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Essays on family and labor economics
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Essays on family and labor economics
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Essays on Family and Labor Economics by Kyoung Eun Kim A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements of the Degree DOCTOR OF PHILOSOPHY (Economics) May 2016 Copyright 2016 Kyoung Eun Kim to my husband and parents ii Acknowledgements I am deeply thankful for the support, patience and guidance I have received from my advisor Moshe Buchinsky. Without his guidance, none of my achievement would have been possible. I am also very grateful to John Strauss for his extremely helpful comments and encouragement. My work has been also beneted from the help of my other com- mittee members, Geert Ridder and Gary Painter. I am also deeply indebted to Changsik Kim for his enormous support and guidance. During my years at USC, I received abundance of help and support from Young Miller, Morgan Ponder and the entire sta of the economics department. My deep- est thanks to my friends Mihye, Ahram and Kunhwa for being sincere friends at all times. I would like to thank Jonathan for having been there and sharing every moment with me. Finally, I am sincerely grateful to my parents for their invaluable support and trust. iii Table of Contents Dedication ii Acknowledgements iv List of Tables vi List of Figures vii Abstract viii Chapter 1 Introduction 1 Chapter 2 A Structural Study of Marital Dissolution, Fertility and Female Labor Supply 5 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.4 Dynamic Programming Solution . . . . . . . . . . . . . . . . . . . 30 2.5 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.6 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.7 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.8 Policy Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Chapter 3 Marital Mobility and the Characteristics of Successive Husbands 67 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.2.1 Comparison of the Two Husbands' Wages . . . . . . . . . . 70 3.2.2 The Associations between the Two Husbands' Wages . . . . 77 3.3 Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.5 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.5.1 Comparison of the Two Husbands' Wages . . . . . . . . . . 86 3.5.2 The Associations between the Two Husbands' Wages . . . . 96 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 iv References 108 Appendix Chapter A Bayesian Update 113 v List of Tables Table 2.1 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . 38 Table 2.2 Estimates of Log-Wage Function Parameters . . . . . . . . . 42 Table 2.3 Estimates of Utility Function Parameters . . . . . . . . . . . 45 Table 2.4 Chi-square Goodness of Fit Test . . . . . . . . . . . . . . . . 50 Table 2.5 Goodness of Fit Comparison - With or Without Learning . . 53 Table 2.6 Policy Simulation Results . . . . . . . . . . . . . . . . . . . . 56 Table 3.1 Changes in Hourly Wages of First Husbands . . . . . . . . . . 87 Table 3.2 Dierences in the Two Husbands' Wages . . . . . . . . . . . . 89 Table 3.3 Dierences in the Two Husbands' HWSEIs & NPBOSSes . . 91 Table 3.4 Dierences in the Two Husbands' ERSes & Occupation Mean Wages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Table 3.5 Dierences in the Two Husbands' EDSes & PRENTs . . . . . 93 Table 3.6 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . 97 Table 3.7 Association between Two Husbands' Wages . . . . . . . . . . 99 Table 3.8 Association between Two Husbands' Wages . . . . . . . . . . 101 Table 3.9 Association between Two Husbands' Predicted and Unpre- dicted Wages . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 vi List of Figures 2.1 Rate of Divorce, Birth and LFP of Married Women . . . . . . . . 11 2.2 Fertility Rate by a Woman's Marital Status . . . . . . . . . . . . 12 2.3 Marital Status of Women in the Labor Force . . . . . . . . . . . . 13 2.4 Hours of Work and LFP of Separated Couples . . . . . . . . . . . 14 2.5 Actual and Predicted Proportions by Choice Alternatives . . . . . 49 2.6 Actual and Predicted Proportions - Working, Married, and Birth . 51 2.7 Simulated Proportions by Choice Alternatives . . . . . . . . . . . 57 2.8 Simulated Proportions - Ever Mar'd/Div'd, Working and Birth . . 59 2.9 Simulated Proportions - Subsidy for Single Mothers . . . . . . . . 63 3.1 Age Matching Patterns in First and Second Marriages . . . . . . . 74 3.2 Age Dierences Between Spouses in First and Second Marriages . 75 vii Abstract This dissertation asks two empirical questions : How would a woman's marriage, fertility and labor supply decisions vary depending on the changes in the social and cultural environment, and how would a remarried woman's second husband be dierent from her rst husband in terms of his economic ability. The goal of chapter 2 is to quantify the eects of changes in the work environment and the divorce related policies on a woman's marriage, fertility and labor supply decisions. Acknowledging the fact that a woman makes decisions considering their eects on her lifetime utility, the chapter uses a structural dynamic model as a tool of analysis. The chapter rst construct and estimate a model which ts the existing data on a woman's behavior. By assuming a woman as a Bayesian learner of her husband's unobserved economic ability, the model allows a divorce to be a gradual process rather than a sudden unexpected event. The results show that my model ts the data well, and the learning in particular improves the t of women's birth giving pattern. The chapter then performs counterfactual analyses on the four dierent policies which represent the changes in the labor market opportunities for women and the changes in the society's attitude to divorce. The results indicate that the increase in female wage and reduced divorce cost make a marriage a less stable institution, leading to higher labor force participation and the divorce rate while lowering the fertility rate for married women. However, when the labor market (re-)entry cost is reduced, it allows a woman to manage her career path more exibly, thus the divorce rate decreases while the fertility rate and the labor force viii participation of older women increases. The results indicate that a woman's career and her role as a mother and a wife are not incompatible, and in the environment that allows a woman to manage her career path exibly, the female labor force participation would increase without deteriorating the family related statistics. Chapter 3 is interested in a remarried woman and her rst and second husband. The nancial hardship that a woman typically undergoes following divorce is often ameliorated by remarriage and thus, the economic status of men who are available for remarriage is of particular concern for the woman. This chapter investigates the new husband's wage in relation to that of the rst husband. Controlling for age, I found that the second husband is economically less competent than the rst for a woman who remarries a man of the same age. However, a woman who marries a man outside of her age group in either or both of her marriages avoids this downward mobility. In addition, I found a strong positive association between the rst husband's predicted wage and the second husband's unpredicted wage where the prediction is made based on the husbands' observable characteristics. These ndings imply that given the limited pool of potential husbands, a female divorcee re-prioritizes her preferences, trading other characteristics of her spouse for his unobserved economic ability. ix Chapter 1 Introduction This dissertation consists of two essays. The essays are independent as they are addressing dierent research questions, but are related in the sense that they both deal with divorce. The second essay can be used as an empirical evidence when modifying the rst essay's model assumption that denes how a woman forms her (potential) husband's future wage stream. I wish the essays provide helpful impli- cations for the future studies. The rst essay, \A Structural Study of Marital Dissolution, Fertility and Female Labor Supply", is an empirical study which discusses how a woman changes her decisions on marriage, fertility and labor supply in response to changes in the social environment. The study uses a structural dynamic model as a tool of analysis in order to address the endogeneity issue. In addition, the model assumes a woman to be a Bayesian learner of her husband's unobserved economic ability in order to allow a divorce to be a gradual process rather than an sudden unexpected event. 1 The model constructed and estimated in this study ts the observed pattern of women's behavior well, and the learning in particular improves the t of women's birth giving pattern. Based on the model estimation, the study performs various counterfactual anal- yses. The main ndings are as follows. First, when the female wage increases or the divorce cost is reduced, a woman tends to work more and invest less in her marital- specic capital during the marriage, thus the divorce rate increases. Second, since reducing the labor market (re-)entry cost gives a woman a chance to manage her career path more exibly, she concentrates on her family duty when she and her children are young and returns to the labor market once her children passes the period of high demand. Third, in the environment where the negative shock from divorce is reduced, a woman's precautionary motive decreases, thus the deceleration rate of the woman's pre-divorce fertility and the acceleration rate of her pre-divorce labor supply become slower. The second essay, \Marital Mobility and the Characteristics of Successive Hus- bands", compares a remarried woman's two husbands in terms of their economic ability. Since the nancial hardship that a woman typically undergoes following divorce is often ameliorated by remarriage, the economic status of men who are available for remarriage is of particular interest for the woman. The study inves- tigates whether the second husband earns more than the rst husband, even after controlling for the two husbands' age dierence. 2 The main ndings are as follows. Controlling for age, the second husband is economically less competent than the rst for a woman who remarries a man of the same age. However, a woman who marries a man outside of her age group in either or both of her marriages avoids this downward mobility. In the additional analysis which examines the association between the two husbands' wage, a strong positive association between the rst husband's predicted wage and the second husband's unpredicted wage is found where the prediction is made based on the husbands' observable characteristics. The nding implies that given the limited pool of potential husbands, a female divorcee re-prioritizes her preferences, trading other characteristics of her spouse for his unobserved economic ability. The dissertation is organized as follows. Chapter 2 consists of nine sections. Section 2.1 gives an introduction and section 2.2 reviews past studies. Section 2.3 describes the structural model, and is followed by section 2.4 which explains how the paper derives a dynamic programming solution. Section 2.5 summarizes the data and the denitions of the variables, while section 2.6 explains some estimation strategies. Section 2.7 and 2.8 presents estimation results and the results of policy simulation, respectively. Section 2.9 summarizes the ndings and concludes. Chapter 3 has six sections. Section 3.1 gives an introduction, while section 3.2 reviews past studies. Section 3.3 explains the empirical strategies, and is followed by section 3.4 which summarizes the data and the denitions of the variables. Section 3.5 examines the woman's mobility between the rst and the second marriages, 3 and also investigates the determinants of the gain of the remarriage. Section 3.6 summarizes the ndings and concludes. 4 Chapter 2 A Structural Study of Marital Dissolution, Fertility and Female Labor Supply 2.1 Introduction Over the past few decades, the labor market opportunities, the wage relative to men, and the average level of attained education have increased for women in the United States. In the meantime, the general attitude towards divorce has been changed as well, in a way that the level of stigma attached to divorcees has been mitigated, thus divorce is considered more of a choice rather than a failure nowadays. Related to these social and cultural changes, the average woman's behavior have also been changed; between 1960 and 1980, the number of divorces per thousand married 5 women increased from 9.2 to 22.6, while the number of births for these women decreased from 156.6 to 97. During the same period, the labor force participation rate of married women increases from 31.9% to 49.8%. Compare to half a century ago, married women these days are more likely to work or divorce and less likely to have children. Based on above facts, one may claim that the liberalized marital culture, the improved work environment for women and the increasing female labor force par- ticipation account for the increase in divorce rate and the decrease in fertility rate. However, the claim is easy to make but not so easy to prove or quantitatively support. This is because; rst, a social or cultural change occurs gradually by interacting with public needs, thus it is dicult to pinpoint how and when it hap- pened; second, a woman's labor supply, marriage and fertility depend on her lifetime planning, thus changes in her environment aect her decisions on all three of them comprehensively. In other words, since a woman's work, marriage, and fertility are variables that are endogenous and thus are mutually interrelated, analyzing eects of policies or social changes on those based on a naive reduced form framework is likely to be invalid. A more appropriate analysis should be based on a model which can address above concerns. In this paper, I examine how changes in the work environment and/or divorce related policies aect women's marriage, fertility and labor supply using a structural dynamic model. In the model, a woman is assumed to be a forward-looking agent who makes decisions on her labor force participation, marital status and childbirth 6 knowing that her decisions today aect her current and future utilities as well as her decisions in the future. The model is an extension of discrete choice model, which allows one to specify the woman's decision rule, thus to deal with the endo- geneity issue. In addition, the structural dynamic framework allows one to perform counterfactual analyses, thus to quantify the eects of changes in the social environ- ment without pinpointing the timing or the magnitude of the changes that actually happened in the history. While the past literature has assumed the contraception, which is an indirect way of controlling childbirth, as a woman's decision, this paper allows the woman to make direct decisions on her childbirth. By modeling the childbirth as a woman's choice, the paper enables quantifying the direct eects of various policy changes on fertility. In addition, the model assumes a woman to be a Bayesian learner of her husband's unobserved economic ability. The assumption adds a more realistic aspect to the model as it allows a divorce to be a gradual process rather than an sudden unexpected event. This allows us to observe women's behavior before divorce, such as their fertility and labor force participation, in more detail and examine how changes in policy aect it. This type of analysis could not be performed without the Bayesian assumption. The paper rst focuses on constructing and estimating a structural dynamic model that resembles the patterns of existing data on women's labor supply and family structure. The estimation results indicates that the model successfully ts the data, and that Bayesian learning plays an important role, especially in tting 7 women's birth giving pattern. Setting up the estimated model as the baseline, the second part of the paper performs policy simulations. The eects of following four policies are examined: (i) reducing the labor entry cost, (ii) reducing the divorce cost, (iii) increasing the female annual wage, and (iv) providing a subsidy to a single mother. In the rst scenario, a woman can concentrate more on her family duty when her children are young and returns to the labor market once her children pass the period of the high demand since the policy helps her manage her career path more exibly. As a result, although the labor supply of young women tends to decrease, that of older women increases, and the family related statistics also improves, i.e. fertility rate increases and divorce rate decreases. In addition, the drastic changes in women's pre-divorce fertility and labor force participation tends to slow down, implying that women are less concerned about their post-divorce lives since it becomes easier to nd a job under the new policy. The changes in women's pre-divorce fertility and labor force participation are also less drastic in the second and the third scenarios where the divorce cost is reduced and the female wage increases. Meanwhile, women tend to invest less in their marital-specic capital during the marriage in both scenarios, i.e. they tend to avoid having children and becoming housewives. This is because: (i) the reduced divorce cost makes marriage a less stable institution in the second scenario, and (ii) the increased female wage makes a marriage a less attractive option for a woman in the third scenario. 8 In the last scenario where all divorced mothers are subsidized, due to the fact that the policy is biased towards women with children, the overall fertility increases and the speed of pre-divorce fertility deceleration slows down. Reduced concern about post-divorce child support induces more mothers to divorce, thus the pro- portion of mothers among divorced women increases. Since mothers have stronger incentive to work than women without children when husbands are not present in the households, the pre-divorce labor force participation accelerates faster, and the proportion working among divorced women increases compared to the baseline sce- nario. Therefore, by taking advantage of maternal instincts, the policy increases the labor force participation of divorced women without providing any explicit stimulus to work. The rest of the paper is organized as follows: The next section reviews past studies. The third section describes the structural model, and is followed by the fourth section which explains how the paper derives a dynamic programming so- lution. The fth section summarizes the data and the denitions of the variables, while the sixth section explains some estimation strategies. The seventh and eight section presents estimation results and the results of policy simulation, respectively. The last section summarizes the ndings and concludes. 2.2 Literature Review The changes in structure of the American family for the past few decades draws attention among the labor economists to the importance of household structure in 9 the study of individual and family labor supply. One of the main changes is the increase in divorce rate. The number of divorces per thousand married women age 15 and older increased from 9.2 in 1960 to 22.6 in 1980 (see Figure 2.1). During the same period, the fertility of married women decreased dramatically; the number of live births per thousand married women between age 15 and 44 decreased from 156.6 in 1960 to 97 in 1980. Notice that the decrease in birth rate is observed only for married women. As we can see from Figure 2.2, the birth rate has increased for unmarried women. Meanwhile, the married women's labor force participation rate increased from 31:9% in 1960 to 49:8% in 1980 and this rate of increase is sustained until the early 90's. Although the labor force participation of never married women has also increased, the increasing trend is steeper for married women (see Figure 2.3). These simultaneous trends in divorce, fertility, and labor force participation rates give rise to the conjecture that there is a possible dependence among married women's divorce, fertility and labor supply decisions. Changes in labor market opportunity for women may account for the increase in divorce rate a . Better labor market opportunities provide women an option to support their lives other than marriage. As the access to the labor market becomes easier for women, married women who work may have less incentive to maintain marriages than married women who do not work, thus they are more likely to a This labor market opportunities encompasses various aspects of labor market conditions such as the degree of openness of the labor market to women, the types of jobs that are available to women, and the wages of those jobs relative to men. 10 Figure 2.1: Rate of Divorce, Birth and LFP of Married Women Notes: Per 1,000 women older than 14 for divorce rate, between 15-44 for birth rate, and % of married women older than 15 for LFP. Source: U.S. National Center for Health Statistics, Vital Statistics of the United States, National Vital Statistics Reports (NVSR) and Current Population Survey. 