Female Labour Market Outcomes and Parental Leave Policies

Transcription

1 Female Labour Market Outcomes and Parental Leave Policies Hamish Low University of Cambridge, IFS Virginia Sánchez-Marcos Universidad de Cantabria April 2013 Abstract There is substantial variation in the labour market gender gaps throughout developed countries. Family policies aimed at reconciling family and work are considered to be responsible for such variations. We use a quantitative life-cycle model of the female labour supply and savings decisions made by households to assess the role of differences in parental leave policies between the US and the Scandinavian countries in accounting for differences in labour market gender gaps. Our findings show that a generous paid parental leave policy has a substantial effect on mothers employment rate while causing a modest impact on differences in wages between genders. 1 Introduction Gender gaps in the labour market are still substantial in many developed countries. Firstly, the employment rate gap between sexes was about 20.6% in 2009 for the average of the OECD countries and it was more pronounced during child-bearing ages. Secondly, the average wage of women is in general below men s, the gap averaging about 15.8% in 2009 in the OECD countries. However, differences across countries in these respects are remarkable and then the question of what their determinants are naturally arises. Family policies aimed at reconciling family and work Virginia Sánchez-Marcos thank the Spanish Ministry of Science and Technology for Grant ECO

2 during child-bearing periods are sometimes argued to be key to account for differences in gender gaps across countries. In particular, parental leave policies may potentially affect female labour supply and wages. Paid parental leave provides an insurance against wage loss during women s spell from the labour market and a cash benefit that preserves household earnings during this period. As a consequence parental leave coverage may speed the mothers return to work, who would otherwise have left the labour market altogether for a lengthy period of time. 1 In addition, as argued by Ruhm (1998) females that would not otherwise participate in the labour market may choose to be active prior to childbirth in order to subsequently qualify for maternity leave benefits. As regards the effect on female wages, Waldfogel (1998a) argues that parental leave coverage may raise women s pay by raising women s retention during the period of child-rearing, and then increasing their work experience and job tenure and thereby allowing them to maintain good job matches. The fact that displaced workers suffer important wage losses has been documented by Jacobson, LaLonde, and Sullivan (1993) and more recently by Couch and Placzek (2010). Jacobsen and Levine (1995) document the negative impact on female earnings due to intermittent labour supply. Furthermore, they find evidence of differences in labor market experience between mothers and childless women being key to account for motherhood wage penalties, see for instance Waldfogel (1998b) or Budig and England (2001). However, a the introduction of parental leave on wages can also be negative due to at least three different reasons. First, women that are self-selected into the labour market after the implementation of maternity leave may be on average less productive than women already working. Second, employers may pass the cost of parental leave policies to mothers by lowering their wages. However, this is less likely to be the case in those countries which mandate maternity leave provided as a tax-funded social insurance benefit. Finally, long lasting leaves may erode female human capital, even if job their is protected. There is abundance of empirical evidence of the effect of maternity leave policies on female labour supply, and female wages based on quasi-experiments or cross-country analysis. Waldfogel, 1 Note however that in the case of long maternity policies there may be some women that stay out of the labour market longer than what they would have been in the absence of such coverage. 2

3 Higuchi and Abe (1999) find that family leave coverage increases the likelihood that a woman will return to her employer after childbirth in the US, Britain and Japan. Furthermore, there is evidence both in the US and Britain (Waldfogel (1998a)) that women who maintain employment continuity over childbirth have higher pay than those who do not. So those countries that lack access to job-protected maternity leave would in principal be observed to have higher mother wage penalties. This fact is consistent with studies finding no family penalty for women with children in the Scandinavian countries (see Rosholm and Smith (1996) for Denmark TO BE CHECKED). Ruhm (1998) finds that in nine European countries parental leave legislation raises female employment rate, mostly affecting women of childbearing age. In particular rights to 40 weeks of job-protected paid leave are predicted to raise female employment to population ratios by 4.2 percent, but reduces hourly wages by 2.7 percent. According to him, about one quarter of the employment effect may be accounted by mothers on parental leave being counted as employed. However, some studies find that extensions of paid maternity leave in Europe may reduce maternal work while the mother is eligible for leave. Lalive and Zweimller (2009) explore the case of extensions in paid leave from 1 to 2 years in Austria and they found that it decreased maternal employment 8 years after birth. Howev, this may be the result of the incentives of the Austrian system for mothers to compress their fertility to maintain eligibility for leave. Merz (2004) attributes many of the changes in the labour supply of married women with children since the mid seventies in Germany to institutional modifications in the federal legislation governing parental leave that occurred up until Schnberg and Ludsteck (2011) analyze the impact of five major expansions in maternity leave coverage in Germany on mothers labour market outcomes after childbirth. Each expansion in leave coverage reduced mothers post-birth employment rates in the short-run. Four out of the five expansions in leave coverage had only a small effect on women s employment rates and labour market income six years after childbirth (the common feature of these reforms is that the job protection period is as long as, or even exceeds the maternity benefit period). The reform that extended the maternity benefit period beyond the job protection period, in contrast, worsened women s position in the labour market after childbirth. In the US, an evaluation of the 12 weeks of unpaid job-protected leave under the Family and 3

