Documento de Trabajo - 2016/10

Family Job Search and Wealth: The Added Worker Effect Revisited

J. Ignacio García-Pérez Universidad Pablo de Olavide and FEDEA

Sílvio Rendon The Federal Reserve Bank of Philadelphia

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J. Ignacio García-Pérez, (Universidad Pablo de Olavide and FEDEA) Sílvio Rendon, (The Federal Reserve Bank of Philadelphia)

Las parejas casadas son el grupo más numeroso dentro de la población activa en los Estados Unidos. Según la Oficina de Estadísticas Laborales de este país, el 77% de la mano de obra civil estadounidense está casada y convive con el cónyuge dentro del hogar. Sin embargo, la mayoría de los análisis teóricos y empíricos de políticas sociolaborales se llevan a cabo en el marco tradicional de oferta de trabajo individual. Solo muy recientemente se ha empezado a considerar la existencia de más de un trabajador dentro del hogar, pero en estos casos el análisis económico se ha centrado normalmente en la elección conjunta de las horas de trabajo bajo un enfoque colectivo dentro del hogar. El objetivo de estos estudios suele ser estudiar la división del trabajo y el ingreso dentro del hogar (ver Blundell et al., 2007). En los últimos años, unos cuantos estudios han extendido este análisis a las decisiones laborales de los hogares en presencia de fricciones derivadas de la existencia de incertidumbre cuando se busca empleo y también de la que se deriva de la excesiva rotación de puestos de trabajo existente en la mayoría de mercados de trabajo actuales. Ninguno de los trabajos previos en la literatura de búsqueda ha considerado el efecto del ahorro en la búsqueda de empleo familiar.

En este trabajo, damos un paso más dentro de esta literatura y proponemos un modelo de búsqueda de empleo dentro del hogar donde dos agentes toman decisiones de búsqueda y ahorro conjuntamente. Concretamente proponemos un modelo en el cual la riqueza es común y los salarios de un agente permiten que el otro agente sea más selectivo y busque más tiempo un trabajo que se ajuste a sus preferencias. En consecuencia, las transiciones del desempleo al empleo y los salarios aceptados van a depender fundamentalmente de la riqueza y de la situación laboral y salarial de los cónyuges dentro del hogar. Encontramos además una base teórica clara para el llamado efecto trabajador añadido: cuando un cónyuge es despedido, el salario de reserva del otro cónyuge se ajusta a la baja y su probabilidad de aceptación de ofertas y por tanto de salida del desempleo aumenta sustancialmente. Esto ocurre especialmente en situaciones de recesión económica, cuando las pérdidas de empleo de un cónyuge son compensadas por el aumento de la actividad económica en el mercado de trabajo del otro miembro del hogar.

En este trabajo también se demuestra la importancia de tener en cuenta la riqueza y el ahorro cuando se modeliza la búsqueda de empleo en el contexto familiar. Si la riqueza no se incluye explícitamente en un modelo de búsqueda de empleo en el hogar y, por consiguiente, se omite en la estimación correspondiente del mismo, se estimará con error la interconexión entre los procesos individuales de búsqueda de empleo. Además, esta omisión lleva a no tener en cuenta, por desaparecer de la ecuación a estimar, el efecto trabajador añadido lo que haría, por ejemplo, que el efecto de las prestaciones por desempleo en la duración del mismo y sobre los salarios aceptados sea mayor al que realmente predice el modelo aquí desarrollado.

Utilizando datos del Survey of Income and Program Participation (SIPP), que contiene un historial de trabajo detallado para una muestra de hogares estadounidenses para el periodo 1996-2010, y que incluye además información sobre su renta salarial y su riqueza, estimamos estructuralmente el modelo por el método de Simulación de Momentos. En nuestra muestra de estimación existe una notable asimetría en la situación laboral entre maridos y mujeres. Así, por ejemplo, encontramos que en alrededor del 21% de los casos, el marido está empleado y la esposa está desempleada, mientras que sólo en el 4% de la muestra es la esposa la que está empleada y el marido desempleado.

Los valores de los parámetros estimados hacen que los datos sean replicados por el modelo de manera bastante razonable, particularmente en términos de dinámica laboral, salarial y de riqueza. Así, una vez estimado el modelo, el siguiente ejercicio que realizamos es, evaluar sus predicciones bajo tres escenarios de simulación o contrafactuales: (i) una recesión económica sufrida alternativamente por cada uno de los miembros del hogar, (ii) una relajación de las restricciones de endeudamiento del hogar y (iii) mayores transferencias de desempleo. El primer cambio de régimen tiene como objetivo evaluar el efecto trabajador añadido, el segundo evalúa el efecto de las restricciones de liquidez sobre la oferta de trabajo del hogar y el tercero evalúa los cambios en la política de asistencia al desempleo.

Todos estos cambios de régimen muestran importantes efectos que no estarían presentes en un marco de agente individual. El primer cambio de régimen revela que una vez que un miembro del hogar es golpeado por un shock adverso en el mercado de trabajo, se observa un efecto trabajador añadido importante sobre el cónyuge, que decide ajustar a la baja su salario de reserva y que, por tanto, reduce el tiempo en que está desempleado para compensar la pérdida de renta del cónyuge. El segundo cambio de régimen muestra que cuando el hogar enfrenta restricciones de endeudamiento más holgadas, la actividad laboral de la esposa aumenta, logrando así condiciones más igualitarias dentro del hogar. El tercer cambio de régimen muestra que los aumentos en las transferencias por desempleo generan el conocido efecto sobre el beneficiario directo, esto es, alarga su estancia en el desempleo al subir su salario de reserva pero hace, a su vez, que su salario aceptado sea mayor. Sin embargo, el efecto sobre la pareja es lo contrario: sus tasas de desempleo y sus salarios aceptados serán inferiores porque querrá re-emplearse cuanto antes para compensar el comportamiento más “relajado” del cónyuge. El efecto deseado de las prestaciones por desempleo establecidas por modelos de agentes individuales, aumentando los salarios a expensas de más desempleo, se deshace parcialmente, por tanto, cuando los receptores de esta prestación más generosa son miembros de un hogar donde ambos cónyuges están activos en el mercado de trabajo.

Finalmente, también mostramos que el efecto trabajador añadido aumenta con el número de hijos en el hogar. Si un trabajador pierde el empleo, la búsqueda de trabajo del cónyuge es tanto más rápida cuantos más hijos hay en el hogar. Sin embargo, con más niños, el efecto contrario del aumento de las transferencias de desempleo sobre el desempleo de los miembros del hogar desaparece para la esposa; Es decir, si el marido recibe las transferencias por desempleo, aumenta (no disminuye) la tasa de desempleo de la esposa. El origen de este resultado es que el aumento de los ingresos del marido mientras está desempleado hace que la esposa decida pasar más tiempo con los niños, lo que se refleja en el modelo en una mayor valoración del ocio en la presencia de un mayor número de niños.

