Family job search and wealth: The added worker effect revisited

García Peréz, José Ignacio; Rendón, Sílvio Article Family job search and wealth: The added worker effect revisited Quantitative Economics Provided in Cooperation with: The Econometric Society Suggested Citation: García Peréz, José Ignacio; Rendón, Sílvio (2020) : Family job search and wealth: The added worker effect revisited, Quantitative Economics, ISSN 1759-7331, The Econometric Society, New Haven, CT, Vol. 11, Iss. 4, pp. 1431-1459, https://doi.org/10.3982/QE1092 This Version is available at: https://hdl.handle.net/10419/253571 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/ Quantitative Economics 11 (2020), 1431–1459 1759-7331/20201431 Family job search and wealth: The added worker effect revisited J. Ignacio García-Pérez Department of Economics, Universidad Pablo de Olavide and FEDEA Sílvio Rendon Federal Reserve Bank of Philadelphia We propose and estimate a model of family job search and wealth accumulation with data from the Survey of Income and Program Participation (SIPP). This dataset reveals a very asymmetric labor market for household members who share that their job finding is stimulated by their partners’ job separation. We uncover a job search-theoretic basis for this added worker effect, which occurs mainly during economic downturns, but also by increased nonemployment transfers. Thus, our analysis shows that the policy goal of increasing nonemployment transfers to support a worker’s job search is partially offset by the spouse’s cross effect of decreased nonemployment and wages. The added worker effect is robust to having more children and more education in the household and does not just result as a composition of heterogeneous individuals. We also show that the interdependency between household members is understated if wealth and savings are not considered. Finally, we show that gender equality in the labor market not only improves women’s labor market performance, but it also increases men’s accepted wages and nonemployment rates. Keywords. Job search, asset accumulation, household economics, consumption, nonemployment, estimation of dynamic structural models. JEL classification. C33, E21, E24, J64. J. Ignacio García-Pérez: [email protected] Sílvio Rendon: [email protected] A preliminary version of this paper was titled “Family job search and consumption: the added worker effect revisited.” We thank Christopher Flinn, Zvi Eckstein, Barbara Brynko, and participants of the following conferences for their comments and suggestions: the European Society for Population Economics, the Society of Economic Dynamics, the New York State Economics Association, the North-American Summer Meetings of the Econometric Society, and seminars at Queen’s University, CEMFI, University of Pennsylvania, New York University, and University of Edinburgh. Our special thanks to three anonymous referees. This research started before Rendon joined the Federal Reserve System. All errors and omissions are solely ours, and our views are not necessarily those of the Federal Reserve Bank of Philadelphia or the Federal Reserve System. J. Ignacio García Pérez acknowledges the support from research projects SEJ-1512/ECON, P18-RT2135 (Fondo Europeo de Desarrollo Regional, Junta de Andalucía), PID2019-104452RB-I00 and ECO201565408-R, and ECO2015-65408-R (MINECO/FEDER). ©2020 The Authors. Licensed under the Creative Commons Attribution-NonCommercial License 4.0. Available at http://qeconomics.org.https://doi.org/10.3982/QE1092 1432 García-Pérez and Rendon Quantitative Economics 11 (2020) 1. Introduction Married couples are the largest group within the U.S. labor force,1yetmostemployment analyses and policy designs are undertaken under the individual-agent framework. When multiple workers within the household are considered, the economic analysis focuses on the choice of hours that they work in a frictionless labor market,2which is particularly enlightening for an evaluation of tax schemes and social programs. The evaluation of employment policies toward households, however, requires extending this analysis to household labor decisions in the presence of search frictions. This paper adds to the recent literature on household job search with an analysis and estimation of the added worker effect not just as a result of economic downturns, but also of increased nonemployment transfers. We propose and estimate a two-agent job search model in which an agent’s reservation wages depend on common wealth and the spouse’s wage. This setup is flexible enough to mimic observed employment transitions, wages, and household wealth levels. We find a search-theoretic basis for the observed added worker effect: When an agent separates from his job, the partner’s reservation wage declines and his or her job finding rate increases. This result reflects the observed cyclicality of household job flows, when during economic downturns job loss for one agent is compensated by the spouse’s job finding, a switch in breadwinner roles that is shown to occur mostly at low levels of wages and household wealth. We also show that the added worker effect is the result of rising individual non-employment transfers that increase workers’ nonemployment and wages but have the opposite effect on their spouses. An important policy implication of our analysis is thus that the desired goal of nonemployment transfers is partly undone by the spouse’s opposite behavior in the labor market, a result that is absent in individual job search or household labor supply frameworks. Our approach stems from the literature on job search with wealth accumulation3 and from the recent research on family job search4related to common health-insurance (Dey and Flinn (2008)), long-term welfare inequality (Flabbi and Mabli (2018)), equilibrium effects (Ek and Holmlund (2010)), and household members’ job turnover (Guler, Guvenen, and Violante (2012)). None of these studies have considered the effect of savings on family job search. Recent macroeconomic research shows that family job 1According to the Bureau of Labor Statistics (BLS), individuals whose declared marital status is “married, spouse present” represent around 77% of the civilian labor force (BLS (2016, Table 5)). 2This framework, basically under the collective approach (see Blundell et al. (2007)), studies the division of labor and of labor income within the household. One of its main conclusions is that the spouse’s wage matters for an individual’s labor supply but only through its impact on the income sharing rule set within the household, that is, through an income effect. Blundell and Macurdy (1999) and Browning, Chiappori, and Weiss (2014) reviewed the literature on family economics. 3Our approach grows out from Mortensen (1977) and Burdett and Mortensen (1998) and includes wealth accumulation as in Danforth (1979), Acemoglu and Shimer (1999), Costain (1999), Rendon (2006), Lentz (2009), and Lise (2013). 