4 Medical Leave Act 2 found small or inconsistent impacts of the length of leaves (Baum (2003); Han and Waldfogel (2003); Waldfogel (1999); Klerman and Leibowitz (1997)), while it did not affect post-pregnancy employment or wages (Klerman and Leibowitz (1997), Baum (2003) and Waldfogel (1999)). In Canada, Baker and Milligan (2005) focused on identifying the impact of extensions of job-protected leave, by exploiting variations in provincial dates. As in the US, this research found that short unpaid mandates (12 to 18 weeks) had no impact on maternal work, while later expansions in 1990/1991 and 2000/2001 had larger impacts on maternal work during the period of eligibility for leave. Finally, Rossin-Slater, Ruhm and Waldfogel (2011) found that California s first in the nation Paid Family Leave (PFL) program affected leave-taking by mothers following childbirth, as well as subsequent labour market outcomes. They find robust evidence that the California program more than doubled the overall use of maternity leave, increasing it from around three to six or seven weeks for the typical new mother with particularly large growth for less advantaged groups who had relatively low levels of baseline use. This contrasts starkly with the results for other state family leave laws (most of which extend rights to unpaid leave beyond those in the 1993 Family and Medical Leave Act, where the estimated effects are much larger for college-educated and married women than for their less advantaged counterparts (Han, Ruhm and Waldfogel (2009)). These authors also find evidence that PFL increased the usual weekly work hours of employed mothers of children aged 1 to 3 by 6 to 9% and that their wage incomes rose by a similar amount. The evaluation of parental leave policies cited above is based on quasi-experiments or crosscountry comparisons. Meyer (1995) offers an excellent survey of this kind of methodology and about the difficulties that are common in its application. In general, changes in policies implemented through time and across countries may simultaneously occur with other policy reforms that can reinforce or counteract some of the effects of the policy being analyzed. This causes difficulties when trying to isolate the effect of the policy in question. Furthermore, finding control groups to implement difference-in-difference type of analysis is difficult in many cases. Finally, 2 Under the Family and Medical Leave Act, firms employing at least 50 persons within 75 miles of the work site are required to offer eligible workers 12 weeks of job protected but unpaid time off work to care for newborn or newly adopted children. 4

5 in the particular case of maternity leave polices, some of the studies cited above focus on the effect of maternity leave policies that are not mandatory but only adopted voluntarily by firms. In those cases, self-selection into maternity leave policies is not random and therefore its effects on female employment and wages cannot be generalized. In spite of the aforementioned difficulties, quasi-experimental analysis is sometimes the only way to evaluate the effect of certain policies. Nevertheless, in the case of paid parental leave policies, an analysis based on quantitative life-cycle models of the female participation decision can be undertaken to complement empirical evidence. This is precisely the aim of this paper. We contribute to the discussion on the effects of parental leave policies by evaluating the impact of the introduction of a one-year paid parental leave in the US. More specifically, the aim of this paper is to assess the extent to which differences in parental leave policies between the Scandinavian countries and the US can account for differences in female labour market performance between these countries, both in terms of employment and wages. The analysis is carried out in a similar framework as Attanasio, Low and Sánchez-Marcos (2008). In particular we pose a life-cycle model of the savings and female labour participation decisions that accounts for the trade-offs of labour market participation during child-bearing, including the loss of human capital that results from labour market spells. We calibrate our model economy to be consistent with mothers employment rates at different child ages, with observed females life-cycle wage growth and with the wage gender gap and the fraction of motherhood wage penalty that can be attributed to labour market interruptions in the US economy. Then we look in detail at the impact of paid parental leave on mothers labour supply and wages. Of course, this analysis is also subject to several limitations. First, it is silenced about the potential reaction of firms to the introduction of parental leave benefits. If the policy imposes any cost for firms hiring mothers, firms may try compensate through lower wages or may modify their hiring policy with respect to men and women. In this sense our estimation of the impact of the policy is an upper bound of the effect on female employment and wages. Second, we are not considering how benefits for mothers on paid maternity leave are funded. This could be done for instance through a general income tax. 5

6 Our paper is related to a strand of the quantitative macroeconomic literature that have focused on family issues and in particular on the evaluation of the effect of different types of policies on two-earner households. Among others, Guner, Kaygusuz and Ventura (2012) and Kaygusuz (2010) evaluate the effect of different income tax reforms in the US with a special focus on joint versus separate taxation of spouses. Kaygusuz (2010) evaluates the impact on female labour supply of changing survivors pensions in the US. Bick (2011) quantifies the effect of policy reforms regarding the supply of subsidized child care for children aged zero to two in Germany and Domeij and Klein (2012) explore optimal day care subsidizing policies in Germany. However, the most closely related paper to us is Erosa, Fuster and Restuccia (2010) who analyze the welfare consequences of alternative maternity leave policies in the US within a general equilibrium model with labour market frictions where households make employment and fertility decisions. Our paper is less ambitious in the sense that we do not undertake a general equilibrium analysis, however, our purpose is different. We wish to understand to what extent differences in female gaps in the labour market between the US and the Scandinavian countries, both in terms of employment and wages, can be accounted for by differences in maternity leave policies. In our analysis we assume exogenous fertility, but as we argue below, total fertility rates are similar across the countries of interest. Different from Erosa, Fuster and Restuccia (2010), households in our model economy face uncertainty with respect to husbands and wives earnings and they are allowed to save and borrow against their minimum future income. Without the saving choice, the only way to substitute consumption intertemporally would be through changing labor supply. However, saving is potentially a more flexible tool for intertemporal substitution and therefore ignoring it might overstate the importance of labor supply choices in smoothing earnings shocks. Furthermore, saving allows households to smooth the effect of the fixed cost of working for mothers that would otherwise affect labour supply differently. The effect of parental leave policies may be different in a context in which savings are not allowed. Our results support a substantial effect of a one-year paid parental leave policy on mothers employment rate, in particular of mothers of children aged 0 to 2. This is both due to women being more likely to participate in the workforce in order to be eligible for parental leave and 6

