Effects of parental leave policies on female career and fertility choices

Yamaguchi, Shintaro Article Effects of parental leave policies on female career and fertility choices Quantitative Economics Provided in Cooperation with: The Econometric Society Suggested Citation: Yamaguchi, Shintaro (2019) : Effects of parental leave policies on female career and fertility choices, Quantitative Economics, ISSN 1759-7331, The Econometric Society, New Haven, CT, Vol. 10, Iss. 3, pp. 1195-1232, https://doi.org/10.3982/QE965 This Version is available at: https://hdl.handle.net/10419/217166 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/ Quantitative Economics 10 (2019), 1195–1232 1759-7331/20191195 Effects of parental leave policies on female career and fertility choices Shintaro Yamaguchi Faculty of Economics, University of Tokyo This paper constructs and estimates a dynamic discrete choice structural model of female employment and fertility decisions that incorporates job protection and cash benefits of parental leave legislation. The structural model is used for ex ante evaluation of policies that change the duration of job protection and/or the arrangement for cash benefits. Counterfactual simulations indicate that introducing an initial 1-year job protection policy increases maternal employment significantly, but extending the existing job protection period from 1to 3years has little effect. In addition, the employment effects of cash benefits seem modest. Overall, parental leave policies have little effect on fertility. Keywords. Parental leave, female labor supply, discrete choice model, structural estimation. JEL classification. J13, J22, J24. 1. Introduction Parental leave (PL) is mandated in most developed countries, but the generosity of PL legislation varies significantly across countries. Figure 1presents international differences in the duration of job-protected leave and the replacement rate of cash benefits, that is, the percentage of employee compensation that is payable during PL. The US mandates only 12 weeks of unpaid job-protected leave, but many other countries, including Germany, France, and Finland, mandate job-protected leave for 3years or more. The generosity of cash benefits also differs considerably across countries. The US is the only developed country where no mandated benefit is paid, while Mexico, Spain, and Poland pay 100% of pre-leave earnings to PL takers. Policy makers in countries that mandate shorter job-protected leave and/or less generous cash benefits may be interested in expanding their PL policies to resolve the conflict between work and family life, which may lead to a higher fertility and labor force participation rate of mothers of young children. Predicting likely outcomes before a policy reform could help policy makers, but it is not necessarily straightforward. One can Shintaro Yamaguchi: [email protected] I am thankful for the comments from participants of seminars at Buffalo, Maryland, Rochester, Calgary, Guelph, Ottawa, Waterloo, Chuo, Hitotsubashi, Keio, Kyoto, Osaka, and Tokyo and the conferences of Canadian Economic Association, Econometric Society, Society of Labor Economists, and Southern Economic Association. This study uses the data from the Japanese Panel Survey of Consumers conducted by the Institute for Research on Household Economics. The author is grateful for the financial support from JSPS KAKENHI Grant 16K21743, the Japan Centre for Economic Research, and Tokyo Centre for Economic Research. ©2019 The Author. Licensed under the Creative Commons Attribution-NonCommercial License 4.0. Available at http://qeconomics.org.https://doi.org/10.3982/QE965 1196 Shintaro Yamaguchi Quantitative Economics 10 (2019) Figure 1. International comparison of parental leave legislation. Quantitative Economics 10 (2019) Effects of parental leave policies 1197 learn from the experiences of countries where the most generous PL policies are already mandated, but their experiences may not be fully generalizable to other countries because of differences in institutions, etc. Another way to assess the policy effects is to conduct a small-scale social experiment, but this may be costly and politically infeasible. Yet another approach to ex ante policy evaluation is to construct and estimate a structural model and conduct counterfactual simulations, which is the approach taken in this paper. In the present paper, I construct and estimate a structural dynamic discrete choice model of women’s employment and fertility that incorporates job protection and cash benefits of PL. In each period, a woman decides on her employment sector, PL takeup, and conception. When a mother of a young child works, she not only pays child care costs, but also derives negative nonpecuniary utility of work because she values the time with her young child. Human capital increases with work experience through learning-by-doing, but it depreciates when she remains at home for PL. The model also incorporates the entry cost to employment for women who have stayed at home in the previous period. These features can be seen in some of the previous papers in the literature on the life-cycle model of female labor supply. Examples include, but are not limited to, Eckstein and Wolpin (1989), van der Klaauw (1996), Altug and Miller (1998), Francesconi (2002), Sheran (2007), Keane and Wolpin (2007,2010), Adda, Dustmann, and Stevens (2017), and Gayle and Miller (2012). The contribution of this paper is to model job protection and cash benefits of PL legislation. Job protection provided by PL allows mothers of newborns to stay at home without losing their jobs. In the model, PL takers can return to the pre-leave employment sectors without paying the entry costs, while those who quit their jobs without taking PL must pay to reenter employment. Cash benefits of PL replace only a percentage of her pre-leave earnings while on PL and affect her decisions through the budget constraint. The model is applied to panel data on Japanese women for the period 1993 to 2011. During that period, Japan experienced a series of PL reforms that expanded the coverage of the PL legislation and raised cash benefits. These policy variations allow me to identify the model without relying solely on functional form assumptions, which is a criticism to the structural estimation approach. The estimation algorithm is based on the sequential algorithm proposed by Kasahara and Shimotsu (2011). Because the model allows for permanent unobserved heterogeneity using finite mixture, the Kasahara–Shimotsu algorithm is combined with the Expectation-Maximization (EM) algorithm developed by Arcidiacono and Jones (2003). To further accelerate computation, I also approximate the value function based on sieves using the method suggested by Arcidiacono, Bayer, Bugni, and James (2013). As far as I know, this is the first paper that combines these three methods. The proposed algorithm makes estimation tractable, despite the model’s complexity. Our model is relevant particularly for countries where the labor market is segmented, such as southern European countries and Korea. In these countries and Japan, one sector consists of better-paid permanent jobs, while the other sector consists of lower-paid jobs that provide no security of continued employment. The model explicitly 1198 Shintaro Yamaguchi Quantitative Economics 10 (2019) takes this aspect of the labor market into account and allows me to simulate a PL policy to see how PL policies influence the relative importance of each sector for women’s career decisions. The estimated model is used for counterfactual simulations to assess PL policies. In the first set of simulations, I evaluate the effects of job protection. This is particularly relevant in the context of real policy; the Prime Minister of Japan, Shinzo Abe, proposed extending the duration of job protection from 1to 3years to raise female labor force participation and the birth rate.1This proposal initiated a heated debate on whether Japan should reform its PL policies. The likely outcomes of the yet to be legislated