4The job search literature also includes work by Gemici (2011), who proposes and estimates a model of household migration that results in family ties hindering mobility and wage growth. Though different in their purpose, the analysis of search by committee proposed by Albrecht, Anderson, and Vroman (2010) can be also considered as part of the literature on job search by more than one agent. Quantitative Economics 11 (2020) Family job search and wealth 1433 search can explain that participation rates are not sensitive to business cycles (Mankart and Oikonomou (2017)), intrahousehold insurance (Fernández-Blanco (2017)), labor supply of secondary earnings, sons and daughters (Gonçalves, Menezes-Filho, and Narita (2018)), countercyclical unemployment rates for women (Wang (2019)), household inequality (Pilossoph and Wee (2019a)), and the marital wage premium, that is, higher wages for married men than bachelors (Pilossoph and Wee (2019b)). Mankart and Oikonomou (2017) and Wang (2019) considered wealth within a household search model, but with a unique wage that is determined in a competitive market. We have two gender-specific wage distributions and on-the-job search, plus quits and layoffs, which are able to account closely for their empirical counterparts. We also focus on asymmetric nonemployment transfer increases on family members’ nonemployment rates and wages. Our model is a unitary framework in which both employed and nonemployed agents are engaged in job search and their labor markets are connected by their common wealth and consumption and joint employment decisions. The underlying mechanism for the added worker effect in this framework is similar to Guler, Guvenen, and Violante’s (2012) “breadwinner’s cycle.” However, while they remark that an employed agent’s job separation results from the partner’s finding a job, the added worker effect that we highlight is rather that the nonemployed agent’s job finding results from the employed partner separating from his or her job. The Survey of Income Program Participation (SIPP) contains a detailed work history of individuals in the U.S. from 1996 until 2010, including their employment transitions, wages, and wealth. We find a strong labor market attachment of men and a high job turnover of women, which are not indicative of a cycle in which breadwinners’ roles constantly switch. There is a noteworthy asymmetry reflected in that, in around 20% of couples, only the husband works, while in only 45% of couples, only the wife works. Additionally, the job finding rate for the husband is around 17%, with a job separation rate of around 11%, while the wife’s job finding rate is around 35%, and her job separation rate is around 09%. On the other hand, in our data for both partners, nonemployment and wages tend to increase in the spouse’s wages; we do not find the “gender asymmetry” found by Lentz and Tranæs (2005), Lentz (2009), and Marcassa (2014), that the nonemployment duration of the wife (and, therefore, her reservation wage) is increasing in the husband’s wage, while the nonemployment duration of the husband is decreasing in the wife’s wage. We estimate this model structurally by a Simulated Method of Moments (SMM) with reasonable fit to the data on wealth, wages, employment, and employment transitions. By modifying the recovered behavioral parameters, we evaluate three counterfactual scenarios, which show important household effects that would not be present in an individual-agent framework. The first counterfactual scenario reveals that, once a household member is hit by an adverse labor market shock, the partner substantially decreases his/her nonemployment rate. Stephens (2002), for example, presented evidence of this effect in the American economy, while Wang (2019) found a similar result by linking the added worker effect to countercyclical search intensity of unemployed partners. The second 1434 García-Pérez and Rendon Quantitative Economics 11 (2020) counterfactual scenario is a relaxation of borrowing constraints, which implies increases in both spouses’ nonemployment. The third counterfactual scenario shows that the desired policy effect of nonemployment transfers established by models of individual agents, increasing wages at the expense of more nonemployment, is partially undone, especially at low levels of wages and household wealth. We also show that the omission of wealth and savings in the family job search implies underestimating the interconnection between individual job search processes and misunderstanding on how married workers react to their spouses’ job loss and increased nonemployment transfers. We show as well that the added worker effect caused by the spouses’ job loss and increased nonemployment transfers is robust to having more children in the household and more educated families. Moreover, we show that this effect is not simply a compositional result of heterogeneous agents. Finally, we show that, if wives had the same labor markets as their husbands, not only would they have similar wages and nonemployment rates as their husbands, but also their husbands would experience increases in their wages and nonemployment rates. Our model has the limitation, shared with all existing household job search models, that it is a unitary framework wherein the household is a planner that does not admit any spouse’s individual decision-making. In the context of labor supply models, this framework is not supported by the data. Under search frictions, a similar limitation may be present by means of the related reservation wages. Addressing this limitation requires modeling household job search in a nonunitary framework, which is beyond our current purpose.5 The remainder of this paper is organized as follows. In Section 2,weexplainthe model and its main implications; in Section 3, we describe the data and the selection criteria used to construct the sample; in Section 4, we detail the estimation method and identification; in Section 5, we present the estimation results and assess the model’s fit to the data; in Section 6, we analyze counterfactual scenarios; in Section 7,weevaluate the effects of omitting wealth and savings in family job search; in Section 8,wediscuss the effects of the number of children and education on family job search; in Section 9, we analyze the effects in the household of equalizing labor markets for husbands and wives; and in Section 10, we summarize our main conclusions. Appendices B–E may be found in the Online Supplementary Material (García-Pérez and Rendon (2020)) where we provide details about the numerical solution to the model. 