11 Figure 2.2: Fertility Rate by a Woman's Marital Status Notes: Births per 1,000 women between 15-44 Source: National Vital Statistics Reports, Volume 60, Number 1 12 Figure 2.3: Marital Status of Women in the Labor Force Notes: For civilian non-institutional population older than 15. Source: Current Population Survey 13 Figure 2.4: Hours of Work and LFP of Separated Couples Source: Johnson and Skinner (1986) divorce. Conversely, women who anticipate divorces may freely increase their labor supply in order to accumulate work experience and ensure her life after divorce. This implies the increase in women's labor supply before the occurrence of divorce. The implied positive correlation between divorce probability and female labor supply is supported by the empirical evidence provided in Johnson and Skinner (1986) (see Figure 2.4). Using a sample of separated couples in Panel Study of Income Dynamics (PSID), Johnson and Skinner (1986) examined the changes in labor supply of women who experienced marital separation during the survey period. They found that the annual hours of work increased from 635 seven years before the separation to 1024 one year before the separation. A large part of the increase was induced by the 14 increase in labor force participation; the participation rate increased from 62% to 76% during the same time period. Fertility is also likely to be related to divorce. According to Becker et al. (1977), the gain from marriage increases as the marital-specic capital is accumulated, and children are considered one of the main component of marital-specic capital. The decrease in fertility implying lower marital gain relative to being single, thus implies higher divorce probability. However, the causation may running both ways; the decreased fertility reduces the gain from marriage thus raising the probability of divorce. Conversely, women who anticipate divorce in the near future suppress birth giving to reduce the economic burden after the anticipated divorce. While many of the past studies consider only one-way relationships, Johnson and Skinner (1986) and Koo and Janowitz (1983) studied the interrelationship between divorce and female labor supply, and between divorce and fertility, respectively. Letting the divorce probability (or the future divorce decision) and women's hours of work depend on each other, Johnson and Skinner (1986) estimated the static simultaneous model. Their result illustrated that women's work decision had a positive but insignicant eect on the divorce probability, and the divorce proba- bility had a signicant positive eect on the women's hours of work if they included women's past work experience and fertility, which are possibly endogenous, in the regression model. Also, in the additional test they conducted, the endogeneity of divorce probability is rejected in the hours of work equation but it was not rejected 15 in the labor force participation equation. Similarly, Koo and Janowitz (1983) exam- ine the interdependency between marital dissolution and fertility using the static simultaneous logit model. Their result showed that the recent fertility does not have a signicant eect on divorce, and the divorce probability did not aect recent childbearing either. It would be interesting to extend the above studies in a dynamic framework and reexamine the interrelationship between marital dissolution, female labor force par- ticipation and fertility altogether. Since the fertility decision typically has long-term consequences and the labor force participation behavior is known to be persistent, it would be appropriate to examine the interrelationships among the three in the dynamic rather than static framework. Specically, I will use a structural dynamic discrete choice model, which explicitly addresses the interdependence among dif- ferent choice alternatives and their dependence on past decisions, for the analysis. The model is structural in the sense that the parameters that will be estimated are derived from economic primitives such as the utility function and the budget constraint. Once the model is estimated, one can use it for predicting the long-term patterns of marital dissolution, labor force participation, and fertility of women with dierent characteristics, such as education, race, and (potential) earnings. It can also be used for policy analysis; that is, how changes in the parameters or exogenous variables change women's joint decisions regarding the three issues. Structural dynamic discrete choice models have been applied to various economic problems in which the present decision aects future decisions. The female labor 16 supply problem is one of those since the current participation in the labor force may alter the future wage, thus aecting the future participation. An application of a structural dynamic discrete choice model to the female labor supply problem can be found in Eckstein and Wolpin (1989). They restricted their attention to married women who were beyond childbearing age to avoid a complication of jointly mod- eling women's fertility and labor force participation decision. Another application can be found in Francesconi (2002). However, dierent from Eckstein and Wolpin (1989), he estimated a structural dynamic model of labor force participation of married women in conjunction with their fertility choice. These studies, however, restricted their attention to married women only and did not incorporate the possi- ble relationship among the decisions of their interest (labor force participation, and fertility) and marital status in their models. The inclusion of the marital status decision in the structural dynamic discrete choice model was accomplished relatively recently. Van der Klaauw (1996) rst at- tempted to study women's joint decision on marital status and labor supply b . When incorporating marital status as the women's decision in the model, a possible source of complication was the modeling of the husbands choice. Van der Klaauw (1996) resolved this issue by assuming that the (potential) husband was solely characterized b Fertility is not modeled as a women's choice here. Rather, it is assumed to be determined stochastically where the probability of have at least one child depends on women's marital sta- tus. The author calls it indirectly endogenous since fertility depends on marital status, which is endogenous in the model. 17 by his wage earnings. Then, he assumed that a woman predicted her (potential) husband's wage based on the wage equation in which the husband's wage depends on the woman's characteristics and her past decisions. Following this work, Sheran (2007) and Ma (2010) also estimated a structural dynamic model which incorpo- rates women's marital status decisions. Sheran (2007) estimated a dynamic model in which a woman makes labor supply, marital status, contraception, and schooling choice jointly, and Ma (2010) estimated a model in which a woman makes occu- pational (professional, non-professional, and non-market work), marital status, and contraception decisions. In both works, the way they characterized the husbands choice and the husband's wage equation was similar to Van der Klaauw (1996). All the previous works mentioned above did not model how people process a divorce decision. This is true not only for the models which only concerned married women, but also the models which incorporated marital status choices. In the previous models with marital status choices, as with other decisions, the divorce decision is made either based on a dynamic programming solution or because of a transitory shock which is serially uncorrelated. In other words, if a woman is divorced, it means that the reason for her divorce is either: 1) due to a life plan made previous to marriage or 2) an unexpected occurrence that is specic to a period. However, another major cause of divorce is imperfect information. As mentioned in Becker et al. (1977), even after prolonged dating, newly married persons face tremendous uncertainty about their own or their mate's needs, their capacity to get along with each other, and so on. I assume that the major uncertainty associated 18 with marriage is the uncertainty about the match/husband's quality. This quality is uncertain since it cannot be directly observed, but is revealed slowly over the course of a marriage through a woman's information gathering process, which is similar to the notion of `intensive search' in Becker et al. (1977). Thus in our model, divorce occurs not only due to the two reasons presented above, but also because the accumulated information indicates that the quality of current husband/match is suciently low. The idea presented above about marital match quality was rst formulated in Jovanovic (1979) in the form of job match. He constructed a model of permanent job separation which can explain the observed phenomenon such as the negative relationship between quits (or layos) and job tenure. In his model, a job is consid- ered an experience good, which means that the only way to determine the quality of a particular match with a particular rm or employer is to form the match and experience it. The quality is unknown for an employee at any time, but she can ob- serve the output of the rm that she works for. The output stochastically depends on the match quality; if the match quality is good, it is more likely to generate high output. Thus, the output can be interpreted as a noisy signal of match quality. Each period, the employee observes the output, infers the match quality based on the output and decide whether to quit or not. The major reason for turnover is thus, the arrival of new information about the current job match. Brien et al. (2006) applied the theoretical model of Jovanovic (1979) in their structural dynamic model. Their model is a dynamic extension of the ordered 19 discrete choice model, in which a woman chooses whether to be single, to cohabit with a partner, or to be married. In their model, the true match quality with a current partner is unknown to the woman, but she receives a noisy signal of it in each period. Based on this signal, the woman decides whether to form a relationship with the current partner or not, and if she does, what form the relation should take (cohabitation or marriage). Once a relationship is formed, the woman receives signals of the match quality with the same partner as long as she remains intact with him. The decision to remain in or change the form of relationship is made then, based on the accumulated signals. We similarly apply this theory of Jovanovic (1979) in the problem of marriage formation and dissolution in our model. The objective of this paper is to construct and estimate a structural dynamic model that can t the observed data on women's divorce, fertility and labor force participation behaviors. The model constructed in this paper can be thought of as an extension of Van der Klaauw (1996) with an additional fertility decision. In the model, a woman makes decisions on her marital status, labor supply, and fertility jointly in each period, in order to maximize her life-time utility. However, the distinction from Van der Klaauw (1996) and many of the past literature on the dynamic discrete choice model of female labor supply is that we adopt the model of uncertain match quality formulated by Jovanovic (1979). This model has been applied to the structural dynamic model of marital status by Brien et al. (2006). I follow the way they applied it with a simplication. By adding this part to the model, I expect to see whether it improves the model t, and how the learning 20 about the match/husband's quality aects women's divorce, fertility, and labor supply decisions. 2.3 Model The model assumes discrete time (t = 1; 2;:::;T ), where the length of each period t is set to be a year. The model assumes nite time horizon where a woman enters to the model in the year she rst leaves school, and exit from it when she turns 60 c . Due to the dierences in achieved levels of education, the total length of time a woman stays in the model (T ) varies across women. In any given period, a woman's objective is to maximize the present value of her expected lifetime utility. She can achieve it by choosing whether or not to work, marry, or give birth. She can also decide how much to consume. Let h t = 1 if she decides to work, m t = 1 if she decides to marry, b t = 1 if she decides to give birth in period t, and zero otherwise. Let c t be the woman's consumption in period t. Then, the expected lifetime utility of a woman is dened as E T X t=1 t1 [U(h t ;m t ;b t ;c t ;X t ;h t1 ;exp t1 ;m t1 ;md t1 ;N t )] (2.1) c Notice that the model treats the attained level of education as an exogenous variable. By doing so, it assumes that a women makes decisions on her work and family structure only after she nishes schooling. Considering the fact that the proportion of female students who are married or work fulltime are less than 3% in my sample, the assumption is quite realistic. 21 which is the expected sum of the discounted period utilities where 2 [0; 1] is the woman's subjective discount factor. Throughout the paper, is set to be 0.95 d . The utility in periodt depends on the woman's choices at the time (h t ;m t ;b t ;c t ) and several other factors. More specically, U(h t ;m t ;b t ;c t ;X t ;h t1 ;exp t1 ;m t1 ;md t1 ;N t ) =a 1t h t +fa 2t +a 4t b t + (a 3t +a 5t b t )h t gm t + 6 h t (1h t1 ) + 7 m t (1m t1 ) + 8 (1m t )m t1 + 9 m t md t1 +c t +(h t ;m t ;b t ) (2.2) where for k = 1;:::5, a kt =X 0 t k1 +N 0 t k2 ; (2.3) and (h t ;m t ;b t ) = 1t (1h t )(1m t )(1b t ) + 2t h t (1m t )(1b t ) + 3t (1h t )m t (1b t ) + 4t h t m t (1b t ) + 5t (1h t )m t b t + 6t h t m t b t : (2.4) d Although it is theoretically possible to identify the discount factor, it is at most poorly iden- tied in reality (See Rust (1987) and Aguirregabiria and Mira (2010).). 22 Here,X t is the vector that contains the woman's demographic characteristics, such as the her age, attained level of education and race, all of which are assumed to be exogenous to the model. The variables exp t1 and md t1 are her work expe- rience and marriage duration respectively, both of which are accumulated before the beginning of period t. Lastly, N t is the 21 vector consisting of n yt and n ot which indicate the number of young (age below 6), and older (age 6 to 18) children that a woman has, respectively. Notice that exp t1 , md t1 and N t are endogenous variables in the sense that they are determined by the woman's past choices. More specically, exp t = exp t1 +h t md t = m t (md t1 +m t ) n yt+1 = n yt +b t where in the beginning of the model,exp 0 =h 0 = 0,md 0 =m 0 = 0 andN t = (0; 0) 0 . Although the above specication seems awfully too complicated, it is simply an extension of the latent variable framework, which is often used to explain binary choice models. Think of modeling a car purchasing decision. In this case, the latent variable framework assumes that a person buys a car if the net utility from it exceeds that of not buying a car, where in many cases the latter is normalized to zero. If a researcher thinks that the decision depends on the decision maker's individual characteristics, such as his/her age, education, and income, the researcher 23 can assume the utility to vary by these characteristics, given the availability of the data. Then, other factors that are likely to aect the car buying decision but are unobserved to the researcher, such as the individual preference, are introduced in the model as an error term. Depending on the assumption that is made on the structure of the error term, the model would have dierent names, such as probit or logit. Equation (2.2) can be thought as an extension of the binary model to a multi- nomial choice case in a given time period t. The combination of binary variables h t , m t , and b t gives a woman 8 mutually exclusive choices. Normalizing the utility from choosing not to work, not to marry, or not to give birth (h t =m t =b t = 0) to zero, the rest of the mutually exclusive choices give a woman dierent levels of net utility; if she decides only to work or only to marry, she enjoys the direct utilities of a 1t anda 2t , respectively. If she decides to do both, she enjoysa 3t on top ofa 1t +a 2t , where the terma 3t captures the (dis-)utility that might be incurred due to the role con ict (the role as an employee and that as a wife). Being pregnant and expecting a childbirth may incur medical expenses or expenses regarding baby supplies to the woman, but would also bring happiness to her. This net utility of having a new- born is captured by a 4t . Finally, since a working woman may have more medical needs or may experience more physical hardship during her pregnancy compare to a housewife, a 5t captures this possible dierences e . The net utility associated with each choice alternatives is likely to vary by a woman's observable characteristics; for instance, a woman's preference to work may 24 become stronger as her level of attained education increases; an older woman may value her marriage more than a younger woman; a non-white woman may have stronger preference towards having children than a white woman; a woman with young children may benet more from staying at home than a woman without children. In order to incorporate these ideas into the model, the alternative specic net utilities, a kt;k=1;:::;5 , are assumed to vary depending on a woman's individual characteristics and the number of children she has, as shown in equation (2.3). Deviating from the static point of view, due to the dynamic nature of the model, the net utility from each alternative may change depending on a woman's position in her life course; for example, the utility from working may be lower in the year the woman returns to the labor market than the rest of periods in her career because adjusting herself to the new work environment and purchasing new work gears are costly. Similarly, the utility from being married (being single) may be lower during the rst year of her marriage (her divorce) than the rest of her marriage duration (her life) since a couple typically goes through an adjustment phase during the period (since she may feel the sense of loss during the period). These ideas are summarized in the costs of (re-)entering labor market ( 6 ), the cost of marriage ( 7 ) and the cost of divorce ( 8 ), respectively. In addition, considering the fact that a married couple typically builds attachment to their spouses as the marriage duration increases, the utility from marriage is allowed to vary by its duration ( 9 ). e I intentionally excluded 2 choice alternatives which give a unmarried woman an option to give birth. This assumption is made in order to keep the size of the state space small. I will explain further in detail about this issue later in the estimation section. 