7 due to women being more likely to participate as a result of the higher accumulation of human capital during child-bering. The effect is also substantial on the employment rate of mothers of children aged 3 to 5. Finally, the impact on the employment rate of mothers 6 to 14 is mild. We find a modest impact on the wage gender gap. In spite of the increase in females labour market experience that goes in the direction of increasing females wages with respect to males, new participants are relatively less productive (conditioning on human capital) and they help to erode average female wages. The rest of the paper is organized as follows. Section 2 describes the facts from which our question arises. In section 3 we present the model economy we use for the analysis and explain the parental leave policy we evaluate. The calibration of the model economy to align it with the US economy can be found in section 4. Policy analysis is carried out in section 5. Finally, section 6 concludes. 2 Data In this section we provide empirical evidence that motivates the question we address in this paper. First we describe child-birth related policies in the countries of interest. Second we describe female labour market performance along several dimensions. Statistics provided in this section correspond to the period and they will be helpful in section 4 in order to map out the model economy to the US economy. We start by providing a description of the maternity and parental leave policies in the US and the Scandinavian countries. 3 There are three types of child-birth related leave polices. Maternity leave that can be enjoyed by the mother after birth, paternity leave that can be enjoyed by the father after birth and parental leave that may be enjoyed by either of them 4 and that, in general follows maternity leave policy. Across countries there are substantial variation in the number of 3 We take the average of Sweden, Finland, Norway and Denmark. See Appendix 8.1 for the numbers for each country. 4 However, according to Haataja (2009) a father s share of total compensated parental leave is about 9% in the Scandinavian countries (table 3). 7

8 Table 1: Full Rate Equivalent Leaves (weeks) Maternity Parental Total Scandinavian countries US Source: OECD Family Database. weeks and in the benefit relative to the last earnings of the entitlement. In order to make policies comparable across countries, the OECD calculates the duration of the full-time equivalent of the leave period if paid at 100% of an employee s last earnings (Full Rate Equivalent, FRE). In the OECD countries the average length of duration of FRE paid maternity leave policy is 12.8, whereas paternity leave is only 3.1. FRE paid parental leave policy is on average 18.5, but there is huge variation across countries. Here we focus only on paid maternity and parental leave polices. As reported in table 1, whereas the Scandinavian countries enjoy almost 40 weeks of FRE maternity and parental leave in total, in the US mothers are not entitled to even a week of paid leave. Next we report several statistics from the OECD Family Database that describe female s performance in the labour market. First we show there are interesting differences in labour supply at child-bearing ages between the countries of interest. Second we show that the wage gender gap differs substantially between the two groups of countries. We summarize empirical evidence in the following two facts. Fact 1: In table 2 we report the female employment rate according to children s age from the OECD Family Database that uses the EU-Labor Force Survey. 5 Differences are substantial between the US and the Scandinavian countries 6 for mothers of children under 6. The gap 5 In principle, all women on maternity or on statutory paid parental leave (legal or contractual) are counted as employed. EU-guidelines stipulate counting parents on parental leave as employees absent for other reasons: they should be counted as employed if the period of absence is less than 3 months or if they continue to receive a significant portion of their previous earnings (at least 50%). 6 We take the average of Sweden, Finland, Norway and Denmark. See Appendix 8.1 for the statistics for each country. In the case of Norway maternal employment rates are not available in the OECD Family 8

9 Table 2: Employment Rate of Mothers by Children s Age Scandinavian countries US Source: OECD Family Database. Table 3: Mothers with children 2, In-work On leave Total Scandinavian countries US Source: OECD Family Database. is smaller for mothers with children aged 6 to 14. Since there are substantial differences in paid maternity/parental leave policies across countries it is worth reporting what the fraction is of women that are in work and the fraction of women that are on maternity/parental leave conditioning on the the age of children. This is shown in table 3. Interestingly, the fraction of mothers aged 0 to 2 in work is similar across countries. Then, the whole difference in the employment rate between countries at the age group 0 to 2 is accounted for by considering those individuals on paid maternity/parental leave in the Scandinavian countries. The comparison across countries of female employment rate in the age group 3 to 5 is not affected by the incidence of paid maternity/parental leave policies since the total length of paid leaves is less than one year. However, the gap in the employment rates between countries for this group of mothers is substantial. Finally, as we said above, the gap is narrow for the group of mothers of children aged 6 to 14. Fact 2: There is another important dimension in which countries differ. As we report in table 4 according to the OECD, the gross wage gender gap in the US is about 20%, whereas it Database so we obtain them from the EU-Survey of Income and Living Conditions. 9