2. Model Consider a household of two members, husband and wife,6that derives utility from consumption and leisure. They maximize expected lifetime utility by choosing a common 5A nonunitary extension of the household search model requires an individual outside option that is a divorce threat point in household bargaining. Furthermore, in a dynamic framework, a problematic issue is the commitment for future allocations of resources, as exposed by Chiappori and Mazzocco (2017). 6To facilitate the exposition of the model and to further relate it to the data, we describe our two-agent job search model as consisting of husband and wife, but this framework is applicable to any household composed of two individuals. Quantitative Economics 11 (2020) Family job search and wealth 1435 level of consumption and acceptable wage offers that determine their individual employment status as employed or nonemployed. If a spouse is nonemployed, the household receives transfers bi, which are nonlabor income and transfers that are not the result of any previous job search process, utility from leisure ϑi,7and a wage offer with probability λifrom a wage offer distribution Fi,i=12.8Additionally, if both spouses are nonemployed, the household enjoys an extra utility ϑ3, which reflects the complementarity between partners’ leisure time spent together. Employed spouses can be either laid off with probability θior receive a job offer with probability πi.9If agents accept an offer, they work for the new employer; otherwise, they remain in their current employment status. Agents can always quit their job to become nonemployed. Individual arrival and layoff rates and wage offer distributions are independent; yet, the model is able to account for correlated spouses’ employment transitions and wages, because their reservation wages are interconnected. In each period, given individuals’ employment status, wages, and current common wealth A, the household decides on a level of consumption, which determines a level of wealth for the next period A. The rate of return for saving and borrowing is the same and constant r, while the subjective discount factor is β∈(01). There is no restriction for savings, but borrowing is limited by a fraction s∈[01]of the natural borrowing limit, defined as the present value of the lowest possible secured income: B=−s(1+r)(b1+b2) r. Here, smeasures the tightness of borrowing constraints, and the limit case s=1occurs when there are no borrowing constraints. The household’s problem is contained in four value functions, which depend on wealth holdings, employment status, and the wages of its members. The value function when both members are nonemployed is the following: V(A00) =max A≥BUA+b1+b2−A 1+r+ϑ1+ϑ2+ϑ3 +βλ1λ2maxVAx1x2VAx10VA0x2 VA00dF2(x2)dF1(x1) +λ1(1−λ2)maxVAx10VA00dF1(x1) 7The value of leisure includes the direct enjoyment of free time as well as the enjoyment of nonmarket goods produced at home using this time, that is, home production. See Aguiar, Hurst, and Karabarbounis (2012). 8This model can be extended to account for geographical mobility by allowing for offers from other locations, moving costs and preference for location, as in Rendon and Cuecuecha (2010), Guler, Guvenen, and Violante (2012), and Gemici (2011). 9We tried to extend this model to allow for a costly search effort that increases arrival rates (as in Wang (2019)). Since this extension did not improve model fit of the data, we kept the simple version of the model with exogeneous arrival rates. This extension is available from the authors upon request. 1436 García-Pérez and Rendon Quantitative Economics 11 (2020) +(1−λ1)λ2maxVA0x2VA00dF2(x2) +(1−λ1)(1−λ2)V A00(1) Equation (1) shows that the family is receiving utility of consumption and of leisure, as well as the discounted value of all possible future joint employment statuses. There are similar expressions for V(Aw 10)and V(A0w2), the value function when one household member is employed and the other is nonemployed and for the value function when both members are employed, V(Aw 1w2). The specific expressions for these functions are in Appendix A. A policy rule for wealth accumulation solves each of these four equations; we concisely express them by A=A(Aw1w2). Reservation wages emerge from comparing value functions for each possible employment status with each other. We define reservation wages as a function of wealth and the spouse’s wage. For the husband, this reservation wage is w∗ 1(A w2)=w1|maxV(Aw 1w2) V (Aw10)=maxV(A0w2) V (A 00) and there is a similar definition for the wife’s reservation wage, w∗ 2(A w1).Eachagent’s reservation wage is defined as a function of the partner’s acceptable wage. For any wage below the partner’s reservation wage, as the partner is nonemployed, an agent’s reservation wage is expressed as w∗ 1(A 0)and w∗ 2(A 0). We also define the following reservation wage set: w∗∗ 1(A)w∗∗ 2(A) =w1w2|V(Aw 1w2)=V(Aw 10)=V(A0w2) This reservation wage set defines the lowest wage combination for both individuals to be employed, which we call joint-employment reservation wage. There is no joint employment at wage combinations in which at least one wage wiis below its corresponding reservation wage w∗∗ i. However, joint employment does not need to occur above this wage set; it can happen that only one partner is employed Because this model does not admit a closed-form solution, we solve it numerically, for which we assume a specific functional form for the utility function, a constant relative risk aversion (CRRA) type, where γis the coefficient of risk-aversion: U(C)=C1−γ−1 1−γ (if γ= 1and U(C)=ln(C),ifγ=1). The wage offer distribution is a truncated lognormal Fi(x):lnw∼N(μσ2|w w);0<w<w<∞,i=12. Wealth is treated as a continuous variable, while wages are discretized.10 Accordingly, we use the Euler equation and an interpolation algorithm to solve for wealth next period, and we integrate the value functions over wages by a weighted summation. The dynamic problem is solved recursively, iterating the value function until convergence is attained. In Appendix B, available online, we explain in detail the numerical solution to the model. For ease of understanding, the following discussion is based on solving the model assuming the same labor markets 10The lognormal distribution is truncated because the discretization of wages for the numerical solution requires a maximum level. We also need to discard implausible very low wage offers that do not allow couples to accumulate wealth in the way that is observed in the data. Quantitative Economics 11 (2020) Family job search and wealth 1437 Figure 1. Joint employment status by wages of husband and wife, conditional on wealth level A. for both household members, same arrival rates, wage offer distributions, nonemployment transfers, and zero leisure values. Figure 1shows the two individual reservation wages as a function of the spouse’s wage, where the husband is indexed by 1and the wife by 2. An individual’s reservation wage is unreactive to the