = γ m1;s Pfm1s1s ; Rfm1s1s ; Pfm2s1s Rfm2s1s . Utility functions Um1;s and Um2;s are defined in Appendix B. They are functions of these reservation values as well as the payoff matrix parameters given in Tables 1 and 2.

3.4. Reaction Functions within a Steady State Equilibrium The solutions to the optimization problems are the reservation characteristics set by different groups (old and young, low and high ability, and low f f f f and high schooling) of men and women. They are Rm1;l1;l , Rm1;h1;l , Rm2;l1;l , Rm2;h1;l , f1;l f1;h f2;l f2;h m1;l m1;h m2;l m2;h m1;l m1;h m2;l m2;h Rm1;h , Rm1;h , Rm1;h , Rm1;h , Rf1;l , Rf1;l , Rf1;l , Rf1;l , Rf1;h , Rf1;h , Rf1;h , and Rf1;h . In equilibrium, high and low ability young men and women should set an optimal reservation value so that they are indifferent between marrying when young and remaining single until the second period. These equilibrium conditions can be depicted as follows: m

m

m

m

kð1 þ βÞRf1;l1;l = kð1 þ βÞRf1;l1;h = kRf1;l2;l = krRf1;l2;h = βUf2;l

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A Biological Basis for the Gender Wage Gap

m

m

m

m

kð1 þ βÞRf1;h1;l = kð1 þ βÞRf1;h1;h = kRf1;h2;l = krRf1;h2;h = βUf2;h kð1 þ βÞRfm1;l1;l = kð1 þ βÞRfm1;h1;l = Rfm2;l1;l = rRfm2;h1;l = βUm2;l kð1 þ βÞRfm1;l1;h = kð1 þ βÞRfm1;h1;h = Rfm2;l1;h = rRfm2;h1;h = βUm2;h The four left hand terms in each equation indicate the respective low and high ability female and male utilities when marrying young and old, low and high ability males in the first period. These values are obtained from parameters contained in the payoff matrices in Tables 1 and 2, multiplied by the respective x and y values of the spouses quality (i.e., the reservation quality given that these are uniformly distributed between zero and one). The far right-hand term of each equation is the utility a low or highly educated male and female would have in period two if each put off marriage until that time period. Because both low and highly educated males m2s 1s and females set reservation characteristics to zero (i.e., Rm f2s = 0, Rf2s = 0, Rfm1s2s = 0, and Rfm2s2s = 0, meaning each will take anyone because there is no other chance to get married), each obtains a utility equal to what would be obtained from the average quality spouse ðy or xÞ weighted by the product of the probability of meeting each type spouse and the respective utility augmentation parameter (k, r, and e) taken from Tables 1 and 2. These (derived in Appendix B) are:   m m m m Uf2;l = pf2;l1;l þ pf2;l1;h þ pf2;l2;l þ pf2;l2;h r y   m m m m Uf2;h = Vf2;h = pf2;h1;l þ pf2;h1;h þ pf2;h2;l þ pf2;h2;h r y   Um2;l = pfm1;l2;l k þ pfm1;h2;l k þ pfm2;l2;l þ pfm2;h2;l r x   k k Um2;h = pfm1;l2;h þ pfm1;h2;h þ pfm2;l2;h þ pfm2;h2;h r x e e Solving the above yield reaction functions in which reservation qualities become functions of the parameters and meeting probabilities.

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From these reaction functions, one can derive the effect of exogenously increasing the demand for children on the spousal reservation qualities one would set. As such, f

∂Rm1;h1;l