Unemployment Duration of Spouses: Evidence From France

Unemployment Duration of Spouses: Evidence From France Stefania Marcassa∗ Abstract This paper analyzes the conditional probability of leaving unemployment of French married individuals from 1991 to 2002. We find that the effect of spousal labor income on unemployment duration is asymmetric for men and women. In particular, the probability of men to find a job is increasing in wife’s labor income, while it is decreasing in husband’s earnings for women. To adjust for endogenous selection into marriage, we use the quarter of birth as an instrumental variable for the spousal wage. Finally, we show that introducing a breadwinner stigma in a joint job search model generates the positive correlation observed for men in the data. Keywords: unemployment duration, hazard models, labor income, marriage, joint search theory JEL Classification: J12, J64, J65 ∗ Université de Cergy-Pontoise THEMA (UMR CNRS 8184), 33 boulevard du Port, 95011 Cergy-Pontoise cedex, FR. Email: [email protected]. 1 1 Introduction An important factor affecting unemployment duration is the time elapsed in searching for an offer. The determinants of the search time are several, and mostly include the labor market conditions and the socio-economic characteristics of the searcher, who is usually assumed to be acting individually. But in a society where more than 60 percent of the agents are married or live in couples, it is important to consider how the individual’s decisions depend on the characteristics of the partner. We know that the possibility of sharing economic and social resources is an important reason that leads to marriage, or any other form of partnership.1 In particular, marriage is seen as a sort of small insurance pool against life’s uncertainties, reducing the spouses’ need to protect themselves from unexpected events. Hence, during a period of unemployment, we expect that the effort exerted to find a job by a married individual depends on individual and local characteristics, but also on spousal income. We find a significant elasticity of unemployment duration to spousal earnings, and the effect is shown to be asymmetric for men and women. In particular, the elasticities of 1.27 for men and -0.24 for women are found to be significant for the entire sample. In other words, a 10 percent increase in a worker’s wage is associated with a 12.7 percent increase in the husband’s hazard rate of leaving unemployment, and with a 2.4 percent decrease in the wife’s hazard rate. The coefficients on the other characteristics (demographics and labor market conditions) have the expected signs for both spouses. Most notably, we find that being a recipient of unemployment benefits decreases the hazard rate of exiting unemployment. The econometric analysis is carried out using data from the French Labor Force Survey from 1991 to 2002. Endogeneity bias is surely a concern in this study because it is reasonable to believe that spouses do not select themselves randomly, and couple formation may be subject to assortative mating. At the same time, the asymmetric results that we find for men and women cannot be easily viewed as the consequences of positive or negative assortative mating. In both cases, we would expect 1 An example is provided by Waite (1995). 2 symmetric reactions of husband and wife unemployment duration to their spousal labor income. To support this reasoning, we show that our results persist when we add an instrumental-variables-type technique to adjust for endogenous selection into marriage on unobservables. We instrument for the spousal wage using her (or his) quarter of birth, following the analysis of Grenet (2010).2 He shows that French men born at the end of the year incur a small but significant penalty in terms of labor market outcomes, in the form of lower wages and higher unemployment rates. The contribution of our paper is twofold. First, it provides an empirical investigation of the relevance of the spousal characteristics on the probability of finding a job. Second, it proposes a stylized model which builds on the existing theory of job search to ground the empirical findings. The paper adds to the rich empirical literature on individual job search by incorporating the characteristics of the partner. One can find numerous empirical studies on the effect of wealth, unemployment benefits, and other characteristics on unemployment duration. An example is the seminal paper of Meyer (1990) which studies the individual behavior during the weeks just prior to the end of the unemployment insurance, and shows the negative effect of unemployment benefits on the probability of leaving unemployment. Danforth (1979) and Bloemen and Stancanelli (2001) find that high levels of wealth result in higher reservation wages, and thus lower probability of leaving unemployment. Related works from Lentz and Tranas (2005) and Lentz (2009) estimate empirically the optimal savings and job search behavior of a risk averse worker as she moves back and forth between employment and unemployment. A general study on the determinants of individual unemployment durations in Britain is provided by Arulampalam and Stewart (1995). All these papers show the importance of wealth and unemployment benefits in determining the hazard rate of leaving the unemployment state. But none of them includes the spousal income which plays an important role in the intra-household risk sharing, and consequently in eliminating part of the uncertainty faced by the couple. From a theoretical point of view, the literature on joint search is still preliminary. Burdett (1978) has been the first contributor to the topic, laying out a two-person search model and some 2 See also Ponzo and Scoppa (2011) for the case of Italy. 3 characterization of its solution. Only recently, Garcia-Perez and Rendon (2004) have numerically simulated a household search model in which consumption and job search decisions are made jointly. Dey and Flinn (2008) extend the standard partial equilibrium labor market search model to a multiple searcher setting with the inclusion of multi-attribute job offers, where some of the attributes are treated as public goods within the household. Gemici (2011) estimates a rich structural model to assess the implications of joint location constraints on the migration patterns, labor market outcomes, and marital stability of men and women. Finally, a mostly theoretical work by Guler et al. (2012) analyzes a joint search and location problem of a household formed by a couple who pools income. They characterize the reservation wage behavior of the couple and compare it to the single-agent problem. We build on Guler et al. (2012) to explain the asymmetric response in spousal income. We show that, in an environment where both spouses are risk neutral and perfectly pool their income, the presence of a stigma or breadwinner cost bear by the husband may generate a negative correlation between his reservation wage and the labor income of his wife. A justification for this social cost can be found in the sociological literature (Sayer et al. (2011)) where it has been documented that while social pressure discouraging women from working outside home has weakened, pressure on husbands to be breadwinners largely remains. We also use the theoretical model to draw some tentative conclusions on the effect of unemployment insurance. The exercise shows that the reservation wages of both spouses depend positively on their own unemployment benefits, but the size of their changes may be different. This may suggest the implementation of a gender-based unemployment policy. In this environment, a policy directed to reduce the unemployment duration establishes an unemployment insurance scheme more generous for men than for women, as the elasticity is lower for the former. Note that quantifying the direction or the size of policy effects is not the goal of the analysis, as the model has not been structurally estimated. Nonetheless, the empirical evidence for a breadwinner effect may have important implications for welfare due to the fact that it represents a social norm that may prevent agents from implementing optimal allocation rules. For example, even if the 4 efficient time allocation for the household entails the wife working in the labor market and husband at home, the couple might not be able to implement this as an equilibrium allocation due to the fact that a home-maker husband is frowned upon for not being the breadwinner.3 The paper is organized as follows. The description of the data is in section 2. Next, section 3 contains the empirical analysis. In particular, in section 3.1, we specify the econometric model. The results are presented in section 3.2. The endogeneity issue is discussed in section 3.3, and the instrumental variable model is in section 3.4. The theoretical joint search model is described in section 4. Section 5 concludes. Figures, Tables, and Proofs are relegated to the Appendix. 