spouse’s wages below his or her reservation wage, and an increasing curve for the spouses’s acceptable wages. The reservation wages of both spouses cross each other and divide this space into four areas, each corresponding to the four joint employment statuses. The area of joint nonemployment, uu, is a rectangle, while the areas for one nonemployed and one employed household member, eu and ue, the area under the curves, are convex sets. However, interestingly, the area of joint employment, ee, is a nonconvex set, which implies that, when both spouses work, there can be voluntary quits to nonemployment, if one spouse receives a high wage offer. Only when both household members are employed having wages that are higher than the highest possible reservation wage w∗ i(A w), there are no voluntary job separations at a given wealth level. These results are consistent with Guler, Guvenen, and Violante (2012) in what they have called “the breadwinner’s cycle,” with the following differences. In models of job search and wealth accumulation, as opposed to classic job search models, quits are possible even in individual-agent setups: Over time, once-acceptable wages are overtaken by reservation wages that increased with wealth accumulation (Rendon (2006)). Thus, individuals who managed to increase their wealth position separate voluntarily from their current job to search for better jobs while nonemployed. In our model, this effect is present as well but for the couple: As the household accumulates wealth, the rectangular area uu and both areas ue and eu of Figure 1expand over the graph, implying that some wage offers and current wages are no longer acceptable. Another important difference with Guler, Guvenen, and Violante’s model is that, in our framework, joint employment 1438 García-Pérez and Rendon Quantitative Economics 11 (2020) is not an absorbing state; agents can still be dismissed or quit to nonemployment. Accordingly, quits from employment to non-employment not only switch who is the breadwinner from ue to eu or from eu to ue, but also from ee to eu and from ee to ue. In the figure, when the couple is in the area ee and the husband is employed at wage  w1,ifthe wife receives a high wage offer w2, then she accepts it, and because  w1<w ∗ 1(A w2),he quits. Breadwinner switches can thus go on even when both household members are employed, until both wages are at least w∗ i(A w). As we show in the next section on data, we find evidence that job finding triggers job separations and role switching within the household. However, asymmetric labor markets by gender, characterized by a strong labor market attachment for men with a high turnover for women, more than indicating a cycle of constant switching between breadwinners rather suggest episodes of role switching, mostly triggered by job separation than by job finding of one spouse. When an employed household member faces a job separation, the nonemployed partner experiences a drop in his or her reservation wage and is more likely to accept wage offers. Job separations of one agent thus encourage job finding of the partner. Hence, this analysis provides a search-theoretic explanation for the added worker effect observed in the data. Figure 2shows that reservation wages are increasing in wealth, which coincides with Danforth’s (1979) result for a model of an individual job searcher. In our context of household job search, the joint-employment reservation wage is also increasing in wealth and, moreover, it converges to the reservation wage set. This implies that switching breadwinner roles within the household occurs at low levels of wealth, but it diminishes as wealth accumulation takes place, so that wage disparity within the household decreases in wealth. At low levels of wealth, and especially under tight borrowing constraints, the household smooths consumption over economic downturns by more active breadwinners’ turnover, while with more wealth, the household can smooth consumption by wealth decumulation. Figure 2. Reservation wages of the wife when the husband is nonemployed as a function of wealth. Quantitative Economics 11 (2020) Family job search and wealth 1445 find jobs sooner and accordingly exhibit shorter duration of nonemployment. Unobserved heterogeneity in mean logwages also allow us to identify some segments of the joint wage distribution, particularly those segments in which the wife’s wages are higher than the husband’s, a relatively infrequent yet nonnegligible event.18 The SMM procedure is based on a weighted measure of distance between sample and simulated moments as a function of a parameter set S(Θ) =mW−1m,where m =(ma−mp)is the distance between sample and simulated moments and Wis a weighting matrix. As in Dey and Flinn (2008), the matrix Wis a diagonal matrix consisting of the standard deviation of each empirical moment ma, obtained by bootstrap methods, from 10,000 random samples of the data. The estimated behavioral parameters are thus  Θ=argminS(Θ). We minimize this function by means of the Powell algorithm, as in Press et al. (1992), who use direction set methods in their optimization algorithm.19 Asymptotic standard errors are calculated by the gradient estimator, which requires first derivatives. We compute them numerically using a polynomial that requires five function evaluations, obtained by proportionally varying the parameter values around their estimated value. This polynomial smooths the criterion function, whose surface has discontinuous areas. The parameters’ asymptotic standard errors are then the square root of the main diagonal of this matrix. 5. Results The estimates and their corresponding asymptotic standard errors are reported in Table 3. These estimates reflect the gender asymmetry in labor markets in which arrival rates are much higher and layoff rates are much lower for the husband than for the wife. As we used monthly data in the estimation, the reported rates are also monthly and are in line with the employment transitions reported in Table 2. Job finding and job-to-job transitions are certainly lower than their corresponding estimated arrival rates because some job offers are not accepted. Similarly, job separations are higher than the estimated layoff rates, especially for the husband, as there is a relatively high proportion of voluntary job separations. Utility-maximizing search models have the feature of producing voluntary quits, as explained in Section 2, moreover so in this environment of household job search in which an individual’s employment status is highly correlated with the partner’s status. Accepted offers that made an individual leave nonemployment may no longer be acceptable in the next periods, as household wealth accumulates and the spouse accesses better paying jobs. The annualized arrival rates while nonemployed are 8755% 18An additional source of heterogeneity is by age and by marital duration. Younger and recently married couples may face different search frictions and unobserved heterogeneity than couples who are older and have longer marriage duration. We leave this matter for future research, yet in the online Appendix D, we show that age in our sample is fairly dispersed, and thus is potentially important. 