25 Once all these parameters are dened, the error terms 1t ;:::; 6t in equation (2.4) capture the variations in the utilities that occur due to changes in factors that are unobservable to economists but observable to the woman. Throughout the paper, these terms are assumed to be independent across time and individuals. Turning our attention to the consumption, it is necessary to introduce the follow- ing three equations into the model: (i) the woman's budget constraint, (ii) her wage equation, and (iii) her husband's wage equation. Once these equations are specied, the woman's problem becomes to maximize the objective function (Equation (2.1)) subject to the three equations. Starting with the woman's budget constraint, the constraint is specied as follows and is assumed to be satised period by period f : c t =m t [w h t +h t w f t ] + (1m t )h t w f t (2.5) where w f t is the woman's wage in period t, and w h t is that of her husband's. If the woman is single, her wage income is the sole source of her consumption. If she is married, the source becomes the pooled income, which is the sum of her and her husband's wages. However, while the woman has full claim on the source when she is single, she can only claim a portion ( ) of the pooled income when she is married. f Due to this assumption, women in this model cannot directly choose how much to consume. However, they can indirectly decide the consumption amount by making decisions on her work and marital status. This point will become clear once the two wage equations are specied. 26 Throughout the paper, I assume women can claim half of pooled income, and this is the same across time and individuals g . The following equation species how a woman's wage at period t is determined: ln(w f t ) =X 0 t 1 + 2 h t1 + 3 exp t1 + 4 exp 2 t1 +u f t : (2.6) The woman's wage depends on her education, work experience, race, age, and whether she worked in the previous period. Here, the age captures the eect of the experience outside of the labor market, and h t1 captures the eect of recent work experience on wage. Lastly, u f t represents the random uctuations in earn- ings, which is assumed to be independent across time and individuals and have zero mean. Due to the existence of this randomness, the woman does not know the exact realizations of her future wages. Now for each woman, her (potential) husband's wage equation is specied as ln(w h t ) =X 0 1t 1 + 2 exp t1 + 3 hexp t1 + 4 hexp 2 t1 +u h t (2.7) g In reality, how much a woman can claim from the pooled income would depend on her bar- gaining power in the household, which is likely to vary by a woman's work and fertility status. For example, a woman who works or has children may have stronger bargaining power compare to a woman who does not. However, since I do not have data which allows me to identify and estimate the bargaining power, I assume it to be equal to 0.5 (see Browning et al. (1994)). 27 where X 1t is equivalent to X t excluding a woman's age, and hexp t1 is a proxy for the husband's experience which is dened as the dierence between the woman's age and education. This type of equation, which assumes the husband's wage depends on his wife's characteristics, is called \the matching equation" (Van der Klaauw (1996)). This equation does not necessarily describe how male wages are actually determined in the labor market. Rather, it denes how a woman forms her expectation regarding her (potential) husband's earnings given her demographic features and work history. She compares herself to women in the marriage market who have the same observable characteristics as hers and refers to their husbands' average earnings when forming the expectation. If no further assumptions are made on the stochastic component of the matching equation (u h t ), Equation (2.7) completes the description of how a woman forecasts her husband's future wages. The husband's wage forecast based on equation (2.7) may be reasonable for single women, but it is less so for the married. In fact, critical information about a spouse, which determines the quality of the marriage, is often revealed only after marriage, and the spouse's true wage earning ability is a good example of it. Thus, a reasonable model of divorce must incorporate in the model the fact that a woman learns about her husband's wage earning ability throughout her marriage. Ignoring this learning process may signicantly bias the value of the marriage, thus weaken the model's prediction power. 28 In this model, a woman is assumed to be a Bayesian learner of her husband's true wage earning ability. I formulate this idea by dening the following equation: u h t = + t (2.8) which is a simplied version of the learning equation presented in Brien et al. (2006). Here, represents the husband's true ability which is assumed to be unknown or unobserved to any woman in the model at any time. However, women are provided with information that helps the inference of their husbands' ability. The rst is the noisy signal of their husband's ability, u h t , where the noise is denoted by t . The second is the distribution of, which indicates how the ability is distributed among the males in the marriage market. The last is the distribution of the noise and the fact that the noise is independent across time and individuals. How equations (2.7) and (2.8) summarize a woman's marital decision process can be explained in the following way: In the beginning of period t, a single woman randomly meets a potential husband and observes his wage, which contains a signal of his true ability. Based on this observation, she updates her belief about his ability and his future wages h . She then decides whether to marry this man or not. If she decides not to marry him, the wage signal from him is forgotten, and she continues to search for another partner until the next period t+1. If she decides to marry him in period t, she consumes a portion ( ) of his wage during the period h The detailed Bayesian update process is presented in the Appendix. 29 and observes his wage in the beginning of the next period. She adjusts her belief based on the new observation and decides whether to remain married or not. This updating process continues as long as the woman stays in the marriage; therefore, the true ability will gradually be revealed over the course of the marriage. I close the model by dening the error structure. The stochastic part of the utilities, t = ( 1t ;:::; 6t ) is assumed to be jointly normal with mean zero and co- variance matrix . The random uctuation of a woman's wage, u f t , is assumed to be normally distributed with mean zero and variance 2 u . The true ability, , is assumed to be normally distributed with mean zero and variance 2 and indepen- dent among the males in the marriage market. The noise, t , is assumed to follow i.i.dN(0; 2 ). Finally, each of the above structural error terms, t ;u f t ;, and t are assumed to be independent of each other for all t = 1;:::T . 2.4 Dynamic Programming Solution For the discussion of the dynamic programming solution, it is convenient to rst dene the mutually exclusive alternatives and the state space. As mentioned earlier, combined work, marital status and fertility choices yield six mutually exclusive alternatives in this model. I let alternative 1 and 2 correspond to not working and working status for a single woman (h t = 0 or 1 form t =b t = 0),3 and 4 correspond to not working and working status for a married woman who did not give birth in periodt (h t = 0 or 1 form t = 1;b t = 0), and 5 and 6 correspond to not working and working status for a married woman who gave birth (h t = 0 or 1 for m t =b t = 1). 30 The state space consists of all factors, known to the decision maker, that aect current rewards or the probability distribution of any of the future rewards (Keane and Wolpin (1994)). In this paper, the factors are a woman's demographic charac- teristics, her past choice history, the stochastic components of period utilities and wage equations as well as the information regarding her husband's ability. Dene S t as a vector consists of variables that are constructed based on a woman's past choice history, i.e. S t = (h t1 ;exp t1 ;m t1 ;md t1 ;N t ). Then the state space at time t, denoted as Z t , is dened as Z t =fX t ;S t ; t ;u f t ;u h t ; ^ md t1 g where ^ md t1 represents the information about her husband's ability accumulated until the beginning of t i . Dened jt;j=1;:::;6 to be a dummy variable which gives 1 if alternativej is chosen at time t, and 0 otherwise. Also, dene R jt;j=1;:::6 , the alternative-specic utilities for each of the six alternatives. The alternative-specic utility is obtained by com- bining the period utility (2.2) and the budget constraint (2.5), and substituting the i See Appendix for a detailed description of how ^ mdt1 summarizes the accumulated informa- tion. 31 two wage functions (2.6) and (2.7) into the budget constraint. For example, the alternative-specic utility for alternative 2 is: R 2t = Z 0 t a 1 + exp(X 0 1t 1 + 2 exp t1 + 3 exp 2 t1 +u h t ) + 2t where Z t is a vector consists of X t and S t . Here the rst term in the RHS ( Z 0 t a 1 ) represents the direct utility relevant to alternative 2, the second term is obtained by replacing the woman's wage with her wage equation. Once the R jt s are dened, the woman's problem reduces to: max d jt E " T X t=1 t 6 X j=1 R jt d jt # and I can dene the value function at time t given Z t as V (Z t ;t) = max d jt E " T X =t t 6 X j=1 R j d j jZ t # : The value function V (Z t ;t) can be rewritten as the maximum over alternative- specic value functions, each of which obeys the Bellman equation: V (Z t ;t) = max j fV j (Z t ;t)g 32 where the alternative-specic value function is dened, for each j = 1;:::; 6, as V j (Z t ;t) = R jt (Z t ) +E[V (Z t+1 ;t + 1)jZ t ;d jt = 1]; t<T; (2.9) V j (Z T ;T ) = R jT (Z T ): The expectation in equation (2.9) is taken over the distribution of the random component ofZ t+1 conditional onZ t andd jt = 1. More specically, the expectation is taken over the unconditional joint distribution off t+1 ;u f t+1 g, and the distribution of u h t+1 conditional on ^ md t1 and u h t . Thus, it is equivalent to write equation (2.9) in the following manner: V j (Z t ;t) =R jt (Z t ) +E[V (Z t+1 ;t + 1)j Z t ; ^ md t1 ;u h t ;d jt = 1]: The dynamic optimization problem is solved by backward recursion; starting from the last period T, the value function should be evaluated at each element in the state space until the initial period. It is generally recommended to use full- solution method when it is feasible since it yields unbiased estimators. However, there are two conditions in this model which prevents me from using the full-solution method: First, the error structure follows the normal distribution which makes it practically impossible to yield a closed form solution when evaluating the condi- tional expectation of the value function (represented by the second term of RHS in equation (2.9)). Second, the state space is extremely large in our case, thus even when we can obtain closed form solution, it might be computationally too costly 33 to evaluate it at every point in the state space. This paper tackles these issues by simulation and interpolation method which is similar in spirit to Keane and Wolpin (1994). Simulation resolves the diculty of solving multi-dimensional integration. Interpolation allows me to handle the \curse of dimensionality" problem. The simulation and interpolation method takes the following steps: First, for randomly picked states at period T, their value functions are simulated based on 150 random draws on the set of error terms. Then, for the rest of states at period T, their value functions are approximated using a quadratic function of deterministic elements of the state space. Moving backwards to the previous period T-1, the sim- ulation procedure is almost the same as the one in period T except that it involves the period T's value functions. Therefore, at the end of period T, the simulated values and the coecient estimates in the approximation function should be saved and passed to the simulation in period T-1. Once the simulation is completed, the approximation procedure is implemented in the same manner as in period T. The process is continued until it reaches to the initial period. When it comes to multidimensional approximation, a well-known method is to use complete polynomial. The approximation based on complete polynomial is as accurate as the one that is based on tensor product but the former is more ecient than the latter (Judd (1998)). Since the deterministic part of the state space, which is used for the approximation, consists of 10 variables (X t ;S t ; ^ md t1 ), it is costly to increase the order of the base higher than 2. Thus, quadratic function of the 10 34 variables is used for the approximation. If the state space was small, the approxi- mation method that Keane and Wolpin (1994) suggested could be implemented in our paper, since their method tends to perform well in tting the data. However, when the state space is large as in this paper, the method is infeasible since their approximation function involves the next period's value function which is costly to save. Although frequently used in many applications, quadratic approximation does yield approximation errors. As Keane and Wolpin (1994) noted, any approximation errors in value functions enter nonlinearly in the conditional choice probabilities, thus cause inconsistency in the estimators of structural parameters. According to their experiment, the in-sample t of the quadratic approximation is not very consis- tent across dierent data sets, and the method can produce some biased estimates. However, as pointed out in Aguirregabiria and Mira (2010), the computational gain from using the method has allowed researchers to estimate complicated models with large state spaces, produces interesting implications, that would be otherwise impossible. 2.5 Data The data is taken from the Panel Study of Income Dynamics (PSID). The PSID started its rst survey in 1968 and has been continued over four decades. The initial sample consists of 18,230 individuals who are the members of 4,802 households. Of the 4,802 households, 2,930 are the national representative sample and the rest are 35 the low income sample from the Survey of Economics Opportunity. The survey interviews heads of household annually (bi-annually from 1997) and collects socio- economic and demographic information of their households members. Individuals who are added to a household either due to childbirth or due to adoption are also considered to be sample persons. All sample persons are followed even after they split o from the original household and establish their own families. This paper utilizes 1976-1993 survey years. Surveys after 1997 could not be uti- lized since the bi-annual data is not suitable for estimating the model with Bayesian update. Surveys between 1993 and 1997 could not be used as well because the wage of a unmarried woman who is not the head of a household (for instance, a single woman who is living with her parents) is not reported. The baseline sample of my analysis consists of women from the national representative sample who are 11 to 19 years old in 1976 survey year. Considering their ages, most of these women are daughters or granddaughters of household heads who are interviewed in the initial survey year. It is my intention to select relatively young women as my sam- ple because that way I can follow each of them from the year they leave school. Since the timing of nishing schooling is dierent across women, the resulting panel data becomes unbalanced. The nalized sample consists of 587 women and 6,637 person-year observations j . j Of the 618 women for whom I could observe the post-schooling behavior, 31 are excluded due to the following reasons: (1) 16 of them are married while they are in school; (2) 2 of them are widowed; (3) 10 of them have missing data on certain variables. 36 The achieved education level of a woman is the highest grade completed at the time she leaves school. A woman is dened to be working (work = 1) at a certain period if her annual hours of work exceeds 1,000. Once the woman is dened to be working, she is assumed to be working full-time during the given year. Thus, her annual wage earning is dened to be the average hourly earning multiplied by 2000 hours k . The annual wage earning for the husband is calculated in the same way. The woman is dened to be married if she is reported to be legally married and lives together with her husband at the time she is interviewed. The woman is dened to give birth in a certain survey year if the birth year of a children coincide with the survey year. The race is dened to be 1 if a woman is non-white and 0 otherwise. Table 2.1 summarizes the mean and standard deviation of the variables dened above. Women in my sample are on average observed for 11 years, nish schooling when they are 19 years old and attain 13 years of education. About 16% of the women are non-white, 92% of them have ever worked, and 68% of them have ever been married during the sample period l . Of the ever married, 27% of them have k The annual wage is constructed following Van der Klaauw (1996) and Sheran (2007). l The sample represents U.S. women pretty well. For example, the fact that slightly less than 70% of the women in my sample are ever married by their age 29 is consistent with 1990 CPS data. According to CPS, 69% of women who are between 25 and 29 are ever married in 1990. In addition, both 1968 and 1976 PSID survey indicate that about 15% of the households heads from the national representative sample are non-white which is consistent with my sample. 37 Table 2.1: Descriptive Statistics Variable N Mean S.D. (Freq.) Sample of 587 Individuals Years in Sample 587 11.31 3.93 Age in 1st period 587 19.12 1.93 Education 587 12.79 1.87 Race 587 0.16 (94) Ever Worked 587 0.92 (542) Experience for Ever Worked 542 7.14 3.60 Ever Married 587 0.68 (401) Marriage Duration for Ever Married 401 7.18 4.30 Ever Divorced 401 0.27 (108) Ever Gave Birth 401 0.70 (279) Sample of 6637 person-year observations Age 6637 24.71 4.12 Work 6637 0.64 (4241) Married 6637 0.48 (3173) Birth 6637 0.08 (529) Working & Married 6637 0.24 (1,594) Working & Single 6637 0.37 (2437) Not-working & Married 6637 0.16 (1,050) Not-working & Single 6637 0.15 (1,027) Wage($) 4241 17,701 9,872 Husband Wage($) 3173 25,557 16,886 Note: The annual labor income is CPI adjusted, using 1990 as the base year. 38 divorced and 70% of them have ever given birth. The average length of marriage for ever married and the average work experience for ever worked are both about 7 years. Averaging over the person-year observations, women are working about 60% of the time, married about half of the time, and giving birth about 10% of the time during the sample periods. The average wages of working women during the sample periods is a little less than 18,000 dollars, and that of husbands for married women is about 8,000 dollars higher than that. 2.6 Estimation Many eorts have been made in order to reduce the computational burden and make the estimation feasible. First, as described in the earlier section, the simulation and interpolation technique is adopted when evaluating the value function m . Second, I impose several restrictions on a woman's choice set in order to reduce the size of the state space. The list of assumptions is given as follows: (i) A woman is assumed to become biologically infertile from age 40; (ii) A marriage with duration longer than ten years is treated the same as a marriage with exactly ten years of duration n ; (iii) The maximum number of children a woman can have is restricted to three; (iv) A unmarried woman, either divorced or never married, cannot give birth; and (v) A divorced woman cannot get remarried. Among the assumptions, m See Rust (1997). n Consistent with this assumption, the learning process stops at the tenth year of the marriage. 