reform are not well understood. Based on the structural estimation approach, the simulations in the present paper provide the best estimates for its effects. The counterfactual simulations indicate that 1-year job protection increases maternal employment after childbearing with effects that last for several years, compared with no mandated PL. Without job protection, many women quit their jobs at childbirth and slowly (or even never) come back to work. Job protection allows women to suspend working prior to childbirth without losing their jobs. Because PL takers maintain their employment contracts and do not pay entry costs, they return to work quickly after childbearing. However, extending the duration of job protection from 1to 3years has little effect. This is because the nonpecuniary utility of work is very negative when the child is newborn but becomes much smaller as the child grows to age 1year or older. New mothers therefore take PL, but as their child grows beyond 1year of age, they return to work, even if they are eligible for PL for 3years, because the utility loss falls below the utility gains from being employed. The simulations also indicate that policy effects on fertility seem modest for both 1-and3-year job protection. In the second set of simulations, I evaluate the effects of cash benefits. The simulation results indicate that raising the rate of cash benefits that accrue with job-protected PL has modest effects on maternal work and fertility. Overall, neither the duration of job protection nor cash benefits in the current PL legislation create a binding constraint for mothers of young children. Most previous papers on PL policies and maternal labor supply identify the policy effects using a difference-in-differences (DID) estimator (Ruhm (1998), Baum (2003a), and Baker and Milligan (2008a)) or regression discontinuity designs (Lalive and Zweimüller (2009), Schönberg and Ludsteck (2014), and Lalive, Schlosser, Steinhauer, and Zweimüller (2014)). The present paper differs from these previous papers by using a structural estimation approach to evaluate potential PL reforms. Another difference from previous papers is that the structural approach sheds light on the mechanism by which the PL policies affect mothers’ labor supply. Understanding the mechanism is important when interpreting the lessons from a particular country. The key finding of the present paper is that the nonpecuniary utility of work is a large negative for mothers of newborns, which is why 1-year job protection helps women return to work after childbirth. This finding on the non-pecuniary utility of work is consistent with international evidence, including that from the US.2It should be noted, how- 1See Abe (2013). 2See the discussion in Section 6.1 and papers cited there. Quantitative Economics 10 (2019) Effects of parental leave policies 1199 ever, that differences in child care and labor market institutions can affect the effectiveness of PL policies. On the one hand, job protection may be more effective in countries such as the US where child care is not heavily subsidized, if other things remain equal. On the other hand, job protection may be less effective in the US because the labor market is more flexible and the entry costs to the employment sector are apparently smaller. The structural model helps one understand how PL policies affect maternal work and speculate about the potential policy effects in a given country. The remainder of the paper is structured as follows. Section 2describes the institutional background. Section 3describes the data. Section 4lays out the structural model. Section 5outlines the estimation method. Section 6presents the estimates of the structural parameters. The model’s ability to fit to key aspects of the data is also demonstrated. Section 7shows the effects of job protection and the cash benefits of PL through counterfactual simulations. Section 8concludes the paper. Details regarding the data, estimation methods, and additional results are available in the Appendices. 2. Institutional background The employment sector in Japan consists of two subsectors: the regular and nonregular employment sectors. Regular employment is typically under a permanent contract and a full-time job, while nonregular employment is typically under a limited-term contract and a part-time job. Regular jobs are usually superior to nonregular jobs in terms of hourly wages, nonwage benefits, employer-sponsored training, and eligibility for mandated PL (see Kambayashi and Kato (2013)). Women are predominant in the nonregular sector. PL in Japan was first enforced in 1992. The legislation mandated job protection until the child reached age 1, with no cash benefits. At the time, to be eligible for the mandated leave, individuals must have been employed in the regular employment sector and were expected to return to work after the completion of PL.3 Cash benefits were first introduced in 1995 with the replacement rate at 25%,and subsequently raised to 40% in 2001. Like many other countries, including Austria, Canada, and Germany, cash benefits are not financed directly by employers, but rather by employment insurance. An important difference from some other countries is that cash benefits are tied to the job from which PL is taken. In other words, PL takers are expected to return to the pre-leave job in order to receive cash benefits, although PL takers can reduce their hours of work if they wish. This requirement is imposed to encourage women to stay in the labor market after childbearing. PL takers must apply through employers to receive cash benefits so that employers provide proof of expectation of returning to work. Although there is no legal penalty for not returning, about 90% of PL takers are employed 1year after childbearing (see Table 5). 3Strictly speaking, the legal eligibility for PL is determined by whether the employment contract is limited or indefinite term. The data do not ask the term of the employment contract, but do ask whether the job is regular or non-regular employment. Because indefinite term employment is usually regular employment and vice versa, I determine eligibility by employment type. 1200 Shintaro Yamaguchi Quantitative Economics 10 (2019) Table 1. Changes in parental leave policies. Eligibility Years Regular Nonregular Job protection Replacement rate Legislated on Enforced on 1992–1994 1Year 0% 1991/05/15 1992/04/01 1995–2000 1Year 25% 1994/06/29 1995/04/01 2001–2004 1Year 40% 2000/05/12 2001/01/01 2005–2006  1Year 40% 2004/12/08 2005/04/01 2007–2012  1Year 50% 2007/04/23 2007/04/01 The next major PL reform took place in 2005, when nonregular workers became eligible for mandated PL for the first time. Since then, PL legislation has treated regular and nonregular workers equally. In 2007, the replacement rate was raised to 50%.Table 1summarizes the changes in PL policies. There are two other relevant issues regarding PL. First, if a PL taker gives birth during her leave, she can renew the PL and receive cash benefits. Second, not only mothers, but also fathers, are eligible to take PL; however, very few fathers do so. In 2010, the PL takeup rate among fathers was 138%, and more than half of male PL takers were on leave for only 1week. 3. Data 3.1 Overview of the data structure The analysis is based on data from the Japanese Panel Survey of Consumers (JPSC) conducted by The Institute for Research on Household Economics. The JPSC started in 1993 with a representative sample of 1500 women aged 24–34 years and asks respondents about marriage, fertility, and their and their spouse’s work every survey year. The JPSC added 500 women aged 24–27 years in 1997, 836 women aged 24–29 years in 2003, and 636 women aged 24–28 years in 2008. As of 2008, the JPSC had sampled 2284 women. Observations from the JPSC from 1993 to 2011 are used for this study. From this representative sample of young women, I drew a sample of married women who completed schooling and were not self-employed. After omitting observations with missing values except for self-earnings, I took the