2 Data and Descriptive Statistics The data used are from the Enquête Emploi, the French Labor Force Survey. Conducted by the INSEE (National Institute of Statistics and Economics) since 1950, the Labor Force Survey is a longitudinal panel survey that measures unemployment in the sense of the ILO (International Labor Organization). In March of every year until 2002, members of around 65,000 French households are interviewed. One third of the household sample is renewed each year, so that a given individual is interviewed in three consecutive years. We use the data of those who entered the survey in 1991, 1994, 1997, and 2000. The survey provides information on the professions, on the activity of women and young people, working hours, and casual employment. Moreover, extensive information is collected on the labor market behavior of individual respondents in the year preceding the moment of the interview. The respondents are asked to report the main labor market state they were in, for each month in that year, including the month of the interview.4 Some measurement errors may arise as a respondent who has worked less than 50 percent of the time in a month may declare to be unemployed for 3 We thank an anonymous referee for bringing this point to our attention. Respondents are asked to choose one among the following states: (1) employed for an unlimited period; (2) on his own or helping a family member in her activity; (3) fixed-term contracts, temporary job, training, seasonal work; (4) Vocational Training, or another paid internship; (5) unemployed; (6) student, or unpaid internship; (7) military; (8) retired, early retirement, out of business, housewife, other. 4 5 the entire month. Also, a respondent may declare to be unemployed even if he is not registered as such at the public employment agency (Agence nationale pour l’emploi ). By comparing individual labor market states of consecutive months in the periods from March 1990 to March 2002, individual unemployment durations can be constructed as a number of calendar months. The initial and final number of individuals for the survey years used in the analysis are in Table 1. We select men and women older than 14 and younger than 60 years old, who are married or cohabiting, and who reported inflow into unemployment at least once during the observation period. We create an inflow sample of unemployment durations for spouses (husbands and wives) with available information on spousal labor earnings and other labor market and demographic characteristics.5 We only include spells starting within the mentioned period to avoid problems related to left censored observations.6 The resulting unbalanced panel of four waves consists of 1,945 husbands and 6,807 wives. The number of transitions from unemployment to employment is 1,981 for the former, and 4,859 for the latter.7 These data are collected in Table 2. The labor earnings of the spouses are computed as the median of the deflated hourly wages earned over the years in which the data are available. Following Laroque and Salanié (2002), we exclude from the samples the observations with an hourly wage lower than two-third of the minimum wage of the respective year.8 The hourly labor earnings of the spouses are computed from the monthly salary that includes non-monthly premiums, and divided by the usual hours worked in a month.9 Tables 4 and 5 describe our sample. From the last interview in March 1993, 1996, 1999, and 2002, we select a set of control variables 5 To organize the data set for the empirical analysis, we followed the procedure described by Cleves (1999). At each interview, the respondents describe their labor market history of the past 12 months. Consider the following case. Two answers are available on the labor market state of March 1991 as the same question is asked retrospectively in the survey of 1992. Most of the studies that use the French Labor Force Survey data discuss the the existence of recall errors. See Lollivier (1994), Magnac (1994), and van den Berg and van der Klaauw (2001) for an extensive discussion. We assume that if two answers on the labor market state in March differ, then the most recent one is correct. 7 The empirical implications of the substantial higher number of unemployment spells for women than men are discussed in section 3.2, and in Appendix C. 8 See Table 3 for details on the minimum legal hourly wage (SMIC). 9 Consistently with the existing literature (e.g., Olivetti and Petrongolo (2008)), data exhibit a significant gender wage gap: men earn about 14 percent more on average than women. Results of the estimation are available upon request. 6 6 that are assumed to be time-constant over the three years in which the individuals are followed. In general, the expected completed duration of an unemployment spell depends upon the probability of receiving (and accepting) a job offer. The probability of receiving a job offer is determined by some observable factors which make a specific worker more attractive to an employer such as demographic characteristics, local demand conditions, and labor market situation before unemployment. Demographic characteristics. Age is likely to influence the number of job offers as well as the individual search intensity. Both aspects are crucial for the likelihood of leaving unemployment. The corresponding covariate “age” captures the age of the respondent at the beginning of the spell, measured in years. We expect hazard rates to rise with education levels due to employer preferences for skilled workers. The set of explanatory variables also includes several indicator variables for being legally married and having children younger than 18 years old. Having children may affect the duration of unemployment, decreasing the time spent searching for work. It is also important to distinguish between having the French nationality or not. In general, immigrants suffer from an inadequate transferability of skills from their home country. As a consequence, formal qualifications of natives and immigrants tend to have a different relevance for labor market outcomes. Furthermore, immigrants are likely to face discrimination by employers, which likely reduces chances to leave unemployment. We also differentiate between real estate owner and renters. Blanchflower and Oswald (2013) present evidence of the links that may exist between the housing and the labor markets. The authors argue that high rates of regional or national home-ownership are responsible for high levels of unemployment. Their hypothesis relies on the proposition that home-owners are less mobile than renters. Therefore, the increase in the number of home-owners has for consequence to decrease matching between job seekers and job vacancies. Concretely, mobility constraints specific to home-owners reduce job search efficiency for individuals that are concerned by this residential status. Local demand conditions. We include dummies for living in a certain region of France and the regional unemployment rate. The latter is computed as the average of the regional unemployment rate over the three years. The literature differs in its conclusions on how duration dependence 7 varies with the labor market conditions. Imbens and Lynch (2006), for instance, find that duration dependence is stronger when local labor markets are tight. By contrast, Dynarski and Sheffrin (1990) find that duration dependence is weaker when markets are tight. Still others find that the interaction effect between market tightness and unemployment duration varies over the length of the spell. For instance, it may be positive for some unemployment durations and negative for others (Abbring et al. (2001)). At the time of the last interview, husbands are on average 44 years old, and the majority of them (about 68 percent) have (at least) a high school diploma. Eighty percent of them are legally married, geographically located in the north of France, and owners of the house where they have been interviewed. Wives have similar characteristics: they are about 40 years old; have the French nationality, mostly legally married, and 65 percent of them are (at least) high school educated. The majority of them live in the north of France, and are owners of their house. Labor market situation before unemployment. To control for the labor market situation before the last unemployment spell, we include several variables, such as: the labor market status (employment or inactivity), the occupation, and the employment status (self-, government or other employed). Men are equally likely to come from a permanent or temporary employment condition than from a non participation status. On the contrary, women are more likely to enter unemployment from a state of inactivity. Both men and women have been previously employed in low skilled occupations, and only a small percentage (17-18 percent) have been self- or government employed. The set of control variables also includes (the logarithm of) the amount of unemployment benefits received during the spell, and a dummy variable that indicates the registration at the National Employment Agency (Agence National Pour l’Emploi (ANPE)). About 30 percent of the unemployed husbands and wives have declared to be registered at the ANPE.10 In addition to these observable characteristics, we have to deal with endogeneity issues due to 10 The ANPE was the French government agency which provided counseling and aid to those who are in search of a job or of training. In 2008, a new public agency was created, resulting from the merging of the ANPE with the Undic administration. 