Por tanto, la conclusión fundamental de estos ejercicios de simulación es que el diseño óptimo de las prestaciones por desempleo debe tener en cuenta no solamente la situación del hogar en términos de número de miembros adultos dentro del mismo, sino también en términos del número de hijos dependientes de los agentes que puedan caer en riesgo de desempleo dentro del hogar.

J. Ignacio GarcÌa-PÈrez Universidad Pablo de Olavide and FEDEA

SÌlvio Rendon Federal Reserve Bank of Philadelphia

December 2016

Abstract

We develop and estimate a model of family job search and wealth accumulation. Individualsí job Önding and job separations depend on their partners job turnover and wages as well as common wealth. We Öt this model to 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 Önding is stimulated by their partnersí job separation, particularly during economic downturns. We uncover a job search-theoretic basis for this added worker e§ect and Önd that this e§ect is stronger with more children in the household. We also show that excluding wealth and savings from the analysis and estimation leads to underestimating the interdependency between household members. Our analysis shows that the policy goal of supporting job search by increasing unemployment transfers is partially o§set by a partnerís lower unemployment and wages.

Keywords: job search, asset accumulation, household economics, consumption, unemployment, estimation of dynamic structural models.

JEL ClassiÖcation: C33, E21, E24, J64.

Our emails: jigarper@upo.es and rensilvio@gmail.com. A previous preliminary version of this paper was entitled ìFamily job search and consumption: the added worker e§ect revisited.îWe thank Christopher Flinn and Zvi Eckstein and participants of the following meetings for their comments and suggestions: the European Society for Population Economics, Athens, June 2001; the Workshop on Numerically Intensive Economic Policy Analysis, Queenís University, Kingston, Canada, May 2004; the CentrA-Fundacion Areces Conference ìLabor Market Policy Evaluation,î Seville, May 2004; seminar at CEMFI, Madrid, May 2004; the Society of Economic Dynamics, Florence, July 2004; Conference in honor of Ken Wolpin, University of Pennsylvania, September 2012; and the Annual Meeting of the New York State Economics Association, Farmingdale, October, 2012. All errors and omissions are solely ours. This research started before Rendon joined the Federal Reserve System. The views expressed in this paper are those of the authors and not necessarily those of the Federal Reserve Bank of Philadelphia, the Federal Reserve System, or the O¢ ce of the Comptroller of the Currency. J. Ignacio GarcÌa PÈrez acknowledges the support from research projects SEJ-1512/ECON and ECO2015-65408-R (MINECO/FEDER).

1 Introduction

Married couples are the largest group within the U.S. labor force,¹ yet most employment 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.² In recent years, a few studies have extended this analysis to household labor decisions in the presence of search frictions that drive job o§er uncertainty and job turnover.

In this paper, we analyze two-agent job search in connection with savings decisions. We propose a model in which common wealth and an agentís wages allow the other agent to be more selective and search longer for a job. Consequently, employment transitions and wage outcomes depend crucially on wealth and on the partnerís employment status and wages. We Önd a search-theoretic basis for the ìadded worker e§ectî: when an agent faces a job separation, the partnerís reservation wage declines and his or her job Önding rate increases substantially. This occurs especially in economic downturns, when the job loss increases for one agent are compensated by the spouseís increased labor market activity. By the same mechanism, raising unemployment transfers increases workersíunemployment and wages but decreases their spousesíunemployment and wages. A policy implication of our analysis is that the desired e§ect of unemployment transfers is partly undone by the spouseís behavior in the labor market.

We show the importance of wealth and savings in family job search, which has not been considered by earlier work on this type of model. If wealth is not included explicitly in a family job search model and, accordingly, is omitted in the corresponding estimation, the interconnection between individual job search processes will be underestimated. Moreover, this omission leads to neglecting the added worker e§ect and to miscalculating the policy e§ect of increasing unemployment transfers.

Our approach stems from the literature on job search with wealth accumulation³ and from the recent research on household job search. We allow for a twofold interaction whereby each household memberís reservation wage depends on the partnerís labor market status and wages as well as on wealth. Previous work on family job search⁴ has analyzed family job search related to common health insurance (Dey and Flinn 2008), long-term welfare inequality (Flabbi and Mabli 2010), equilibrium e§ects (Ek and Holmlund 2010), and household membersíjob turnover (Guler, Guvenen, and Violante 2012). None of these studies has considered the e§ect of savings on family job search.

¹ According to the Bureau of Labor Statistics (BLS) individuals whose declared marital status is ìmarried, spouse presentî 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 spouseís wage matters for an individualís labor supply but only through its impact on the income sharing rule set within the household, that is, through an income e§ect. Blundell and Macurdy (1999) and Browning, Chiappori, and Weiss (2014) include reviews of the literature on family economics. The labor supply approach of the household has been particularly important to understand the household reaction to tax schemes and social programs.

³Our approach grows out from Mortensen (1977) and Burdett and Mortensen (1998) and includes

In our model, both employed and unemployed agents receive job o§ers arriving randomly from a known wage o§er distribution. Employed agents face the risk of being laid o§ from their current job. Labor market environments of the household members are unconnected; however, wealth and consumption are common to the household, which links the household membersí employment decisions. Thus, the employed partnerís income supports the other family memberís selectivity in accepting a job. But, at the same time, if the partner becomes unemployed, an agent cannot a§ord to be so selective, and he or she has to accept lower wage o§ers, which generates the added worker e§ect.

The underlying mechanism of this e§ect is similar to Guler, Guvenen, and Violanteís (2012) ìbreadwinnerís cycleî in that it relies in the dependence between household membersíreservation wages. These authors remark the employed agentís separation from his or her job resulting from the unemployed partner Önding a job. The ìadded workerî e§ect also involves a switch of breadwinner roles, but it rather remarks the unemployed agentís job Önding resulting from the employed partner separating from his or her job.

Using data from the Survey of Income Program Participation (SIPP), which contains a detailed work history of individuals in the U.S. from 1996 until 2010 including their employment transitions, wages, and wealth, we Önd evidence for both of these mechanisms. Yet, given the strong labor market attachment of men and the high job turnover of women, these interactions are not indicative of a cycle in which roles constantly switch. This noteworthy asymmetry is reáected in that, in around 21% of the sample, the husband is employed and the wife is unemployed, while in only 4% of the sample the wife is employed and the husband is unemployed. Additionally, the job Önding rate for the husband is around 14% with a job separation rate of around 1%, while the wifeís job Önding rate is around 4% and her job separation rate is around 2%. However, in our data for both partners, unemployment and wages increase in the spouseís wages; we do not Önd a ìgender asymmetryî, as Lentz and TranÊs (2005), Lentz (2009), and Marcassa (2013), who Önd that while the unemployment duration of the wife (and, therefore, her reservation wage) is increasing in the husbandís wage, the unemployment duration of the husband is decreasing in the wifeís wage.