39 the rst and second assumptions are not unrealistic. The third assumption is not very harmful since less than 4 percent of mothers have more than 3 children in my sample. The fourth assumption might not be too harmful as well, since only about 12% of women in my sample ever given birth to her children when they were not married. However, the fth assumption might be too restrictive, since almost half of ever divorced women usually get remarried according to the past research. In order for my research to have more realistic implications, the estimation should be performed after relaxing the assumption. This is left as a future task. Although ^ md t1 is a continuous variable theoretically, a discretization of it is necessary in order to draw a recursive solution of the dynamic programming prob- lem. Since ^ md t1 is dened to be a linear combination of u h t s, I discretize u h t to have only three values, low, middle and high, where their cumulative probabilities are 0.2, 0.5 and 0.8 in the standard normal distribution. I then assign each of the value the probability mass in a way that probability of observing `low' and `high' are equal to 0.3 while that of observing `middle' is equal to 0.4. Once all the above assumptions are made, the model is estimated using Simu- lated Maximum Likelihood. The likelihood consists of the probability of observing certain wages and the probability of choosing certain alternatives given relevant wages, both of which are conditioned on state variables. When constructing the likelihood, it is dicult to directly calculate the probability of choosing an alter- native because it involves a multi-dimensional integration which does not have an 40 analytic solution in our case. In order to deviate the pain of calculating the proba- bility, the paper instead simulates it. The simulation is performed using the GHK simulator o with 300 random points. 2.7 Estimation Results Table 2.2 and 2.3 present estimates of the model parameters. Starting with the female wage equation in Table 2.2, we can see that a white woman tends to receive higher wage than a non-white woman. The wage increases as a woman attains higher education level and/or accumulates work experiences. When two women have identical years of education and experience, the labor market prefers a woman with more continuous work experience; the positive eect of lagged work indicates that a woman who has been working continuously from the previous year receives higher wage than a woman who is coming back to work. In addition, the negative eect of age on wage indicates that as a woman spends more time outside of the labor market, her work is compensated less given her experience and all else being unchanged. Moving on to the husband's wage equation, I nd that being a white and attain- ing higher education raise not only the chance of earning more for a woman, but also that of marrying a man with higher wage. Also, since `hexp', a proxy for the husband's work experience, largely depends on a woman's age, the fact that it has o See Judd (1998) 41 Table 2.2: Estimates of Log-Wage Function Parameters Variable Estimate Std. Err. Women's Constant 8.1132** 0.0077 Age -0.0240** 0.0003 Non-white -0.1813** 0.0189 Education 0.1328** 0.0006 Lagged work status 0.1259** 0.0092 Experience (Exp) 0.0799** 0.0014 Exp 2 =100 0.0628** 0.0154 Error Std. Dev. 0.4668** 0.0038 Husband's Constant 8.6143** 0.0071 Non-white -0.5026** 0.0249 Education 0.0551** 0.0006 Exp 0.0165** 0.0014 hexp 0.0808** 0.0005 hexp 2 =100 -0.2270** 0.0031 Std. Dev. Of 0.3668** 0.0210 Error Std. Dev. 0.3422** 0.0033 Note: **=5% signicance level;hexp =AgeEducation 6. 42 a positive eect on male wage indicates that a husband's wage tends to increase as a woman gets older. From these results, notice that a woman's race, education and (potential) experience are performing as if they are proxies for the corresponding variables of husbands; the estimation results resembles those of a typical male log- wage equation, such as a racial dierence in wage, positive return to education, and increasing and concave experience to earnings prole. The resemblance seems to be the consequences of assortative matching and is observed in the past structural studies on women's life-cycle as well p . In addition to above ndings, the estimation results of the husband's wage equa- tion also indicate that there is a positive association between a woman's work expe- rience and her husband's wage. This result is in line with studies which emphasize the economic role of women. While traditional perspective views a woman as a homemaker and a man as a breadwinner, more recent studies on marital matching claim that the earnings and the occupational status of a woman are becoming more important in determining her position in the marriage market (Sweeney and Can- cian (2004), Kalmijn (1994), Hout (1982)). Since a woman's earnings increase as she accumulates experiences, the positive eect of her experience on her husband's p See Van der Klaauw (1996), Francesconi (2002), Sheran (2007), and Ma (2010). Past literature on marital matching has reported that people tend to marry ones that are similar to themselves in terms of ethnicity, age, educational attainment and so on (See Becker (1973), Becker (1974), Becker (1981), Jacobs and Furstenberg (1986), Mare (1991), Kalmijn (1998), Greenwood et al. (2014) etc.). 43 wage can be added as another supporting evidence of increasing importance of a woman's economic status in the marriage market. Moving on to the utility function parameters, the rst ve rows in Table 2.3 show the results for a single working woman (alternative 2). While a more educated woman draws larger utility from working, women in general experience a loss of utility from working as they get older. In addition, a working single mother would struggle more in raising a child under 6 compare to a single mother who stays at home. Interestingly, however, she tends to enjoy higher utility from working when her children are older. The next ve rows show that being married is not necessarily a more attractive option for a woman with higher education level or a woman who has a child under 6. However, it seems to be benecial for a woman who has older children, although the eect is signicant only under 10% level. Finally, similar to working, marriage becomes less and less attractive option for a woman as she gets older. When a married woman works, her period utility might not be a simple sum of utility from working and that from being married; it might be higher than the sum if her husband supports her career and lower than the sum if her two roles con ict with each other. The next ve rows in Table 2.3 presents this extra (dis- )utility generated when a married woman works. In order to derive the working married woman's utility, the extra utility should be added to the sum of utility from working and utility from being married. Once the utilities are summed up, the results indicate that while serving both roles becomes more tiring than serving 44 Table 2.3: Estimates of Utility Function Parameters Variable Estimate Std. Err. Working Constant 3,709** 1,511 Age -538** 62 Education 2,094** 120 # of children (age<6) -6,288** 2,033 # of children (6age18) 19,550** 2,995 Married Constant -23,300** 1,875 Age -296** 81 Education 237 149 # of children (age<6) 4,029 2,822 # of children (6age18) 11,134* 5,778 Working & Married Constant -14,065** 1,782 Age 0 72 Education 430** 140 # of children (age<6) -1,185 2,101 # of children (6age18) -11,715** 3,513 Married & Birth Constant -42,578** 2,127 # of children (age<6) -12,500** 2,593 # of children (6age18) -100,625** 5,230 Working, Married & Birth Constant -40,000** 3,537 Labor Entry -72,969** 2,102 Marriage 10,181** 2,418 Divorce -130,469** 2,970 Marriage Duration 1,922** 587 Error Std. Dev. 66,878** 883 Note: *= 10% signicance level; **= 5% signicance level 45 either of the roles as a woman gets older, a more educated woman is more likely to enjoy serving both roles. A possible explanation would be that educated women in general prefer to retain their career after they are married, or since an educated woman tends to marry a man who is more understanding about her career. The extra dis-utility from having an older child and the utility gain from it for a not- working married woman cancel out, a working woman draws about the same amount of utility from having an older child regardless of her marital status. As birth giving is a life-changing experience for women, the model estimates its impact on a woman's utility. The results are presented in the next four rows in the table q . For a married woman who is not working, the utility that she draws during her birth giving year is the sum of the utility from marriage and the extra utility from birth. The corresponding utility for a working married woman, however, is dened to be the sum of all the utilities that I have discussed so far, i.e. the utility from working, marriage, serving two roles, and birth, and the additional utility that a working woman bears when she gives birth. As shown in the results, having and preparing for a newborn consumes lots of energy and nancial resources, especially when a woman is working. Also, the larger utility loss from birth when having an older child than a younger one indicates that while it is dicult to have an q The table only shows the estimates of coecients that are identiable based on my data. The- oretically, the coecients on age, education and number of young and old children for alternative 5 and 6 should be identied. However, due to the low frequency of observed births in the data it was impossible to identify and estimate all those variables. 46 additional child when a young child exists in the family, postponing the decision until the child grows up does not make things better. This is probably because a woman cannot enjoy the economy of scale that she could have enjoyed when the age dierence between the newborn and the existing child is small. The estimate of labor entry cost indicates that a woman bears substantial amount of physical and mental cost when she (re-)enters to the labor market. The cost includes investment in her new work gears such as suits and shoes, time spent to adjust herself to the new environment and more importantly, any kind of diculties that she goes through during the process of job searching r . Although it is known that the process of getting married demands lots of money and energy from people who are involved, the net utility that a woman draws in the beginning of marriage is positive. In contrast, the high cost of divorce indicates that although divorce is a way to change for the better, the legal process it involves, such as reaching an agreement with regard to child custody, child support, and division of property, makes a woman exhausted through out the process. Lastly, the utility gain from being married increases as the marriage duration gets longer, thus the probability of marital dissolution decreases as the length of one's marriage increases. r Notice that the labor cost is an inferred cost, meaning that the parameter is estimated based on how frequently the entering or re-entering to the labor market happens among the women in the sample. In the case where the unemployment rate is high and involuntary unemployment is prevalent, the parameter estimate is likely to have large value indicating the diculty of job searching. 47 Before performing various counterfactual simulations based on above results, it is necessary to rst examine how well the estimated model ts the actual data. As a graphical presentation of the model t, I plot the actual and predicted proportions of women who choose each alternatives in Figure 2.5 as well as the proportions of women who choose to work, marry, or give birth in Figure 2.6. The sequences of predicted proportions are constructed in the following way: First, I categorize women in my sample based on their characteristics in the year they leave school. The characteristics are determined based on a woman's race, the years of schooling, and the age at the time she leaves school. Then for each category, I simulate 10,000 choice sequences from the rst year the women in the category leave school to the year they are last observed in the sample. Then for each year, I calculate the weighted average of these simulations where the weight is given as the year's distribution of the categories in the sample. The parameter estimates reported in Table 2.2 and 2.3 are used throughout the process. The model resembles the reality fairly well. In Figure 2.5, the gradual increase in the proportion of housewives as well as the slow decrease in the proportion of working single women are well captured by the model's prediction. Also, the model successfully predicts the initially increasing and then attening proportion of working married women although it tends to undershoot the proportion at the end of the prediction years. Since the prediction is quite close to the actual data for each of choice alternatives, it is not surprising that the model successfully predicts the percentage of working women as well as that of married women (see Figure 48 Figure 2.5: Actual and Predicted Proportions by Choice Alternatives Note: X-axis indicates years since leaving school. 2.6). Finally, despite the low frequency of observed births in the data, which made it dicult to identify the some utility parameters in the model, the model ts the overall trend of the births quite well. 49 Table 2.4: Chi-square Goodness of Fit Test Yrs since Single Married, No birth Married, Birth leaving Not working (Alt. 1) Working (Alt. 2) Not working (Alt. 3) Working (Alt. 4) Not working (Alt. 5) Working (Alt. 6) Row school Obs. A P 2 A P 2 A P 2 A P 2 A P 2 A P 2 2 1 587 0.281 0.358 14.94** 0.477 0.449 1.79 0.106 0.076 7.47** 0.099 0.074 5.34** 0.032 0.034 0.05 0.005 0.009 1.11 23.59** 2 576 0.217 0.195 1.86 0.453 0.487 2.65 0.118 0.083 8.99** 0.153 0.161 0.31 0.036 0.044 0.77 0.023 0.030 1.02 13.09** 3 569 0.172 0.150 2.26 0.413 0.454 3.90** 0.116 0.099 1.73 0.220 0.205 0.72 0.058 0.048 1.24 0.021 0.043 6.72** 13.78** 4 555 0.132 0.125 0.20 0.404 0.414 0.25 0.108 0.112 0.10 0.267 0.247 1.12 0.056 0.054 0.06 0.034 0.047 2.13 3.34 5 543 0.123 0.118 0.15 0.357 0.383 1.47 0.134 0.130 0.09 0.263 0.259 0.05 0.072 0.060 1.41 0.050 0.051 0.01 2.49 6 529 0.129 0.114 1.04 0.344 0.359 0.51 0.140 0.140 0.00 0.267 0.268 0.01 0.079 0.068 1.05 0.042 0.051 0.93 3.11 7 506 0.136 0.110 3.72 0.336 0.349 0.38 0.152 0.151 0.00 0.269 0.274 0.08 0.057 0.067 0.74 0.049 0.049 0.00 4.32 8 483 0.141 0.110 4.72** 0.317 0.338 0.98 0.168 0.168 0.00 0.280 0.279 0.00 0.062 0.064 0.03 0.033 0.040 0.66 5.51 9 463 0.121 0.108 0.81 0.339 0.338 0.00 0.199 0.180 1.05 0.233 0.280 5.06** 0.056 0.057 0.01 0.052 0.036 3.31 8.43 10 428 0.107 0.108 0.00 0.343 0.338 0.05 0.215 0.182 3.09 0.257 0.291 2.34 0.047 0.050 0.09 0.030 0.031 0.01 4.32 11 371 0.132 0.110 1.82 0.318 0.336 0.54 0.224 0.193 2.27 0.261 0.290 1.45 0.027 0.044 2.57 0.038 0.027 1.60 8.85 12 321 0.134 0.112 1.53 0.330 0.339 0.11 0.209 0.195 0.36 0.290 0.286 0.02 0.016 0.042 5.66** 0.022 0.025 0.12 7.28 13 260 0.138 0.115 1.45 0.327 0.338 0.14 0.227 0.199 1.31 0.250 0.287 1.76 0.023 0.040 1.86 0.035 0.022 1.88 7.30 14 196 0.138 0.116 0.87 0.281 0.335 2.56 0.235 0.214 0.50 0.306 0.281 0.60 0.020 0.038 1.67 0.020 0.016 0.26 5.16 15 139 0.151 0.129 0.62 0.281 0.329 1.48 0.201 0.220 0.29 0.353 0.267 5.16** 0.014 0.039 2.26 0.000 0.015 2.17 9.86 16 80 0.138 0.152 0.14 0.250 0.310 1.34 0.238 0.244 0.02 0.325 0.244 2.88 0.025 0.040 0.47 0.025 0.010 1.70 5.37 Sum 6606 0.155 0.146 3.87** 0.367 0.383 6.79** 0.158 0.144 10.74** 0.239 0.240 0.02 0.048 0.051 1.36 0.032 0.035 2.13 20.04** Note: ** 5% signicance level. A: actual proportion, P: predicted proportion. 50 Figure 2.6: Actual and Predicted Proportions - Working, Married, and Birth Note: X-axis indicates years since leaving school. Another evidence to support the model's explanatory power is given in Table 2.4. It examines for each year and choice alternative how congruent the actual and predicted choice frequencies are using chi-square goodness of t test. The results show that while the data and the prediction tends to disagree in the beginning of the observation year, this disagreement disappears for the later observation periods s . Overall, the model's prediction is a good approximation of the reality. A nal note on the role of learning is given before closing the section. In order to examine how learning improves the model's explanatory power, I compare the s Notice that sample size decreases towards the end of the observation period. Since the test is sensitive to the scale of observation, although the dierence between actual and prediction is relatively large at the end of the observation period (as shown in the above two gures), the dierence might not be statistically signicant due to the scale eect. 51 t of my model to that of the model without learning. The dierence between the two models is that the no-learning model treats the error term in the male wage equation (equation (2.8)) as a pure noise, thus assumes that a woman does not adjust the projection of her husband's wage stream even after she marries. In order to perform goodness of t test for the no-learning model, I rst set the parameter values in the no-learning model the same as those in the learning model except the variance for the male wage equation. The variance is then replaced by the sum of the variances of husband's ability and that of the noise in the learning model. Once the parameters values are given, I simulate the choice sequences for the no-learning model, and construct Chi-squared test statistics based on the simulated sequences for each observation year. Table 2.5 presents the test results for the model with and without learning. It shows for each model the distance between the actual and predicted proportions of women who are married, working and giving birth over the observation periods. As we can see, the learning improves the model t, particularly the t of the proportion giving births, meaning that a woman greatly considers her husband's \ability" in making her birth decision t . In order to further examine the role of learning, I perform a nested model test. The log-likelihood of the model with learning is 8968.7, while that of the model without learning is 8940.9. The likelihood test t The nding is in line with Rossin-Slater (2012) who claimed that women tend to be sensitive to their partner's quality as a father, which implies a close relationship between a woman's fertility and her husband's quality. 52 Table 2.5: Goodness of Fit Comparison - With or Without Learning Years since With Learning Without Learning leaving school Working Married Birth Working Married Birth 1 5.50** 9.04** 0.48 11.66** 0.86 21.72** 2 6.49** 0.35 1.81 1.49 2.60 24.28** 3 6.53** 0.84 1.01 1.30 1.30 17.54** 4 0.05 0.04 0.72 1.04 1.98 9.25** 5 1.22 0.86 0.70 0.07 0.02 4.12** 6 1.60 0.00 0.02 0.95 0.50 5.63** 7 0.76 0.38 0.40 0.56 1.52 2.13 8 1.70 0.18 0.44 2.40 0.89 1.46 9 1.83 0.38 1.14 3.51 1.04 6.41** 10 1.63 0.04 0.09 4.54** 0.26 1.04 11 2.08 0.02 0.23 6.30** 0.15 0.35 12 0.10 0.22 4.54** 1.42 0.32 1.87 13 1.44 0.17 0.07 3.53 0.18 0.08 14 0.51 0.84 0.66 1.17 0.97 0.35 15 0.27 0.38 4.34** 0.04 0.53 3.71 16 0.43 1.79 0.00 0.26 2.09 0.01 Sum 11.23** 1.31 3.50 6.95** 4.24** 10.01** Note: ** 5% signicance level. 