8 unobserved variables. The data do not include variables that allow to identify the preferences in marital partners, or the elements that have determined the choice of a particular spouse. The standard argument is that these unobserved variables affect both unemployment duration and the spousal earnings, causing spurious correlation between unemployment duration and spousal earnings. We will tackle these endogeneity difficulties accounting for unobserved heterogeneity and using an instrumental variable. Nonparametric Kaplan-Meier estimates of the survival functions for men and women in couples are plotted in Figure 1. In all cases, there is evidence of negative duration dependence. That is, the longer an individual remains in the initial state, the smaller the hazard of exiting from the state becomes. The hazards are highest towards the beginning of a spell and mostly decline monotonically thereafter. It is also true for both men and women. As expected, the probability of surviving in the risk pool (i.e. to remain unemployed) is higher for women than for men. 3 Duration Analysis 3.1 Baseline Estimation and Unobserved Heterogeneity We estimate a duration model that incorporates the available information about a worker’s jobless spell. Our goal is to provide an insight into the nature of duration dependence in transitions out (or into) employment, together with an appreciation of the extent to which these transitions are influenced by observed characteristics, controlling also for unobserved heterogeneity. The information available to us on durations is highly discrete: we only know the monthly employment status. This makes continuous time duration models inappropriate. For this reason, we estimate a standard discrete time proportional hazard model.11 The estimation approach used here is based on Meyer (1990). The shape of the hazard is semi-parametrically estimated. The method entails several advantages. First, the probabilities of surviving each period are constrained 11 More precisely, this is defined as a grouped specification in the literature. 9 to lie between 0 and 1; second, it helps avoiding inconsistent estimations of covariate coefficients due to misspecified baseline hazard; and third, it is relatively easy to extend the model to test for unobserved heterogeneity. Let Ti be the length of individual i’s unemployment spell. Then, the hazard rate for individual i at time t, λi (t), is defined by lim+ h→0 P r[t + h > Ti ≥ t|Ti ≥ t] = λi (t). h (1) The hazard is parameterized using the proportional hazard form λi (t) = λ0 (t) exp[Xi′ β], (2) where λ0 (t) is the unknown baseline hazard at time t; Xi is a vector of explanatory variables for individual i, and β is a vector of parameters to be estimated. The probability that a spell lasts until time t + 1 given that it has lasted until t is written as a function of the hazard  Z P r[Ti ≥ t + 1|Ti ≥ t] = exp − t+1  λi (u)du = exp t = exp [− exp(Xi′ β + γ(t))] ,  − exp(Xi′ β) · Z t+1 λ0 (u)du t  (3) where γ(t) = log Z t+1  λ0 (u)du . t (4) The log-likelihood for a sample of N individuals can be written as a function of (3) L(γ, β) = N X i=1 " δi log [1 − exp {− exp [Xi′ β + γ(ki )]}] − kX i −1 t=1 # exp [Xi′ β + γ(t)] , (5) where γ = [γ(0)γ(1) · · · γ(T − 1)]′ . Define Ci to be the censoring time. Hence, δi = 1 if Ti ≤ Ci and 0 otherwise; ki = min(int(Ti ), Ci ). The first term is non-zero (i.e. δi = 1) when a spell ends 10 between ki and ki + 1. The second term represents the probability that a spell lasts at least until ki . As explained by Meyer (1990), we make no assumptions about the baseline hazard. For a nonparametric baseline, we create duration-interval-specific dummy variables, one for each spell month at risk of failure, defining the failure event as exiting the unemployment state. The estimation is implemented with a discrete complementary log-log (cloglog) proportional hazard model.12 To account for unobserved heterogeneity between individuals, we incorporate a random variable θi with unit mean and a certain probability distribution function µ(θi ). Moreover, θi is assumed to be independent of Xi . Then, the instantaneous hazard rate becomes λi (t) = θi λ0 (t) exp[Xi′ β]. (6) The log-likelihood for the augmented model is L(γ, β, µ) = "Z N X i=1 " exp −θ kX i −1 t=0 # exp {Xi′ β + γ(t)} dµ(θ) − δi Z " exp −θ ki X t=0 # # exp {Xi′ β + γ(t)} dµ(θ) . (7) In this study, the existence of unobserved heterogeneity (frailty) is tested by estimating a cloglog model which incorporates a normally distributed random effects term with mean zero to summarize unobserved frailty connected to each spell. The random effects term describes unexplained heterogeneity, or the influence of unobserved risk factors in the model. The assumption of a normal distribution is usually the most convenient in the case of discrete duration models for computational reasons. The results are reported in Tables 6 and 7. Each Table reports the estimated coefficients of five models: (1) and (2) refers to a discrete complementary log-log proportional hazard model; (3) reports the results of a probit model. The results in column (4) are discussed in the section 3.3. In Table 6, we show the results of models (1) to (3) from the merged sample of men and women. 12 We also provide the results of a probit estimation, where the hazard has been adequately changed. 11 3.2 Discussion In this section we discuss the results of our estimations. Tables 6 and 7 report the values of β that maximize equations (5) and (7). Note that a positive coefficient indicates a positive effect on the hazard rate, so that the unemployment duration is expected to be decreasing in the relevant independent variable.13 More precisely, the estimated coefficient on the logarithm of the spousal labor income should be interpreted as the elasticity of the hazard rate with respect to her/his wage. We estimate the models on three different samples: men, women, and the pooled sample. In this latter case, the coefficient of the spousal wage for women is found as the difference between the coefficient on the spousal wage for men and the interaction term between the spousal wage and the indicator variable for the gender. The difference is tested to be significantly different than zero, using a standard Student’s t-test. The result is reported at the bottom of Table 6. For men, a 10 percent increase in the wife’s hourly earnings is associated with a 0.8 percent increase in the hazard in specification (1), up to 14.9 percent in specification (2). For women, a 10 percent increase in husband’s hourly earnings corresponds to a 1 percent decrease in the hazard, up to 2.4 percent from specification (3). These results imply that while the unemployment duration of men is expected to be decreasing in their wife’s labor earnings, the unemployment duration of women is expected to increase in their husbands’ wage.14 Figure 2 shows the estimated hazard rate, or probability to exit unemployment, as a function of spousal income, resulting from specification (1). Panel (a) shows that the probability of leaving unemployment for men is constantly higher when their wives’ wages are in the highest percentile. The opposite is true for women, as shown in panel (b). Tables 10 and 11 report the complete estimates. The signs of the coefficients on the remaining independent variables are in line with those found in the literature. Let us focus on the results of Table 7, the most complete specification (2), where 13 The hazard rate can be found by taking the exponential of the coefficient of interest. These results are robust to anticipated changes in household expenditure. The gender asymmetry remains if the sample is limited to households that experienced an increase in the number of children. Regression results are available upon request. 14 12 we control for unobserved heterogeneity.15 The coefficients on the unemployment benefit have the expected signs and are significantly different than zero. Hence, being an UI recipient is found to have a negative effect on the probability of leaving unemployment, as established by Meyer (1990). The hazard rate also falls with age. The coefficient on the marital status (marriage vs cohabitation) is negative indicating that marriage is expected to increase unemployment duration, but it is not significant. The coefficients on the education level, when significant, are positive. This implies that a having schooling degree increases the probability of exiting unemployment.16 The significant hazard rates of unemployed spouses with children differ for fathers and mothers. While the hazard of leaving unemployment of men is increasing in the number of children, it is decreasing for women. In particular, the coefficient is significantly negative for mothers of three or more children. Hence, children provide incentives to fathers to accelerate their return to activity, but their presence is quite costly for unemployed mothers. The coefficients on the occupation before entering unemployment shows that the unemployment duration is expected to increase for high skilled professions, with respect to skilled worker. It takes longer to exit unemployment the higher is the qualification level of the profession in which they were employed before the last unemployment spell. Moreover, being self-employed before the last unemployment spell decreases the expected unemployment duration with respect to other forms of employment. The coefficient on the inflow from employment into unemployment is significantly positive. Note that, the inflow from employment alone could be capturing the effect of being unemployed after employment and not being registered to the ANPE. The reason is that we are simultaneously controlling for employment status before unemployment and registration to the ANPE. The coefficient on the regional unemployment rate is significant and has a positive sign. This means that a rise in the unemployment rate for a given region is associated with a shortening of unemployment spells in that region. An explanation for this result is that layoffs are counter cyclical: in recessions the fraction of unemployment due to layoffs rises, and layoff spells tend to be shorter. 15 16 Similar conclusions can be drawn from the results of specification (3). The reference group is composed by agents with no diploma. 