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 di§erent 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.

We estimate this model structurally by a simulated method of moments (SMM). The model Öts reasonably well with the data on wealth, wages, employment, and employment transitions. With the recovered behavioral parameters, we evaluate the dynamics of employment, employment transitions, wages, and wealth accumulation under three counterfactual scenarios: i) an economic downturn for one household member, ii) a relaxation of borrowing constraints, and iii) higher unemployment transfers. We accomplish these scenarios by modifying the underlying parameters that we estimated previously: higher layo§ rates, looser borrowing constraints, and higher unemployment transfers. The Örst regime change aims to assess the ìadded worker e§ect,îthe second regime change determines the e§ect of borrowing constraint on the household labor allocation, and the third regime change evaluates the policy of increasing unemployment transfers.

All of these regime changes show important household e§ects that would not be present in an individual-agent framework. The Örst regime change reveals that once a household member is hit by an adverse labor market shock the partner decreases substantially his/her unemployment rate, which corroborates the ìadded worker effectî (see, for example, Stephens 2002). The underlying mechanism for this e§ect is that once the partner separates from his or her job, the spouseís reservation wage declines, thereby speeding up the partnerís transition from unemployment to employment. The second regime change shows that when the household faces looser borrowing constraints the labor market activity of the wife increases, accomplishing thereby more equal conditions within household members. The third regime change shows that increases in unemployment transfers generate the well-known labor market e§ect in the direct beneÖciary, namely that unemployment rates and accepted wages increase. The e§ect on the partner is, however, the opposite: unemployment rates and wages decrease. Increasing unemployment transfers increases the beneÖciaryís reservation wage while simultaneously decreasing the partnerís reservation wage which, again, accelerates his or her job Önding. The desired policy e§ect of unemployment transfers established by models of individual agents, increasing wages at the expense of more unemployment, is thus partially undone when the receivers are household members who are active in the labor market.

To understand the importance of wealth and savings in family job search, we Öt a model that excludes wealth and savings to a restricted sample of only employment and wage data. This omission implies underestimating the coe¢ cient of risk aversion, the only parameter that creates interdependence between individual actions within a household. This would lead to a misunderstanding on how married workers react to their spousesíjob loss and increased unemployment transfers.

Finally, we also show that the ìadded worker e§ectîincreases based on the number of children in the household. If a worker experiences job loss, the spouseís job Önding increases more the more children there are in the household. However, with more children the opposite e§ect of increasing unemployment transfers on household membersíunemployment disappears for the wife; that is, if the husband receives the unemployment transfers, the wifeís unemployment rate increases. The likely reason for this result is that the increase in the husbandís income while unemployed implies that the wife is spending more time with the children, which the model reáects in her higher valuation of leisure.

The remainder of the paper is organized as follows. In Section 2, we explain the 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 identiÖcation; in Section 5, we present the estimation results and assess the modelís Öt to the data; in Section 6, we analyze counterfactual scenarios; in Section 7, we evaluate the e§ects of omitting wealth and savings in family job search; in Section 8, we discuss the e§ects of the number of children on family job search; and in Section 9, we summarize our main conclusions. In the Appendix we provide details on the numerical solution to the model.

2 Model

Consider a household of two members, husband and that derives utility of consumption and leisure. They maximize expected lifetime utility by choosing a common level of consumption and acceptable wage o§ers that determine their individual employment status as employed or unemployed. Labor markets for these household members are separated and independent from each other. If household members are unemployed, each of them receives transfers and a wage o§er with probability from a wage o§er distribution . If they are employed, they can be either laid o§ and become unemployed with probability or receive a job o§er with probability . If agents accept an o§er, they work for the new employer; otherwise, they remain in their current employment status. Agents can always quit their job to become unemployed. If an agent is unemployed, the household enjoys an agent-speciÖc utility from leisure , and if both are unemployed they enjoy an extra utility which reáects the complementarity between partnersíleisure time spent together.

In each period, given individualsíemployment status, wages and current common wealth the household decides on a level of consumption, which determines a level of wealth for the next period . The rate of return for saving and borrowing is the same and constant while the subjective discount factor is . There is no restriction for savings, but borrowing is limited by a fraction of the natural borrowing limit, deÖned as the present value of the lowest possible secured income: . Here s measures the tightness of borrowing constraints, and the limit case occurs when there are no borrowing constraints.

The householdís problem is contained in four value functions, which depend on wealth holdings, employment status, and wages of its members. The value function when both members are unemployed is the following:

\[\begin{array}{l} V (A, 0, 0) = \max _ {A ^ {\prime} \geq B} \left\{U \left(A + b _ {1} + b _ {2} - \frac {A ^ {\prime}}{1 + r}\right) + \vartheta_ {1} + \vartheta_ {2} + \vartheta_ {3} \right. \\ \quad \quad + \beta \left[ \lambda_ {1} \lambda_ {2} \int \int \max \left[ V (A ^ {\prime}, x _ {1}, x _ {2}), V (A ^ {\prime}, x _ {1}, 0), V (A ^ {\prime}, 0, x _ {2}), V (A ^ {\prime}, 0, 0) \right] d F _ {2} (x _ {2}) d F _ {1} (x _ {1}) \right. \\ \quad \quad + \lambda_ {1} (1 - \lambda_ {2}) \int \max [ V (A ^ {\prime}, x _ {1}, 0), V (A ^ {\prime}, 0, 0) ] d F _ {1} (x _ {1}) \\ \quad \quad + (1 - \lambda_ {1}) \lambda_ {2} \int \max [ V (A ^ {\prime}, 0, x _ {2}), V (A ^ {\prime}, 0, 0) ] d F _ {2} (x _ {2}) + (1 - \lambda_ {1}) (1 - \lambda_ {2}) V (A ^ {\prime}, 0, 0) ] \}. \end{array}\]

⁵ To facilitate the exposition of the model and further relate it to the dat we describe our twoagent job search model as consisting of husband and wife, but this framework is applicable to any household composed of two individuals.