53 statistics is2 (8940:9 8968:7) = 55:6 which is greater than the critical value of the chi-square distribution with 5% signicance level and 1 degree of freedom. Therefore, I conclude that the inclusion of learning helps improve the model t. 2.8 Policy Simulations As mentioned earlier, the relative option value of working compare to marriage and the degree of post-divorce hardship that a woman bears largely vary by the cultural or social environment. Since observed decisions of a woman can be though as an outcome of her eorts to maximize her utility stream given the circumstance, her decisions would depend on the environment. In this section, I examine the eects of various social policies on a woman's choices by simulating her choices under the new policy. The paper exploits the merit of structural dynamic approach by tracking a woman's responses to a policy change over a period of time, rather than checking it at a specic point in time. This allows me to observe the change in the timing of divorce as well as changes in labor supply and fertility behavior for a prolonged period before divorce. The procedure of constructing simulated choice sequences is similar to that of constructing predicted proportions which is described in the previous section. In- stead of selecting a specic category of women as a subject of simulation, I maintain the sample distribution of categories and perform simulation on it u . Thus, my paper 54 is interested in what happens to the population of women that has the distribu- tion of characteristics the same as my sample distribution when a new policy is implemented. The policies that are examined in this section are as follows: (i) Reduction of the labor entry cost to 50% of its baseline level, (ii) Reduction of the divorce cost to 50% of its baseline level, (iii) $5,000 increase in the female annual wage, and (iv) Annual subsidy of $3,000 per child for a single mother. The rst and the third policies represent the changes in social environment regarding a woman's labor market opportunities. The other two policies represent the changes in social environment regarding divorce. The simulation results are summarized in Table 2.6 and Figure 2.7 to 2.9. The rst scenario deals with the case where the labor entry cost is reduced to 50% of its baseline level which is equivalent to about $36,500 increase in utility for a woman who is (re-)entering to the labor market. Recall that the cost involves hurdles of any kind that prevents a woman from returning to work, such as the diculties that come from job searching process. Thus, such policies as creating jobs (although it does not specically target women) or subsidizing rms for hiring a woman who comes back from prolonged maternity leave would be examples of policies that substantially decrease the labor entry cost v . u However, some of the past studies used a target category as a subject of their simulation. For example, Van der Klaauw (1996) used an 18-year-old white woman who nished high school and does not live in south as a target type. 55 Table 2.6: Policy Simulation Results Single Mom (1) (2) (3) (4) (5) Baseline Labor Divorce Wage All Working Experience 9.57 -0.43 0.40 0.65 0.13 0.17 Ever married 93.62 -0.15 3.13 -1.72 0.81 0.59 Among ever married: Ever divorced 39.36 -3.06 36.64 6.17 11.78 8.61 Age at marriage 23.50 0.03 -0.66 0.41 -0.50 -0.36 (i) Never divorced 24.58 -0.12 0.86 0.96 0.47 0.35 (ii) Divorced 21.84 0.05 0.18 0.11 -0.79 -0.64 Pre-marriage exp. 3.14 -0.11 -0.47 0.47 -0.34 -0.25 (i) Never divorced 3.79 -0.22 0.51 0.87 0.20 0.15 (ii) Divorced 2.13 -0.05 0.02 0.21 -0.48 -0.39 Ever had a child 69.38 1.47 -8.94 -5.59 4.73 3.37 (i) Never divorced 75.32 0.68 -5.50 -5.60 -1.86 -1.34 (ii) Divorced 60.23 1.60 -2.75 -3.53 14.50 11.19 Number of children 1.88 0.00 -0.13 -0.08 0.02 0.02 (i) Never divorced 1.93 0.00 -0.07 -0.09 -0.07 -0.05 (ii) Divorced 1.79 0.00 -0.09 -0.06 0.15 0.14 Mar. dur. at 1st child* 2.53 0.00 -0.49 -0.11 -0.30 -0.22 (i) Never divorced 3.02 -0.06 0.09 0.00 0.09 0.09 (ii) Divorced 1.60 0.04 0.04 -0.05 -0.19 -0.16 Among ever divorced: Marriage duration 5.15 0.10 -0.44 -0.49 0.16 0.19 Mar. dur.>1 80.95 0.31 -2.54 -2.59 5.09 4.04 Mar. dur.>2 66.66 0.48 -3.80 -4.29 6.85 5.51 % Working (rate of4) ** divorce -1 yr 67.84 -7.49 -2.39 2.29 -5.60 -2.56 (10.82) (5.20) (8.27) (10.28) (12.13) (14.04) divorce -2 yrs 62.27 -5.29 -0.57 3.06 -4.55 -2.65 (1.71) (-0.69) (2.05) (2.27) (3.98) (4.13) divorce -3 yrs 61.22 -3.85 -0.76 2.38 -5.71 -3.97 % Birth (rate of4) ** divorce -1 yr 12.22 0.12 1.63 1.04 7.06 4.60 (-39.46) (-38.27) (-36.14) (-36.75) (-36.25) (-39.08) divorce -2 yrs 17.32 0.86 1.32 1.18 8.76 6.05 (-14.18) (-9.03) (-14.04) (-11.73) (-13.78) (-15.33) divorce -3 yrs 20.18 -0.19 1.50 0.78 10.06 7.42 Note: The baseline column shows the predicted values when the simulation is performed based on the estimated model. The rest of the columns display the baseline prediction subtracted from the prediction under the relevant policy except the rows that contain `rate of4'; *Calculated only for women who ever had a child; **Calculated only for the divorced whose marriage duration is longer than 2 years (md>2). Rate of changes is dened to be the percentage change since 3 years before divorce. 56 Figure 2.7: Simulated Proportions by Choice Alternatives Note: X-axis indicates years since leaving school. 57 When the labor entry cost is reduced and returning to work becomes easier, a woman can manage her career path more exibly. This improved exibility gives a married woman chances to better serve her family duty without forgoing her career. The woman is more likely to put her optimal family plan into practice when she is young, thus a planned childbirth is less likely to be forgone or delayed. Consequently, the overall divorce rate decreases by 3%, the proportion of women who have ever given a birth increases by 1.5%, and, the timing of birth tends to concentrate more towards the peak time of the baseline model as shown in Figure 2.8. Meanwhile, as it becomes less of a burden for a woman to take maternity leave or to temporarily quit her job, more women choose to become fulltime mothers when their children are young. As a result, the labor participation of women becomes lower during this period which leads to a severe loss of female labor force during the same period. However, ease of returning to work draws more women to the labor market as their children grow up, and this leads to the higher labor participation rate for the middle age women (See Figure 2.8.). Lastly, regarding pre-divorce behavior, a fulltime housewife with a high probability of divorce can now concerns less about her post-divorce livelihood, thus the tendencies to nd a job before divorce and to avoid childbirth before divorce both become slower as shown in Table 2.6. v Although the model does not distinguish the (re-)entering cost for a mother from the cost for a woman without children, reducing the cost for mothers would lead to a substantial de- crease in overall (re-)entry cost, since one of the main reasons for female career discontinuity is childbearing/childrearing (See Blau and Kahn (2013) and Bertrand et al. (2010)). 58 Figure 2.8: Simulated Proportions - Ever Mar'd/Div'd, Working and Birth Note: X-axis indicates years since leaving school. 59 The second simulation investigates the consequences of reduced divorce cost. The cost includes any kinds of mental and pecuniary damages that arise from mar- ital dissolution which range from the sense of loss to the expenditure on legal pro- cessing of divorce. Thus, a cultural change such as the lowered level of stigma on divorcees and the change in legislation from mutual-consent to unilateral divorce law are good examples of the lowered divorce cost. A woman becomes relatively less tolerant of marital con icts once the divorce cost is reduced, thus more women decides to divorce at the earlier stage of their marriages; therefore, about three quarters of marriages end in divorce, and the average duration of these marriages becomes 5 months shorter (See Table 2.6). Now, higher risk of divorce and lightened weight of marital commitment bring several side eects to the society: First, it makes a young single woman to become more hasty in entering into a marriage, which result in increasing marriage rate and lowering the average age at marriage. Second, since a marital relationship is not as stable as before, a woman tends to reduce her investment in the so-called `marital-specic capital', meaning she avoids having kids and refuses to be a housewife during the period she is married; the 9% decrease in the proportion of women who ever had a child in Table 2.6 and the higher proportion of working married women in Figure 2.8 supports this idea. However, since a woman expect less negative shock from divorce, her precautionary motive becomes weaker, thus the tendencies to increase labor participation and to avoid childbirth before imminent divorce becomes slower. 60 When the average female wage increases, it makes working a more attractive option for women. Thus, women tend to work more regardless of their marital status, and this results in 8 month increase in the average work experience. As the relative gain from marriage decreases, a woman has less incentive to remain married which leads to 1.72% decrease in marriage rate, 6.17% increase in divorce rate as well as a half year decrease of the average marriage duration. Also, a woman tends to postpone marriage by 5 months on average and devotes this time to her career so that the pre-marriage experience increases about the same amount of time. The lowered marriage rate and shortened marriage duration naturally induces lower fertility rate, thus the percentage of women who ever had a child decreases by 5.59%. However, since now women work more and receive higher wage in general, women with high risk of divorce tend to concern less about their post-divorce lives, so that their tendency to avoid having a newborn and to increase labor participation before imminent divorce becomes slower. The last scenario deals with the case where the government provides single mothers with subsidies. The policy can be thought as a way to support poverty population considering the fact that the large proportion of the population consists of households headed by single mothers (Duncan and Homan (1985)) as well as a way to lower the cost of divorce. The paper compares eects of two dierent policies, subsidizing all single mothers versus subsidizing working single mothers only, in order to address the concern that the former might discourage a woman's 61 willingness to work. In both of the cases, a single mother is assumed to be subsidized with $3,000 for each of her child a year. In the scenario where single mothers are provided with subsidies regardless of their labor force participation, both the marriage and divorce rates increase since the subsidy dilutes the negative shock from divorce. However, since the policy is favorable to women with kids, dierent from the reduced divorce cost case, the proportion of women who have ever given birth increases. Here, a point worth noticing is that there is some degree of asymmetry in the proportion ever given birth between the divorced and the never divorced; while the proportion increases for the divorced, that of the never divorced decreases. A possible explanation would be that since the concern about child support has been mitigated due to the subsidy, mothers who were hesitant to divorce in the previous regime now decide to divorce. In other words, the asymmetry in women's behavior is induced by the asymmetry in the policy. The policy has some interesting implications on women's pre-divorce behavior; since the policy is biased towards mothers, the tendency to avoid giving birth before imminent divorce weakens, thus the deceleration of pre-divorce fertility becomes slower in the given scenario than in the baseline case. Meanwhile, as the proportion of mothers consisting the group of divorced women increases, the group's sense of responsibility towards its post-divorce life becomes stronger, which gives them more incentive to work. Therefore, women tend to accelerate their pre-divorce labor force participation faster than the baseline level, which leads to higher labor participation 62 Figure 2.9: Simulated Proportions - Subsidy for Single Mothers Note: X-axis indicates years since leaving school. 63 rate of single women towards the end of the simulation periods as shown in Figure 2.9. When the subsidy is given to single mothers conditional on their labor force participation, women need to meet more conditions in order to receive the subsidy. This gives women less incentive to change their behavior. Thus, although the di- rection of changes in women's behavior is the same as that of the above policy, particularly for the marriage and divorce rates, the overall fertility rate and the asymmetry in fertility between the divorced and the never divorced, the magnitude of these changes are smaller. Similarly, since women are less beneting from giving birth before divorce in this scenario than the above, the rate of decelerating pre- divorce fertility is smaller. However, the additional condition does give women the incentive to work more, thus the proportion working under this policy is consis- tently higher (see Figure 2.9), and the speed of accelerating pre-divorce labor force participation is faster in this scenario than in the above scenario. 2.9 Conclusion This paper focuses on analyzing how a woman's sequence of decisions varies depend- ing on the social environment. Acknowledging the fact that the a woman makes decisions on her marital status, fertility and labor supply considering their eects on her lifetime utility, the paper uses a structural dynamic model as a tool of analysis. In the rst part of the paper, the goal is to construct and estimate a model that resembles the existing data on women's labor supply and family structure. In order 64 for the model to t the data better, the paper assumes a woman to be a Bayesian learner of her husband's unobserved economic ability. The assumption adds a more realistic aspect to the model as it allow a divorce to be a gradual process rather than a sudden unexpected event. The estimation results indicates that my model successfully ts the data, and that Bayesian learning plays an important role in tting women's birth giving pattern. In the second part of the paper, I perform several counterfactual experiments based on the estimated model. Four of the policies which represent the changes in the labor market opportunities for women as well as the changes in the society's attitude to divorce are examined. In the rst scenario where the labor market (re- )entry cost is reduced, a woman is able to manage her career path more exibly, thus can freely allocate her time between her family duty and her career. As a result, the marriage becomes compatible with career, thus the family related statistics improves, i.e. fertility rate increases and divorce rate decreases. Also, the drastic changes in women's pre-divorce fertility and labor force participation tends to slow down, implying that the ease of nding a job makes a woman less concerned about her post-divorce living. The changes in women's fertility and labor force participation behavior before divorce are also less drastic in the second and the third scenarios where the divorce cost is reduced and the female wage increases. However, women tend to invest less on her marital-specic capital during the marriage in both scenarios, i.e. they tend to avoid having children and becoming housewives. This is because: (i) the reduced 65 divorce cost makes marriage a less stable institution in the second scenario, and (ii) the increased female wage makes a marriage a less attractive option for a woman in the third scenario. In the last scenario where all divorced mothers are subsidized, due to the fact that the policy is biased towards women with children, the overall fertility increases and the deceleration speed of pre-divorce fertility decreases. Reduced concern about post-divorce child support induces more mothers to divorce, thus the proportion of mothers among divorced women increases. Since mothers have stronger incentive to work than women without children when husbands are not present in the house- holds, the pre-divorce labor force participation accelerates faster, and the proportion working among divorced women increases compare to the baseline scenario. There- fore, by taking advantage of a maternal instinct, the policy increases the labor force participation of divorced women without providing any explicit stimulus to work. 66 Chapter 3 Marital Mobility and the Characteristics of Successive Husbands 3.1 Introduction A woman tends to experience a substantial decrease in her economic status following divorce. One way to resolve this post-divorce nancial diculty is to remarry. Indeed, a divorced woman's nancial situation largely improves after remarriage; her family income and her family income-to-needs ratio recovers according to past studies. However, this does not necessarily imply that the economic status of her new husband is the same as that of her rst husband. Although the economic status of a second husband would be of particular interest for a divorced woman, this issue 67 has not been directly addressed in the past literature. This study attempts to ll this gap by focusing on the comparison of the two husbands' economic status. A proper way to address the issue requires comparing the two husbands at the same life stage. However, since a rst husband is not tracked after divorce, a second husband, who is observed only after remarriage, is likely to be observed at an older age. Even if the two husbands are assumed to be simultaneously observed, they are likely to be from dierent age groups and thus at dierent stages of life. In order to avoid any obscurity that comes from age dierence, the two husbands' wages are compared after controlling for their ages. The empirical results suggest that the current spouse of a remarried woman is economically less competent than her previous spouse; the subsample of women who consistently marry men of the same age are responsible for this downward mobility. Meanwhile, a woman who is exible about her husband's age and is willing to match outside of her age group avoids this economic loss. This implies that the marriage market faced by divorced women is not as good as the one that they encountered when they have never been married; the men who are available for remarriage in their age group have low economic status. Searching for a spouse outside of the age group typically allows a woman to equal her previous husband's economic status, but not surpass it. In the second half of the paper, I investigate the associations between the two husbands' wages controlling for women's observable characteristics. In particular, I decompose wages into the part that is predicted and unpredicted, and examine their 68 self- and cross-association between the two husbands. The predicted wage is con- structed based on a husband's observable traits, such as his education, occupation, experience, and race, and can be thought as his earning potential. The unpre- dicted wage, on the other hand, is the gap between the realized and the potential wage, which varies depending on the husband's characteristics that are unobserved. Unobserved traits might include his diligence or time devoted to extra work. By analyzing the associations between the two dierent parts of wages, this paper ex- amines how women's preferences for observable and unobservable characteristics persists/changes between marriages. The empirical results exhibit a positive self-association for both of the predicted and unpredicted wages; this supports the idea that the women's preferences for each type of traits persists. However, a unexpected nding is that the cross-association between the rst husband's predicted wage and the second husband's unpredicted wage is the strongest among all the associations. In other words, women who married men with higher wage potential (due to higher education and/or better occupation) are now remarrying someone with a higher realized wage. This robust cross-association might be evidence that women prioritize their husbands' multi- dimensional characteristics. The outline of this paper is as follows: The next section reviews past studies. The third section explains the empirical strategies and is followed by a summary of the data and the variables. The fth section compares wages of remarried women's 69 successive husbands and examines the association between their wages. The last section summarizes the ndings and concludes. 3.2 Literature Review 3.2.1 Comparison of the Two Husbands' Wages Past studies have found a decline in women's economic status following marital dissolution, and a large recovery of it following remarriage a . While the family income and the income-to-needs ratio of intact marriages increase over time, women who divorce typically experience 30 percent decrease in the family income, and more than 6 percent decrease in the income-to-needs ratio following divorce (Homan (1977); Duncan and Homan (1985); Weiss (1984); Weitzman (1985); Homan and Duncan (1988)). However, for the women who remarry within 5 years, both their family income and income-to-needs ratio were comparable to those of intact couples (Duncan and Homan (1985)). This implies a large contribution of husbands income on the women's economic status through its contribution to the family income. The importance of husband income to family naturally lead us to the next question: what would the second husbands' economic status be like compare to that of the rst husbands? Since the information on the composition of the family a Of course, the selection bias issue exists. Using Heckman's two-stage method (Heckman (1979)), Duncan and Homan (1985) showed that the gain from remarriage is not as large for the women who did not remarry as for the women who remarried. 