13 In order to further support the results for married agents, we run a separate regression for single agents to check whether the coefficient on non-labor income is different for men compared to that of women. Since non-labor income is not available in the dataset, we use the indicator variable “owner of real estate” as a proxy for it. This dummy has already been included in the regressions for married agents, and it has not altered the gender asymmetry in the spousal wage coefficients. In Table 8, we report the results of the regression run for single women and men. In both cases, the coefficients on the variable “owner of real estate” are not significant. This result shows that the gender asymmetry for married agents is related to marriage and not to differences in preferences, technology or labor market conditions. In another exercise, we restrict the sample to breadwinner women, i.e. to women who earn more than their husbands, and estimate their hazard rates. The results are in Table 9. The breadwinner effect does not hold for wives who are primary earners in the household, and the coefficient on the spousal wage is still significantly negative. Hence, the breadwinner effect is specific to married men. A remark is in order. Restricting the sample to “richer” women generates a problem of endogeneity. In fact, we could think of this group of women as a selection of workers who have been particularly lucky in their job hunt. In a standard search model, these women got a high draw and should leave unemployment faster than the average women. So, if anything, the selection bias on the hazard rate estimate is likely to be positive. Thus the negative coefficient resulting from the regression should be a lower bound, which reinforces our findings that there is not breadwinner effect for married women. 3.3 Endogeneity Endogeneity bias is a concern in this study because it is reasonable to believe that spouses do not select themselves randomly. In other words, couple formation may be subject to assortative mating. At the same time, the asymmetric results that we find for men and women cannot be easily viewed as the consequences of positive or negative assortative mating. In both cases, we would expect symmetric reactions of husbands and wives. To be more clear, let us consider few examples that 14 lead to negative or positive correlation between the labor market conditions of the two spouses. We may observe a negative correlation when men who have high labor market productivity marry women who work fewer labor market hours. The lower (or zero) labor market hours of these women may suggest a high reservation wage relative to their potential market wage. This may, in turn, reflect a high valuation of leisure, a high shadow wage in home production, or a low potential market wage. A negative correlation between wife’s work hours and husband’s wage might also reflect income effects. Marriage to high earning husband makes it possible for wife to work fewer hours, while marriage to a low earning husband causes the wife to work more hours. In addition, marriage to a high earning wife makes it possible for the husband to work fewer hours, in which case his lower wage may then reflect the lower productivity of part-time work, or to take a more pleasant, lower-paying job. But assortative mating could also push the correlation in the opposite direction. Men who have a high labor market productivity may marry women who also have high labor market productivity. This type of marital matching would actually lead to a positive relationship between wife’s work hours and husband’s wages. Marriage to a high earning wife makes the husband able to search longer and achieve a better job match if the wife is working and providing income during his job search. We would expect a similar behavior from the wife, and hence a positive correlation between the number of hours that she works and her husband’s wage. From all of these examples, we can see that assortative mating does not automatically predict an asymmetric behavior of husbands and wives, but rather a similar response to each other spousal income, either positive or negative. In our view, regardless of the type of assortative mating into marriage, the source of the asymmetry has to be searched in a particular characteristics of a spouse’s utility function that leads him (her) to react differently than his spouse (as in the model we propose), or in a gender specificity of the labor market (as in the model of Guler et al. (2012)). In the next section, we present an instrumental variable specification to corroborate a causal effect interpretation of the main results. In particular, we instrument for hourly wage of the spouse 15 using a set of dummies for her (his) quarter of birth. 3.4 Estimation With Endogeneity To empirically address the endogeneity issue, we consider a set of instrumental variables that affect the spousal hourly earnings but are not correlated with her (his) spouse variation in the possibility to exit unemployment. We use the quarter of birth of the spouse, which through the institutional features of educational systems can have effects propagating to labor market outcomes. To motivate our choice, we refer to recent work by Grenet (2010), where he shows that French men born at the end of the year incur a small but significant penalty in terms of labor market outcomes, in the form of lower wages and higher unemployment rates. The French educational system provides a particularly valuable empirical setting to analyze date of birth effects, since it combines both the extensive use of grade retention and the practice of early secondary school tracking, two features that are likely to affect pupils differently depending on their date of birth. From a methodological point of view, as Kuhn and Skuterud (2002) stress out, there is no widely-used technique for estimating a duration model with an endogenous variable. Following Kiefer (1988), the integrated baseline hazard is γ(t) = −(Xi′ β + yi′ α) + νi , (8) where yi (previously included in Xi ) is the logarithm of the hourly earnings of agent’s i spouse, with coefficient α. Moreover, yi is defined as yi = Zi′ λ + vi , (9) where Zi is a vector of exogenous, non-time varying covariates Xi , plus an instrumental variable excluded from Xi . The error term (νi , vi ) follows a bivariate normal distribution, which implies that 16 also the conditional distribution of ν given v is normal ν|v, Z ∼ N (ρv, 1 − ρ2 ). (10) With the exception of the interval nature of our duration measure, our approach follows a standard instrumental variable probit estimation method. The results are reported in columns (4) of Table 7. They confirm a significant positive elasticity of 1.71 of unemployment duration of married men to their wife’s hourly earnings, and a negative elasticity of -0.49 of unemployment duration of married women to their husband’s hourly earnings. Moreover, the size of the coefficients in columns (4) diverges away from those of the potentially biased estimation in columns (3). The asymmetry between men’s and women’s coefficients being wider under the IV strategy suggests that if there is an endogeneity bias, it works towards making the asymmetry smaller rather than bigger. We can conclude that our findings are not due to some kind of selection. 4 Model In this section, we propose a simple theoretical mechanism that replicates the empirical findings. The asymmetry is generated by assuming that the utility of husbands depends negatively on the difference between the spouses’ wages. We call this gap a stigma, or breadwinner cost. A rationale for this stigma can be found in the sociological literature where it has been documented that while social pressure discouraging women from working outside home has weakened, pressure on husbands to be breadwinners largely remains. Recent work by Sayer et al. (2011) claims that men’s nonemployment is a serious violation of the gendered norm of male breadwinning, and that gender change has been so asymmetric that even if women’s employment has grown, the norm mandating men’s employment is still fully in force.17 17 See also http://www.sciencedaily.com/releases/2011/06/110620183244.htm. 17 An alternative source of asymmetry is described by Guler et al. (2012). They provide a numerical example of a joint search framework with multiple locations that replicates the gender asymmetry, under the assumption that married women have a higher exogenous separation rate than men. The parameters are calibrated to the U.S. data. They show that, when the unemployed wife receives an offer from the outside location, she turns it down or she accepts it and the couple lives apart, for almost all husband’s wages. Instead, when the unemployed husband receives an outside offer, there is a wide range of wife’s wage where she chooses to quit her job and moves to a new location with her husband. This asymmetry is induced by the larger separation rate for the wife. In fact, it is rarely the optimal choice for the husband to quit a high wage job to follow his wife on a precarious job in a different location. Our model builds on the theoretical framework of Guler et al. (2012). However, we focus on the breadwinner cost, because of the existing evidence of low geographical mobility in Europe provided by David et al. (2010). We consider an economy populated by married couples who participate in the labor force. Agents are either employed or unemployed. Time is continuous and there is no aggregate uncertainty. An unemployed worker is entitled to an instantaneous benefit b, and receives wage offers w at rate α from an exogenous wage offer distribution G(w) with support [0, 1). There is no recall of past wage offers. The worker observes the wage offer w and decides whether to accept it or reject it. If she (he) rejects the offer, she (he) continues to be unemployed and to receive job offers. If she (he) accepts the offer, she (he) becomes employed at wage w. A couple is defined as an economic unit composed of two individuals, a female f and a male m, who may have different preferences. The two individuals perfectly pool income to purchase a market good which is jointly consumed by the couple. We assume that individuals have not access to risk-free saving, and are not allowed to borrow. Couples make their job search decisions in order to maximize their common welfare. A couple can be in three labor market states. First, both spouses are unemployed and searching (dual-searcher couple). Second, both spouses are employed (dual-worker couple). Given our assumption of absence of job destruction, this is an absorbing state. Thirdly, one spouse is employed and the other is unemployed (worker-searcher couple). 