When the husband is employed and the wife is unemployed, the value function is:

\[\begin{array}{l}V \left(A, w _ {1}, 0\right) = \max _ {A ^ {\prime} \geq B} \left\{U \left(A + w _ {1} + b _ {2} - \frac {A ^ {\prime}}{1 + r}\right) + \vartheta_ {1} \right.\\\quad + \beta \left[ \pi_ {1} \lambda_ {2} \int \int \max \left[ V \left(A ^ {\prime}, x _ {1}, x _ {2}\right), V \left(A ^ {\prime}, w _ {1}, x _ {2}\right), V \left(A ^ {\prime}, x _ {1}, 0\right), \right. \right.\\\quad \left. \right.\left. V \left(A ^ {\prime}, w _ {1}, 0\right), V \left(A ^ {\prime}, 0, x _ {2}\right), V \left(A ^ {\prime}, 0, 0\right)\right] d F _ {2} (x _ {2}) d F _ {1} (x _ {1})\\\quad + \pi_ {1} \left(1 - \lambda_ {2}\right) \int \max \left[ V \left(A ^ {\prime}, x _ {1}, 0\right), V \left(A ^ {\prime}, w _ {1}, 0\right), V \left(A ^ {\prime}, 0, 0\right) \right] d F _ {1} (x _ {1})\\\quad + (1 - \pi_ {1} - \theta_ {1}) \lambda_ {2} \int \max \left[ V \left(A ^ {\prime}, w _ {1}, x _ {2}\right), V \left(A ^ {\prime}, w _ {1}, 0\right), V \left(A ^ {\prime}, 0, x _ {2}\right), V \left(A ^ {\prime}, 0, 0\right) \right] d F _ {2} (x _ {2})\\\quad + (1 - \pi_ {1} - \theta_ {1}) (1 - \lambda_ {2}) \max \left[ V \left(A ^ {\prime}, w _ {1}, 0\right), V \left(A ^ {\prime}, 0, 0\right) \right]\\\quad + \theta_ {1} \lambda_ {2} \int \max \left[ V \left(A ^ {\prime}, 0, x _ {2}\right), V \left(A ^ {\prime}, 0, 0\right) \right] d F _ {2} (x _ {2}) + \theta_ {1} (1 - \lambda_ {2}) V \left(A ^ {\prime}, 0, 0\right) ] \}.\end{array}\]

A similar expression corresponds to , the value function when the husband is unemployed and the wife is employed. And, Önally, the value function when both members are employed has the following expression:

\[\begin{array} { l } V \left( A , w _ { 1 } , w _ { 2 } \right) = \operatorname* { m a x } _ { A ^ { \prime } \geq B } \left\{ U \left( A + w _ { 1 } + w _ { 2 } - \frac { A ^ { \prime } } { 1 + r } \right) \right. \\ + \beta \left[ \pi _ { 1 } \pi _ { 2 } \iint \operatorname* { m a x } \left[ V \left( A ^ { \prime } , x _ { 1 } , x _ { 2 } \right) , V \left( A ^ { \prime } , w _ { 1 } , x _ { 2 } \right) , V \left( A ^ { \prime } , x _ { 1 } , w _ { 2 } \right) , \right. \right. \\ \left. \quad V \left( A ^ { \prime } , w _ { 1 } , w _ { 2 } \right) , V \left( A ^ { \prime } , x _ { 1 } , 0 \right) , V \left( A ^ { \prime } , w _ { 1 } , 0 \right) , V \left( A ^ { \prime } , 0 , x _ { 2 } \right) , \right. \\ \left. \quad V \left( A ^ { \prime } , 0 , w _ { 2 } \right) , V \left( A ^ { \prime } , 0 , 0 \right) ] d F _ { 2 } \left( x _ { 2 } \right) d F _ { 1 } \left( x _ { 1 } \right) \\ + \pi _ { 1 } \left( 1 - \pi _ { 2 } - \theta _ { 2 } \right) \int \operatorname* { m a x } \left[ V \left( A ^ { \prime } , x _ { 1 } , w _ { 2 } \right) , V \left( A ^ { \prime } , w _ { 1 } , w _ { 2 } \right) , \right. \\ \left. \quad V \left( A ^ { \prime } , 0 , w _ { 2 } \right) , V \left( A ^ { \prime } , x _ { 1 } , 0 \right) , V \left( A ^ { \prime } , w _ { 1 } , 0 \right) , V \left( A ^ { \prime } , 0 , 0 \right) ] d F _ { 1 } ( x _ { 1 } ) \right. \\ + \pi _ { 1 } \theta _ { 2 } \int \operatorname* { m a x } \left[ V \left( A ^ { \prime } , x _ { 1 } , 0 \right) , V \left( A ^ { \prime } , w _ { 1 } , 0 \right) , V \left( A ^ { \prime } , 0 , 0 \right) ] d F _ { 1 } ( x _ { 1 } ) \\ + ( 1 - \pi _ { 1 } - \theta _ { 1 } ) \pi _ { 2 } \int \operatorname* { m a x } \left[ V \left( A ^ { \prime } , w _ { 1 } , x _ { 2 } \right) , V \left( A ^ { \prime } , w _ { 1 } , w _ { 2 } \right) , \right. \\ \left. \quad V \left( A ^ { \prime } , w _ { 1 } , 0 \right) , V \left( A ^ { \prime } , 0 , x _ { 2 } \right) , V \left( A ^ { \prime } , 0 , w _ { 2 } \right) , V \left( A ^ { \prime } , 0 , 0 \right) ] d F _ { 2 } ( x _ { 2 } ) \right. \\ + ( 1 - \pi _ { 1 } - \theta _ { 1 } ) ( 1 - \pi _ { 2 } - \theta _ { 2 } ) \operatorname* { m a x } [ V ( A ^ { \prime } , w _ { 1 } , w _ { 2} ) , V ( A ^ { \prime } , w _ { 1 } , 0 ) , \\ V ( A ^ { \prime } , 0 , w _ { 2} ) , V ( A ^ { \prime } , 0 , 0 ) ] \\ + ( 1 - \pi _ { 1 } - \theta _ { 1 } ) \theta _ { 2 } \operatorname* { m a x } [ V ( A ^ { \prime } , w _ { 1 } , 0 ) , V ( A ^ { \prime } , 0 , 0 ) ] \\ + (\theta _ { 1 } {\pi_ { 2}} {\int} {\max} [ V ( A ^ { \prime }, 0, x _ { 2} ) , V ( A ^ { \prime }, 0, w _ { 2} ) , V ( A ^ { \prime }, 0, 0 ) ] d F _ { 2 } ( x _ { 2} ) \\ + (\theta _ { 1 } ( 1 - {\pi_ { 2 }} - {\theta_ { 2}} ) {\max} [ V ( A ^ { \prime }, 0, w _ { 2} ) , V ( A ^ { \prime }, 0, 0 ) ] + (\theta_ { 1} {\theta_ { 2}} V ( A ^ { \prime }, 0, 0 ) ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .. . . . . . .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |\]