10 Table 4: Wage Gender Gap Scandinavian countries 11.9 US 19.8 Source: OECD Family Database. Table 5: Total Fertility Rate Scandinavian countries 1.94 US 1.93 Source: OECD Family Database. is below 14% in the Scandinavian countries. Before going on, it is worth mentioning that the set of OECD countries in which we are focusing here, all share a similar total fertility rate (see table 5): 1.93 in the case of the US and 1.95 in the case of the Scandinavian countries. So differences in fertility behavior do not seem to be behind the differences in female labour supply that we report here. Family policy differences across the countries of interest go beyond differences in maternity and parental leave policies that we reported above. As we show in table 6 there are substantial differences in child care costs. Average child care fees for a two year old in the US is more than twice than that of the Scandinavian countries considered as a fraction of average worker earnings. This may be the result of differences in subsidizing child care policies. Furthermore, in the US, family benefits with children aged 3 to 12 are almost half of the average of those in the Scandinavian countries. As we mentioned above there are several papers in the literature that evaluate the effect of child care costs on mothers labour supply. According to Attanasio, Low and Sánchez-Marcos (2008) a reduction of 20% in child care cost increases participation of mothers with children younger than 3 by 18 percentage points. Nevertheless differences in chid care costs are an alternative explanation to the one we pursue here to account for differences in female s performance in the US labour market with respect to the Scandinavian countries. 10

11 Table 6: Other family policies Child Care Fee 2-year Old to Earning Annual Benefit Child 3-12 Scandinavian countries 6 1,540 US 20 1,056 Source: OECD Family Database. 3 Model We consider two setups for the analysis. First, an economy without parental leave and essentially the same features as the model economy in Attanasio, Low and Sánchez-Marcos (2008). Second, we extend this economy to allow for paid parental leave 7 resembling the features of this policy in the Scandinavian countries. 3.1 An economy without parental leave In our model unitary households maximize expected lifetime utility. The utility function is intertemporally separable and instantaneous utility depends on household consumption per adult equivalent and the labour supply choice of the wife. We assume that all households have two adults who remain married and that husbands always work and receive earnings that are determined by a stochastic process introduced below. We do not model fertility choices and children do not have a direct effect on utility (except for deflating consumption by their adult equivalent). However, we calibrate the arrival of children to make it similar to what we observe in the data and we assume children affect the fixed cost of work. We assume that there is no correlation between productivity (male or female wages) and fertility types. 8 7 From now on I will refer to paid parental leave in a general sense, including both paid maternity leave and parental leave. I will assume also that it is the mother who is entitled to it. 8 Interestingly, Waldfogel (1998b) finds little difference in early wages between childless women at the age of 21 and childless at 30 and those childless at the age of 21, but mothers at

12 The household is assumed to maximize lifetime expected utility, max V t = E t c,p T β s t u(c s, P s ; e s ) s=t where β is the discount factor, E t the expectations operator conditional on information available in period t., P t is a discrete {0, 1} female labour supply choice, c t is total household consumption and e t is the number of adult equivalents in the household. We consider a retirement period after which neither of the members of the household participate in the labour market and the household receives a pension proportional to the husband s earnings after retirement in period T T R. It is important to include the retirement savings motive in our model to have a realistic amount of savings so that the potential role of female labour supply as a private insurance mechanism is not overestimated. The intertemporal budget constraint for a household that is not eligible for maternity leave has the form ( ( ) ) A t+1 = R A t + y f t F (a t ) P t + y mt c t (1) where A t are beginning of period assets t, R is the interest rate, F the fixed cost of work which depends on a t, the age of the first child born to the female. Female earnings are given by y f t, and husband earnings are given by yt m. In any period, individuals are able to borrow against the minimum income they can guarantee for the rest of their lives. It is important to allow for saving and borrowing since this is a way to smooth the effect of fixed cost of the labour supply for mothers that would otherwise affect labour supply differently. We denote the child care units needed by a family whose first child is age a t by G(a t ) and the price of each unit of child care by p. Therefore, the total child care cost faced by a household 12

13 when females participate in the labour market is given by F (a t ) = pg(a t ) (2) Female earnings are given by ln y f t = ln y f 0 + ln h f t + v f t (3) where h t is the level of human capital at the start of the period and ν f t is the permanent productivity shock. Human capital evolves with employment decisions in the following way ln h f t = ln h f t 1 + η t I (P t 1 = 1) δi (P t 1 = 0) We think of δ as the permanent depreciation in human capital associated with non-participation. However, we assume human capital cannot fall below its initial value. This means that the marginal loss of human capital associated with a year out of the labour force becomes zero for a sufficiently long unemployment spell. Evidence of wage losses by displaced workers have been reported in the literature by LaLonde, and Sullivan (1993) and more recently by Couch and Placzek (2010). 9 Jacobsen, Joyce and Laurence (1995) document the impact on female earnings of intermittent labour supply. They find evidence that spells from the labour market have lasting negative effects on mothers, of even 10% after years of the spell. As regards as the process of human capital accumulation, we assume, as in Olivetti (2006), that the increase in human capital depends on age only. We calibrate the depreciation rate and the human capital function parameters so that our model matches certain moments of the data that we discuss below. 9 They find estimated earnings reductions of more than 30% at the time of job loss and about 12 to 15% six years later. 13