19This algorithm first calculates function values for the whole parameter space and then searches for the optimal parameter direction in the next iteration for function minimization. Once a new set of parameters is obtained, the algorithm goes back to calculate a new function value, and the process is repeated until a convergence criterion is satisfied. 1446 García-Pérez and Rendon Quantitative Economics 11 (2020) Table 3. Parameter values and asymptotic standard errors in parentheses. High school. 0or 1 child. Estimate Parameter  ΘHusband Wife Individual: Arrival rate nonemployed: λ01594 (0000996)00393 (0000274) Arrival rate employed: π00758 (0000835)00517 (0000908) Layoff rate: θ00057 (0000031)00104 (0000046) Standard deviation of logwages: σ05653 (0013680)09123 (0015301) Nonemployment transfers: b11881 (310)00165 (328) Individual heterogeneous: Mean logwages, low: μ141553 (0230736)54987 (0046765) Mean logwages, high: μ266076 (0019680)79038 (0246300) Leisure, low: ϑ100000 (735776025)00101 (0000226) Leisure, high: ϑ200000 (81059089)00188 (0011735) Common: Relative risk aversion: γ13600 (0002269) Borrowing constraint: s00205 (0000548) Leisure: ϑ3−00190 (0002899) Types’ proportions: Low–Low: p11 03948 (0006383) High–Low: p21 05905 (0009414) High–High: p22 00140 (0004411) for the husband and 3819% for the wife, while the annualized arrival rates when employed are 6117% and 4711%, respectively. The annualized layoff rate is 663% for the husband and 1179% for the wife. Unobserved heterogeneity is contained in “high” and “low” types, represented by the values of individual mean logwages and leisure.20 We find that heterogeneity is relevant essentially only for husbands; there is a very low proportion of the high type for wives, 14%, and is only matched with the high type of the husband. Individual leisure values are only positive for the wife and have relatively low values, while for the husband they are zero. The “low” type of wife is matched to the “high” type of husband for 59% of the total and to the “low” type of husband for 40% of the total. This relative large homogeneity for the wife is compensated with the large dispersion of her wage offer distribution.21 Given these parameters, in general, the husband receives higher wage offers than the wife, but there is an important segment for which the wife receives higher wage offers. Nonemployment transfers only exist for the husband, while the wife’s main support when nonemployed is her husband’s wages. In models of individual agents, these 20Without imposing any constraint in the estimation, values of leisure turn out to be higher when the mean logwage is higher and smaller when the mean logwage is smaller. 21Having two types of partners, and thus four types of couples, certainly helps for the identification of the heterogeneous parameters as well as their proportions. The results of this specification, in particular that heterogeneity only matters for the husband, suggest that the estimation would not improve much from allowing for more types or in the limit assuming a continuum of types. Quantitative Economics 11 (2020) Family job search and wealth 1447 nonemployment transfers are mainly nonlabor income and the partner’s income. In our framework, we are accounting explicitly for both nonlabor income that comes from wealth and for the partner’s income, which we endogenize as accepted wages resulting from the joint job search process.22 Larger values of leisure for the wife than for the husband capture the household’s higher incentive for the wife not to work. However, when both are nonemployed, the common leisure parameter has a negative sign with a relatively high value, which reflects that there is net disutility from joint nonemployment. The coefficient of constant relative risk aversion is estimated at 136, which is in line with previous estimates of utility-maximizing job search models. The estimated borrowing constraint is very tight; essentially, the household cannot borrow. The estimated model is able to replicate very closely the observed trends in joint and conditional individual employment transitions, wages and wealth by employment status, and wealth variations by employment transitions, as we can see in Tables 1and 2, as well as in E1 and E2. Certainly, in Table 1, wealth is estimated less accurately because of the very noisy wealth data. Yet, predicted average wealth is closer to actual average wealth when both partners are nonemployed or both are employed. In Table E1, the increasing trend of nonemployment rates and wages by the wage segment of the spouse is well replicated by the estimated model, which conforms to both reservation wages being increased in the spouse’s wage. Predicted household employment transitions, shown in Table E2, also exhibit a close proximity to their actual counterparts. Table 2also reassures that individual employment transitions conditional on the spouse’s employment transitions are fairly well replicated by the model, particularly for the most frequent spouse’s employment transitions. As in the actual transitions, job finding and job separations for household members tend to be higher when their partners experience employment status changes. The model’s prediction for both spouses job-to-job flows is very close to the actuals at the total level. However, conditional on the spouse’s employment transitions, the model performs well only when the spouse’s employment status does not change. The model underpredicts job-to-job transitions when the spouse changes his or her employment status; it also overpredicts quits. Altogether, the model delivers a fairly good replication of the observed data, particularly for employment and wages. This good replication is extensive to several conditional moments by the spouse’s employment transitions both joint and conditional, in particular, the connection between household members’ job finding and job separations. The model replicates well for the large dispersion of the wealth data and their trend to depend mainly on the husband’s labor market activity. 6. Downturns,credit,and nonemployment income We perform three counterfactual experiments: worsening each household member’s labor markets, relaxing borrowing constraints, and increasing nonemployment transfers. 22As discussed previously, the nonemployment transfers parameters are mainly identified by accepted wages and employment transitions. In further research, these results can be corroborated by incorporating data of observed income during nonemployment spells of each household member. 