A policy rule for wealth accumulation solves each of these four equations; we concisely express them by . Reservation wages emerge from comparing value functions for each possible employment status with each other. We deÖne reservation wages as a function of wealth and the spouseís wage:

\[\begin{array}{l l l} w _ {1} ^ {*} \left(A, w _ {2}\right) & = & \left\{w _ {1} | \max \left[ V \left(A, w _ {1}, w _ {2}\right), V \left(A, w _ {1}, 0\right) \right] = \max \left[ V \left(A, 0, w _ {2}\right), V \left(A, 0, 0\right) \right] \right\}, \\ w _ {2} ^ {*} \left(A, w _ {1}\right) & = & \left\{w _ {2} | \max \left[ V \left(A, w _ {1}, w _ {2}\right), V \left(A, 0, w _ {2}\right) \right] = \max \left[ V \left(A, w _ {1}, 0\right), V \left(A, 0, 0\right) \right] \right\}. \end{array}\]

Each agentís reservation wage is deÖned as a function of the partnerís acceptable wage. For any wage below the partnerís reservation wage, as the partner is unemployed, an agentís reservation wage is expressed as and . We also deÖne the following reservation wages:

\[w _ {1} ^ {* *} (A), w _ {2} ^ {* *} (A) = \left\{w _ {1}, w _ {2} \mid V (A, w _ {1}, w _ {2}) = V (A, w _ {1}, 0) = V (A, 0, w _ {2}) \right\}.\]

This reservation wage set deÖnes 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 is below its corresponding reservation wage . However, above this wage set joint employment does not need to occur, being possible that only one partner is employed.

As this model does not admit a closed-form solution, we solve it numerically, for which we assume a speciÖc functional form for the utility function, a constant relative risk aversion (CRRA) type, where is the coe¢ cient of risk-aversion: , and . The wage o§er distribution is a truncated lognormal : ln : We allow wealth to be continuous while we discretize wages. 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 the Appendix, we provide a detailed explanation of the numerical solution to the model. The following discussion is based on solving the model assuming the same labor markets for both household members, same arrival rates, wage o§er distributions, unemployment transfers, and zero leisure values.

Figure 1 shows the two reservation wages as a function of the spouseís wage, where the husband is indexed by 1 and the wife by 2. The wifeís reservation wage is a horizontal line that becomes an increasing curve as the husbandís wage increases. The husbandís reservation wage is a vertical line that becomes an increasing curve as the wifeís wage increases. These crossing reservation wages divide this space into four areas, each corresponding to the four joint employment statuses. The area of joint unemployment, uu, is a rectangle, while the areas for one unemployed and one employed household member, eu and ue, is the area under the curves, a convex set. However, interestingly, the area of joint employment, ee, is a nonconvex set. Notice also that there is a ceiling on acceptable wages for both partners who are employed: if the wage of one partner is very high, then the other household member will not work. This shape implies that a household with both employed members can experience voluntary quits to unemployment, if one household member receives a high wage o§er. Only when both household members are employed at wages that are higher than the highest possible reservation wage , there are no voluntary job separations at a given wealth level.

These results are consistent with Guler, Guvenen, and Violante (2010) in what they have called ìthe ìbreadwinnerís cycle,îwith the following di§erences. 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 unemployed. In our model, this e§ect is present as well but at the couple level: as the household accumulates wealth, the rectangular area uu and both areas ue and eu of Figure 1 expand over the graph implying that some wage o§ers and current wages are no longer acceptable. Another important di§erence with Guler, Guvenen, and Violanteís model is that in our framework joint employment is not an absorbing state; agents can still be dismissed or quit to unemployment. Accordingly, quits from employment to unemployment not only switch who is the breadwinner from ue to eu or from eu to ue but also from to eu and from ee to ue. In the Ögure, when the couple is in the area ee and the husband is employed at wage , if the wife receives a high wage o§er , then she accepts it, and because he quits. Breadwinner switches can thus go on even when both household members are employed, until both wages are at least

As we will see in the next section on data, we Önd evidence that suggests that job Önding 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 point out episodes of role switching, mostly triggered by job separation than by job Önding of one spouse. When an employed household member faces a job separation, the unemployed partner experiences a drop in his or her reservation wage and is more likely to accept wage o§ers. Job separations of one agent encourage thus job Önding of the partner. Hence, this analysis provides a search-theoretic explanation for the well-known ìadded worker e§ect.î

[Figure 2 here]

Figure 2 shows that reservation wages are increasing in wealth. This result coincides with Danforthís (1979) result for a model of an individual job searcher for which employment is a terminal state. 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. Switching directly between employment statuses ue and eu occurs mostly at low levels of wealth. As wealth accumulation takes place, there is less room for a rotation of breadwinners within the household. Consequently, the internal disparity of wage income within the household is decreasing in wealth.

[Figure 3 here]

Figure 3 exhibits the husbandís reservation wages as a function of both the wifeís reservation wage and wealth as level curves. Because there are wage and wealth combinations for which the wife is not employed, we also show the wifeís reservation wage functions of Figure 2. We show four levels, L, of the husbandís reservation wage, which are increasing both in wealth and the wifeís wage, so that they exhibit a decreasing shape and are relatively áat. That is, for the husbandís reservation wage to remain constant an increase of one dollarís worth in the wifeís wage has to be compensated by a decrease in wealth of more than one dollar. In the area between the wifeís reservation wage and the joint-employment reservation wage , the husbandís reservation wage increases only in the wifeís wage but not in wealth.⁶

⁶Notice that in Figure 1 an expansion of wealth will not variate substantially the increasing reservation wage curve in the segment between the upper-right corner of the rectangle uu and the point ).

In the area under the wifeís reservation wage, , the husbandís reservation wage only increases in wealth at a wifeís given wage and is unreactive to the wifeís wages in that location, as these wages are unacceptable.

[Figure 4 here]

Figure 4 illustrates the joint employment e§ect of an increase in the husbandís unemployment transfers. The husbandís increased reservation wage produces a reallocation of joint employment statuses in three ways. First, there is a reallocation from joint employment to the husband being unemployed and the wife being employed (ee to ue). Second, there is a household role switch from the husband being employed and the wife unemployed to the husband being unemployed to the wife being employed (eu to ue). Third, a reallocation from the husband being employed and the wife unemployed to both spouses being unemployed (eu to uu). In these three reallocations, the husband separates from his job, but the wifeís employment status is unchanged in two, whereas in one reallocation she transitions from unemployment to employment. Hence, an increase in a husbandís unemployment transfers increases his unemployment rate while it tends to decrease her unemployment rate. This e§ect will be important when we assess the policy implications of our model in Section 6.