longest spell of consecutive observations for each individual. In total, the sample comprises 1826 women and about eight observations per person (14,907 person-year observations in total). The empirical definitions of eligibility for PL and PL take-up are detailed in Appendix A.1 in the Online Supplementary Material (Yamaguchi (2019)) along with other variables, including decision variables for employment sectors and fertility, sectorspecific experiences, etc. Table 2presents summary statistics for the pooled sample. The age of sampled individuals ranges from 24–52 years, which means the sample covers more than 89% of childbirths, according to Vital Statistics 2011.4Average years of education is 13211, while 4In total, 89% of children are born to mothers aged 25 years or older. Quantitative Economics 10 (2019) Effects of parental leave policies 1201 Table 2. Summary statistics. Mean Std. Dev. Min. Max. Individual Characteristics Age 35239 5976 24 52000 Education 13211 1634 9 18000 Years in Home 5580 4791 0 26000 Years in Reg Work 6573 5091 0 34000 Years in Non-Reg Work 3271 4135 0 26000 No. of Children 1720 0966 0 4000 Husband’s Earnings 5103 2027 0 45000 Earnings 0859 1423 0 8964 Employment and Fertility Choices Home 0503 0500 0 1000 Reg Work 0188 0391 0 1000 Non-Reg Work 0292 0455 0 1000 PL 0017 0130 0 1000 Pregnancy 0081 0274 0 1000 No. of Obs. (Person-Year) 14,907 No. of Persons 1826 Note: The sample includes married women who completed schooling and are not self-employed. Earnings are in million yen (≈10,000 USD) in 2010 constant price. The earnings of those who do not work are counted as zero. Source: JPSC. average years spent at home since completing education and experiences in the regular and nonregular sectors are 5580,6573,and3271, respectively. Average number of children is 1720. The average earning of husbands is 5103 million JPY, which is approximately equal to 51,030 USD. The average earning of the wives is 0859 million JPY. 3.2 Descriptive analysis 3.2.1 Life-cycle profiles Table 3shows average labor market and fertility outcomes by age. The percentage staying at home at age 30 years is high, at 59%, but this gradually decreases with age. At age 45 years, 31% of married women stay at home. These statistics are comparable with those from the Labor Force Survey 2010.5Similar percentages of mothers work in the regular and nonregular sectors at age 30 years (178% and 194%, resp.). While the percentage of regular workers slowly increases after age 35,thatofnonregular workers grows much more rapidly. At age 45, the percentage of regular workers is 235%, but that of nonregular workers is higher, at 454%. These statistics suggest that women gradually return to the labor market after childbearing, but largely to nonregular employment. The percentage of PL takers is small, at 37% at age 30 years, and gradually decreases with age. The percentage of pregnant women is 166% at age 30 years, and this decreases to 53% at age 35 years. No women aged 45 years in the sample were pregnant. Self and 5According to the Labor Force Survey in 2010, 56%,45%, and 33% of married women aged 30–34 years, 35–39 years, and 40–44 years, respectively, are out of the labor force. 1202 Shintaro Yamaguchi Quantitative Economics 10 (2019) Table 3. Labor market and fertility outcomes by age. Age 30 35 40 45 N=916 N=907 N=592 N=293 Home 0591 0535 0419 0311 (0016)(0017)(002)(0027) Reg Work 0178 0172 0208 0235 (0012)(0013)(0017)(0025) Non-Reg Work 0194 0276 0367 0454 (0013)(0015)(002)(003) PL 0037 0018 0007 0 (0006)(0004)(0003)(–) Pregnancy 0166 0053 0012 0 (0012)(0008)(0004)(–) Earnings 0673 0755 1067 1302 (0041)(0044)(0067)(0102) No. of Children 1407 1867 2007 2089 (003)(0031)(0036)(0051) Husband’s Earnings 4482 5172 5723 6022 (0062)(006)(0093)(0136) Note: The sample includes married women who completed schooling and are not self-employed. Earnings are in million yen (≈10,000 USD) in 2010 constant price. Standard errors are in parenthesis. They are clustered at individual level and calculated by bootstrapping with 1000 replications. Source: JPSC. husbands’ earnings increase over time. A woman’s earnings are 0673 million JPY at age 30 years, but this increases to 1302 million JPY at age 45 years as more and more individuals participate in the labor force. Husbands’ earnings grow from 4482 million JPY at age 30 years to 6022 million JPY at age 45 years. The number of children of married women at age 30 years is 1407. This grows over time, and the completed fertility rate (at age 45 years) for married women is 2089. 3.2.2 Employment transitions Table 4shows the transition matrix for employment choices. The rows indicate employment choices in year t−1, the columns indicate employment choices in year t. Employment choices are serially correlated except for PL. Forthosewhostayedathomeint−1,886% stay at home in tagain. Similarly, 826% of those who worked in the regular sector and 847% of those who worked in the nonregular sector in year t−1work in the same sector in year tagain. This serial correlation can be driven by heterogeneity, state dependence, or both. Sector-specific human capital is a possible explanation for state dependence. Individuals lose their sector-specific human capital when they leave the current employment sector, which discourages them from switching sectors. Another possible explanation is an entry barrier to employment sectors. If finding new employment requires a significant search effort, the chance of entering a new employment sector is low. For those who stay at home, entering the regular sector seems harder than entering the non-regular sector. Among those who stay at home during a year, 109% begin working in the non-regular employment sector, but only 10% find a job in the regular employment sector. Quantitative Economics 10 (2019) Effects of parental leave policies 1209 Cash benefits To be eligible for cash benefits, a mother must apply for job-protected PL that maintains the employment contract. Tying cash benefits to job-protected PL is the key difference from other countries such as Canada and Germany. In these countries, mothers must have worked before childbearing, but they do not need to take jobprotected PL to maintain their employment contract. Cash benefits replace a fraction Rtof pre-leave earnings up to 5112 million JPY (≈51,120 USD) per year, net of the bonus. In the JPSC, gross labor earnings including bonuses are reported, so they have to be scaled downward. According to the Basic Survey on Wage Structure 2008, regular workers’ bonuses per year are worth about the same as 3months of earnings,13 while that of nonregular workers was worth about the same as 1month of earnings. Given these statistics, earnings net of the bonus for a regular worker is 12/15 of gross earnings, while that for a non-regular worker is 12/13 of gross earnings, as reported by the JPSC. Formally, the cash benefits of PL are given by bit =Rtmin5112drit−1 12 15 ˆ yrit +dnit−1 12 13 ˆ ynit(7) where Rtis the replacement rate and ˆ yjit (j=i n) is the predicted earnings in sector j, which is based on the current state variables and earnings equation (6). Because the exact pre-leave salary is not included in the state variable to reduce computational burden, it is approximated by the predicted earnings in year t. Changes in the replacement rate of the cash benefit Rtover time are summarized in Table 1. Earnings of husband The earnings of husbands are modeled by a flexible function of state variables with little emphasis on a structural interpretation. It is specified as ymit =ωmi1+ωm2ymit−1+ωm3(ait)+ωm4(akitnit)+ωm5(dit) +ωm6URt+ηmit(8) The first term ωmi1varies across individuals to allow for the difference in the husband’s unobserved permanent skills. The lagged earnings of the husband are included to allow for serial correlation. The third term is a quadratic function of the age of the wife. The fourth term is a function of the age of the youngest child and the number of children. The fifth term is the current labor supply and fertility choices. The sixth term is the effect of the unemployment rate