14 Since we assume men always work, male earnings are given by ln y m t = ln y m 0 + h m t + v m t (4) h m t = α m 1 t + α m 2 t 2 (5) We estimate directly from the data the parameters of the human capital accumulation function for males. 10 Both female and male earnings, y f t and yt m, in the household are subject to permanent shocks, v f t and v m t, that are positively correlated. This is the only source of uncertainty that households face. They are assumed to have perfect foresight regarding fertility, child care costs, the process for human capital accumulation and the fact that they will remain married. In particular we assume v f t = v f t 1 + ξ f t vt m = vt 1 m + ξt m where ξ t = (ξ f t, ξt m ) N ( µ ξ, σξ 2 µ ξ = ( σ2 ξ f 2, σ2 ξm 2 ) and σ2 ξ = ) σ2 ξ f ρ ξ f,ξ m ρ ξ f,ξ m σ2 ξ m (6) (7) In each period, the value function for a working woman is given by ( Vt 1 A t, vt m, v f t, h f t max c t ) = u (c t, P t = 1; e t ) + βe t max Vt+1 0 V 1 t+1 ( ) A t+1, vt+1, m vt+1, f h f t+1 ( ) A t+1, vt+1, m vt+1, f h f t+1 (8) 10 As for married men labour market participation is very high, selection bias in this estimation is expected to be small. 14

15 However, if she chooses not to participate, the value function is given by, ) Vt (A 0 t, v mt, v ft, h t = max c t u (c t, P t = 0) + βe t max Vt+1 0 V 1 t+1 ( ) A t+1, vt+1, m vt+1, f h f t+1 ( ) A t+1, vt+1, m vt+1, f h f t+1 (9) Therefore, the decision of whether or not to participate in period t is determined by comparing Vt 0 A t, vt m, v f t, h f t and Vt 1 A t, vt m, v f t, h f t. The participation choice and the ( ) ( ) consumption choice in t determines the endogenous state variables (assets and human capital) at the start of the next period. The non-concavity in the value function induced by the discrete participation decision is smoothed out by the presence of sufficient uncertainty. We confirm that this holds in the numerical solution of the problem, as discussed in the Appendix. 3.2 An economy with paid parental leave In this section we extend the previous model to allow for a paid parental leave with the following features. First parental leave guarantees job protection that we model here as human capital being constant during leave, therefore human capital is prevented from depreciation. Second a cash benefit is provided to eligible mothers during leave. We set it equal to a fraction s of the corresponding earnings as if they were still working. So during parental leave eligible households face the following budget constraints. ) A t+1 = R (A t + sy ft + y mt c t (10) We assume that in order to be eligible for parental leave, a female has to be employed in the period previous to her child s arrival. This implies that in this economy we have to keep track of female labour supply decisions at that period in order to determine eligibility later on. This adds an additional state variable during the periods in which mothers are potentially eligible for maternity leave. Except for this the household problem is identical to the one in the previous 15

16 section. 4 Calibration We now proceed to restrict the model economy in order to produce a quantitative statement of the effect of the parental leave policy we describe below. We align the model economy with the US economy in a number of dimensions by obtaining a vector of parameters that produces the desired set of properties. The calibration is intended to capture the tradeoffs of spells from the labor market as well as life-cycle wage growth that are key to determine female labour supply decisions. 4.1 Functional forms We use a utility function of the form u(c t, P t ; e t ) = ( c t e t ) 1 γ 1 γ ψp t (11) The equivalence scale for consumption is given by e t which depends on the age and number of children. We use the McClements scale, according to which a childless couple is equivalent to 1.67 adults, a couple with one child is equivalent to 1.9 adults if the child is less than 3, to 2 adults if the child is between 3 and 7, 2.07 adults if the child is between 8 and 12 and 2.2 adults if the child is between 13 and 18. As we explain below, we assume that each couple has two children who arrive at a predetermined age and leave at age 18. We allow heterogeneity in the age of first child s arrival, but we assume the second child comes 3 years after. 11 Regarding the child care cost function G(a t ) we build it directly from data provided by State Child Care Resource and Referral Network offices for pre-school children. 12 According to the information they provide average annual full-time child care cost for an infant in a Center varies 11 We assume 3 years time between births to be consistent with NLSY79 and Natality Detail Files (see Buckles and Munnich (2012)). 12 See Child Care Aware of America (2012). 16