Summarizing, in this model both common wealth and the partnerís wages allow individuals to be more selective and search longer for a suitable job. If an employed agent separates from his or her job, the unemployed partner cannot a§ord to be so selective and will be more likely to accept job o§ers and become employed. The model allows, thus, for an ìadded worker e§ect.î It also produces the well-known e§ect of unemployment transfers on the receiving household member, higher unemployment, and higher wages; yet at the same time it produces an opposite e§ect on the spouse, namely, lower unemployment and lower wages.

3 Data and descriptive statistics

We are Ötting our model to a sample of couples coming from SIPP. This data set contains information on socio-demographic characteristics and labor market variables, such as income; labor force and public programs participation, including child care; wealth; utilization and cost of health care; disability; school enrollment;and taxes. SIPP was constructed primarily to measure the e§ectiveness of existing federal, state, and local programs. As it collects information on several variables at the household level, this survey is unique in allowing us to construct a household labor market history.

SIPPís design is based on a continuous series of national panels, with a sample size of approximately 36,700 interviewed households. We are using the 4-year 1996 panel, which covers the period 1996ñ1999, a period of relative economic stability. The survey is based on monthly interviewing and uses a 4-month recall period, with approximately the same number of interviews being conducted in each month of the 4-month period for each wave. Hence, we have three observations per year during the 1996ñ1999 span, that is, 12 waves.

As we are interested only in households with two members present, we select one-family households of married couples where both spouses are present and meet certain requirements regarding age and education. We restrict our sample to those aged between 26 and 50, who are high school graduates, not currently enrolled in school, not self-employed or ever retired, not disabled, not contingent workers, not receiving any kind of welfare beneÖts or social program, not owners of any kind of business, and not in the armed forces. We exclude from the sample couples who have two children or more; our sample consists only of couples that do not have children or who have only one child. These selection criteria restrict our sample to 32,485 observations on 1,050 married couples.⁷

We categorize any individual in the sample as either employed or unemployed.⁸ In order to determine the labor status in each of the 12 waves included in the sample, we use the monthly labor status information o§ered. If that information is not available, we compute monthly wages from the regular hourly wage and the number of hours they work per week.

We use total wealth information reported by SIPP and exclude couples that lack wealth data. All wages and wealth observations are in dollars of 1982ñ1984. Nominal values in SIPP are deáated using the Consumer Price Index reported by the BLS.⁹

[Table 1 here]

⁷ This stringent sample selection is usual in structural estimations. It is particularly similar to Dey and Flinn (2008) , who also use SIPP and restrict their sample to 1,267 married couples.

⁸In the absence of good information on search intensity, we are not able to distinguish between being out of the labor force and unemployment, a distinction that is relevant especially for women Like Dey and Flinn (2008) , we use unemployment synonimously with nonemployment.

⁹See Table 24 in the Historical Consumer Price Index for All Urban Consumers (CPI-U): U. S. city average, all items-Continued (1982ñ1984=100, unless otherwise noted).

Table 1 shows employment status, wages, and wealth by the employment status of the spouse. It illustrates a noteworthy asymmetry between the employment statuses of the household members.¹⁰ In 21% of the sample, the husband is employed and the wife is unemployed, compared to only around 4% in which the husband is unemployed and the wife is employed. On the other hand, the most frequent employment status is that both are employed, which occurs in around 74% of the observations, while joint unemployment is very infrequent, with only 0.5% of the observations. That is, in 95% of the observations the husband is employed compared with 78% of the observations in which the wife is employed. Within the household, the husband is clearly better established as an employed worker than the wife.

For both household members, the unemployment rate is clearly much higher, twice as much, when the spouse is employed than when he or she is unemployed. For the husband, the unemployment rate is around 2.5% when his wife is unemployed and becomes 5.6% when she is employed. The same happens for the wife, at much higher levels. The wifeís unemployment rate is around 10.8% when her husband is unemployed and becomes 21.7% when he is employed.

On the contrary, wages are higher when the spouse is unemployed than if he or she is employed. Husbandsímonthly wages are on average $1,996 when his wife is not working, and $1,685 when she is working. Wivesí average monthly wages are $1,243 when her husband is not working and $1,182 when he is working. That is, husbandís wages are fairly sensitive to the wifeís employment status whereas wifeís wages are pretty unreactive to the husbandís employment status. A consequence of this asymmetry is that the gender wage gap for these married couples is larger when the spouse is unemployed than when he or she is employed.

Wealth data are very noisy, yet there are some clear di§erences by household employment status. Wealth is the highest with joint unemployment, which suggests that higher wealth allows couples to hold on to unemployment and wait for better wage o§ers to arrive. When only one household member works, there is also a clear asymmetry in wealth, depending on who is working. Wealth is higher when only the husband works than when only the wife works. Moreover, when only the wife works, wealth level is the lowest, whereas when only the husband works, the wealth level is as high as when both work. These associations between wealth and joint employment status suggest that wealth accumulation is mainly dependent on the husband working than on the wife working, another asymmetry within the household.

¹⁰ In these tables, we also report predicted statistics, which we will discuss in detail in Section 5 when we assess model Öt.

[Table 2 here]

Table 2 reports unemployment rates and average wages of each household member by the spouseís wage segment and when the spouse is unemployed. The general pattern is very clear: unemployment rates and average wages tend to be higher when the partnerís wages are higher. At this level of aggregation, we do not Önd a ìgender asymmetryîas found by Lentz and TranÊs (2005), Lentz (2009), and Marcassa (2013) that would imply that the wifeís unemployment and wages are decreasing in the husbandís wage. We observe, however, nonmonotonicities in several segments. It is also noteworthy that the unemployment rate when the partner is employed is higher than when the partner is unemployed, even in the lower wage segment, which does not happen for average wages. Average wages when the partner is unemployed are lower than when the partner is employed at the lowest wage segment.

[Table 3 here]

In Table 3 we report the household employment transitions as a percentage of all transitions. The main áows happen within the same joint employment status. Flows from joint unemployment are persistent and very small, as joint status is not very frequent. So is the case with the transition from only the husband being unemployed. Most of the o§-diagonal single transitions represent less than 0.5% of all transitions. One transition that exceeds 1% happens when the husband stays unemployed and the wife separates from her job or, equivalently, from joint employment to only the wife being unemployed. As these employment transitions are generally small, the data for wage and wealth variations occurring within these employment transitions contain very few observations.