in year tto capture the overall labor market conditions. The last term ηmit is an i.i.d. income shock that follows a normal distribution with a zero mean and variance σ2 m. Cost for child care The cost for child care CC(akit )is a function of the age of the youngest child. The Survey of Regional Child Welfare Services 2003 reports the average monthly fees for nonaccredited child care by child’s age. The actual child care costs vary by individuals for a variety of reasons, but using the reported child care costs raises the 13For regular workers, the average monthly earnings without a bonus were 243,900 JPY, and the average bonus in 2008 was 724,000 JPY. For nonregular workers, the average monthly earnings without a bonus were 170,500 JPY and the average bonus in 2008 was 140,800 JPY. 1210 Shintaro Yamaguchi Quantitative Economics 10 (2019) concern of endogeneity biases. My approach is to use the average of the list prices. The child care cost is given by CC(akit )=I(akit =0)·43,739 +I(akit =1)·40,660 +I(akit =2)·38,179 +I(3≤akit ≤5)·34,181×12/1,000,000(9) where I(·)is an indicator function that takes the value of one if the condition in the parenthesis is satisfied and takes zero otherwise. The monthly child care cost for children under 1year of age is only 43,739 JPY (≈437 USD), because it is heavily subsidized. The fee tends to be lower for older children, but the fee difference across ages is not large. 4.4 Utility maximization The objective of a married woman is to maximize the present discount value of her lifetime utility. Her value function Vis recursively defined as V(S it εit )=max dit u(Cit nit dit )+drit vrit +dnit vnit +dlit vlit +dfit vfit +εit (dit ) +βEV(S it+1εit+1)|Sit dit (10) where βis a discount factor. Her current payoff is also affected by a preference shock εit (dit )specific to a choice dit , which are allowed to be correlated among them as described below, but are independent of all other variables. The choice-specific shocks follow a generalized extreme value distribution so that they can be correlated with each other. The choice probability is modeled by the generalized nested logit model that allows for overlapping nests, following Wen and Koppelman (2001). Eight choices are grouped by whether to work and whether to conceive. There are four nests of alternatives labeled as B1B4.NestB1includes alternatives for nonconception (dfit =0) regardless of labor supply choices, nest B2includes alternatives for conception (dfit =1) regardless of labor supply choices, nest B3includes alternatives for work (drit =1or dnit =1) regardless of fertility choices, and nest B4includes alternatives for nonwork (dhit =1or dlit =1) regardless of fertility choices. A detailed explanation of the generalized nested logit model is given in Appendix B.1 in the Online Supplementary Material. 4.5 Unobserved heterogeneity Permanent unobserved heterogeneity is modeled as a finite mixture. Individuals are one of the Ktypes, but the type of an individual is not observed. Following Wooldridge (2005), to address the initial condition problem, I allow for the probability of being type kto depend on the observed characteristics and choices in year t=τ(i) that is the first year when individual iis observed in the data. Define ziτ(i) as a vector of observed characteristics and choice in year τ(i):ziτ(i) =(diτ(i)Siτ(i)edui)where eduiis years of education. Note that education is time-invariant in the model and included here to allow Quantitative Economics 10 (2019) Effects of parental leave policies 1211 for the correlation between education and unobserved skills and preference.14 The state variables in the first year seen in the data or year τ(i) include age, years in home, regular, and nonregular sectors, the interactions of age and years in home, regular, and nonregular sectors, husband’s earnings, number of children, and age of youngest child. The probability that individual iis type kis given by pk(ziτ(i))=expπ kziτ(i) K  κ=1 expπ κziτ(i) (11) For normalization, the parameters for the first type is set to zero so that πκ=1=0. 4.6 Comparison with previous structural models A few previous structural estimation papers model and/or simulate PL policies. Gayle and Miller (2012) simulated the effects of cash benefits on fertility and labor supply, but the role of job protection or PL take-up is not considered. Adda, Dustmann, and Stevens (2017) included job protection and cash benefits in their model, but they do not model PL take-up behavior and assume that all women giving birth take PL and receive job protection and cash benefits. In addition, Adda, Dustmann, and Stevens (2017) did not study the effects of PL policies specifically. Modeling PL take-up is fruitful if PL is not universal or if the take-up rate is less than 100%. The Family and Medical Leave Act (FMLA) in the US provides job protection, but it applies to public sector employment and to private companies with 50 or more employees. Although PL is universal, the takeup rate15 is about 50% in Germany, according to Schönberg and Ludsteck (2014). Given these facts, not modeling PL take-up and instead assuming that all women take PL may result in biased estimates for the effects of PL policies. Lalive et al. (2014) appeared to be the structural estimation paper closest to the present paper. Their model, however, is based on the continuous-time job search model of Frijters and van der Klaauw (2006) instead of the discrete choice framework adopted by this paper. This paper differs from Lalive et al. (2014) in three important ways. First, I model PL take-up, the importance of which is explained above. Second, I allow for fertility choice. If a PL reform affects fertility decisions as in Lalive and Zweimüller (2009) and fertility affects labor supply decisions, then the estimated policy effects on maternal labor market outcomes may be biased if fertility is assumed exogenous. Third, I consider not only labor force participation decisions, but also occupational choices (regular vs. nonregular jobs). The simulation results below indicate that the policy effects differ between the two jobs. 14Education could be included in the intercepts of the utility and earnings functions as an alternative specification, but doing so expands the state space. Remember that computational cost exponentially rises with the size of the state space. My preferred choice is to introduce time-invariant unobserved skills and preferences and allow for correlation with education, which saves computational burden. 15Measured by the number of PL take-ups divided by the number of births. 1212 Shintaro Yamaguchi Quantitative Economics 10 (2019) 5. Estimation strategy 5.1 Estimation algorithm The model is estimated by the maximum likelihood method. I describe the details of the likelihood function in Section B.1 for interested readers. The maximum is found by combining the three algorithms that accelerate computation. The main algorithm is developed by Kasahara and Shimotsu (2011), and their algorithm sequentially updates the parameter and the value function estimates. For each likelihood evaluation, the value function is iterated for a small number of times rather than until convergence, which significantly reduces the computational time. To accelerate the computation for the value function iteration in evaluating the likelihood, the value function is approximated by sieves using the method proposed by Arcidiacono et al. (2013). When the state space is large, this sieve approximation can reduce the computational time dramatically. To account for unobserved heterogeneity modeled as a finite mixture, I combine the sequential algorithm above and the expectation-maximization algorithm with a sequential maximization step developed by Arcidiacono and Jones (2003). Combining these algorithms makes the model estimation tractable. The details are described in Section B.2. Because the computation of standard errors for the proposed algorithm is analytically complex, I take the converged estimates from this algorithm as a starting value for the full information maximum likelihood with the nested fixed-point algorithm. 