17 between $14,009 in the state of New York (that is about 16% of state median income for two parent families) and $4,591 in the state of Mississippi (7%). Child care cost for a 4-year-old child is about 20% cheaper, $11,585 in the case of New York and $3,911 in the case of Mississippi. Given this information on the relative cost depending on age and considering that in our model all women with children have two of them separated by 3 years we shape G(a t ) such that it captures the evolution of household s child care cost with the age of the first child. As we discuss below, we calibrate the price p using our model. 4.2 Parameter values There are two set of parameters that characterize the model economy. The first set is measured directly from the data or taken from previous estimates in the literature. The second set is calibrated by solving the model. In this case a nice feature of the approach to identify parameter values is that for all the statistics that involve female labour market outcomes we implicitly control the self-selection process that is operative in our model. Therefore both in the data and in the simulations, the women on which these statistics are computed are from a selected sample of the population. All women in our model begin their lives at age 23 with zero assets and they live for 50 periods. Duging the last 10 periods they have to be retired from the labour market, as is the case for their husbands. We fix the rate of return to savings to equal the average real return on three monthly T-bills at and we assume a discount factor equal to In the utility function (11), the coefficient of relative risk aversion, γ, is set to 1.5, which is consistent to the evidence on the elasticity of intertemporal substitution in the US provided by Attanasio and Weber (1995). We allow three different groups of women according to the age at which they have their first child. According to the OECD 15% of women never have a child and this is what we assume here to be the first group. 13 Then in order to be consistent with the average age of 25 at a woman s first birth that the OECD reports for the US, 14 we assume that 42.5% of women have their first 13 See OECD family database Chart SF2.5B Definitive childlessness. 14 See OECD family database Chart SF2.3.A: Mean age of women at the birth of the first child. 17

18 child at age 24 (we call this group young mothers) and 42.5% have their first child at 27 (we call this group old mothers). Then, as we said above, all mothers have a second child after three years. The deterministic component of the male earnings process is consistent with wage growth as reported from the NLSY79 (that follows a sample of the cohort of individuals born between 1957 and 1964). In particular we target average annual wage growth of 0.03 from 30 to 39 and of 0.01 from 40 to 46. This gives a wage growth of 0.04 from 25 to 29 also consistent with NLSY Both the innovations in male earnings and those in female wages are assumed to have a unit root, consistent with the evidence about men found by MaCurdy (1983) and Abowd and Card (1989). The standard deviation of the innovation for a husband s earnings is assumed to be This number is similar to the variances estimated using PSID data by Carroll and Samwick (1997) or Low, Meghir and Pistaferri (2006). There is not much evidence on the variability of female wages and/or earnings. Assuming that the variance of female wages innovations is the same as that of men s earnings, we compute the implied coefficient of variations of female earnings in our simulations, which comes out at So it turns out to be quite similar to the value of 0.65 reported by Hyslop (2001) for female earnings. 16 We therefore settled for the value of We assume that the correlation coefficient between the two shocks (for husband and wife) is equal to 0.25 as estimated by Hyslop (2001). There remain six parameters to be calibrated: the utility cost of working ψ ; the price of child care p; the depreciation rate δ; the initial wage gender gap y f 0 /y m 0 ; and, finally, two parameters of the human capital accumulation function, η 0 that would apply to females up until the age of 39 and η 1 for females aged 40 to 60. Then we choose six statistics to target (see the first panel of table 7). We select two labour market participation statistics from OECD Family Database: employment rate of childless women, 0.77, and employment rate of mothers of children aged 0 to 2, We also target the 0.8 gross wage gender gap and the female wage growth at 15 See 16 Hyslop (2001) assumes a different process for wages, as he includes individual fixed effects in the process for female wages, rather than persistent innovation. 18

19 different ages as measured from NLSY79. Average female wage growth from 25 to 39 is 0.03 and from to 46. Finally, we align the model gross motherhood wage penalty (average wage of mothers relative to average wage of childless women) with the fraction of the gross motherhood wage penalty that in the data is accounted for by differences in labour market experiences between mothers and childless women. There are several papers in the literature that explore the driving forces of the motherhood wage penalty. Among those forces, differences in human capital, including both labour market experience and education, but also lower effort, discrimination or segregation are found to be important. Waldfogel (1998b) 17 finds that for mothers of two children wage penalty is about 13.2% after controlling by education, year, age and race. However, the gap goes down to 8.1% once differences in labour market experience are taking into account. 18 So this implies a 5.1% motherhood wage gap related to lower attachment to the labor market by mothers and this is what we target here. 19 model. In the second panel of table 7 we report parameter values that are calibrated by solving the The calibrated value for the price of child care implies that child care costs paid for an infant is about 22% of a two-earner household s mean earnings. This is, according to the National Association of Child Care Resource and Referral Agencies, above the cost reported in the least-affordable states of the US (16%). However, since we do not specify any other time or monetary child-related costs for working mothers our model requires this relatively high price of child care in order to target the employment rate of mothers of young children. Note also that we assume zero child care cost for school children (older than 4). The ratio of initial offer wages for men and women is calibrated to 0.77, so it is lower than the observed gender gap. This is as a result of the positive self-selection of women into the labour market that our model implies. Positive self-selection is consistent with Olivetti and Petrongolo (2008) that find that 17 She uses data from NLSY-YW. She considers an early and a late wage separated on average by about 8 years. 18 Budig and England (2001) find that there is a penalty of about 12% that is due to differences in human capital and education. Anderson, Binder and Krause (2002) find that the penalty is higher among non-college women. 19 Note that in our model there are not be other sources of differences in wages between mothers and childless women besides differences in labour market experiences. In particular, motherhood is an exogenous state in our model. So it would not make sense to target the gross motherhood wage gap here. 19