[Table 4 here]

Table 4 presents employment transitions between joint employment statuses conditional on the current status. We see that the exit from joint unemployment depends mainly on only the husband Önding a job, which happens in 19% of the transitions compared with 3% for only the wife Önding a job and 3% for both Önding a job. If one of the household members is unemployed and the other is employed, the main o§-diagonal transition is to joint employment, that is, that the unemployed partner Önds a job while the employed partner remains unemployed. However, there is a large quantitative di§erence in these transitions: if only the wife works, the probability of transitioning to joint employment is around 13%. But if only the husband works, the probability of transitioning to joint employment is only around 4%. If both work, the most likely event next to staying in the current status is that the wife loses her job, which occurs in around 2% of the transitions.

[Table 5 here]

Table 5 shows individual employment transitions, job Önding, and job separations, both total and by the spouseís employment transitions. This table illustrates how one spouseís transitions are ináuenced by the transition of the partner. The husbandís job Önding is the highest when the unemployed wife Önds a job. Job Önding is also high, much higher than the unconditional job Önding rate, when the employed wife separates from her job. For the wife, job Önding is the highest when the employed husband separates from his job and is next highest when the unemployed husband Önds a job. More active job Önding is thus strongly ináuenced by job separations and by job Önding by the partner.

On the other hand, for both partners job separations are more intense with the partnerís job separation rather than with the partner job Önding. Accordingly, the coincidence of job separations between household members is more important than job separations triggered by the partnerís job Önding. For both household members, job Önding and job separations are more active when the spouse experiences an employment status change, job Önding or job separation. The wife is more likely both to Önd a job and to separate from her current job when the husband separates from his job. The husband is more likely to Önd a job when the wife Önds one and is more likely to separate from his job when the wife separates from hers. Altogether, this evidence supports that job Önding is triggered by job separations, especially for wives, the ìadded worker e§ect,î and that job separations are triggered by job Önding as remarked by Guler, Guvenen, and Violanteís (2012).

This table also shows wage and wealth variations for the transition from employment to employment, the most frequent transition, depending on the spouseís employment transition. Very clearly, wage increases for each spouse are higher if the partner separates from his or her current job. The wage variation in the husbandís wage is an increase of $656 if the wife separates and only of $46 if the wife keeps her job. The wage variation in the wifeís wage is an increase of $149 if the husband separates and only of $24 if the husband keeps his job. The husbandís wage increase is particularly higher than the wifeís increase. Thus, both job Önding and wage increases mostly happen when the partner separates from his or her job, which corroborates the ìadded worker e§ect.

Variations on the householdís wealth caused by the spouseís employment transitions are smaller when the husband stays employed than when the wife stays employed. When the husband keeps his job, there is a relatively stable wealth accumulation, which does not depend substantially on the wifeís employment transitions. Moreover, wealth increases when the husband keeps his job are the highest when the wife separates from her job. When the wife stays employed, household wealth áuctuations depend strongly on the husbandís job turnover. These áuctuations decrease when the husband changes his employment status, particularly when the husband separates from his job, an important drop of around $1,738. Thus, household members employment transitions ináuence wealth accumulation very asymmetrically. Wealth accumulation increases the most when the husband keeps his job and the wife loses hers, while wealth deccumulation increases the most when the wife keeps her job and the husband separates from his.

In sum, these trends suggest a clear asymmetry between husband and wifeís employment status, and support that there is an ìadded worker e§ectî: when one household member separates from employment, it is more likely that the partner becomes employed and wage increases are higher. On its turn, wealth accumulation is mainly dependent on the husbandís employment stability.

4 Estimation

By SMM, we recover the parameters of the theoretical model. From the month that we Örst observe wealth onward, we use the policy rules that solve the dynamic programming problem and random numbers for the stochastic components e.g., job o§ers, layo§s, and wage o§ers, to generate simulated data. We compute some selected moments that are then matched to actual moments. At each iteration of the parameter computation, we construct a measure of distance between the observed and the simulated moments. This criterion function is then minimized by the parameter

estimates of the theoretical model.

We Öx the rate of discount at 0.9957 and the interest rate at 0.0041, which are the monthly values that match annual values of 0.95 and 0.05, respectively. The parameters to estimate are then , with 2 . The moments used in this estimation are the following: joint employment status, wage means and standard deviations by joint employment status, wealth holdings by joint employment status, joint employment transitions, means and standard deviations of wage variations by joint employment transitions, and means and standard deviations of wealth variations by joint employment transitions. Most of these moments are reported in Tables 1 through 6.

These moments are selected to allow identiÖcation of the behavioral parameters of the model. The parameters of the standard search model are identiÖed from the reservation wage rule by the observed transitions, accepted wages, and wealth level (Flinn and Heckman 1982). Fixing the interest rate r and the discount factor enables identiÖcation of arrival rates and layo§ rates by the employment transitions, job Önding, and job separations. The observed accepted wages identify the parameters of the wage o§er distributions as well as the transfers while unemployed. Since we do not keep track of employers, the arrival rate while employed is identiÖed by wage variations. The other parameters that are speciÖc to a utility-maximizing job search model with wealth accumulation, and are pinned down by the observed evolution of wealth by employment status and wages. Wealth data also allow identiÖcation of the leisure values separately from unemployment transfers, which in risk-neutral job search is identical to the value of leisure. Unlike nonpecuniary leisure values, higher unemployment transfers a§ect directly observed wealth accumulation over employment transitions.

The SMM procedure is based on a weighted measure of distance between sample and simulated moments as a function of a parameter set:

\[S (\Theta) = \Delta m ^ {\prime} W ^ {- 1} \Delta m,\]

where is the distance between sample and simulated moments and is a weighting matrix. As in Dey and Flinn (2008), the matrix W is a diagonal matrix consisting of the standard deviation of each empirical moment obtained by bootstrap methods, from 10,000 random resamples of the data. The estimated behavioral parameters are thus . 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.¹¹ Asymptotic standard errors are calculated by the gradient estimator, which requires Örst derivatives. We compute them numerically using a polynomial that requires Öve function evaluations, obtained by proportionally variating the parameter values around their estimated value. This polynomial smooths the criterion function, whose surface has discontinuous areas. The parametersíasymptotic 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 6.

[Table 6 here]

The estimated labor market parameters reáect the asymmetry in individual labor markets. Arrival rates are much higher and layo§ 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. The corresponding annual rates for the arrival rate while unemployed are 0.9267 for the husband and 0.5093 for the wife, and 0.6246 and 0.0424, respectively, for the arrival rate when employed. The annualized layo§ rate is 0.0595 for the husband and 0.0753 for the wife. Notice that these rates are in line with the employment transitions reported in Table 5. Job Önding is certainly lower than the arrival rate when unemployed, as some job o§ers are not accepted. By contrast, job separation is higher than the layo§ rate, as some transitions from employment to unemployment are not produced by dismissals. We do not have the reason for leaving a job to verify this mechanism in this data; however, as explained in Section 2, utility-maximizing search models do have the feature of producing voluntary quits, moreover so in this environment of household job search in which an individualís employment status is highly dependent on the partnerís status. Accepted o§ers that made an individual leave unemployment may no longer be acceptable in the next periods, as household wealth accumulates and the spouse accesses better paid jobs.