5.2 Identification In this subsection, I discuss identification issues. Although a formal identification argument may not be possible for a complicated structural economic model, an informal argument may help me understand what variations of the data identify which parameters along with parametric assumptions. There are two policy variations in the data: changes in the eligibility condition and the replacement rate. Nonregular workers became eligible for mandated PL in 2005, which generates variation in the eligibility variable ELGit (see Appendix A.1.1 for the precise definition). The variation in this variable helps me identify the effects of legal eligibility on the nonpecuniary utility from PL take-up, which is parameter νl3in equation (4). Changes in the replacement rate affect consumption while on PL through the budget constraint. This variation identifies the marginal utility of consumption while staying at home or taking up PL, which is measured by parameter α1in equation (1). For a greater value of the parameter α1, women’s PL take-up is more elastic to a change in cash benefits. Hence, the variation in PL cash benefits help me identify parameter α1. The intercepts of the nonpecuniary utility functions (equations (3), (4), and (5)) are time-invariant and vary by individuals. They are identified by the panel structure of the data. Given the parametric assumption that the intercepts are time-invariant, the remaining parameters in the nonpecuniary utility are identified by the variations of observed variables such as the age of the youngest child, number of children, and lagged Quantitative Economics 10 (2019) Effects of parental leave policies 1213 decision variables. The heterogeneous intercept and lagged decision variable have similar effects on choice in the sense that both generate a serial correlation in choice, which can be seen in Table 4; however, they can still be distinguished. This is because the intercept is time-invariant and hence has permanent effects, while the effect of the lagged decision variable diminishes over time. The intercepts of the earnings functions (equations (6)and(8)) are also timeinvariant and vary by individuals. Similar to the argument above, they are identified by the panel structure of the data, while the remaining parameters are identified by variations in observed variables such as experiences. One might consider the DID approach to be more suitable, at least for ex post policy evaluation, but it may not necessarily be superior to structural estimation in this context. In DID estimation, a researcher may consider that the treatment group comprises those in the eligible (i.e., regular) sector and the control group comprises those in the ineligible (i.e., nonregular) sector. However, this approach may result in a biased estimate because eligibility, or the worker’s sector, is determined by past career decisions. In structural estimation, selection into sectors is modeled to avoid this bias. Another reason why DID may not be a better method than structural estimation in this context is the small sample size. Because the employment rate prior to childbirth is low, the sample size for the DID approach is small, which results in imprecise estimates. The structural estimation approach avoids this problem by taking advantage of the economic model and knowledge about institutions. While misspecification of the structural model is a legitimate concern, I assess the model’s internal validity by examining whether the model’s predictions are consistent with some important features of the data. Of course, this is by no means a proof for identification; some of the assumptions may not be correct. 6. Estimation results 6.1 Parameter estimates Marginal utility of consumption Table 6reports the parameter estimates for the marginal utility of consumption. The estimated marginal utility of consumption is positive, but decreases when women work either in regular or nonregular sectors. This is consistent with the fact that a wife’s labor force participation decreases with her husband’s earnings, all else being equal. The estimates also indicate that the marginal utility of consumption increases with the number of children, which implies that labor supply increases with the number of children. Table 6. Parameter estimates for marginal utility of consumption. Estimate S.E. Home or On-Leave 0074 0013 Reg. −0030 0006 Non-Reg. −0037 0007 Sqrt. of No. Children 0049 0005 1214 Shintaro Yamaguchi Quantitative Economics 10 (2019) Table 7. Parameter estimates for nonpecuniary utility from labor supply and fertility choices. Reg. Non-Reg. PL Fertility Estimate S.E. Estimate S.E. Estimate S.E. Estimate S.E. Intercept (Type 1) 0172 0155 −0115 0144 −2701 0752 0501 1019 Intercept (Type 2) −0064 0110 0272 0061 0468 0305 −0753 0319 Intercept (Type 3) 0372 0114 0570 0093 −0810 0346 0354 0301 Intercept (Type 4) 0076 0103 0159 0065 0043 0305 −0098 0321 Reg. 0705 0192 Non-Reg. 0243 0196 Lagged Home −4755 0649 −2611 0352 Lagged PL in Reg. −0292 0230 Lagged PL in Non-Reg. 0349 0437 Lagged Reg. Empl. −1594 0319 0780 0380 Lagged Non-Reg. Empl. −2322 0385 PL Legally Eligible 1388 0407 Lagged PL * Ineligible 0788 0390 Sqrt. of No. Children 0003 0028 0090 0026 −0594 0368 Child Age 0−2614 0396 −2798 0383 −0361 0439 Child Age 1−0080 0180 −0432 0109 1084 0405 Child Age 2−0157 0166 −0498 0106 1235 0398 Child Age 3–5−0081 0074 −0206 0051 0916 0362 Child Age 6–11 −0016 0060 −0139 0047 0295 0339 Age −0059 0042 Age-sq −0239 0060 Unempl. Rate −0056 0028 0011 0031 Nonpecuniary utility of work There are two important findings from the estimates of the non-pecuniary utility of work shown in Table 7. First, the entry costs to employment sectors from home are large, which is particularly true for the regular employment sector. This is suggested by the large negative nonpecuniary utility of entering the regular sector from home (−4755), which is the most negative of all factors in the model. The large entry cost implies that returning to work after quitting a job is difficult, and hence, job protection is expected to help mothers of young children return to the labor market quickly. Second, having a young child decreases the nonpecuniary utility of work in both sectors, and the negative effect is particularly large when the child is less than 1year of age. This is consistent with empirical evidence that maternal work in the first year of a child’s life may have negative effects on both children and mothers themselves. Waldfogel, Han, and Brooks-Gunn (2002), Baum (2003b), and James-Burdumy (2005)found that maternal work during the first year of a child’s life has a negative effect on the child’s test scores. Baker and Milligan (2008b) find that maternal work can prevent breastfeeding, which improves the health of both children and mothers according to the World Health Organization.16 Moreover, Wray (2011) argued that mothers need a year to fully recover from childbirth and be ready to work. If mothers care about the development 16World Health Organization recommends exclusive breastfeeding for the first 6months. Quantitative Economics 10 (2019) Effects of parental leave policies 1215 of their children and their own health, and believe that maternal work has detrimental effects on these outcomes, the nonpecuniary utility from work will be very negative in the first year of the child’s life.17 The large negative effect of a newborn on the nonpecuniary utility of work implies that PL is valuable for mothers of children aged less than 1year because it allows them to be off work and stay with their new baby without losing their job. However, PL may not be as valuable for mothers of children aged 1year or older because the negative effect on the nonpecuniary utility quickly fades after the child’s first birthday. This difference between newborns and older children explains why 1-year job protection increases female labor supply but expanding it to 3years does not based on counterfactual simulations in Section 7. Other estimates are also worth mentioning. As expected, the