1448 García-Pérez and Rendon Quantitative Economics 11 (2020) The first change aims to assess the effect of an asymmetric downturn on a worker’s labor market outcomes and, more precisely, evaluate whether the spouse increases his or her labor market activity once the partner becomes nonemployed, that is, the added worker effect. This change is attained by increasing layoff rates by 1percentage point. The second change consists of decreasing tightness of the borrowing constraint by 5percentage points to evaluate the effect of access to credit on family job search. The third experiment is increasing nonemployment transfers of each spouse by $100 atatimeandthen increasing both transfers by $50 at the same time, so that we can assess to what extent nonemployment transfers can also generate the added worker effect. For these counterfactuals, we recompute all moments from the same starting point in time but with the new setup. We are comparing two different economies rather than comparing an economy before and after a policy change. In Table 4, we report the variations of several selected observables caused by these changes. The response to worsening of a spouse’s labor market can be seen in the first two columns. When there is a downturn for the husband by a higher layoff rate, there is an increase of both joint nonemployment and nonemployment for the husband, associated with a decrease of joint employment and nonemployment for the wife. This evidently translates into higher total nonemployment for the husband but less evidently into a lower nonemployment for the wife. There is a clear added worker effect for the wife: She becomes more active in the labor market when labor market conditions for her husband worsen. Underlying these changes in outcomes are the household members’ reservation wage variations. An economic downturn increases an agent’s nonemployment and thereby undermines the support for the partner’s reservation wage, thus becoming more likely to accept a job. On their turn, average wages of both spouses Table 4. Variations of employment, wages, and wealth of three counterfactuals: (i) an economic downturn, (ii) relaxing borrowing constraints, and (iii) increasing nonemployment transfers. High school. 0or 1child. Economic Downturn Nonemployment Transfers Husband +θ1 Wife +θ2 Increase Debt Limit +s Husband +b1 Wife +b2 Both +b1,+b2 Variable Joint employment status (%) uu 105 028 −000 076 −004 028 ue 360 −033 001 042 −002 018 eu −141 657 002 −079 078 006 ee −321 −651 −000 −037 −070 −050 Nonemployment rate∗(%) Husband 458 005 001 053 002 026 Wife −042 691 002 −056 081 017 Wages∗($) Husband −66 0 −17−11 0 Wife −2−20 0 0 6 3 Wealth∗∗ ($)85 −804 1034 978 46 498 Note:∗if the spouse is employed. ∗∗ if both are employed. Quantitative Economics 11 (2020) Family job search and wealth 1449 tend to decrease when their layoff rates increase. Wealth holdings increase if the husband’s layoff rate increases, which indicates the predominance of the precautionary motive for savings’ effect over the effect of higher nonemployment for the husband, whereas wealth holdings decrease if the wife’s layoff rate increases, thus suggesting that the higher nonemployment effect is stronger. This added worker effect does not exist for the husband when the wife faces an economic downturn. The second counterfactual change, increasing the debt limit, generates increases in both spouses’ nonemployment rates, with negligible wage effects. The increased credit limit increases the couple’s wealth holdings: As more access to credit increases nonemployment currently and in the future, the predominant effect is that couples prefer to be cautious and increase their wealth position. The third counterfactual exercise is reported in the last three columns of Table 4. Increases in nonemployment transfers increase nonemployment and wages of the beneficiary spouse, but it has an ambiguous effect on nonemployment and wages of the spouse who does not receive them. Increasing the husband’s nonemployment transfers has the usual effect in the labor market of the husband but the opposite effect on his wife, that is, the cross effect is negative, and there is an added worker effect as discussed in Section 2. If the wife is the beneficiary of the increased nonemployment transfers, her nonemployment increases, but her husband’s nonemployment increases slightly. Splitting individual nonemployment transfers in half and increasing both spouses’ nonemployment transfers implies increasing both agents’ nonemployment rates, but this increase is quantitatively split between the two spouses. Additionally, this change increases wealth holdings, as agents increase their permanent income. As these counterfactual exercises impact a heterogeneous population, it is instructive to decompose their effects for each type of couple, as shown in Table E3. The added worker effect for the wife is present in all types of couples; whereas for the husband, it is absent in any type. The effect of relaxing borrowing constraints is so small in all types that we do not report it in this table. When the husband’s nonemployment transfers increase, there is an increase in his nonemployment but a decrease in his wife’s nonemployment across all types. We, thus, have an added worker effect of nonemployment transfers for the wife in all types. This negative cross effect does not happen when the wife’s nonemployment transfers increase. When the nonemployment transfers are split between husband and wife, nonemployment of both partners tends to increase for all types, except for the low–low type, for which the negative cross effect predominates. In sum, this decomposition by types shows that the main total effects occur for each type of couples, so that they are not just the result of the composition of different types. These counterfactual scenarios corroborate, thus, the existence of the added worker effect for the wife, both as a result of the husband’s increased layoff rates and increased nonemployment transfers. 7. No wealth and savings To understand the importance of wealth and savings in family job search, we perform a reestimation excluding wealth and savings both in the model and in the data; that is, 1450 García-Pérez and Rendon Quantitative Economics 11 (2020) Table 5. Parameter values and standard errors in parentheses. No wealth. High school. 