18 4.1 Value Functions Denote by U the value function of a dual-searcher couple; Ωi (wj ) the value function of a workersearcher couple, for i, j = f, m, when the worker’s wage is wj ; and T (wf , wm ) the value function of a dual worker couple earning wages wf and wm . Let r be the subjective rate of time preference, and u(·) the instantaneous utility function. We assume that workers randomly meet employers and then change state from unemployed to employed. This event is modeled using a Poisson process: as time ǫ goes to zero, the couple receives at most one offer. The flow value in the three states becomes rT (wf , wm ) = u (wf + wm ) ; rU (11) Z wf = u (bf + bm ) + αf max {Ωm (wf ) − U, 0} dG (wf ) 0 Z wm n o max Ωf (wm ) − U, 0 dG (wm ) ; +αm (12) 0 rΩf (wm ) = u (bf + wm ) Z wf n o +αf max T (wf , wm ) − Ωf (wm ) , Ωm (wf ) − Ωf (wm ) , 0 dG (wf ) ; (13) 0 rΩm (wf ) = u (wf + bm ) − s (wf − bm ) Z wm n o m f m +αm max T (wf , wm ) − Ω (wf ) , Ω (wm ) − Ω (wf ) , 0 dG (wm ) , (14) 0 where s (·) is an increasing and convex function of the gap between the wife’s wage wf and the husband’s unemployment benefit. This function can be interpreted as a stigma or breadwinner cost that the husband faces when unemployed and having a working wife. When both spouses are employed, their flow value is equal to the total instantaneous earnings of the household (equation (11)). When they are both unemployed, their flow value is equal to the total utility of consumption (which equals the total amount of unemployment benefits) plus the expected gain in case a wage offer is received (equation (12)).18 The value functions of a worker-searcher couple require a bit more of an explanation as they are less standard. Let us analyze equation (13) where the husband is working and the wife is searching 18 Since time is continuous, the probability of both spouses receiving offers simultaneously is negligible and hence ignored. 19 for a job. Upon receiving a wage offer, the couple faces three choices. First, the unemployed spouse can accept the job offer and both spouses become employed, which increases the value by T (wf , wm )−Ωf (wm ). In this joint search model, the reservation wage of each spouse may depend on the income of the other spouse. Second, when there is a transition in the job status, the reservation wage of the previously employed spouse may also change, which could lead to exercising the quit option. Hence, the second term in the max operator represents the gain in the case where the unemployed spouse accepts the wage offer wf and the employed spouse simultaneously quits his job and search for another one. Third, the unemployed worker can reject the offer, in which case there is no change in value. A symmetric reasoning can be conducted for equation (14), where the husband is unemployed. 4.2 Characterizing the Couple’s Decisions Consider the problem of a worker-searcher couple where the spouse j is unemployed. Let us assume that it is not optimal to exercise the quit option upon acceptance, i.e. Ωi (wj ) < T (wi , wj ), for i, j = f, m. In this case, a job offer wj will be accepted when T (wi , wj ) ≥ Ωj (wi ). The associated reservation wage function φj (wi ) solves T wi , φj (wi )
= Ωj (wi ) . (15) Now, suppose that it is optimal to quit upon acceptance, Ωi (wj ) ≥ T (wi , wj ). Then, the job offer will be accepted when Ωi (wj ) ≥ Ωj (wi ). A similar reasoning is valid if the spouse i is unemployed. Proposition 1. With risk-neutral preferences, i.e. u′′ (·) = 0, the reservation wage function of the worker-searcher couple is independent of the husband’s wage when the unemployed spouse is the wife, and it is decreasing in the wife’s wage when the unemployed spouse is the husband. Moreover, it is never optimal to exercise the quit option. Proof. See the Appendix. 20 By conjecturing that the quit option is never exercised and using the value functions described above, the problem of the wife boils down to a standard single search model, where the reservation wage function depends on the utility from leisure and not on the husband’s earnings. Hence, she does not exercise the quit option, confirming the conjecture. When the unemployed spouse is the husband, the presence of the breadwinner cost in his utility function generates a negative relationship between his reservation wage and the wage of his wife. This implies that he will never exercise the quit option, as the acceptance of a wage offer by his wife decreases his reservation wage. Unemployment insurance. Using a similar strategy, we can also show that the reservation wage of the unemployed worker depends positively on his (her) own unemployment benefit. But the elasticity to changes in unemployment benefits is of different size for men and women. With risk-neutral preferences, the derivative of the men’s reservation wage function (19) with respect to unemployment benefits is 1 + ∂s/∂bm ∂φm (wf ) 1 + ∂s/∂bm = > 0, = αm m ∂bm 1 + r [1 − G (φ )] 1 + Hm (16) where Hm is the hazard rate of men. For women, the derivative of (18) is equal to ∂φf (wm ) = ∂bf 1+ αf r 1 1 > 0, = f 1 + Hf [1 − G (φ )] (17) where Hf is the hazard rate of women. The comparison between (16) and (17) shows that the size of the increase in the reservation wages depends on the breadwinner cost and on the arrival rate of jobs.19 If (1 + Hm )/(1 + Hf ) > [1 + ∂s/∂bm ], the elasticity of the husband’s reservation wage to unemployment benefits is lower than the elasticity of his wife’s reservation wage. The comparative static exercise shows a reaction to changes in unemployment insurance that is symmetric (i.e. positive for both spouses) but different in size. This may suggest the implementation 19 Here we assume that the job offer distribution is the same across gender. 21 of a gender-based unemployment policy.20 In this environment, a policy directed to reduce the aggregate unemployment duration would be less generous with women than men, as the elasticity is higher for the former. A planner that aims to exploit the difference in elasticities could implement an unemployment insurance scheme that transfers unemployment benefits from women to men. Each transferred euro would generate an increase in the search intensity of women that overcomes the decrease in men’s search effort. Note that these theoretical results are supported by the empirical findings. In fact, in all of the estimations, we obtain that being a recipient of unemployment insurance decreases the hazard rate of women more than the hazard rate of men. For example, in specification (2) of Table 7, a 10 percent increase in unemployment benefits decreases by 1.5 percent the hazard rate of men, and by 3 percent the hazard rate of women. However, it is important to point out that these policy suggestions are only tentative. Quantifying the elasticity of unemployment benefits requires a structural estimation of the theoretical model, which is relegated to future research. 5 Conclusion In this paper, we document the existing asymmetry in the probability of leaving unemployment between French married men and women. We show that the results are robust when controlling for unobserved heterogeneity and endogeneity of the explanatory variables. Most of the literature on household economics studies the intra-household behavior of husbands and wives, and the different incentives schemes that lead them to participate or not in the labor market. A vast literature is dedicated to the consequences of fertility choices, or exogenous differences in the labor market, on the labor market choices of married women. But there is no intersection with the standard search theory, that mostly focuses on single-agent problems. Not too much space has been dedicated so far to models where labor market frictions generate asymmetric reactions of married men and women, as the ones we observe empirically in this study. 20 The denomination is borrowed from Alesina et al. (2011) in their description of the gender-based taxation system. 22 We propose a first step in that direction by building on existing works to provide a simple theoretical model of joint search that replicates the gender asymmetry observed in the data. In particular, we show that the presence of a breadwinner stigma generates a negative correlation between the husband’s reservation wage and his spouse’s labor income. The theoretical model suggests the potential need for a gender-based unemployment policy, in line with the emerging literature on gender-based policies, as proposed by Alesina et al. (2011). Further research should strive to bring a richer model of household bargaining to micro data and quantify the importance of joint search, and a more accurate design of unemployment insurance schemes that take into consideration the labor market situation of the household members, and not only the individual wage history. 