costs of returning from PL are small and not significantly different from zero in both sectors. The costs of switching between employment sectors are large, although they are smaller than the costs of entering from home. The unemployment rate is negatively related to the nonpecuniary utility of work in the regular employment sector, while it has almost no effect in the nonregular sector. Transaction cost of PL take-up The nonpecuniary utility of PL take-up varies greatly by unobserved type, as presented in Table 7: PL is generally unpleasant for type 1women, but it is less so for other types. For type 1women, the financial incentives of PL are likely to be irrelevant because of the large negative nonpecuniary utility of PL take-up. Legal eligibility for PL reduces the transaction cost of PL take-up, which is implied by its positive effects on nonpecuniary utility. Even though some employers grant PL voluntarily, mandating it can increase PL take-up. The transaction cost of PL take-up is also found to be lower in the regular sector than in the nonregular sector. This is because regular workers are more skilled and harder to find than nonregular workers, and hence, employers are more willing to offer additional PL to retain regular workers. Utility from children The last column in Table 7reports parameter estimates for utility from children received as a lump sum at the time of conception. Utility decreases with the number of existing children and when the mother has a child aged less than 1year. It also decreases with the mother’s age at the quadratic rate. Correlation structure of error terms Table 8presents the parameter estimates that govern the correlation structure of the error terms. The correlation of the error terms is modeled by the generalized nested logit. Four overlapping nests are constructed depending on the work and fertility alternatives (see Section 4.4 for details). Equation (22) in Appendix B.1 of the Online Supplementary Material shows the choice probabilities using these parameters. 17The literature does not fully agree on the effects of maternal work on child development. For example, using the changes in PL legislation, Baker and Milligan (2010,2015) and Dustmann and Schönberg (2011) found no effects for Canada and Germany, while Carneiro, Løken, and Salvanes (2015) found negative effects of maternal work in Norway. In addition, Baker and Milligan (2008b) found no effects of breastfeeding on self-reported maternal and child health. Even if maternal work has no effect on these outcomes, mothers derive large negative utility from work if they believe it has detrimental effects. 1216 Shintaro Yamaguchi Quantitative Economics 10 (2019) Table 8. Parameter estimates for error terms. Estimate S.E. Dissimilarity Parameter λ10612 0112 λ20810 0129 λ30651 0487 λ40927 0228 Allocation Parameter μ10784 0178 Note: Dissimilarity parameters measure the degree of independence among alternatives within the nest and take the value between zero and one. λ1is a dissimilarity parameter for the nest that includes alternatives for nonconception (dfit =0) regardless of labor supply choices. λ2is for the nest that includes alternatives for conception (dfit =1) regardless of labor supply choices. λ3is for the nest that includes alternatives for work (drit =1or dnit =1) regardless of fertility choices. λ4is for the nest that includes alternatives for nonwork (dhit =1or dlit =1) regardless of fertility choices. The allocation parameters measure the extent to which an alternative is a member of each nest. It is assumed that μ1=μ2,μ3=μ4,and1−μ1=μ3.See equation (22) in Appendix B.1 of the Online Supplementary Material for choice probabilities using these parameters. The dissimilarity parameters λ1λ4measure the degree of independence among alternatives within the nest and take a value between zero and one. The estimates are smaller than one, implying that choices are correlated within each nest. The allocation parameter μbmeasures the extent to which an alternative is a member of nest b.The estimate is significantly above zero and below one, implying that the nests overlap. Ignoring this correlation structure, or the use of the multinomial logit model, biases the parameter estimates of the utility functions and can make unrealistic predictions arise from the assumption of independence from irrelevant alternatives. Earnings functions The parameter estimates for the earnings functions are shown in Table 9. For both the regular and nonregular sectors, experience in an individual’s own sector increases earnings. Experience in the other sector also increases earnings, but at a lower rate than experience in one’s own sector. Years at home reduce earnings in both sectors, which implies earnings capacity depreciates while at home or on leave. A temporary earnings penalty was also observed for those who stayed at home or had been on leave in the last year. New workers switching from the non-regular to the regular sector earn less than those already in the regular sector. By contrast, workers newly switching from the regular to the nonregular sector earn more than those already in the nonregular sector. Husband’s earnings and type probability functions The parameter estimates for the husband’s earnings and type probability functions and the share of each unobserved type are reported in Appendix C of the Online Supplementary Material, because they do not have structural interpretation. 6.2 Model fit I now present evidence on how well the model fits selected features of the data. I took the initial observations for each individual in the data, that is, her employment and fer- Quantitative Economics 10 (2019) Effects of parental leave policies 1217 Table 9. Parameter estimates for log earnings functions. Reg. Non-Reg. Estimate S.E. Estimate S.E. Intercept (Type 1) −0431 0158 −2459 0066 Intercept (Type 2) 1039 0128 −1356 0061 Intercept (Type 3) 0349 0131 −0623 0059 Intercept (Type 4) 0723 0139 −0021 0061 Years in Reg. 0030 0006 0023 0002 Square of Years in Reg./100 −0028 0013 Years in Non-Reg. 0010 0003 0087 0006 Square of Years in Non-Reg./100 −0269 0027 Years in Home −0025 0017 −0049 0009 Square of Years in Home/100 0060 0176 0107 0078 Lagged Home or On-Leave −0487 0043 −0677 0020 Lagged Reg 0165 0054 Lagged Non-Reg. −0288 0062 Unempl. Rate 0031 0028 −0006 0012 tility choices, earnings, and earnings of her husband. I then ran 30 simulations using the model until the period ending with the last appearance of each individual in the data. Figure 2shows the observed and predicted age profiles of choice probabilities, her own and her husband’s earnings, and the number of children. The solid lines are observed profiles and the dashed lines are predicted profiles. In all eight panels in the figure, the predicted age profiles are similar to the actual age profiles, although the profiles for both left and right tails are noisier because of the small sample size for these age groups. Tables 10 and 11 show the model fit for employment transitions and PL take-up rates along with employment status around childbearing. For both sets of statistics, the model is able to predict the observed patterns in the data. The model is identified by increases in the availability and generosity of Japan’s PL policies as well as the parametric assumptions. Among the policy changes, the most notable is the expansion of job protection to nonregular workers in 2005. Table 12 presents how well the model fits selected features of the data before and after this major reform in 2005. The PL take-up rate among those who give birth increased from 0140 to 0249 after the reform, which is consistent with the expected effect of the PL reform. The model matches closely this increase in the PL take-up rate. The employment rate 1year after PL take-up decreased slightly from 0922 to 0880, which is also well matched by the model. Because the 2005 reform is targeted at nonregular workers, the non-regular employment rate is expected to have increased after the reform; in fact, it increased from 0088 to 0160 in the data. The model’s prediction closely tracks these changes. 