0or 1 child. Estimate Parameter  ΘHusband Wife Individual: Arrival rate nonemployed: λ01116 (0000404)00452 (0000189) Arrival rate employed: π00807 (0000477)00319 (0000260) Layoff rate: θ00057 (0000031)00104 (0000044) S.D. of logwages: σ05653 (0006930)11412 (0053780) Nonemployment transfers: b12758 (588)15938 (445) Individual heterogeneous: Mean Logwages, low: μ160973 (0009371)48968 (0163914) Mean Logwages, high: μ268898 (0014129)52017 (0142827) Common: Relative risk aversion: γ09240 (0094522) Types’ proportions: Low–Low: p11 06645 (0333731) Low–High: p12 00920 (0333779) High–High: p22 02435 (0001880) assuming that all household income is consumed at every period, as in Dey and Flinn (2008), Ek and Holmlund (2010), Guler, Guvenen, and Violante (2012), and Flabbi and Mabli (2018). This is the exercise performed by Blundell et al. (2016) in their analysis of female labor supply. As in excluding a relevant variable in any other estimation, this exercise implies a biased estimation of the remaining parameters. As shown in Table 5, the omission of savings reduces the estimated coefficient of risk aversion, which accounts for the labor market interdependence between household members. This parameter declines substantially, from 1360 to 0924.Thisresult is around earlier structural estimations of this parameter in the absence of wealth data, which also find lower estimates. Dey and Flinn (2008), using full-time data, part-time data, and employer-provided health-insurance data from the 1996–1999 panel of SIPP estimate this coefficient at a low value: 0474. Flabbi and Mabli (2018) used full-time and part-time data from the 2001–2003 panel of SIPP and estimate this coefficient at a higher value, 09744. Despite the nonlinear utility function, without data on hours of work or monetary transfers, in a model without savings, it is not possible to distinguish between the value of leisure and nonemployment transfers. Accordingly, we exclude the leisure parameters from the estimation that increases substantially the estimated nonemployment transfers.23 Omitting wealth also implies a reduction in the mean logwages in the main type: 23In this model, we are abstracting from the option of workers to choose hours of work, either by receiving wage rate offers and choosing hours directly, as in labor supply models, or by receiving job offers as wage-hours package offers as in Hwang, Mortensen, and Reed (1998), Gorgens (2002), Dey and Flinn (2008), Aizawa and Fang (2013), Flabbi and Moro (2012), Meghir, Narita, and Robin (2015), Flabbi, Mabli, and Salazar (2016), Flabbi and Mabli (2018). None of these papers has attempted to separately identify Quantitative Economics 11 (2020) Family job search and wealth 1451 Table 6. Variations of employment, and wages of two counterfactuals: i. An economic downturn, and ii. increasing nonemployment transfers. No wealth. High school. 0or 1child. Economic Downturn Nonemployment Transfers Variable Husband +θ1Wife +θ2Husband +b1Wife +b2Both +b1,+b2 Joint employment status (%) uu 102 037 053 046 042 ue 431 −037 203 −044 158 eu −101 632 −052 610 −041 ee −430 −630 −202 −610 −157 Nonemployment rate∗(%) Husband 537 000 253 −011 196 Wife 004 668 −002 646 −002 Wages∗($) Husband −64 0 37 4 29 Wife 0−20 0 67 0 Note:∗if the spouse is employed. from a type of 66for husbands and 55for wives, with a proportion of 59%,to61for husbands and 49for wives, with a proportion of 66%. There is a lower fraction of high mean logwages for wives, which is compensated by an increased dispersion of logwages, from 091 to 114. Other parameters of the model, such as the arrival rates, do not present large variations because they do not present heterogeneity and are well identified from the observed employment transitions. Table 6presents the effects of two counterfactual changes in the constrained model. An asymmetric downturn increases nonemployment and job separations and decreases wages of the affected spouse, without any added worker effect as in the unconstrained model with wealth. On the other hand, the added worker effect of nonemployment transfers is present even in a household search without savings: Increasing non-employment transfers increases the beneficiary nonemployment rate while decreasing his or her partner’s nonemployment rate. Thus, wealth data, even if they present a large dispersion, contribute to the estimation of a family job search model. Omitting wealth in an estimation of this model implies a lower estimated coefficient of risk aversion, which understates the interdependence between household members’ job search and thus obscures the added worker effect. 8. Children and education What is the effect on the family job search of having more children or more education? We can answer this question by reestimating our model using samples of similar charpecuniary from nonpecuniary compensations during nonemployment. In SIPP, there are data on unemployment insurance and other government transfers as well on the hours of work by each household member. However, as it happens in other datasets used in the estimation of structural job search models, these observed transfers are very low for the model to match observed nonemployment rates and wealth accumulation. Accordingly, we leave this extension for future research. 1452 García-Pérez and Rendon Quantitative Economics 11 (2020) acteristics to the one that we use in this paper, but with two or more children and with more education, such as college graduates, as we anticipated in Section 3. Table E4 shows descriptive statistics for these three samples. They all exhibit a clear asymmetry in labor markets for husbands and wives as in the high school group with at most one child. Essentially, more children exacerbate this asymmetry by undermining the wife’s labor market activity; that is, decreasing her nonemployment and wages, while increasing the husband’s employment and wages. By contrast, increasing education reduces this asymmetry by deeply increasing the wife’s labor market activity yet also increasing the husband’s employment and wages. As it happens in our main sample, the dispersion of wealth is very high, yet we can see that with more children, wealth is lower for high school graduates, but it is higher for college graduates. In Table 7, we report the estimated parameters for these three groups. For high school graduates with two or more children, the husband’s labor market, contained in arrival and layoff rates, is generally better than in the main sample, whereas the wife’s labor market is generally worse, which is consistent with the lower nonemployment for the husband and the higher nonemployment for the wife. The main difference between the two types of husbands is in leisure values, as their mean logwages are very similar. For this group, there is also little heterogeneity between types of wives, as almost all wives except a very small percentage are of the low type. The coefficient of risk aversion is higher, and the husband’s nonemployment transfers and his value of leisure are also higher, while the wife’s value of leisure and her mean logwages are lower than the estimated parameters of the main sample. However, as in the main sample, the wife’s nonemployment transfers are close to zero and the tightness of the borrowing constraint is very low. For college