23 Figures 0.00 0.25 0.50 0.75 1.00 Figure 1: Kaplan-Meier Survival Estimates 0 10 20 Months Unemployed 30 Women 40 Men Figure 2: Estimated Hazard, Model (1) .5 .25 0 .25 .5 .65 (b) Women .65 (a) Men 0 A 0 5 10 15 20 Duration Bottom 1% 25 30 35 0 Median 5 10 15 20 Duration Bottom 1% Top 1% Top 1% 24 25 30 35 Median B Tables Table 1: Survey Years and No. of Observations After Restrictions Survey Year No. Initial Obs. No. Final Obs. No. Husbands No. Wives 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 137,298 141,053 146,803 151,590 151,146 150,365 148,891 149,132 182,155 182,066 178,143 175,939 966 700 642 683 581 637 2,835 859 781 2,774 797 793 298 216 226 201 195 214 452 199 172 443 155 181 668 484 416 482 386 423 2,383 660 609 2,331 642 612 Table 2: Transition from Unemployment to Employment HUSBANDS Total no. of subjects no. of records (first) entry time (final) exit rate subjects with gap time on gap if gap time at risk total failures 1,945 3,398 1,042 5,431 34,721 1,981 Mean Min Median Max 1.75 0 20,64 1 0 1 2 0 22 8 0 37 3.93 17.85 1.02 1 1 0 1 13 1 35 36 7 1.73 0 26,92 1 0 1 1 0 36 9 0 37 3.24 24.62 0.71 1 1 0 1 34 0 32 36 9 WIVES no. of subjects no. of records (first) entry time (final) exit rate subjects with gap time on gap if gap time at risk total failures 6,807 11,781 3,249 15,609 167,608 4,859 25 Table 3: Salaire minimum interprofessionnel de croissance (SMIC) Year Amount in euros of hourly gross SMIC 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 4.98 5.19 5.31 5.42 5.64 5.78 6.01 6.13 6.21 6.41 6.67 6.83 Source: INSEE 26 Table 4: Summary Statistics - Husbands - Panel 1991 to 2002 Variable Mean (Std. Dev.) Median wives’ hourly wage 6.44 (3.62) Unemployment benefits 617.29 (1,123.76) Age 43.76 (9.95) Married 0.76 (0.42) Schooling Graduate 0.09 (0.28) Undergraduate 0.09 (0.28) High school 0.11 (0.31) Basic technical training 0.32 (0.47) Junior high school 0.08 (0.26) No diploma 0.32 (0.47) Number of children: 0 children 0.47 (0.50) 1 child 0.25 (0.43) 2 children 0.21 (0.41) 3 or more children 0.07 (025) Region of residence: North 0.49 (0.50) South 0.17 (0.37) Center 0.35 (0.47) Nationality: French nationality 0.93 (0.26) Non-French nationality 0.07 (0.26) Real Estate: Owner of real estate 0.55 (0.50) Renter 0.45 (0.50) Labor market status status before last unemployment spell: Inflow after permanent employment 0.48 (0.50) Inflow after any other non participation state 0.52 (0.50) Occupation before last unemployment spell: Agricultural workers 0.00 (0.05) Upper managers 0.05 (0.22) Lower managers 0.15 (0.36) Intermediary occupations 0.27 (0.44) Salaried workers 0.11 (0.32) Skilled workers 0.41 (0.49) Employment status before last unemployment spell: Self-employed 0.06 (0.24) Government employed 0.12 (0.32) Other employed 0.82 (0.38) Registered to the ANPE 0.41 (0.49) Regional unemployment rate 9.31 (2.00) 27 Min. Max. N 3.35 0.10 23 0 99.12 24,985.88 59 1 1,945 527 1,945 1,945 0 0 0 0 0 0 1 1 1 1 1 1 1,945 1,945 1,945 1,945 1,945 1,945 0 0 0 0 1 1 1 1 1,945 1,945 1,945 1,945 0 0 0 1 1 1 1,945 1,945 1,945 0 0 1 1 1,945 1,945 0 0 1 1 1,945 1,945 0 0 1 1 1,945 1,945 0 0 0 0 0 0 1 1 1 1 1 1 1,262 1,262 1,262 1,262 1,262 1,262 0 0 0 0 5.03 1 1 1 1 15.32 1,263 1,263 1,263 1,945 1,945 Table 5: Summary Statistics - Wives - Panel 1991 to 2002 Variable Mean (Std. Dev.) Median husbands’ hourly wage 7.24 (4.39) Unemployment benefits 405.16 (1,044.30) Age 40.03 (8.89) Married 0.82 (0.38) Schooling Graduate 0.05 (0.22) Undergraduate 0.08 (0.28) High school 0.12 (0.33) Basic technical training 0.29 (0.45) Junior high school 0.10 (0.30) No diploma 0.35 (0.48) Number of children: 0 children 0.32 (0.46) 1 child 0.26 (0.44) 2 children 0.26 (0.44) 3 or more children 0.17 (0.37) Region of residence: North 0.48 (0.50) South 0.16 (0.37) Center 0.36 (0.48) Nationality: French nationality 0.93 (0.25) Non-French nationality 0.07 (0.25) Real Estate: Owner of real estate 0.53 (0.50) Renter 0.48 (0.50) Labor market status status before last unemployment spell: Inflow after employment 0.27 (0.44) Inflow after any other non participation state 0.73 (0.47) Occupation before last unemployment spell: Agricultural workers 0.00 (0.04) Upper managers 0.01 (0.12) Lower managers 0.04 (0.19) Intermediary occupations 0.15 (0.36) Salaried workers 0.57 (0.49) Skilled workers 0.22 (0.41) Employment status before last unemployment spell: Self-employed 0.02 (0.15) Government employed 0.16 (0.37) Other employed 0.82 (0.39) Registered to the ANPE 0.29 (0.47) Regional unemployment rate 9.54 (2.20) 28 Min. Max. N 3.34 9.17 20 0 147.02 34,261.03 59 1 6,807 1,114 6,807 6,807 0 0 0 0 0 0 1 1 1 1 1 1 6,807 6,807 6,807 6,807 6,807 6,807 0 0 0 0 1 1 1 1 6,807 6,807 6,807 6,807 0 0 0 1 1 1 6,807 6,807 6,807 0 0 1 1 6,807 6,807 0 0 1 1 6,807 6,807 0 0 1 1 6,807 6,807 0 0 0 0 0 0 1 1 1 1 1 1 4,761 4,761 4,761 4,761 4,761 4,761 0 0 0 0 5.03 1 1 1 1 15.32 4,763 4,763 4,763 6,807 6,807 Table 6: Pooled Sample - Wives and Husbands, Coefficients - The dependent variable is Employment VARIABLES Spousal log(hourly wage) (1=Female)*Spousal log(hourly wage) 1=Female (1) cloglog (2) cloglog u.h. (3) probit u.h. 0.080*** (0.015) -0.182*** (0.017) -0.204*** (0.032) 1.489*** (0.193) -1.508*** (0.221) 1.986*** (0.384) -0.196*** (0.030) -0.028*** (0.004) 0.787*** (0.081) 1.269*** (0.383) -1.505*** (0.210) 2.311*** (0.383) -0.092*** (0026) -0.031*** (0.004) 0.535*** (0.082) 2.020*** (0.154) -1.678*** (0.168) 1.621*** (0.129) 0.570*** (0.076) -1.415*** (0.118) 1.397*** (0.144) -1.606*** (0.198) 1.400*** (0.127) 0.422*** (0.079) -1.256*** (0.137) 1.081*** (0.073) -0.700*** (0.076) -0.149 (0.104) 0.875*** (0.078) -0.753*** (0.083) -0.151 (0.117) log(Unemployment benefits) Age 1=Legally Married Schooling (base: no diploma) Graduate Undergraduate High school Basic technical training Junior high school Number of children (base: 0 children) 1 Child 2 Children 3 and more children Region of residence (base: center) North -0.249*** (0.074) South -0.080 (0.140) 1=French nationality 2.065*** (0.118) 1=Owner of real estate -0.292*** (0.071) 1=Inflow after employment -0.311*** (0.030) Occupation before last unemployment spell (base: agricultural workers) Upper manager 0.179 (0.422) Lower manager -1.617*** (0.120) Intermediary occupations -1.480*** (0.107) Salaried worker -0.807*** (0.080) Employment status before last unemployment spell (base: other employed) Self-employed -2.862*** (0.074) Government employment 1.992*** (0.186) 1=Registered to the ANPE -1.969*** (0.132) Regional unemployment rate 0.334*** (0.018) Duration-interval-specific dummy variables YES YES -0.507*** (0.084) -0.009 (0.120) 1.773*** (0.209) -0.182** (0.080) -0.228*** (0.025) 0.659* (0.398) -1.076*** (0.115) -0.954*** (0.113) -0.565*** (0.077) -2.758*** (0.432) 1.480*** (0.149) -1.357*** (0.041) 0.266*** (0.010) YES Test: [Spousal log(hourly wage) + (1=Female)*Spousal log(hourly wage) = 0] -0.102*** -0.020 -0.236* (0.134) (0.009) (0.124) Log likelihood -72274926 -16312.889 Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1 29 -27390.919 Table 7: Separated Samples, Coefficients - The dependent variable is Employment MEN VARIABLES Spousal log(hourly wage) log(Unemployment benefits) Age 1=Legally Married Schooling (base: no diploma) Graduate Undergraduate High school Basic technical training Junior high school Number of children (base: 0 children) 1 Child 2 Children 3 and more children WOMEN (1) cloglog (2) cloglog u.h. (3) probit u.h. (4) probit IV (1) cloglog (2) cloglog u.h. (3) probit u.h. (4) probit IV 0.078*** (0.015) 0.461* (0.244) -0.152*** (0.045) -0.074*** (0.012) -0.028 (0.244) 0.377* (0.213) -0.099*** (0.035) -0.062*** (0.010) -0.079 (0.222) 1.714*** (0.367) -0.026* (0.016) -0.022*** (0.001) 0.074** (0.031) -0.101*** (0.009) -0.068 (0.183) -0.301** (0.131) -0.027*** (0.008) -0.221 (0.136) -0.075 (0.169) -0.254** (0.104) -0.025*** (0.007) -0.215 (0.136) -0.492* (0.287) -0.098*** (0.020) -0.001 (0.003) -0.090*** (0.017) -0.404 (0.588) -0.635 (0.478) 0.704** (0.306) 0.249 (0.230) 0.281 (0.372) -0.185 (0.528) -0.414 (0.396) 0.705*** (0.245) 0.297 (0.200) -0.202 (0.315) -0.464*** (0.132) -0.562*** (0.099) 0.014 (0.081) 0.031 (0.030) 0.040 (0.038) 0.228 (0.457) 0.677*** (0.265) 0.399** (0.017) 0.024 (0.137) 0.123 (0.206) 0.217 (0.413) 0.540** (0.237) 0.277 (0.175) -0.001 (0.136) 0.098 (0.199) 0.263*** (0.052) 0.332*** (0.065) 0.203*** (0.051) 0.040 (0.026) 0.037 (0.038) 0.645*** (0.243) 0.181 (0.256) 0.660 (0.448) 0.543** (0.215) 0.191 (0.227) 0.611* (0.374) 0.062*** (0.025) -0.026 (0.027) 0.142*** (0.033) -0.105 (0.130) 0.020 (0.161) -0.513** (0.210) -0.133 (0.081) -0.006 (0.147) -0.457** (0.193) 0.006 (0.016) 0.061*** (0.017) -0.111*** (0.023) -0.200*** (0.022) -0.204*** (0.031) -0.440*** (0.043) -0.111*** (0.034) -0.045** (0.019) -0.161 (0.145) -0.477*** (0.183) 0.360* (0.193) 0.139 (0.119) -0.209*** (0.022) -0.143 (0.137) -0.415** (0.169) 0.392** (0.172) 0.130 (0.115) -0.245*** (0.018) -0.004 (0.025) -0.059* (0.030) 0.153*** (0.038) 0.151*** (0.028) 0.060*** (0.012) -0.679*** (0.119) -0.289*** (0.071) -0.217*** (0.030) 0.093*** (0.032) -2.375 (2.082) 0.158 (0.456) -0.357 (0.235) -0.185 (0.139) -1.814 (1.851) 0.284 (0.373) -0.278 (0.211) -0.107 (0.138) -0.968*** (0.178) 0.055 (0.102) -0.081 (0.060) -0.066** (0.032) 0.672*** (0.127) 0.128* (0.073) -0.464*** (0.077) 0.011*** (0.006) YES -16896.674 2.394*** (0.655) -0.139 (0.181) 0.029 (0.028) 0.023 (0.031) YES -24948.022 2.013*** (0.547) -0.109 (0.169) 0.038* (0.022) 0.017 (0.027) YES -24504.805 -0.028 (0.138) -0.065** (0.032) 0.004 (0.043) 0.022*** (0.008) YES -41589.007 Region of residence (base: center) North -0.238 -0.208 (0.223) (0.196) South -0.384 -0.316 (0.344) (0.283) 1=French nationality -0.589* -0.505* (0.321) (0.288) 1=Owner of real estate -0.052 -0.020 (0.210) (0.170) 1=Inflow after employment -0.319*** -0.240*** (0.061) (0.049) Occupation before last unemployment spell (base: agricultural workers) Upper manager -1.806 -1.461** (1.204) (0.637) Lower manager 0.340 0.107 (0.352) (0.295) Intermediary occupations -0.227 -0.251 (0.213) (0.191) Salaried worker -0.135 -0.149 (0.354) (0.293) Employment status before last unemployment spell (base: other employed) Self-employed 1.905 1.510** (1.261) (0.749) Government employment 0.731 0.584 (0.741) (0.546) 1=Registered to the ANPE -4.179*** -3.816*** (0.367) (0.314) Regional unemployment rate 0.314*** 0.184*** (0.061) (0.058) Duration-interval-specific dummy variables YES YES YES Log likelihood -17528345 -4808.4855 -4704.4621 Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1 30 YES -54655567 Table 8: Estimation for singles - The dependent variable is Employment VARIABLES log(Unemployment benefits) Age WOMEN MEN cloglog u.h. cloglog u.h. -1.539*** -0.005 (0.455) (0.205) 0.000 -0.019 (0.024) (0.015) Schooling (base: no diploma) Graduate Undergraduate High school Basic technical training Junior high school -1.287 -1.025 (0.962) (0.728) -1.553** -0.256 (0.740) (0.813) 0.197 0.935** (0.793) (0.408) -0.512 0.320 (0.587) (0.303) -0.705 0.497 (0.825) (0.563) Number of children (base: 0 children) 1 Child 2 Children 3 and more children 2.086*** -0.425 (0.572) (0.385) 2.344*** -0.185 (0.705) (0.396) - 0.302 (0.562) Region of residence (base: center) North South 1=French nationality 1=Owner of real estate 1=Inflow after employment 1.548*** 0.354 (0.411) (0.304) 1.429** 0.693* (0.686) (0.362) 1.622 0.106 (1.288) (0.560) 0.493 -0.130 (0.382) (0.262) -0.431*** -0.443 (0.083) (0.765) Occupation before last unemployment spell (base: agricultural workers) Upper manager 5.957* Lower manager Intermediary occupations Salaried worker -3.881*** (3.165) (0.952) 3.380 -4.497*** (3.139) (0.801) 2.390 -3.781*** (3.047) (0.911) 3.044 -3.912*** (2.897) (0.845) Employment status before last unemployment spell (base: other employed) Government employment 1=Registered to the ANPE Regional unemployment rate Duration-interval-specific dummy variables Log likelihood 0.467 -0.443 (0.549) (0.765) -0.962*** -0.298*** (0.140) (0.067) 0.067 0.004 (0.096) (0.057) YES YES -1705.3744 -3693.853 Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1 31 Table 9: Primary Earner Wives, Coefficients - The dependent variable is Employment VARIABLES Spousal log(hourly wage) (1) cloglog (2) cloglog u.h. (3) probit u.h. -0.523*** (0.020) -1.563*** (0.192) 0.167 (0.155) -0.031*** (0.008) -2.429* (1.354) -1.121*** (0.175) 0.049 (0.127) -0.024*** (0.007) -0.911 (1.001) 0.801** (0.361) 1.283*** (0.234) 0.331* (0.191) 0.017 (0.131) 0.196 (0.227) 0.635** (0.299) 0.961*** (0.235) 0.229 (0.173) 0.046 (0.114) 0.153 (0.207) -0.034 (0.137) 0.207 (0.165) -0.269 (0.217) -0.034 (0.124) 0.141 (0.142) -0.146 (0.173) log(Unemployment benefits) Age 1=Legally Married Schooling (base: no diploma) Graduate Undergraduate High school Basic technical training Junior high school Number of children (base: 0 children) 1 Child 2 Children 3 and more children Region of residence (base: center) North -0.058 (0.166) South -0.201 (0.210) 1=French nationality 0.184 (0.258) 1=Owner of real estate 0.255 (0.150) 1=Inflow after employment -0.742*** (0.042) Occupation before last unemployment spell (base: agricultural workers) Upper manager -5.671*** (0.975) Lower manager 0.611 (0.407) Intermediary occupations -1.184*** (0.215) Salaried worker 0.003 (0.136) Employment status before last unemployment spell (base: other employed) Self-employed 3.677*** (0.879) Government employment -0.537** (0.205) 1=Registered to the ANPE 0.304*** (0.053) Regional unemployment rate 0.014 (0.036) Duration-interval-specific dummy variables YES YES -0.073 (0.136) -0.172 (0.174) 0.110 (0.209) 0.239 (0.222) -0.560*** (0.032) Log likelihood -7365.5816 -18316338 -7490.5227 Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1 32 -3.885*** (0.697) 0.714 (0.431) -0.688*** (0.186) 0.068 (0.123) 2.664*** (0.616) -0.426** (0.180) 0.241*** (0.040) 0.025 (0.029) YES Table 10: Estimated Hazard Rates from Model (1), Men Percentiles of Wife Labor Income Spell 1 2 3 4 5 6 7 8 9 10 1 0.5681307 0.5717313 0.5740378 0.5764908 0.5787139 0.5811312 0.5839177 0.5876448 0.592774 0.6059438 2 0.5604966 0.5641105 0.5664497 0.5688965 0.57113 0.573559 0.5763494 0.5800862 0.5852475 0.5985749 3 0.5571887 0.5608156 0.5631503 0.5656064 0.5678342 0.5702754 0.5730643 0.5768151 0.5819847 0.5952938 4 0.5536302 0.5572791 0.5596115 0.5620728 0.5642955 0.5667416 0.5695209 0.5733036 0.5784863 0.5918593 5 0.5509996 0.5546362 0.5569725 0.5594308 0.5616671 0.5641051 0.5668961 0.5706894 0.575868 0.5892816 6 0.5444905 0.5481303 0.5504758 0.5529301 0.5551813 0.5576295 0.5604259 0.5642104 0.5694009 0.5828834 7 0.5395352 0.5431829 0.545523 0.547987 0.5502425 0.5526974 0.5554915 0.5592887 0.5644722 0.5777963 8 0.5352041 0.5388551 0.5411986 0.5436671 0.545929 0.5483875 0.5511767 0.5549907 0.5601676 0.5735053 9 0.5318019 0.5354356 0.5377831 0.5402582 0.5425221 0.5449777 0.547768 0.5515769 0.5567524 0.5699149 10 0.5265662 0.5302137 0.5325739 0.5350459 0.5373055 0.5397544 0.5425658 0.5463824 0.5515658 0.564758 11 0.5217793 0.5254332 0.5278037 0.5302733 0.5325428 0.5349864 0.5377947 0.5416152 0.5467809 0.5597559 12 0.5027835 0.5064085 0.5088045 0.5112942 0.5135554 0.5160317 0.5188348 0.5226634 0.5278106 0.5407566 13 0.4948119 0.498422 0.5008226 0.5033012 0.5055771 0.5080433 0.5108448 0.5146753 0.5198505 0.5327633 14 0.4879692 0.4915859 0.4939741 0.4964631 0.4987415 0.5012123 0.5040281 0.5078547 0.5130255 0.5259783 15 0.479176 0.4827572 0.4851567 0.487635 0.4899217 0.4923852 0.4952142 0.4990305 0.5042086 0.5172048 16 0.4730941 0.4766497 0.4790614 0.48154 0.4838245 0.4862872 0.4891101 0.492926 0.4980984 0.511078 17 0.4684884 0.4720324 0.4744528 0.4769194 0.4791912 0.4816684 0.4844851 0.4882736 0.4934958 0.5064303 18 0.4534361 0.4569623 0.4593696 0.461808 0.4640912 0.4665664 0.4693814 0.4731514 0.4783264 0.4913678 19 0.4460464 0.4495839 0.4519843 0.4544379 0.4566902 0.4591785 0.4619912 0.4657559 0.4709324 0.4837188 20 0.4417643 0.445299 0.4476884 0.4501576 0.452393 0.4548788 0.4576884 0.4614355 0.4666521 0.4794772 21 0.4357459 0.4392814 0.4416672 0.4441426 0.4463797 0.4488621 0.4516466 0.4553932 0.4606106 0.4734035 22 0.4266775 0.4301833 0.4325676 0.4350427 0.4372625 0.4397216 0.4425363 0.446261 0.4514612 0.4641633 23 0.4138257 0.4173026 0.4196711 0.4221213 0.4243448 0.4267859 0.4296009 0.4332944 0.4385009 0.4511648 24 0.3754666 0.3788059 0.3811466 0.3835551 0.3856849 0.3880468 0.3908641 0.3944806 0.3994489 0.4120156 25 0.3582085 0.3614881 0.3637693 0.3661632 0.3682538 0.3706228 0.3734041 0.3769107 0.3818589 0.3943284 26 0.3518749 0.35517 0.3574142 0.3598085 0.3618777 0.3642348 0.3669983 0.3704816 0.3754231 0.3878992 27 0.3339769 0.3372434 0.3394443 0.3418072 0.3438121 0.3461454 0.3488869 0.3522659 0.357148 0.369439 28 0.32317 0.3263699 0.3285543 0.3308679 0.3328564 0.3351689 0.3378757 0.3412064 0.3460085 0.3583547 29 0.3102255 0.313378 0.3155477 0.3178053 0.3197688 0.3220322 0.3247071 0.3279445 0.3327425 0.3448972 30 0.2951666 0.2981949 0.3003323 0.3025364 0.3044707 0.3066905 0.3092993 0.3124786 0.317197 0.3292453 31 0.2829099 0.2858752 0.287985 0.2901557 0.2920518 0.2942285 0.296771 0.299915 0.3045602 0.3162896 32 0.2609091 0.2637556 0.2657937 0.2678964 0.2696988 0.2717883 0.2742665 0.2772525 0.2816981 0.2934355 33 0.2436815 0.2464115 0.2483988 0.250394 0.2521492 0.2541793 0.2565525 0.2594769 0.2637197 0.2750005 34 0.2299429 0.2325699 0.2344849 0.23643 0.2381233 0.2401033 0.2424187 0.2451935 0.2493293 0.2597938 35 0.2144423 0.2169626 0.2188153 0.2206984 0.2223059 0.2242172 0.2264524 0.2291316 0.2331054 0.243238 36 0.1946488 0.1970313 0.1987636 0.2005462 0.2020802 0.2038788 0.2059629 0.2084782 0.2122881 0.2220506 33 Table 11: Estimated Hazard Rates from Model (1), Women Percentiles of Husband Labor Income Spell 1 2 3 4 5 6 7 8 9 10 1 0.4257655 0.4228636 0.4208883 0.4188965 0.4166949 0.4142188 0.4114052 0.4079804 0.4027411 0.3915409 2 0.4203475 0.4174508 0.415485 0.4134957 0.4113034 0.4088293 0.4060268 0.4026149 0.3973958 0.3861973 3 0.4175571 0.4146574 0.4126916 0.4107058 0.4085166 0.4060493 0.4032534 0.3998415 0.3946474 0.3834248 4 0.4161256 0.413218 0.4112482 0.4092665 0.4070799 0.4046152 0.4018229 0.3984147 0.3932185 0.3820349 5 0.4143786 0.4114802 0.4095093 0.4075234 0.4053461 0.4028781 0.4000916 0.3966867 0.3914927 0.3803107 6 0.4064267 0.4035412 0.4015842 0.3996079 0.3974414 0.3949839 0.3922105 0.3888226 0.3836624 0.3725559 7 0.4014196 0.3985325 0.3965817 0.394614 0.3924526 0.3900063 0.387248 0.3838693 0.3787193 0.367629 8 0.3974529 0.3945655 0.3926189 0.3906573 0.3884976 0.3860606 0.3833107 0.379949 0.3748032 0.3637335 9 0.3926073 0.3897487 0.3878029 0.3858483 0.3837048 0.3812673 0.3785323 0.375184 0.37006 0.3590179 10 0.3882492 0.3854072 0.383469 0.3815221 0.3793809 0.3769529 0.3742226 0.3708954 0.3657957 0.3548456 11 0.3819744 0.3791483 0.3772205 0.3752841 0.3731548 0.370735 0.3680271 0.3647199 0.3596554 0.348732 12 0.3703125 0.3674786 0.3655767 0.3636657 0.3615544 0.3591493 0.3564852 0.3531975 0.3482099 0.337308 13 0.3636199 0.3607926 0.3589043 0.3570039 0.3549052 0.3525138 0.3498665 0.346599 0.3416493 0.3307978 14 0.3586284 0.3558216 0.3539453 0.3520496 