20 Table 7: Calibration Targets Model Data Childless Women Employment Rate Mothers 0 to 2 Employment Rate Wage Gender Gap Female Wage Growth (aged 25 to 39) Female Wage Growth (aged 40 to 46) Motherhood Wage Penalty Parameters ψ p y f 0 /y m η η δ 0.04 Other Statistics Model Data Mothers 3 to 5 Employment Rate Mothers 6 to 14 Employment Rate Median duration of Spells 6 5 Female Employment Rate gender wage gaps across countries are negatively correlated with gender employment gaps due to positive self-selection of women into the labour market. Finally, the value of the depreciation rate of human capital is calibrated to 4%, which is above the estimates of Mincer and Olfek (1982) of 2%. However, the implied annualized wage loss due to non-participation in our model is 3%. This lower annualized wage loss arises because the impact of depreciation on human capital is constrained by the assumption that human capital cannot fall below its starting value. Furthermore, positive self-selection into the labour market downward bias the observed annualized wage depreciation. 20

21 Finally, the third panel in table 7 reports other labour market statistics that are helpful to assess the ability of the model to account for female labour supply behavior. The model captures the increasing participation rate with age of children well, although it slightly overestimates both the participation of mothers 3 to 5 and 6 to 14. Average participation in the simulations equals data observation. Finally, according to Jacobsen and Levine (1995), median duration of exits in the data is about 5 years and 85% of exits are due to family responsibilities. 20 In the simulations median duration of the first exit is 6 years and it takes place at a median age of 28 (so it is related to children s arrival). 5 Policy Evaluation In this section we evaluate the effect of a one-year paid parental leave policy. So the 54 weeks of the parental leave we assume here are above the 37 weeks average length of the total FRE paid maternity and parental leave in the Scandinavian countries. However, given the annual frequency of our model economy this is the closest we can get to the actual policy in terms of length. Therefore, in order to make our implemented policy equivalent to the 37 weeks of FRE parental leave, we assume that the cash benefit that mothers on leave enjoy is equal to 0.69 of their corresponding wage if they were at work. We report results in table 8. The female employment rate increases as a result of the policy, and the change in mothers female labour supply is the driving force. Participation of childless women only changes slightly (note that we provide statistics for women 25 to 54 and than participation of women before child arrival is already very high ). There are several forces that change mothers behavior. First, as noted by Ruhm (1998), females are much more likely to participate in the labour market in order to be eligible for parental leave benefits. In our simulations participation in the period previous to a first child s arrival goes from 0.96 to 1 in the case of young mothers and from 0.90 to 1 in the case of old mothers; participation in the period previous to second child arrival goes from 0.44 to 0.79 in the case of young mothers and from 0.65 to 0.84 in the case old mothers (see 20 They used Survey of Income and Program Participation

22 Table 8: Policy Evaluation US US under Scandinavian Baseline 69% Paid Parental Leave countries Mothers 0 to 2 Employment Rate Mothers 0 to 2 in work Mothers 3 to 5 Employment Rate Mothers 6 to 14 Employment Rate Female Employment Rate Wage Gender Gap Motherhood Wage Penalty Table 9: Policy Evaluation: details US US under Baseline 69% Paid Parental Leave Part Before 1st child,y Part Before 1st child,o Part Before 2nd child,y Part Before 2nd child,o Part Afterwards,Y Part Afterwards,O Part After 5 years 2nd child,y Part After 5 years 2nd child,o Part After 10 years 2nd child,y Part After 10 years 2nd child,o

23 Table 10: Policy Evaluation: decomposition Base Job-prot 69% Benefit Mothers 0 to 2 ER Mothers 0 to 2 In Work Mothers 3 to 5 ER Mothers 6 to 14 ER Female ER Wage Gender Gap Motherhood Wage Penalty observed wage, all women -0.7% -2.0% observed wage, women % -4.0% observed wage, women % -0.4% Table 11: Policy Evaluation: Employment Decision Marg.ef. P-value Young mother with young children Old mother with young children Young mother with old children Old mother with old children Young mother with young children*policy Old mother with young children*policy Young mother with old children*policy Old mother with old children*policy Age Age Constant 23