graduates of both groups by number of children, the largest type of couple is low–low, which amounts to around 72%. The low–high type amounts to 13% and the high–high type to 14%. College graduates in general have better labor markets than high school graduates; that is, higher wage offers, higher non-employment transfers, and better arrival and layoff rates. Notably, college graduates have more access to credit, around 19% of their natural borrowing limit. College graduates with more children tend to have a wider difference between mean logwages of husbands and wives than college graduates with at most one child. We can say thus that there is more heterogeneity in the latter than in the former. Yet, with more children, arrival rates are better for the husband than for the wife, and leisure parameters are higher for both household members. Table E5 presents an intrahousehold comparison of actual and predicted wages by segment, which illustrates one of the sources of unobserved heterogeneity across households. Even though wages are mostly higher for men than for women, there is an important fraction of households for which both household members are in the same wage segment and even a fair proportion of households in which women make more than men. This latter proportion is 13% for high school graduates and 21% for college graduates with at most one child, and it declines in the number of children, which reiterates that wives are more impacted by the presence of children than their husbands. Unobserved heterogeneity is especially important to account for the segments in which women have higher wages than men. Quantitative Economics 11 (2020) Family job search and wealth 1453 Table 7. Parameter values and asymptotic standard errors in parentheses. High School College Children: 2or More 0or 12or More Parameter  ΘEst. S.E. Est. S.E. Est. S.E. Husband: Arrival rate non-E: λ01964 (0000427)01598 (0000981)01684 (0000932) Arrival rate E: π00968 (0000424)01029 (0000961)01174 (0001297) Layoff rate: θ00050 (0000044)00032 (0000020)00024 (0000017) S.D. of logwages: σ04274 (0002931)08293 (0007423)07945 (0017344) Non-E income: b12709 (066)41316 (0925286)47789 (1239324) Mean logwages, low: μ160869 (0004560)61512 (0016759)59201 (0039305) Mean logwages, high: μ260880 (0040083)76189 (0046489)80519 (0023882) Leisure, low: ϑ100002 (0000009)00114 (0000233)00117 (0000511) Leisure, high: ϑ200039 (0000251)00269 (0000729)00273 (0001727) Wife: Arrival rate non-E: λ00395 (0000150)00545 (0000337)00362 (0000256) Arrival rate E: π00508 (0000485)00506 (0000458)00469 (0000945) Layoff rate: θ00124 (0000069)00097 (0000042)00094 (0000062) S.D. of logwages: σ09527 (0007963)09104 (0024246)04455 (0013912) Non-E income: b001 (000)10011 (0232403)8983 (0214334) Mean logwages, low: μ154678 (0022529)56433 (0053321)47568 (0147875) Mean logwages, high: μ277302 (0539973)71412 (0029986)71912 (0019105) Leisure, low: ϑ100059 (0000048)00159 (0051790)00161 (0000207) Leisure, high: ϑ200828 (0054676)00338 (0000584)00341 (0000544) Common: Relative risk aversion: γ14945 (0001343)13390 (0003408)13307 (0001869) Borrowing constraint: s00219 (0000163)01902 (0000342)01904 (0000441) Leisure: ϑ3−00247 (0000367)−15621 (0028294)−13942 (0019822) Proportions of types: Low–Low: p11 08140 (0025808)07184 (0022421)07287 (0009206) Low–High: p12 01272 (0013513)01240 (0007752) High–Low: p21 01836 (0025028) High–High: p22 00024 (0003358)01481 (0010396)01412 (0002777) In Table 8, we repeat the three counterfactual exercises for all groups. The added worker effect of an economic downturn exists for both spouses in all groups, except for a downturn in the wife’s labor market in the main sample. Relaxing borrowing constraints increases nonemployment of both spouses for high school graduates; it also decreases husbands’ nonemployment and increases wives’ nonemployment for college graduates. This suggests that more access to credit increases reservation wages, mainly of the husbands. Increasing nonemployment transfers also produces the added worker effect as a negative cross effect on the spouse. For high school graduates, this negative effect exists when the husband is the beneficiary and when the wife is the beneficiary for the sample of two or more children. For college graduates, this effect only exists when the wife is the beneficiary; that is, more transfers for wives increase husbands’ employment rates. 1454 García-Pérez and Rendon Quantitative Economics 11 (2020) Table 8. Variations of individual nonemployment rates, if the spouse is employed for three counterfactuals: (i) an economic downturn, (ii) relaxing borrowing constraints, and (iii) increasing nonemployment transfers. All samples. Increase Debt Limit +s Economic Downturn Nonemployment Transfers Husband +θ1 Wife +θ2 Husband +b1 Wife +b2 Both +b1,+b2 Sample Education Children Spouse High School 0–1Husband 458 005 001 053 002 026 Wife −042 691 002 −056 081 017 High School 2+Husband 353 −017 009 196 −004 125 Wife −133 594 012 −001 172 095 College 0–1Husband 454 −058 −012 026 −011 007 Wife −222 650 011 015 071 043 College 2+Husband 457 −050 −005 027 −000 014 Wife −476 724 017 013 267 119 In sum, these additional samples corroborate the added worker effect both during downturns and as a result of individual nonemployment transfers and, the increased nonemployment reaction to more access to credit. 9. Household gender equality The family job search framework also allows us to evaluate different labor market outcomes if there is full gender equality in the labor market. We simulate the model when wives have the same arrival rates and wage offer parameters (λ,π,θ,μ,σ) and initial employment status and wages as husbands. Results of this exercise for the four samples are shown in Table 9. Labor market homogenization does accomplish gender equality and increased employment, wages, and wealth in the household. For all groups, average wages of husbands and wives are practically identical, with small differences in nonemployment rates by gender. Notice that despite only labor markets for wives were improved, husbands’ wages increased as well, which clearly implies that men’s reservation wages increased and allowed them to access better paying jobs, yet at the expense of increased nonemployment in some segments. As expected, the remaining intrahousehold differences in labor market outcomes by gender are driven by individual values of leisure and nonemployment transfers. 10. Conclusions In this paper, we have developed and estimated a model of family job search and wealth accumulation that is able to mimic observed employment transitions, wages, and wealth levels. We have documented that increasing job separations, particularly during economic downturns, triggers increased job finding by his or her partner, which constitutes the added worker effect, and underlies the countercyclical unemployment