0.3499594 0.3475792 0.3449515 0.3417012 0.3367799 0.3259933 15 0.3528357 0.3500505 0.348186 0.3463009 0.3442183 0.3418553 0.33925 0.3360183 0.3311175 0.3203965 16 0.347139 0.3444085 0.3425518 0.3406779 0.3386083 0.3362566 0.3336699 0.3304579 0.3255977 0.314972 17 0.3436638 0.3409386 0.3390861 0.33722 0.3351557 0.3328167 0.3302409 0.3270471 0.3222086 0.3115838 18 0.3290246 0.3263461 0.324524 0.3226908 0.3206613 0.3183706 0.3158415 0.3127039 0.307963 0.2975289 19 0.3177308 0.3150842 0.3132915 0.3114835 0.3094789 0.3072301 0.3047424 0.3016581 0.2969977 0.2866383 20 0.3074978 0.3049019 0.3031394 0.3013527 0.2993779 0.2971614 0.2947189 0.2916815 0.2870873 0.2769645 21 0.2995199 0.2969762 0.2952367 0.2934671 0.2915168 0.2893275 0.2869168 0.2839148 0.2793944 0.2693389 22 0.290532 0.2880481 0.2863341 0.2845828 0.2826685 0.2804993 0.278136 0.275171 0.2707104 0.260813 23 0.282632 0.2801886 0.2784964 0.2767638 0.2748792 0.2727381 0.2704118 0.2674892 0.263091 0.2533264 24 0.2510592 0.2488792 0.2472816 0.2456616 0.2438947 0.2418664 0.2396977 0.2369534 0.2328072 0.2235105 25 0.2317209 0.2296109 0.2280809 0.2265347 0.2248399 0.2229158 0.2208291 0.2182134 0.2142405 0.2053758 26 0.2210092 0.2189665 0.2174726 0.2159721 0.2143173 0.212451 0.2104188 0.2078778 0.2040229 0.195415 27 0.2097702 0.2077817 0.2063393 0.2048833 0.2032747 0.2014718 0.1995066 0.1970384 0.1933193 0.1849572 28 0.1950365 0.1931366 0.1917554 0.1903611 0.1888242 0.1871033 0.1852221 0.1828593 0.179306 0.1712966 29 0.1839271 0.1820854 0.180748 0.1794095 0.1779309 0.1762707 0.1744598 0.1721788 0.1687616 0.161042 30 0.1625827 0.160885 0.1596568 0.1584199 0.157055 0.1555293 0.1538562 0.1517523 0.1485838 0.1414923 31 0.1409769 0.1394383 0.1383244 0.1371978 0.1359617 0.1345783 0.1330505 0.1311509 0.1282844 0.121893 32 0.1183749 0.1170097 0.116031 0.115029 0.1139403 0.1127195 0.1113685 0.1096919 0.1071649 0.1015571 33 0.0989502 0.0977476 0.0968951 0.0960157 0.0950595 0.09399 0.0928022 0.0913385 0.0891209 0.0842264 34 0.0780899 0.0770991 0.0763827 0.0756481 0.074849 0.0739593 0.0729614 0.0717447 0.0698857 0.0658284 35 0.05477 3 0.0540205 0.0534796 0.0529194 0.052319 0.0516478 0.0508909 0.0499705 0.0485824 0.0455312 36 0.0319394 0.0314539 0.031105 0.0307436 0.0303553 0.0299262 0.0294382 0.0288527 0.0279585 0.0260313 34 C Sample Bias Correction To correct for the possible sampling bias due to the over representation of women in the sample, we adopt two strategies. First, we apply the sample weights EXTRI (Coefficient de pondération des individus) to all of the econometric specifications reported in the paper. Second, we follow Wooldridge (2002), chapter 17, and estimate a (probit) Heckman selection model. The selected sample includes women who are married (or cohabiting) and unemployed for at least one month. In the first stage, using all observations, we estimate a binary probit model, where the binary dependent variable is equal to 1 for selected women. In this stage, we obtain the Mills ratio for each observation. The exclusion variable is a categorial variable that indicates the willingness to work, which is called SOUH in the data set. In the second stage, we run a probit model on the selected sample, where the dependent variable is the binary variable that indicates whether the subject has left unemployment or not in that month. This is the same binary dependent variable that we used in all of the other empirical specifications. Moreover, we add the Mills ratio as explanatory variable. The results are in Table 12. The coefficient of the spousal income in the second stage remains significant and in the range of the coefficients resulting from the other specifications. 35 Table 12: Heckman Selection Model 1st Stage 2nd Stage Dep. Var.: Married or cohabiting Dep. Var.: Employment and unemployed Spousal log(hourly wage) log(Unemployment benefits) Age 0.061** (0.031) 0.121*** (0.023) -0.012*** (0.001) -0.160*** (0.024) -0.076*** (0.022) -0.011*** (0.001) 0.085 (0.061) 0.087* (0.053) 0.337*** (0.034) -0.097*** (0.025) 0.039 (0.043) 0.144*** (0.061) 0.413*** (0.049) -0.035 (0.032) 0.125*** (0.028) 0.201*** (0.042) 0.225*** (0.027) -0.165*** (0.027) -0.439*** (0.039) -0.185*** (0.026) 0.090*** (0.023) 0.195*** (0.035) -0.150*** (0.024) -0.321*** (0.034) 0.193*** (0.039) 0.191*** (0.022) 1.513*** (0.023) -0.179*** (0.017) -0.093*** (0.031) 0.116*** (0.044) 0.045** (0.044) 0.327*** (0.038) -0.039 (0.050) -0.493*** (0.038) -0.339*** (0.025) 0.310*** (0.040) -0.293*** (0.044) 0.036* (0.021) 0.229*** (0.033) 1.821*** (0.030) 0.044*** (0.005) -0.286*** (0.041) -0.336*** (0.023) -0.086*** (0.025) -0.388*** (0.041) -0.020*** (0.005) Schooling Graduate Undergraduate High school Basic technical training Junior high school Number of children 1 Child 2 Children 3 and more children Region of residence: Region of residence: North Region of residence: South French nationality Owner of real estate Inflow after employment Occupation before last unemployment spell: Lower manager Intermediary occupations Salaried worker Employment status before last unemployment spell: Government employment Registered to the ANPE Regional unemployment rate Willing to work1 Not willing to work Inverse Mills Ratio Duration-interval-specific dummy variables Log likelihood YES -3450198.3 -0.719*** (0.047) YES -13104.33 *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in the 1st stage, and bootstrap standard errors in the 2nd stage. 1 The reference category for the exclusion variable (SOUH) is “Already been working”. 36 D Variables Each agent is identified by the variables AIRE, IMLOC, NOI, and S (gender). Spousal hourly wage: monthly earnings are computed from the variables SALRED and (SALFR + PRIMFR*(1/12)) when SALRED is not available. The amounts are deflated using the consumer price deflator available at the web site of the INSEE.21 Weekly hours worked are imputed from DUHAB, and replaced by the average weekly hours worked by men and women if DUHAB is not available but the reported wage is positive. We only considered hourly wages that are at least three quarters of the minimum legal hourly wage of the considered year. See Table (3) for details on the minimum legal hourly wage, or salaire minimum interprofessionnel de croissance (SMIC). Unemployment benefits: this is computed from the variable MFRALC. The amounts are deflated using the consumer price deflator available at the web site of the INSEE.22 Age: the variable is AG. We consider its value at the last interview. Years of education: the variable is DDIPL. No. of children: the variables are ENF3, ENF6, ENF18. Region of residence: the variable RG is split in three more variables that we named North, Center, and South. The north of France includes the following regions: Picardie, Haute-Normandie, Nord-Pas de Calais, Champagne-Ardennes, Lorraine, Alsace, Ile-de-France, Basse-Normandie. Center includes: Pays de la Loire, Bretagne, Centre, Bourgogne, Franche-Comté, Poitou-Charentes, Limousin, Rhône-Alpes, Auvergne. South includes: Languedoc-Roussillon, Provence-Cte d’AzurCorse, Aquitaine, Midi-Pyrénées. French nationality: the variable is N. Owner of real estate: the variable is SO. Inflow after permanent employment, temporary employment, school or military: the variable is FI recorded at the month which precedes the unemployment spell. Occupation: the variable is DCSA. 21 22 http : //www.insee.fr/fr/themes/conjoncture/historiquei pc.asp http : //www.insee.fr/fr/themes/conjoncture/historiquei pc.asp 37 Employment status: the variable is STA. Regional unemployment rate: data available at the INSEE website.23 Registered to the ANPE: the variable is ANPE (Agence nationale pour l’emploi ). Social origin of the father in-law: the variable is CSPP that reports the type of occupation in which the father has been employed. Population weight: the variable is EXTRI that reports sample weights. Willingness to work: the variable is SOUHAITE. E Proof of Proposition 1 (i) Consider the case in which the unemployed worker is the wife. From the definition of the reservation wage function, when the quit option is not exercised, φf (wm ) has to satisfy equation (15) with j = f . We conjecture that under risk neutrality the quit option is never exercised. Then, we can disregard the second term in the max operator in (13). Substituting (11) and (13) into (15), and using the fact that workers are risk neutral, the equation characterizing φf (wm ) becomes αf φ (wm ) = bf + r f Z wf φf (wm )   wf − φf (wm ) dG (wf ) , (18) which does not depend on wm , and satisfies our conjecture. It follows that, when the unemployed husband receives and accepts a wage offer wm , the reservation wage of the wife does not change. Hence, she will not exercise the quit option. (ii) Now, consider the case in which the unemployed worker is the husband. When the quit option is not exercised, φm (wf ) has to satisfy equation (15) with j = m. We conjecture again that under risk neutrality the quit option is never exercised. Then, we can disregard the second term in the max operator in (14). Substituting (11) and (14) into (15), and using the fact that workers are risk 23 See http : //www.insee.fr/fr/themes/tableau.asp?regi d = 99refi d = CMRSOS03311. 38 neutral, the equation characterizing φm (wf ) becomes αm φ (wf ) = bm − s (wf − bm ) + r m Z wm φm ( wf ) [wm − φm (wf )] dG (wm ) , (19) which depends on wf via s (·). Taking the derivative of both sides, the effect of wf on φm is ∂φm (wf ) = − ∂wf 1+ ∂s/∂wf <0 [1 − G (φm )] αm r (20) by the assumption that s′ (·) > 0. It follows that the reservation wage of the unemployed husband is decreasing in his wife’s wage. 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