6.3 Discussion I have imposed several simplifying assumptions to make the model tractable for estimation. Two important assumptions are omitting saving decisions and taking husband’s 1218 Shintaro Yamaguchi Quantitative Economics 10 (2019) Figure 2. Age profiles for labor market outcomes. Note: The solid lines are observed profiles, while the dashed lines are predicted profiles. Quantitative Economics 10 (2019) Effects of parental leave policies 1225 on leave. Human capital depreciation affects the opportunity cost of taking PL, which may explain why the extension of job protection from 1to 3years does not increase maternal employment. Two policy changes are simulated. In the first, 1-year job protection is first introduced, but no cash benefits are paid. In the second, job protection is extended from 1to 3years, as in Section 7.1.1, in which the replacement rate of cash benefits is at 50% and cash benefits are paid only when an individual takes PL. The policy effects of the baseline model are compared with the model without human capital depreciation. In the baseline model, all parameters are at the estimated values. In the model without human capital depreciation, the coefficients for years at home and lagged sectors in the earnings functions (6)aresettozero. In Table 17, Column (2) shows the policy effects in the baseline model, while Column (3) shows those when human capital does not depreciate. Although the policy effects are stronger when human capital does not depreciate, they are similar to those of the baseline model. Hence, human capital depreciation does not explain why most women do not take PL for 3years, even when 3-year job protection is possible. The estimates in Table 9indicate that 1year spent at home decreases earnings by 2 to 5%, which may not be large enough to prevent women from taking PL for an extended period. Human capital depreciation may be crucial for highly skilled women, but it does not seem so for women of average skill. Indeed, only 14% in the sample graduated from a 4-year university. It should also be noted that this result is consistent with previous findings in other countries. For example, Lalive et al. (2014) found no evidence for human capital depreciation among the group of mothers exposed to longer leave regimes. 7.1.3 The cost of entry and job protection policy The simulation indicates that the effect of job protection is concentrated in the regular sector and lasts for several years after childbirth. This is because the cost of entry to regular employment from home is high. Table 17. Policy effects under different setup. Mean Policy Effects (1) Before Change (2) Baseline (3) No HC Depreciation (4) Low Entry Cost No PL →1-Yr JP (w/No Benefit) On PL in t=0012 038 038 030 Work in t=5046 011 013 002 Earnings in t=5087 051 065 014 No of Children in t=10 210 006 008 005 1-Yr JP →3-Yr JP (w/50% + PL Take-Up) On PL in t=0054 003 003 004 Work in t=5059 001 000 −001 Earnings in t=5148 −002 000 −003 No of Children in t=10 218 005 006 003 Note: Column (1) shows mean of outcomes variables before the PL reforms. Columns (2)–(4) show the mean changes of outcomes variables caused by the PL reforms under different assumptions. JP stands for job protection. 1226 Shintaro Yamaguchi Quantitative Economics 10 (2019) To see how entry costs influence the effects of job protection, I simulate the model under the assumption that the entry costs are reduced by 50%. I compare that with the results from the last Section 7.1.2, presented in Table 17. As expected, lower entry costs weaken the policy effects on maternal work relative to the baseline model. This implies that differences in labor market friction and/or flexibility between countries must be taken into account when one tries to generalize the findings of this paper. Lin and Miyamoto (2012) found that the monthly job finding and separation rates in Japan are about 14% and 04%, respectively, while they are 25–32% and 3–5% in the US, according to Yashiv (2008). These statistics suggest both that the labor market is more flexible and that the entry cost is smaller in the US compared with Japan, and hence, the employment effect of job protection is also expected to be smaller. 7.2 Cash benefits I evaluate the effects of PL cash benefits by simulating three scenarios where the duration of job-protected PL is 1year. In the first scenario, no cash benefits are paid. In the second, unlike the actual legislation in Japan, mothers can receive cash benefits even if they do not apply for job-protected PL. This scenario tries to replicate the PL system seen in other countries such as Canada and Germany. In the third, mothers must apply for job-protected PL to receive cash benefits, which corresponds to the current Japanese PL system. In the second and third scenarios, the replacement rate is set at 50%. These scenarios are implemented as follows. In the first scenario, the replacement rate of the cash benefit is set to zero. In the second, cash benefits are paid to women who (1) give birth, and (2) have worked in the previous year before childbirth, but they do not have to take up job-protected PL. The third scenario uses the estimated baseline model that imitates the actual legislation. In the baseline model, to be eligible for cash benefits, a mother must apply for job-protected PL. To be eligible for job-protected PL, she must satisfy the following two conditions: (1) the age of the youngest child is zero, and (2) she has been employed without being on any form of leave, in the eligible sector in the previous year. Cash benefits are expected to increase the number of mothers staying at home in the short run, but the long-run effects on maternal work are ambiguous. On the one hand, cash benefits may increase maternal work because women want to become eligible for cash benefits. On the other hand, cash benefits may decrease maternal work because mothers lose their human capital while on PL. Whether cash benefits are tied to job-protected PL also matters to their labor supply after childbearing. If mothers are required to take up job-protected PL to be eligible for cash benefits, then cash benefits increase the incentive to take up PL, which helps women to return to work. Table 18 summarizes the simulation results.20 The effects on the PL take-up rate are modest. The first column shows the mean outcomes in the first scenario in which no cash benefits are paid. The second column shows the effects of a change from the first to second scenarios, while the third column shows the effects of a change from the second 20Detailed results are available in Appendix C of the Online Supplementary Material. Quantitative Economics 10 (2019) Effects of parental leave policies 1227 Table 18. Marginal effects of cash benefit arrangement. Mean Policy Effects No Benefit 0% →50% 50% →50% +‘Need to Take PL’ On PL in t=0050 002 002 Work in t=5057 001 001 Earnings in t=5138 003 006 No of Children in t=10 215 003 000 Note: The following three scenarios are simulated. In the first scenario, no cash benefit is paid. In the second scenario, mothers can receive cash benefit even if they do not apply for a job protected PL. In the third scenario, mothers must apply for a job protected PL to receive cash benefit. In the second and third scenarios, the replacement rate is set at 50%.Thefirst column labeled as “Mean” shows mean of outcomes variables when no cash benefits are paid (the first scenario). The second column shows the effects of a change from the first to second scenarios, while the third column shows the effects of a change from the second to the third scenarios. to the third scenarios. When the replacement rate increases from 0% to 50%, the take-up rate increases by two percentage points. When cash benefits and job-protected PL are tied together, the take-up rate further increases by two percentage points. The effects on probability of work, earnings, and fertility are also modest, although positive. These results are in line with Asai (2015), who estimates the effects of cash benefits using the DID approach and finds that they have little effect on employment in Japan. Effects on accumulated income, accumulated consumption, and welfare are presented in Table 15 (see rows 2, 5, and 7). Raising the replacement rate from 0% to 50% improves accumulated income, consumption, and welfare. Tying cash benefits to jobprotected PL increases income and consumption but decreases welfare for lost time at home. Yet, tying cash benefits to job-protected PL is preferred over no cash benefits. 