70 income is unavailable, the above studies cannot provide a direct answer to this question. For example, it is possible that the pre-divorce family income is solely contributed by the husband's income, while only the half of the post-remarriage family income is contributed by the husband, and the other half is the women's labor income. In this case, even though the family income is recovered to pre- divorce level after remarriage, the second husbands are in fact, economically less competent than the rsts. While the focus was more on occupational status rather than income, two past studies were interested in the comparison of the two husbands: Mueller and Pope (1980) as well as Jacobs and Furstenberg (1986). Mueller and Pope (1980) compared the occupational status of the two husbands directly and concluded that about 50 percent of the women in the sample experienced upward mobility, and only 20 percent of them experienced downward mobility. However, Jacobs and Furstenberg (1986) pointed out that a high percentage of the upward mobility is due to the fact that remarriages occur later in life, thus the second husbands are older and in a later stage of career development than the rst husbands. They asserted that a proper comparison should control for this dynamic career trend. In their analysis of young women (using NLSYW), they found that the dierence in the occupational status between two husbands is roughly the same as the career change that a man would experience between the rst husband's average age and the second husbands' average age. They did a similar analysis on the mature women (using NLSMW), but their analysis was not as rigorous as their analysis on the young women, and this 71 will be discussed below. Based on their empirical results, Jacobs and Furstenberg (1986) asserted that after an adjustment for age and career trend, women actually experience neither upward nor downward mobility between their rst and second marriages. What was not accounted for in Jacobs and Furstenberg (1986) is the possibility that the two marriages are not identical in terms of their spousal age gap. Assume that the average age of second husbands is 50 and the average time gap between the observation of rst and second husbands is 10 years. Then, in their analysis of mature women, Jacobs and Furstenberg (1986) compares the average dierence in the two husbands' occupational status to the average men's career change between 40 and 50 b . This means they are implicitly assuming the rst husbands to be 40 at the time of the observation. However, there is no guarantee that this assumption will hold, and a violation of this assumption will change the implication of their results. For example, assume that the rst husbands were actually younger than 40, say 35, and the average dierence between two husbands coincides with the average increase in occupational status between 40 and 50. This result indicates that women are actually downward mobile in the second marriages since the career improvement that usually happens in 10 years is now happening in 15 years. Therefore, in order to check whether the conclusion in Jacobs and Furstenberg (1986) is valid, it is necessary to see whether the two marriages of remarried women are identical in terms of their distribution of spousal age gap. b Their analysis of young women does not suer from this issue 72 However, it turns out that the distributions of spousal age gap in the rst and second marriages are not identical. Empirical evidence from past studies have reported larger age discrepancy between spouses in the second marriages of twice married women (Dean and Gurak (1978), Jacobs and Furstenberg (1986), Gelissen (2004), and Shafer (2013a)). The sample of twice married women in the National Longitudinal Survey of Youth 1979 (NLSY79), which will be the subject of our analysis, also adds support to this idea. From Figure 3.1, we can see that women are less likely to be matched to the same age men in the second marriages; while more than 60 percent of rst marriages are the same age match, less than half of the second marriages are the same age match c . In addition, the age dierences in the second marriages tend to be larger than the rst; In Figure 3.2, the left tail is thicker for the second marriage than the rst. While it is not very clear from the graph, the right tail shows the same pattern; the number of cases where the husband is more than 20 years older than the wife is 5 for the rst marriages, while it is 19 for the second marriages. A statistically more rigorous comparison of the two distributions yields the same conclusion; the mean and standard deviation of the spousal age dierence in the rst marriage are 3.18 and 3.99, and those of the second are 2.22 and 6.35. Both the mean and the standard deviation of the second marriage are statistically signicantly dierent from those of the rst marriages. c The same age match is dened to be the match where husbands are no more than 3 years older or 2 years younger than wives. The result was robust to the denition of the same age match. 73 The discordance of the two distributions of spousal age gap indicates a need for reinvestigating the woman's marital mobility between her two marriages. Figure 3.1: Age Matching Patterns in First and Second Marriages In addition, changes in age matching pattern may have in uence on the women's marital mobility. It is likely that the marriage market faced by older, divorced women is more constrained than the market that a young, never-married woman encounters. Thus, women in a more constrained market are more likely to be exible to certain traits of husbands that are less important and this may contribute to the larger variance in age matching in the second marriage. Therefore, in this paper we will examine whether the age matching pattern is associated with women's marital 74 Figure 3.2: Age Dierences Between Spouses in First and Second Marriages mobility. This will be accomplished by grouping women by their age matching pattern in the rst and second marriages, and comparing the marital mobility across dierent groups. Therefore, in the rst part of this paper, I will reinvestigate women's marital mobility. The paper improves the previous studies in two ways; First, the analysis contained in this paper is statistically more rigorous than the previous studies. In adjusting for the career trend, we perform it in a way that is invariant to any assumptions on the distribution of spousal age gap. This can be done by directly comparing the husband of each order to its same age counterpart in the NLSY79 male sample. In addition, since the major concern of this part is the changes in matching pattern between two marriages and their association with women's marital 75 mobility, I examine the marital mobility by age matching pattern in the rst and the second marriages. Any comparison in this paper will go through the statistical test of mean dierence to yield more convincing conclusion on the women's marital mobility. This test was not included in Jacobs and Furstenberg (1986). Second, while only Duncan's SEI score and the education were the variables of interest in Jacobs and Furstenberg (1986), this paper examines the marital mobil- ity in terms of various measures of socio-economic status, such as wage, and ve dierent measure of occupational status. The primary concern of this paper is to compare the two husbands' hourly wage, which is a measure of their economic status. It will be followed by the comparisons of the various dimensions of two hus- bands' occupational status not only because they are meaningful as they are, but also the systematic dierences in the two husbands' occupational status are likely to be associated with the dierence in their wages. In addition, it is likely that ob- servable characteristics of husbands other than occupation, such as their education or age (a proxy for experience), are associated with their wages. To see whether collective dierences in the two husbands' observable characteristics contribute to their wage dierence, we construct a predicted wage for each husband based on his observable characteristics and compare it between the two husbands group. 76 3.2.2 The Associations between the Two Husbands' Wages Following the pioneering work by Becker (1973), researchers have been studying the matching in the rst marriages. Assuming each individuals to maximize their con- sumption of home-production, Becker (1973) argued that it is optimal for couples to match assortatively in general, treating most of the traits as typical comple- ments d . Indeed, empirical evidence supports his idea; Both Becker (1981) and Ja- cobs and Furstenberg (1986) found strong degrees of assortative matching in terms of education and age. Mare (1991) found that the degree of educational assorta- tive matching increases between 1930s and 1980s in the U.S., once the time gap between school leaving and marriage is adjusted. Kalmijn (1998) reported that American immigrants, such as African-Americans, Asians, and Hispanics, tend to show a strong tendency to marry someone in the same ethnic groups. In his other research, Kalmijn (1994) also found that people tend to match others with similar occupation where the similarity is dened based on the level of education that a occupation requires. d An exception is the wage rate, since the advantage of the division of labor is greater as the spousal wage dierence is larger. However, Oppenheimer (1988) argued that as the proportion of women who participate in the labor market increases, their value in the marriage market depends on their socio-economic status more, which implies the positive assortive mating in terms of wage rate. Indeed, Sweeney and Cancian (2004) found that women's earnings became more important in the marriage market in determining their husbands economic ability. 77 The relatively strong degree of sorting in terms of observable characteristics in the rst marriage has certain implication on the women's economic gain from the rst marriages; Dene the gain from marriage as the husband's wage, then the gain's function that represents the association between women's observable characteristics and their husbands' wage will resemble that of male wage equation. For example, given the positive sorting and the well-known positive association between educa- tion and wage, the gain from marriage for a woman who has higher educational achievement is likely to be higher than that of low educational achievement woman. Past studies which constructed the women's marital decision model exploited this implication, and assumed that women in their model predict their (potential) hus- band's future wage stream based on their own observable characteristics (Van der Klaauw (1996), Francesconi (2002), Sheran (2007)). Compare to rst marriages, however, second marital matches are less assortative. According to Jacobs and Furstenberg (1986), the spousal correlations in terms of education, age, and occupational status are lower in the remarriage than in the rst. Dean and Gurak (1978) also found that the degree of homogamy decreases in the second marriage compare to the rst in terms of age, education, and religion. Thus in the higher order marriages, the implication that we derived from above becomes weaken, and the observable characteristics of women are likely to be less associated with the marital gain. The weakened association between the gain and the observable characteristics of women in the higher order marriages bring to the forefront the relative strong 78 association between the gain and women's unobservable characteristics. There- fore, in the second part of this paper, I will investigate the association between a woman's unobservable characteristic and her gain from remarriage. Controlling for the women's observable characteristics, the variation in the gain from rst marriage is thought to be associated with women's unobservable characteristics. Thus, I will use the gain from rst marriage as a proxy of women's unobservable characteristics, exploiting the fact that the wage data of both husbands is available for every woman in our sample. What is unique about this paper is that I separate both gains from rst marriage and remarriage into predicted and unpredicted values. Here, the predicted gain is constructed based on the husband's observable characteristics, and the unpredicted value is dened simply as a residual. The reason behind the decomposition of the gain from rst marriage is to distinguish the women's unobservable characteristics that aects the spousal matching on observable characteristics from the other unob- servables. For example, the decomposition allows us to separate women's preference toward men's education achievement from their preference toward men's extra work hour schedule. Since the role of unobservable characteristics is largely unknown in this issue, I hope this paper helps better understand the association of dierent types of women's unobservable characteristics and their gain from remarriage. However, the predicted and unpredicted gain from rst marriage may take dier- ent channels in their association with the gain from second marriage. For example, since the predicted gain from remarriage is determined by a woman's matching 79 pattern in terms of her observable characteristics, it is likely to be associated more with the predicted gain from rst marriage than the unpredicted gain from it. The same logic applies to the unpredicted gain from rst and second marriages. Thus, I regress the predicted gain from remarriage on the two dierent types of unob- servables, do the same for the unpredicted gain from remarriage, and compare the results of the two regression estimations. 3.3 Empirical Strategy The relative productivity of the two husbands is compared in the following way: For each woman in the sample, we observe her rst husband at divorce and her second husband at remarriage. For woman i, denote her rst husband's age at divorce as A 1i and his wage at divorce as Y 1i . Similarly, her second husband's age and wage at remarriage is denoted asA 2i andY 2i . Then, by averaging over the whole sample, we get the average age of rst and second husbands ( A 1 and A 2 ), and their average hourly wages ( Y 1 and Y 2 ). Meanwhile, using the male sample from NLSY79, we construct the benchmark wage trajectory. We sort the sample men based on their age, and calculate the mean of the wage for each age group. The constructed wage trajectory ranged from age 18 to 54. We denote the average wage of male who are 'a' years old as Y a M . Now, once we have the wage trajectory, we compare the dierence between Y 1 and Y 2 to the dierence in wages between age A 1 and A 2 from the wage trajectory, 80 and test whether the two dierences are statistically dierent. More specically, I test the following null hypothesis: H 0 : Y 2 Y 1 = Y A 2 M Y A 1 M (3.1) The same logic applies to the comparison of two husbands' occupational status, and the comparison across dierent age matching groups. The second part of this paper will investigate the association between the gain from second marriage and the two types of women's unobservable characteristics. Since my study is one of the earliest in this matter, we take reduced form approach rather than a structural one. Denote Y 2i as a woman's gain from remarriage which is equivalent to the second husband's hourly wage at remarriage, X i as the set of women's observable characteristics, and W i as the set of women's unobservable characteristics. We assume that Y 2i is a function of X i , and W i e . Although we cannot directly observe W i , by the availability of rst marriage data, we can use Y 1i as a proxy of W i , where Y 1i is the hourly wage of rst husband at divorce (see Duncan and Homan (1985), and Jacobs and Furstenberg (1986)). For now, the set of women's unobservable characteristics is represented by only one variable Y 1i , thus what Y 1i captures is the mixture of association between the gain from remarriage and various unobservable characteristics. However, a subset of e Of course, there is a selection issue since we do not observe the data from women who chose not to remarry. This issue should probably be dealt with as a sensitivity check. 81 women's unobservable characteristics may have dierent association with the gain from remarriage than the the rest of unobservable characteristics. For example, a woman's preference towards her spouse's education may have larger (smaller) association with the gain from remarriage than her preference towards her spouse's hard working. Thus, we divide the set of women's unobservable characteristics into two categories, one with the characteristics that in uence women's matching with respect to observable traits, and the other with the rest of the unobservable characteristics. The above idea of decomposition is realized in the following way: We decom- pose the gain from rst marriage, Y 1i , into predicted and unpredicted value. The predicted value is constructed using the rst husbands' observable characteristics, such as their age, race, education, and occupational mean wage f . The unpredicted value is simply dened as the predicted value subtracted from Y 1i . Denote ~ Y 1i as the predicted value, and " 1i as the unpredicted value (" 1i = Y 1i ~ Y 1i ). Then, we treat ~ Y 1i as a representative of woman i's unobservable characteristics that in u- ence her matching with respect to observable traits of her husband, and " 1i as a representative of rest of her unobservable characteristics. Then, the rst equation of our interest can be written as: Y 2i = 0 1 X i + 2 ~ Y 1i + 3 " 1i +u i : (3.2) f Since the race of a respondent's spouse is largely missing in NLSY79, I substitute it with the woman's race. 82 However, the two types of women's unobservable characteristics may take dif- ferent channels in their association with the gain from remarriage. For instance, a woman's preference on her spouse's education, which is captured by ~ Y 1i , may only in uence her educational matching in the second marriage, thus is associated only with the predicted gain from remarriage, and not with the gain that is unpredicted. In order to examine whether this is true, I decompose the gain from second marriage using the same method that was used to decompose the rst marriage gain, and separately estimate the following two equations: ~ Y 2i = 0 11 X i + 12 ~ Y 1i + 13 " 1i +u 1i (3.3) " 2i = 0 21 X i + 22 ~ Y 1i + 23 " 1i +u 2i (3.4) where ~ Y 2i and " 2i represent the predicted and unpredicted gain from remarriage, respectively. 3.4 Data The data was obtained from the 1979-2010 waves of the NLSY79. The NLSY79 is a well known panel study which consists of 12,686 nationally representative men and women who were born between 1957 and 1965 in the United States. The respon- dents were followed annually from 1979 to 1994, and biannually thereafter. The 83 survey collected various kinds of information, including demographic characteris- tics, educational attainment, employment history, as well as marital history. If a respondent was married at the time of interview, his/her spouse's information was also recorded in the survey. This paper used the sample of (at least) twice married women whose rst and second husbands were observed during the survey period. Since the survey obtained spouses' data from respondents and not directly from the spouses, the information of spouses was less meticulously recorded than that of respondents. In many cases, women were unable to, or refused to report their husbands' wage or hours of work. This was the major hindrance when constructing the sample since the sample size of twice married women was already small. In order to keep the sample size as large as possible, a woman was included if for each of her two husbands, the wage and the work hours are observed at least for a year. The total sample consisted of 797 women. The hourly wage, which is a measure of a husband's economic ability, was con- structed by dividing his annual labor income by annual work hours. Here, the annual labor income is the sum of the wage income and the income from the farm or the business, which is then adjusted for in ation using Consumer Price Index where the base year is 1990. Since the NLSY79 recorded the annual work weeks and the weekly work hours for a spouse, the annual work hours was constructed by their product. Various measures of occupational status, such as the Hauser-Warren Socio-Economic Index (HWSEI), the Nam-Powers-Boyd Occupational Status Score (NPBOSS), the Occupational Education Score (EDS), the Occupational Earnings 84 Score (ERS), and the occupational mean hourly wage were constructed based on the 1990 occupational classication system. Since the NLSY79 recorded occupations based on 1970 classication system until survey year 2000, and use that of 2000 thereafter, the NLSY79 occupation code was synchronized into 1990 classication rst, and then translated into each of the above occupational indices g . For the occu- pational mean hourly wage, the labor income and the annual work hour data were drawn from 1% sample of 1990 census, and averaged over each occupation. The 1% sample of 1990 census data and the information necessary for synchronization were obtained from IPUMS-USA. The hourly wage, the occupational status, and other observable characteristics of a husband, such as his age, and education, were then extracted from the year of divorce and that of remarriage for the rst and second husband, respectively h . Since the sample women did not report their rst husbands' work related variables after their separations in most cases, the hourly wage at the time of separation was used instead when the timing of the divorce and that of the separation do not coincide. g In the census data, all the indices that were used in this paper were re-calculated over the census years except HWSEI. For now, I use the scores based on 1990. h For the rst husband, the year of rst marriage could not be chosen since the rst year data is missing in many cases (about 30%). Also, the wage at the time of the rst marriage is thought to measure their economic ability less accurately since the husband is younger and his career is less likely to be established at the time. For the second husband, by choosing the year of remarriage, we can less concern about the sample selection issue that is caused by second divorce. 