24 Table 12: Policy Evaluation: Log Wage Coef. P-value Young mother with young children Old mother with young children Young mother with old children Old mother with old children Young mother with young children*policy Old mother with young children*policy Young mother with old children*policy Old mother with old children*policy Age Age Constant Table 9). Note that in the case of second child s arrival the higher human capital of women (due to a previous relatively high labor market attachment and due to job protection during leave) reinforces the effect of women willing to participate in order to be eligible for the second parental leave. Second eligible females are employed during the parental leave period, although they are not in work. This shows up in the higher female employment rate of mothers 0 to 2. Note that for this group of mothers a substantial gap between the employment rate (0.78) and the fraction of women in work (0.48) arises. This goes in the direction of what is observed in the Scandinavian countries. Interestingly, the fraction of mothers of children 0 to 2 in work decreases as a result of the policy. This is in spite of the higher employment rate of women at the time in which the child is 1 and 2 years old. 21 Third, mothers are more likely to work in the period right after the second parental leave (see Table 9). Participation goes up from 0.42 to 0.61 in the case of young mothers and from 0.56 to 0.62 in the case of old mothers. There are two potential reasons for the the higher impact of the policy on young mothers with respect to old mothers. On the one hand, young mothers face a longer lifetime horizon to enjoy the returns to accumulated human capital so they are expected to be more elastic (see Imai and Keane (2008)). On the other hand 21 Employment rate of mothers of newborn children goes from 0.54 to 0.91, whereas the fraction of women at work goes from 0.54 to zero. Employment rate of mothers of children aged 1 year old goes from 0.52 to 0.68 and that of mothers of children aged 2 years old from 0.56 to

25 for young mothers the amount of uncertainty that remains to be resolved is larger than for old mothers so they may be more elastic for this reason as well (see Low (2005)). Forth, mothers of children aged 3 to 5 are more likely to participate after the policy s implementation, their employment rate goes from 0.70 in the baseline economy to 0.74 in the economy with maternity leave. There are two things behind the increase of employment rate for mothers of children aged 3 to 5. On the one hand higher attachment to the labour market before child s arrival encourages mothers to stay in the labour market afterwards. On the other hand, job protection that parental leave guarantees and, that prevents human capital from depreciation during leave, makes mothers more likely to participate. Finally, for the group of mothers of children aged 6 to 14 the employment rate remains stable at In Table 9 we provide statistics to assess the long-run effects of the policy, this is the effect on participation after 5 and 10 years of second child arrival. The long-run impact of job protection only on participation is small both for young mothers and old mothers, about 1 percentage point. Furthermore, parental benefit negatively affects participation in the long-run (income effect). All in all, female employment rate goes up from 0.69 to 0.73 (4 percentage points) as a result of the policy. This is in line with the 3-4 percentage points effect estimated by Ruhm (1998). Consistent with his findings, the effect is substantially higher for women at child-bering ages 25 to 34 (10 percentage poings) than for those aged 45 to 54 (0 percentage points). Ruhm (1998) estimated effect are 8 and 4 respectively. Note that job-protection is one year long in our experiments in contrast with the duration in the sample of countries considered by Rhum (1998). Table 10 decomposes the effect of the policy. Second column reports the effect of parental leave that only provides job-protection and columns third the total effect. The effect of jobprotection is very substantial. So two thirds of the average change in participation are accounted by job-protection dimension of the policy, the parental benefit only adds 1 percentage point. Finally, as a way to summarize the results, we report in table 11 the marginal effects of a probit estimated on the decision of working on a pooled sample of individuals before and after the policy. 22 We include dummies for four different groups of women in the economy: young mothers 22 Note that in our simulations we observe the whole life-cycle employment profile of women before and 25

26 with children under the age of 5 (young children), young mothers with children aged 5 to 16 (old children), old mothers with young children and old mothers with old children. The reference group are mothers with children older than 16 since we remove from our simulated data never mothers that are not going to be affected by the policy. In addition we include as regressors the four group dummies interacted with the policy and age and age squared. As expected mothers of young children work less than the reference group, especially in the case of young mothers. The effect of the policy is larger for this group of women, employment rate going up by 19.1 percentage points as a result of the policy in contrast to 13.9 for the group of old mothers with young children. The effect on mothers of children aged 5 to 16 is not significant. Regarding the effect on female earnings, as reported in table 9 the parental leave policy slightly worsens females average wage relative to males. The wage gender gap goes from 0.80 in the baseline economy to 0.79 percentage points. There are two effects that operate in opposite direction to shape this variation. First, female s higher attachment to the labour market during child-bearing contributes to reducing the wage gender gap through the higher human capital that women accumulate. Second, there is an interesting effect that goes in the opposite direction. As more women participate in the labour market, female s average wage (conditioning on human capital) goes down in our simulations because new entrants are less productive. This is consistent with the positive self-selection of women into the labour market found in Olivetti and Petrongolo (2008). As we mentioned above, they find that positive self-selection delivers a negative correlation between gender wage gaps and gender employment gaps across countries. In our simulations the first effect dominates the second. The motherhood wage penalty also worsens going from 1.06 to Table 9 reports the effect on wages for different age groups. Average wage decreases by 2.0% with respect to the baseline, 4% for women aged 25 to 34 and 0.4% for women aged 45 to 54. The effect on wages estimated by Ruhm (1998) is -2.7%. Note that in the empirical strategy followed by Ruhm (1998) the decrease in wages may be overestimated since it is difficult to assess the impact on future wages of higher human capital of currently young generations. The effect on wages of job-protection only for different age groups is as follows. after the policy. 26