7.3 Other family-friendly policies Parental leave is not the only family-friendly policy that might be expected to affect women’s labor supply and fertility behavior. The simulation results above indicate that PL policies generally have only modest effects on fertility, but large financial incentives directly targeted at fertility may increase the fertility rate. To assess the effects of baby bonuses, I simulate the model in which 1,3,and5mil- lion JPY (≈10,000,30,000,and50,000 USD, resp.) are paid at childbirth. I fix the PL policies at the 2011 level so that 1-year job protection is available for both the regular and nonregular sectors, the replacement rate of cash benefits is 50%, and cash benefits are paid only when an individual takes up job-protected PL. The simulation results are presented in Table 19. The first column shows simulation results for the baseline model in which no baby bonuses are paid. The second to fourth columns show simulation results for the baby bonuses of 1,3,and5million JPY, respectively. The results indicate that baby bonuses increase the fertility rate and that policy effects increase with the size of the bonus. Namely, the baby bonus of 5million JPY increases the fertility rate from 218 to 246. However, the downside of the large baby bonus is that it also decreases the mother’s labor supply and earnings: the baby bonus of 5mil- lion JPY decreases the probability of work and earnings 5years after childbearing from 1228 Shintaro Yamaguchi Quantitative Economics 10 (2019) Table 19. Effects of baby bonus and child care subsidy. Baby Bonus Baseline 1 Mil. JPY 3 Mil. JPY 5 Mil. JPY Free Childcare On PL in t=0054 054 055 055 056 Work in t=5059 059 058 057 063 Earnings in t=5148 147 145 144 162 No of Children in t=10 218 223 234 246 220 Note: In the baseline simulation, the PL policies in 2011 are adopted. Namely, 1-year job protection is available for both regular and nonregular sectors, the replacement rate of cash benefit is 50%, and cash benefits are paid only when an individual takes up a job protected PL. Baby bonuses of 1,3,and5million yen (≈10,000,30,000,and50,000 USD) are paid at childbearing. The child care subsidies cover the full cost of child care and parents do not pay any child care fees. 059 to 057 and from 148 to 144, respectively. This side effect is a logical consequence of increased fertility: baby bonuses increase fertility, and hence, eventually increase the pecuniary and nonpecuniary costs of labor supply. PL legislation generally has few fertility effects, even though it increases mothers’ labor income and household consumption substantially. For example, changing from no PL to 1-year job-protected PL increases the present value of consumption by 338 million JPY (see Table 15). While this increase is comparable to the baby bonus of 3million JPY, PL and the baby bonus have very different effects on fertility and maternal employment. The simulation results suggest that there is a fundamental trade-off between a woman’s career and children, and that promoting both at the same time is quite challenging for policy makers. Job-protected PL increases mother’s employment, and hence her human capital by removing the cost to reenter the labor market after leave, but holding a job and having more human capital increases the opportunity cost of having an additional child. By contrast, baby bonuses raise fertility, but also have a slightly negative effect on mother’s labor supply. This is because having a child increases the pecuniary and nonpecuniary costs of her labor supply. Another family-friendly policy that may promote both fertility and mother’s work is a child care subsidy. However, assessing the effects of a child care subsidy in the Japanese context is not straightforward in the current model for two reasons. First, the model does not allow for the use of free or cheap informal child care arrangements provided by grandparents. Yamaguchi, Asai, and Kambayashi (2018)reportedthatabout10–20% of working mothers of children aged 15–35years take advantage of care by grandparents. For mothers using free child care, the current model overestimates the cost of work. Second, many Japanese parents are unable to find a slot in formal child care centers because the supply of formal child care falls short of the demand in large cities such as Tokyo. For mothers who cannot find a slot, the effective child care price is infinite; the current model cannot capture this feature. Despite these limitations, to assess the role of financial cost in young mother’s labor supply, I conducted counterfactual simulations in which child care is fully subsidized and parents pay no child care fees. The simulation results are presented in the fifth and last columns. Child care subsidies modestly increased both fertility and mother’s labor supply. The effect of providing free child care is modest because child care is already Quantitative Economics 10 (2019) Effects of parental leave policies 1229 heavily subsidized; hence, the policy change does not provide a large additional financial incentive. Yamaguchi, Asai, and Kambayashi (2018) pointed out that providing more child care slots instead of reducing the child care fee has large positive employment effects on mothers of children aged 1to 2years. 8. Conclusion In the present paper, I constructed and estimated a dynamic discrete choice structural model of female employment and fertility decisions. My contribution is to model job protection and cash benefits of parental leave. Job protection allows women to return to work after childbearing without paying entry costs to employment, while cash benefits provide financial incentives to take up parental leave. The model is estimated by the sequential estimation algorithm based on Kasahara and Shimotsu (2011) and the EM algorithm of Arcidiacono and Jones (2003). The sieve approximation for the value function of Arcidiacono et al. (2013)isalsoappliedtofurther reduce computational burden. As far as I know, this paper is the first application that combines these three methods. The estimated model seems to fit selected features of the data. The model is used to conduct counterfactual simulations for evaluating parental leave policies. Effects of 1-year job protection on maternal work are significant, but extending the duration of job protection from 1to 3years has little effect. This is because the nonpecuniary utility of work is very negative only in the first year of a child’s life. Evidence suggests that the large negative nonpecuniary utility of work for mothers of newborns is not specific to Japanese women, but policy effects may depend on labor market institutions. The effect of job protection tends to be strong when the cost of entry to the labor market is high, and hence, job protection may have smaller employment effects in the US, where the labor market is significantly more flexible than in Japan. Nevertheless, the model and estimation method offer a useful tool to predict the potential effects of parental leave in other countries such as the US, where the FMLA offers only 12 weeks of unpaid parental leave. The model could be used to conduct an ex ante evaluation of extending the job protection period and the introduction of cash benefits. One area to examine in future work is the interaction with other pro-family policies intended to support working mothers, such as child care expansion. Such policies are likely to affect the cost of children for labor force participation, and hence, the effects of parental leave policies. References Abe, S. 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