85 If the hourly wage was not observed in the year of separation or remarriage, it was substituted by the data from closest years. Finally, since the average men's wage/career trajectory is needed as a bench- mark, it was constructed using the NLSY79 male sample. From the total of 153,672 person-year observations, the observations that the respondent was older than 18, whose wage and work hours data were available were included in the sample. For occupational standing analysis, observations that are missing with occupation code are excluded from the sample. The resulting sample consisted of 87,958 observations for hourly wage analysis, and 83,966 observations for occupational status analysis. 3.5 Empirical Results 3.5.1 Comparison of the Two Husbands' Wages Before looking at the main results, a reader might cast a doubt about the validity of using wages at divorce as a measure of rst husbands' economic ability. As a signicant loss of income or a loss of job can trigger divorces, it is possible that wages at divorce underestimate the rst husbands' economic ability. If this is true, comparing the two husbands' wages at divorce and at remarriage would overesti- mates the dierences in their economic ability. i To prevent this concern, I checked for any signicant decrease in rst husbands' wages towards divorce. i The idea is similar to the "Pre-programme dip" where earnings tend to drop right before a training program (Ashenfelter (1978)). 86 Table 3.1: Changes in Hourly Wages of First Husbands Year Employed and Unemployed Employed Only since Real Detrended % Real Detrended divorce N wage wage unempl'd N wage wage -3 324 10.18 11.68 8.64 296 11.15 12.78 -2 324 10.75 12.42 6.48 303 11.50 13.28 -1 324 10.81 12.59 7.72 299 11.72 13.64 0 324 10.99 12.91 7.72 299 11.91 13.99 Notes: The table includes only the sample women who report their hus- bands' wages and employment status for 3 consecutive years before divorce. The unemployment is dened to be working less than 600 hours a year. Table 3.1 shows the real and detrended wages of rst husbands for the sample of 324 women who reported their husbands' wages from 3 years before divorce to the year of divorce. The detrended wages are examined in addition to real wages to control for possible obscuration that is caused by the dierence in the timing of divorce across the women j . The table does not exhibit any strong evidence of decreasing in husbands wages near divorce; both real and detrended wages increase monotonously, and unemployment does not increase substantially. The subset of employed husbands do not experience signicant drop in their wages as well. Thus, it does not seem problematic to use rst husbands' wage at divorce as a measure of their economic ability. j Detrending is performed using NLSY79 male sample. I regressed real male wages on dierent order polynomials of time and age, and the detrending is performed using the estimated coecients on time variable only. The model that I reported here is the one with 6th order polynomial and cubic ages which yields one of the highest R-squared. 87 Table 3.2 summarizes the results of the hourly wage comparison. k Overall, the second husbands of remarried women are economically less competent compare to the rsts; The average ages of husbands at divorce and remarriage are about 29 and 36 respectively, and second husbands earns 1.3 more dollars per hour than the rsts. However, the average raise in hourly wages that an average male experience between the ages is 2.35 dollars, which is signicantly higher than 1.3. This phe- nomenon is driven by the women who marry same age husbands in both order of their marriages, who consist the majority of the sample. Meanwhile, women who are exible about their spouses' age thus marry men outside of her cohort in ei- ther of her two marriages could avoid loss in husbands' economic ability in their remarriages. The above results has certain implication about the marriage market a divorced woman faces; the market she faces is not as good as the one that she faced when she was never-married. Men who are available and who are from the same cohort as hers are likely to be the ones with low economic ability. This is consistent with past studies which state that men with low ability are most likely to be remain never-married or to be quickly divorced if they marry. Thus, women who does not k Here, a woman is said to be matched to "older" husband if her husband is three years older, and to "younger" husband if he is two years younger. The rest is considered as the same age match. In Table 3.2 and subsequent tables, the cases in which rst husbands are younger than the sample women are omitted since the sample size is too small. However, these cases are included in calculating the averages for the entire sample. 88 Table 3.2: Dierences in the Two Husbands' Wages (a) (b) (c) (d) (e) 1st Husband 2nd Husband (b) (a) 4 avg. male wage (c) (d) Entire Sample Age 29.29 35.64 (N=802) Hourly Wage 11.08 12.38 1.30 2.35 -1.04*** (Std. Err) 0.2636 0.2743 0.3208 0.2292 0.3943 1st Marriage: Same age husband 2nd Marriage: Younger husband Age 28.25 30.16 (N=117) Hourly Wage 10.55 11.31 0.75 0.75 0.00 (Std. Err) 0.5977 0.5679 0.7174 0.1674 0.7367 Same age husband Age 26.67 33.29 (N=234) Hourly Wage 10.64 11.47 0.83 2.25 -1.42*** (Std. Err) 0.3807 0.4442 0.4853 0.1932 0.5223 Older husband Age 27.37 41.25 (N=155) Hourly Wage 10.06 13.76 3.70 5.57 -1.87** (Std. Err) 0.6199 0.6478 0.7550 0.2820 0.8059 1st Marriage: Older husband 2nd Marriage: Younger husband Age 35.76 29.78 (N=37) Hourly Wage 14.09 12.37 -1.72 -2.35 0.62 (Std. Err) 1.4293 1.3145 1.3981 0.2292 1.4168 Same age husband Age 32.86 33.51 (N=114) Hourly Wage 11.73 11.31 -0.42 0.37 -0.79 (Std. Err) 0.8414 0.6831 0.9729 0.2317 1.0001 Older husband Age 33.14 41.86 (N=120) Hourly Wage 12.58 14.53 1.95 3.50 -1.55 (Std. Err) 0.7796 0.8666 1.0141 0.3582 1.0755 Notes: *** p<0.01, ** p<0.05, * p<0.1. A couple is of same age if -2 Husband's age - Wife's age 3. Each husband's wage is CPI adjusted (base year 1990). I intentionally omit the results for women who marry younger rst husbands since the sample size is too small. 89 explore outside of her cohort are likely to experience a loss in terms of her husband's wage. However, remarrying outside of cohort only matches the economic ability of second husbands to their previous counterparts' level and not surpass it. Are the observed patterns of mobility presented above due to changes in hus- bands' observable characteristics between the rst and the second marriages? One way to answer this question is to compare the occupational status of the two hus- bands. As mentioned in the previous section, ve measures of occupational status are examined: EDS, ERS, HWSEI, NPBOSS, and the occupational mean hourly wage. EDS indicates the percentage of people in a given occupation who have at- tained some college education. ERS indicates an occupation's percentile rank of the median income, and for the occupational mean hourly wage, the name is self- explanatory. HWSEI and NPBOSS are composite measures which are the weighted sum of the occupational education and occupational earnings. Thus, any observed pattern from the analysis of HWSEI or NPBOSS is re-investigated using EDS, ERS, and the occupational mean hourly wage. Both HWSEI and NPBOSS do not seem to capture the pattern of hourly wage comparison. Rather, they are showing their own unique patterns. While the dif- ferences between two husbands are not signicant for both the entire sample of women and the women who marry same age men for both times, the women who are matched to older men for both marriages experience signicant upward mobility . This is mainly due to the fact that the second husbands work at jobs that require higher education level than the rst; While the cell for women who marry older men 90 Table 3.3: Dierences in the Two Husbands' HWSEIs & NPBOSSes HWSEI NPBOSS (a) (b) (c) (d) (e) (a) (b) (c) (d) (e) 1st Husband 2nd Husband (b) (a) 4 avg. male wage (c) (d) 1st Husband 2nd Husband (b) (a) 4 avg. male wage (c) (d) Entire Sample Age 29.29 35.64 29.29 35.64 (N=802) SES 33.06 35.18 2.12 1.61 0.50 47.57 51.31 3.74 4.41 -0.67 (Std. Err) 0.4357 0.4685 0.5454 0.3778 0.6635 0.8764 0.8952 1.0724 0.7506 1.3090 1st Marriage: Same age husband 2nd Marriage: Younger husband Age 28.25 30.16 28.25 30.16 (N=117) SES 33.29 34.96 1.67 0.75 0.93 47.77 50.19 2.42 1.44 0.98 (Std. Err) 1.1468 1.1565 1.43 0.3130 1.4648 2.3429 2.3786 2.96 0.6105 3.0175 Same age husband Age 26.67 33.29 26.67 33.29 (N=234) SES 32.10 34.85 2.75 2.43 0.32 45.96 50.86 4.90 5.07 -0.17 (Std. Err) 0.7567 0.8905 0.9600 0.3294 1.0150 1.5580 1.6691 1.93 0.6515 2.0329 Older husband Age 27.37 41.25 27.37 41.25 (N=155) SES 34.33 36.14 1.81 2.96 -1.15 49.45 54.12 4.66 6.71 -2.04 (Std. Err) 1.0237 1.0372 1.2572 0.4071 1.3214 2.0765 1.9705 2.4527 0.7941 2.5780 1st Marriage: Older husband 2nd Marriage: Younger husband Age 35.76 29.78 35.76 29.78 (N=37) SES 34.24 33.57 -0.67 -1.01 0.34 51.71 48.55 -3.15 -2.64 -0.51 (Std. Err) 1.8279 1.8551 1.9607 0.3821 1.9976 3.9491 3.8492 4.1260 0.7476 4.1932 Same age husband Age 32.86 33.51 32.86 33.51 (N=114) SES 31.92 34.33 2.42 0.34 2.07 46.29 49.64 3.35 0.72 2.62 (Std. Err) 1.0040 1.2925 1.4289 0.3931 1.4819 2.1357 2.3893 2.7872 0.7662 2.8906 Older husband Age 33.14 41.86 33.14 41.86 (N=120) SES 33.24 36.81 3.57 1.07 2.50 47.40 53.43 6.03 2.66 3.37 (Std. Err) 1.2541 1.2943 1.5304 0.4453 1.5938 2.3761 2.4084 2.9035 0.8639 3.0293 Notes: *** p<0.01, ** p<0.05, * p<0.1. A couple is of same age if -2 Husband's age - Wife's age 3. The occupational indices are constructed based on 1990 occupational classication. 91 Table 3.4: Dierences in the Two Husbands' ERSes & Occupation Mean Wages ERS Occupational Mean Hourly Wage (a) (b) (c) (d) (e) (a) (b) (c) (d) (e) 1st Husband 2nd Husband (b) (a) 4 avg. male wage (c) (d) 1st Husband 2nd Husband (b) (a) 4 avg. male wage (c) (d) Entire Sample Age 29.29 35.64 29.29 35.64 (N=802) SES 52.22 55.38 3.16 4.61 -1.45 12.74 13.30 0.55 0.75 -0.19 (Std. Err) 0.9055 0.9339 1.1841 0.7664 1.4105 0.1565 0.1587 0.1997 0.1376 0.2426 1st Marriage: Same age husband 2nd Marriage: Younger husband Age 28.25 30.16 28.25 30.16 (N=117) SES 52.73 52.98 0.26 1.52 -1.26 12.74 13.06 0.31 0.30 0.01 (Std. Err) 2.4501 2.5214 3.10 0.6212 3.1576 0.3856 0.3761 0.47 0.1092 0.4783 Same age husband Age 26.67 33.29 26.67 33.29 (N=234) SES 50.49 56.11 5.62 3.66 1.96 12.29 13.32 1.03 0.99 0.04 (Std. Err) 1.6478 1.7705 2.2092 0.6788 2.3111 0.2564 0.2990 0.36 0.1129 0.3776 Older husband Age 27.37 41.25 27.37 41.25 (N=155) SES 52.58 58.09 5.51 7.13 -1.62 12.98 13.57 0.59 1.11 -0.52 (Std. Err) 2.0869 2.0195 2.5746 0.8084 2.6986 0.3322 0.3420 0.4035 0.1418 0.4277 1st Marriage: Older husband 2nd Marriage: Younger husband Age 35.76 29.78 35.76 29.78 (N=37) SES 57.30 50.18 -7.12 -2.72 -4.39 13.22 12.43 -0.79 -0.42 -0.37 (Std. Err) 4.0550 3.6630 4.4963 0.7647 4.5608 0.6740 0.5560 0.6557 0.1358 0.6696 Same age husband Age 32.86 33.51 32.86 33.51 (N=114) SES 52.57 54.41 1.84 0.98 0.86 12.64 13.26 0.62 0.10 0.52 (Std. Err) 2.1952 2.4484 3.1250 0.7836 3.2218 0.3364 0.4600 0.5084 0.1405 0.5275 Older husband Age 33.14 41.86 33.14 41.86 (N=120) SES 51.90 55.80 3.90 2.95 0.95 12.88 13.60 0.72 0.27 0.44 (Std. Err) 2.4312 2.4876 3.3007 0.8828 3.4168 0.4869 0.4637 0.6215 0.1582 0.6413 Notes: *** p<0.01, ** p<0.05, * p<0.1. A couple is of same age if -2 Husband's age - Wife's age 3. The occupational indices are constructed based on 1990 occupational classication. 92 Table 3.5: Dierences in the Two Husbands' EDSes & PRENTs EDS PRENT (a) (b) (c) (d) (e) (a) (b) (c) (d) (e) 1st Husband 2nd Husband (b) (a) 4 avg. male wage (c) (d) 1st Husband 2nd Husband (b) (a) 4 avg. male wage (c) (d) Entire Sample Age 29.29 35.64 29.29 35.64 (N=802) SES 43.95 47.69 3.74 2.94 0.79 41.04 43.00 1.96 2.04 -0.08 (Std. Err) 0.8697 0.8987 1.0421 0.7114 1.2618 0.4308 0.4542 0.5540 0.3770 0.6701 1st Marriage: Same age husband 2nd Marriage: Younger husband Age 28.25 30.16 28.25 30.16 (N=117) SES 44.47 48.66 4.19 1.34 2.85 41.42 42.71 1.29 0.60 0.69 (Std. Err) 2.3325 2.2791 2.85 0.5894 2.9069 1.1536 1.1602 1.43 0.3027 1.4631 Same age husband Age 26.67 33.29 26.67 33.29 (N=234) SES 42.66 46.38 3.72 4.23 -0.51 40.42 42.90 2.48 2.34 0.14 (Std. Err) 1.5292 1.6698 1.8575 0.6263 1.9602 0.7321 0.8210 0.94 0.3216 0.9941 Older husband Age 27.37 41.25 27.37 41.25 (N=155) SES 47.15 49.58 2.44 5.38 -2.94 41.62 44.00 2.39 3.11 -0.72 (Std. Err) 2.0931 2.0351 2.4721 0.7675 2.5885 1.0274 1.0212 1.2960 0.4008 1.3565 1st Marriage: Older husband 2nd Marriage: Younger husband Age 35.76 29.78 35.76 29.78 (N=37) SES 45.77 46.37 0.60 -2.45 3.06 42.67 42.01 -0.66 -1.11 0.45 (Std. Err) 3.9821 4.0316 4.0102 0.7373 4.0774 1.7514 1.8511 2.2010 0.3686 2.2316 Same age husband Age 32.86 33.51 32.86 33.51 (N=114) SES 40.53 45.24 4.71 0.24 4.47 40.34 42.26 1.91 0.46 1.45 (Std. Err) 2.1717 2.4427 2.7962 0.7371 2.8917 1.0565 1.2513 1.4215 0.3829 1.4721 Older husband Age 33.14 41.86 33.14 41.86 (N=120) SES 43.97 51.29 7.32 1.57 5.75** 40.78 44.01 3.24 1.42 1.81 (Std. Err) 2.3105 2.4039 2.6490 0.8334 2.7770 1.2307 1.2810 1.6281 0.4386 1.6861 Notes: *** p<0.01, ** p<0.05, * p<0.1. A couple is of same age if -2 Husband's age - Wife's age 3. The occupational indices are constructed based on 1990 occupational classication. 93 twice in Table 3.4 show no mobility in terms of the occupational earnings score, the same cell in Table 3.5 reports signicant increase in the husband's occupational education score. An interesting nding here is that the occupational earning does not show any signicant mobility for any cell in the table. This implies that the observed down- ward mobility in terms of hourly wage is not due to any systematic change in the occupation but something other than that. Since the results might change depend- ing on which measure is chosen, a robustness check is performed by substituting the ERS with the occupational mean hourly wage. The results are robust to the change in measure, which strengthen the idea that the occupational change was not a main force of the downward mobility. A more comprehensive analysis on the eect of the changes in husbands' observ- able characteristics on the observed pattern of wage dierence is presented: First, I estimate the male wage equation by regressing men's hourly wage on their race, ed- ucation, occupational mean hourly wage, experience, and experience squared using NLSY79 male sample l . Then, I can calculate the predicted wage and the residual for each of the men in the male sample, and construct the trajectory for each of the variable. Now, using the estimates of coecients obtained from the above wage equation regression, I can construct the predicted wage and the residuals for the rst and the second husbands of each of our sample woman m . Then, nally, we can perform the same analysis as before for each of the predicted wage and the residual. l Experience =Ageeducation 6 94 The predicted wage is failed to capture the pattern of the hourly wage; The women who are matched age homogeneously for both of their marriages experience no mobility in terms of the predicted wage, while the entire women sample experi- ence downward mobility. However, the residual resembles the pattern of the hourly wage; downward mobile for the left most cell in the rst row, and no mobility for all other cells. Thus, it is likely that the observed downward mobility is due to the dierence in the rst and second husband's un observable characteristics. How- ever, a caution is needed when interpreting the above results, since any error in the estimation of wage equation can lead to the same conclusion. In sum, our analysis suggests that Jacobs and Furstenberg's conclusion is sup- ported even under the statistically more rigorous setup. Even after relaxing the assumption on the distribution of the spousal age dierence, overall, women do not experience mobility of any direction between their rst and second marriages, both in terms of the husbands' hourly wage and the occupational status. However, in the additional analysis where I grouped the sample women based on their age matching pattern, I found that the women who marry the same age husbands for both times experience a signicant downward mobility in terms of the hourly wage, while the women who marry older husbands for both times experience a signicant upward mobility in terms of the husband's EDS. The unique pattern in the hus- band's hourly wage could not be explained by the systematic change in husbands' m For the husbands' sample, race is substituted by his wife's since NLSY79 does not record husband's race until 2008. 95 observable characteristics, including the occupational status. In conclusion, the downward mobility must be due to the dierence in unobservable characteristics of rst and second husbands, such as their diligence, or amount of time spend on extra work. 3.5.2 The Associations between the Two Husbands' Wages In this section, I examine how a woman's characteristics aects her second husband's hourly wage, treating the hourly wage as the gain from remarriage. Aligning with past studies, this paper includes the ex-husband's hourly wage in a way to control for the eect of a woman's unobservable characteristics. What is new in this paper is that the ex-husband's wage is decomposed into the predicted part and the residual, and added to the regression function separately. Here, the predicted wage is thought to be the proxy for women's unobservable characteristics that aects her (potential) husband's observable characteristics (in a comprehensive way), and the residual is thought to be the proxy for women's unobservable characteristics that aects the husband's unobservable characteristics. For example, the former can be a woman's preference on a man's education and/or occupation, while the latter can be her preference on his extra work hours. Therefore, in this paper, we can distinguish the eect of two dierent types of woman's unobservables, and examine how this separation of the unobservable aects the estimates of other coecients. The eect of each variable on the second husband's wage can take two dierence channels: through the second husband's predicted wage and through their residuals. 96 For example, a woman's unobserved preference towards a men's predicted wage may aect the new husband's predicted wage only, and have no signicant eect on the residual. To examine how each of variable aects the predicted wage and the residuals of the new husband dierently, I run separate regression for each of them. Table 3.6: Summary Statistics Variable Mean Std. Dev. Age 33.49 7.19 Education 12.70 2.21 HWSEI 27.86 18.94 Number of Children 1.16 1.12 Wives Children Younger than 6 0.47 0.50 Divorce to Remarriage 6.67 4.30 Remarried within 1 Year 0.13 0.33 Length of First Marriage 6.93 4.73 Non white 0.31 0.46 Age 29.39 6.48 Education 12.39 2.20 First Occupational Mean Wage 12.66 4.32 Husbands Hourly Wage 11.32 7.89 Predicted Wage 10.99 3.37 Unpredicted Wage 0.34 7.32 Age 35.61 8.89 Education 12.91 2.42 Second Occupational Mean Wage 13.24 4.37 Husbands Hourly Wage 12.51 8.14 Predicted Wage 12.70 3.50 Unpredicted Wage -0.19 7.46 Notes: N=802; First husbands' statistics are observed at di- vorce. Wives' and second husbands' statistics are observed at remarriage. Table 3.6 shows the summary statistics of variables that are included in the regression. The predicted wages and the residuals of each husband is calculated in 97 the same way as described in the previous section. The second husbands tend to be more educated than the rsts; the average year of schooling is 12.91 for the second husbands, while it is 12.39 for the rst husbands. Women's education at the time of remarriage is 12.7 which is higher that that of the rst husbands and lower than that of the second husbands. Also, the women have more than one child a year before remarriage, and about 50% of them have children who are younger than 6. The women are about 33.5 years old when they remarry, their rst marriages are maintained for 7 years, and it takes about 6.67 years for them to remarry n . Finally, about 30% of the sample women are non-white. Table 3.8 compares the regression results with or without the predicted wage. Due to the inclusion of the predicted wage, the wage of the ex-husband in the second column is interpreted as the eect of the residual wage. From column (2), we can see that the inclusion signicantly improves the model t, and both the predicted wage and the residual have signicantly positive eect on the new husband's wage. The inclusion also aects the other estimates, especially the estimates of coecients on education, age, and race. While their signicance or direction do not change n As previously mentioned, the variables related to remarriage are extracted from the year that is closest to remarriage and that has the second husband's records. The variables related to divorce are extracted in the same manner. Thus, the variables Divorce to Remarriage, Length of M1, and Age at Remarriage are not actually measuring what their names indicate. The true average of each variables, which are calculated based on the self-reported years of divorce and remarriage, are 4.11, 8.61, and 32.09, respectively. However the regression results were not sensitive to the denition of the three variables. 98 Table 3.7: Association between Two Husbands' Wages (1) (2) Ex-husbands' Wages Hourly wage 0.197*** 0.155*** (0.0360) (0.0370) Predicted wage 0.443*** (0.109) Women's Characteristics at Remarriage Education 0.535*** 0.376** (0.150) (0.153) HWSEI 0.0475*** 0.0432*** (0.0162) (0.0161) Age 0.156* 0.0359 (0.0804) (0.0849) Divorce to remarriage -0.170 -0.0300 (0.108) (0.112) Remarried within a year -1.370 -1.340 (0.861) (0.853) Length of rst marriage -0.136 -0.128 (0.0910) (0.0902) # of children -0.131 -0.126 (0.342) (0.338) Children younger than 6 0.364 0.439 (0.765) (0.758) Non white -0.881 -0.190 (0.609) (0.626) Constant -0.558 -0.0434 (2.095) (2.078) N 796 796 R-sq 0.134 0.152 adj. R-sq 0.123 0.14 Notes: *** p<0.01, ** p<0.05, * p<0.1. 99 much, their magnitude all decreases. Recall that the corresponding variables of the rst husband are used to construct their predicted wages. Thus, the decreases in the magnitudes of the three variables probably come from the assortative matching in terms of each variable; More specically, due to the assortative nature of the matching in the rst marriage, the predicted wage has the positive correlations with women's age and education, and the negative correlation with the race dummy variable, non-white. Now, to decompose each variable's eect on the new husband's wage, the new husband's predicted wage and the residual are separately regressed on the set of independent variables used in column (2) of Table 3.8. The results are summarized in the rst two columns of Table 3.9. The two columns show quite dierent patterns; First, while many of women's observable characteristics, such as their education, occupational status, age, and race, have signicant eect on the new husband's predicted wage, virtually none of it aects the new husband's residual. Second, the rst husband's predicted wage and his residual have positive and signicant eects in both columns, and the eects on the residual are twice as large as those on the predicted wage for both of the variables. A detailed discussion on these observed phenomenon is given in the following few paragraphs. The fact that the predicted wage has a positive eect on the residual can be justied if we consider the role of the predicted wage as a measure of the husband's earnings potential. In the rst marriage where the (potential) husband is young and 100 Table 3.8: Association between Two Husbands' Wages (1) (2) Ex-husbands' Wages Hourly wage 0.197*** 0.155*** (0.0360) (0.0370) Predicted wage 0.443*** (0.109) Women's Characteristics at Remarriage Education 0.535*** 0.376** (0.150) (0.153) HWSEI 0.0475*** 0.0432*** (0.0162) (0.0161) Age 0.156* 0.0359 (0.0804) (0.0849) Divorce to remarriage -0.170 -0.0300 (0.108) (0.112) Remarried within a year -1.370 -1.340 (0.861) (0.853) Length of rst marriage -0.136 -0.128 (0.0910) (0.0902) # of children -0.131 -0.126 (0.342) (0.338) Children younger than 6 0.364 0.439 (0.765) (0.758) Non white -0.881 -0.190 (0.609) (0.626) Constant -0.558 -0.0434 (2.095) (2.078) N 796 796 R-sq 0.134 0.152 adj. R-sq 0.123 0.14 Notes: *** p<0.01, ** p<0.05, * p<0.1. 101 has little experience of working, the wage prediction based on the husband's ob- servable characteristics provides a woman with a better indication of the husband's future earning than his current wage. However, in the second marriage, since the husband is older and has developed their career, his realized wage provides more accurate indication than his predicted wage. Thus, the positive coecient of the predicted wage in the residual regression implies that the woman's desire to marry a man with higher earning is persistent both in the rst and second marriages, and that the role as a measure of the earnings potential, which was performed by the predicted wage in the rst marriage, is transferred to the realized wage in the second marriage. Also, the fact that the eect of the predicted wage is larger in the residual regression indicates that the main driving force of the higher predicted wage in the rst marriage is the woman's desire to be matched to a man with higher future wages, not their mere preference towards the man's observable characteristics. However, the woman's preference towards the man's observable characteristics persists in the second marriage. The positive signicant estimate of the coecient on the predicted wage in the rst column of Table 3.9 indicates this fact. While some women care about men's education or occupation only because of their eects on the future wage, others may value the education or the occupation itself. Indeed, in the additional regression where we substitute the predicted wage with the set of husband's observable characteristics, the education of the husband had a positive signicant eect on the predicted wage of the second husband. Thus, regardless 102 Table 3.9: Association between Two Husbands' Predicted and Unpredicted Wages Based on Wage eq. 3 Based on Wage eq. 1 (1) (2) (3) Dependent Variable: Predicted wage Unpredicted wage Unpredicted wage Ex-husband's wages Hourly wage 0.0451*** 0.110*** 0.183*** (0.0149) (0.0358) (0.0360) Predicted wage 0.145*** 0.298*** 0.351* (0.0437) (0.105) (0.193) Women's characteristics at Remarriage Education 0.255*** 0.121 0.478*** (0.0617) (0.148) (0.147) HWSEI 0.0223*** 0.0209 0.0472*** (0.00647) (0.0155) (0.0159) Age 0.116*** -0.0796 -0.125 (0.0341) (0.0820) (0.0918) Divorce to remarriage -0.0168 -0.0132 -0.0756 (0.0451) (0.108) (0.116) Remarried within a year -0.199 -1.142 -1.571* (0.343) (0.824) (0.848) Length of rst marriage -0.00489 -0.123 -0.146 (0.0362) (0.0871) (0.0905) # of children -0.236* 0.111 -0.120 (0.136) (0.327) (0.335) Children younger than 6 0.388 0.0508 0.362 (0.305) (0.732) (0.752) Non white -0.955*** 0.766 -0.657 (0.252) (0.605) (0.598) Constant 3.427*** -3.470* -7.113*** (0.835) (2.007) (2.125) N 796 796 796 R-sq 0.259 0.059 0.124 adj. R-sq 0.248 0.045 0.112 Notes: *** p<0.01, ** p<0.05, * p<0.1. 103 of the realized wage, women who preferred educated men in the rst marriage are more likely to do so in their second marriages. Following the above interpretation, the positive coecient of the residual in the residual regression (column (2) of Table 3.9) can be thought as the woman's persistent preference towards the man's unobservable characteristics; A woman who prefers men who works extra hours tends to be matched to such men both in the rst and second marriages. This positive correlation between the residual wage of the rst and the second husbands is consistent with the nding in Astrom et al. (2013). The positive eect of the residual on the second husband's predicted wage needs a bit more discussion. Assume that there are a pool of women who prefer men who work extra hours, and marry such men in their rst marriages. The preference is persistent, so most of these women are matched to men who work extra hours again in their second marriages. Meanwhile, a subset of the women nd the men who are required to work extra hours by their job, and matched to them in their second marriages. The positive eect of the residual on the second husband's predicted wage re ects this eect. o o Another explanation can be given in the following way: The higher residual can be an indi- cation of an out-performer. If the rst husband is an out-performer, he and his wife have more chances to mingle with people who has higher social-status. For example, a successful local en- trepreneur can live in an wealthy neighborhood, where most of the neighbors are accountants, lawyers and doctors. Thus, even after the divorce, this community aects the pool of people the woman meets, which can aects her second marital match. 104 The signicant eects of the woman's observable characteristics in the predicted wage regression have certain implications on the changes in matching between rst and second marriages. To simplify the argument, let's restrict our attention to the women's education for now. Assume two women, who are otherwise identical, have dierent levels of education, with one nished high school education and the other nished college education. In other words, the college graduate was matched down in her rst marriage in terms of husbands' predicted wage. The fact that the education has signicantly positive eect indicates that although we do not know how the matching pattern changes in the second marriage (i.e. whether the woman is matched to a man who is older, more educated, or with a better occupational status), it changes in a way that more educated women are matched to men with higher predicted wage than less educated women. The same logic can be extended to the eect of the occupational status, age, and race. An interesting point here is that older women tend to benet in their second marriages in terms of the new husband's predicted wage; The coecients on "age at remarriage" is positive and signicant (column (1) in Table 3.9). This is inconsistent with the past studies (Duncan and Homan (1985) and Jacobs and Furstenberg (1986)), although they are dierent from this study in many ways p . Since the age is p Duncan and Homan (1985) reported a negative eect of age on the second husband's log wage, although the eect was signicant under 10% level. Jacobs and Furstenberg (1986) also reported negative (but insignicant) eect of age on the second husband's occupational status. However, Jacobs and Furstenberg (1986) was focused on the occupational status, and not on the wage. Duncan and Homan (1985) focused on the wage, but they used dierent data and dierent 105 one of the observable characteristics that is used in the husband's wage prediction, the observed signicance might be due to the fact that the women who remarry when they are relatively older tend to marry older men. The results in the third column of Table 3.9 conrm this conjecture; In this regression, the dependent variable is the residual from the wage equation that has only age and age squared as its regressors. Thus, the dependent variable can be thought as the wage after controlling for the wage trajectory. The eect of the women's age turns to negative in column (3), indicating that the positive eect of the age on the predicted wage is due to the women's matching with older men q . Finally, an additional discussion on the residual regression (column (2) of Ta- ble 3.9) is given. Once the residual and the predicted wage of the rst husband are controlled, virtually none of the women's observable characteristics explains the variation in the second husband's residual wage. Revisiting the example of education introduced in the predicted wage regression, this indicates that a more educated woman who was matched down in her rst marriage in terms of the resid- ual wage does not do better in the second marriage compare to a less educated set of control variables, concentrated only on remarriage happened 5 years after divorce, and had smaller sample size. q In addition, notice that the education and SEI score of women still has signicant positive eects in column (3). This indicates that the positive and signicant eects of the education and SEI in the rst column of the table are because they are matched to men with higher education level or higher occupational level than other women, and not because they are matched to older men. 106 women. Therefore, we can conclude that the residual wage of second husband is de- termined by the woman's unobservable characteristics, and not by their observable characteristics. 3.6 Conclusion This paper investigates the economic status of a remarried woman's current and previous husbands. The comparison of two husbands indicates that although the second husband's economic status is lower than that of the rst in general, a woman who marry a man outside of her age group avoids this downward mobility. The fact that the comparison results vary depending on the woman's age matching pattern raises a possibility that a woman trades a man's other observable characteristics for his wage. In order to further examine this hypothesis, each of the rst and second husbands' wages are decomposed into the part that is predicted by their observed traits and the part that is unpredicted, and examined for self- and cross- associations. The strong cross-association between the rst husband's predicted wage and the second husband's unpredicted wage supports the idea that a woman re-prioritizes her preferences and concentrates on the husband's economic ability in her remarriage. 107 References Aguirregabiria, V. and Mira, P. (2010). Dynamic discrete choice structural models: A survey. Journal of Econometrics, 156(1):38{67. Amato, P. R. (2000). The consequences of divorce for adults and children. Journal of marriage and family, 62(4):1269{1287. Ashenfelter, O. (1978). Estimating the eect of training programs on earnings. The Review of Economics and Statistics, pages 47{57. Astrom, J., Nakosteen, R. A., Westerlund, O., and Zimmer, M. A. (2013). 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The divorce revolution: The unexpected social and eco- nomic consequences for women and children in America. New York: Free Press. 112 Appendix A Bayesian Update A woman's prior belief on her potential husband's wage before she meets a particular man is: ln(w h t )jZ h t N(Z h 0 t ; 2 + 2 ) where Z h 0 t =X 0 t 1 + 2 exp t1 + 3 exp 2 t1 . When she meets a man and observes his wage (w h t , thusu h t ), she updates her beliefs on his ability and future wage as follows (i.e. posterior): ju h t N u h t 2 2 + 2 ; 2 2 2 + 2 ; u h t+1 ju h t N u h t 2 2 + 2 ; 2 2 2 + 2 + 2 ; ln(w h t+1 )ju h t ;Z h t+1 N Z h 0 t+1 + u h t 2 2 + 2 ; 2 2 2 + 2 + 2 : 113 For a woman whose marriage duration is md t1 at time t, her beliefs on her husband's ability and on u h t+1 are: ju h t ;:::;u h tmd t1 N ( P md t1 =0 u h t ) 2 2 + (md t1 + 1) 2 ; 2 2 2 + (md t1 + 1) 2 ! ; u h t+1 ju h t ;:::;u h tmd t1 N ( P md t1 =0 u h t ) 2 2 + (md t1 + 1) 2 ; 2 2 2 + (md t1 + 1) 2 + 2 ! and the belief on her husband's future wage is dened similar to that of u h t+1 . Dene ^ md t1 for md t1 > 0 as: ^ md t1 = ^ md t2 2 +md t1 2 2 + (md t1 + 1) 2 + u h t 2 2 + (md t1 + 1) 2 where ^ 0 =u h t 2 =( 2 + 2 ). Then at time t, given md t1 and ^ md t1 , a woman's beliefs on her husband's ability and future wage are: j ^ md t1 ;md t1 N ^ md t1 ; 2 2 2 + (md t1 + 1) 2 u h t+1 j ^ md t1 ;md t1 N ^ md t1 ; 2 2 2 + (md t1 + 1) 2 + 2 ln(w h t+1 )j ^ md t1 ;md t1 ;Z h t+1 N Z h 0 t+1 + ^ md t1 ; 2 2 2 + (md t1 + 1) 2 + 2 : 114
Abstract (if available)
Abstract
This dissertation asks two empirical questions: How would a woman's marriage, fertility and labor supply decisions vary depending on the changes in the social and cultural environment, and how would a remarried woman's second husband be different from her first husband in terms of his economic ability. ❧ The goal of chapter 2 is to quantify the effects of changes in the work environment and the divorce related policies on a woman's marriage, fertility and labor supply decisions. Acknowledging the fact that a woman makes decisions considering their effects on her lifetime utility, the chapter uses a structural dynamic model as a tool of analysis. The chapter first construct and estimate a model which fits the existing data on a woman's behavior. By assuming a woman as a Bayesian learner of her husband's unobserved economic ability, the model allows a divorce to be a gradual process rather than a sudden unexpected event. The results show that my model fits the data well, and the learning in particular improves the fit of women's birth giving pattern. The chapter then performs counterfactual analyses on the four different policies which represent the changes in the labor market opportunities for women and the changes in the society's attitude to divorce. The results indicate that the increase in female wage and reduced divorce cost make a marriage a less stable institution, leading to higher labor force participation and the divorce rate while lowering the fertility rate for married women. However, when the labor market (re-)entry cost is reduced, it allows a woman to manage her career path more flexibly, thus the divorce rate decreases while the fertility rate and the labor force participation of older women increases. The results indicate that a woman's career and her role as a mother and a wife are not incompatible, and in the environment that allows a woman to manage her career path flexibly, the female labor force participation would increase without deteriorating the family related statistics. ❧ Chapter 3 is interested in a remarried woman and her first and second husband. The financial hardship that a woman typically undergoes following divorce is often ameliorated by remarriage and thus, the economic status of men who are available for remarriage is of particular concern for the woman. This chapter investigates the new husband's wage in relation to that of the first husband. Controlling for age, I found that the second husband is economically less competent than the first for a woman who remarries a man of the same age. However, a woman who marries a man outside of her age group in either or both of her marriages avoids this downward mobility. In addition, I found a strong positive association between the first husband's predicted wage and the second husband's unpredicted wage where the prediction is made based on the husbands' observable characteristics. These findings imply that given the limited pool of potential husbands, a female divorcee re-prioritizes her preferences, trading other characteristics of her spouse for his unobserved economic ability.
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