¹¹This algorithm Örst calculates function values for the whole parameter space and then searches for the optimal parameter direction in the next iteration for function minimization. Underlying the computation of this optimal direction there is an implicit model of the derivative structure of the objective function. 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 satisÖed, namely that the percentage variation of this value falls below a certain value:

Wage o§ers are also higher for the husband than for the wife. The log mean wage o§er is slightly higher for the husband, but the dispersion of the wifeís wage o§er distribution is much higher than the husbandís. These wage o§er distributions are associated with higher unemployment transfers for the husband than for the wife, which are almost zero. This means that these unemployment transfers basically only exist for the husband, while the wifeís main support when unemployed is only her husbandís wages. In models of individual agents these unemployment transfers are mainly non-labor income and the partnerís income. In our framework, we are accounting explicitly for both nonlabor income that comes from wealth and for the partnerís income, which we endogenize as accepted wages resulting from the joint job search process. Because of the design of the sample, consisting only of couples who do not participate in any government programs, these unemployment transfers do not contain income that comes from unemployment insurance. Thus, these unemployment transfers may consist of extensive family transfers, such as transfers from parents to household members.¹² Notice also that these higher unemployment transfers imply a higher truncation point for the wage o§er distribution of the husband, which is consistent with his higher wages, despite the higher dispersion of his wifeís wage o§er distribution.

The value of leisure is positive for both individuals but higher for the wife than for the husband, which captures the householdís higher incentive for the wife not to work. However, when both are unemployed the common leisure parameter has a negative sign with a relatively high value, which implies that there is disutility from joint unemployment.

The coe¢ cient of constant relative risk aversion is estimated at 1.45, which is in line with previous estimates of utility-maximizing job search models. The tightness of the borrowing constraint reveals that households can only borrow around 8% of their natural borrowing limit.

These estimates reproduce 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 1 through 6.

¹²As discussed previously, these parameters are mainly identiÖed by accepted wages and employment transitions. In further research, these results can be corroborated by incorporating data of observed income in unemployed spells of each household member.

The estimated model is able to replicate very closely the household employment status, individual employment status, and accepted wages by employment status of the spouse, as reported in Table 2. Wealth is, however, estimated less accurately, most likely because of the very noisy wealth data. Standard deviations of wealth by employment status are large relative to their corresponding means. The model does reproduce these large variations but certainly with less precision in replicating average wealth. Predicted average wealth is closer to actual average wealth when both partners are unemployed or both are employed. Predicted average wealth holdings when one of the partners is employed and the other is unemployed are pretty far from actual values. Yet, as in the data, average wealth is higher when the husband is working and the wife is unemployed than when the wife is working and the husband is unemployed. Consequently, in the actual and predicted values wealth accumulation depends more on the husband working than on the wife working.

Table 2 shows actual and predicted individual unemployment rate and average wage-by-wage segment of the spouse. Both are relatively well replicated, except for the highest wage segment. Yet, the general increasing trend of both variables is well captured by the estimated model: higher individual wages are associated with higher unemployment rates and average wages of the spouse. We Önd that these trends hold both for husband and wife, suggesting thus that both reservation wages are increasing in the spouseís wage.

Predicted household employment transitions, as shown in Tables 3 and 4, also exhibit a close proximity. This replication is particularly important because many of these numerous household employment transitions have very low values. Accordingly, in the next tables, we concentrate on the wage and wealth variations for the most relevant transitions.

Table 5 presents individual employment transitions and wage and wealth variations conditional on the spouseís employment transitions. The replication of these moments is pretty good, particularly for employment and wage variations for the most frequent spouseís employment transitions. But, once again, the replication is less accurate for the very dispersed wealth data. It is particularly di¢ cult to mimic drops in wealth for the wifeís employment transitions. As in the actual transitions, in all cases unconditional variations are very close to the variations conditional on the spouse staying employed, the most frequent employment transition. An important feature of these predicted transitions is that for both household members job Önding is highest when the partner faces job separations. By contrast, predicted job separations for husbands are the highest when wives Önd jobs, while for wives, as in the data, they are the highest when husbands separate from their jobs. As in the actual transitions, both job Önding and job separations for a household member tend to be higher when their partners experience employment status changes.

In addition to assessing the Öt for the moments used in the estimation, we analyze the hazard rates for the four household employment statuses. We did not include this hazard information in the estimation, yet the model also Öts well these data reasonably well.

[Figure 5 here]

Figure 5 shows the actual and predicted hazard rates of the four joint employment statuses. In the four graphs, the actual data áuctuate around the predicted hazard over time in months. All exhibit a peak around the Öfth month of being in the current joint employment status, which the model is not reproducing. Yet the general level is correctly captured by the estimated model.

[Table 7 here]

In Table 7, we report the proportion of the last joint employment status for each hazard rate. Joint unemployment is mainly receiving the áow from the husband separating from his job when the wife is not working. This status receives 68% of its áow from only the husband being employed. The employment status of only one partner working is fed mainly by joint employment, that is, by job separations of one partner: from joint employment comes 94% of the áow to only the wife working and 89% of the áow to only the husband working. Joint employment comes mostly from only the husband being employed, 58%, and second from only the wife being employed, 41%. The model is able to replicate these áows relatively closely.

[Figure 6 here]

Finally, Figure 6 reports the proportion of exits from the current joint employment status. The model also replicates these exits pretty well in levels, but it does not capture all the proportion áuctuations over time. The main destination for a joint unemployment spell is to only the husband working, followed by only the wife working.

For only one partner working, the main destination is joint employment. However, the second destination di§ers by who the working spouse is. For only the wife working, the second destination is that only the husband works. An employment separation of the wife in this status is associated with the unemployed husband immediately Önding a job, which conforms to the ìadded worker e§ect.î For only the husband working, the second destination is joint unemployment, which implies that the husbandís job separation is not associated with the wifeís immediate incorporation to work. After a spell of joint employment, the main destination is that only one agent separates from her job, mainly the wife.

The model delivers thus a fairly good replication of the observed data, particularly for employment and wages. This good replication is extensive to several conditional moments by the spouseís employment transitions both joint and conditional, in particular, the connection between household membersíjob Önding and job separation. The model replicates well the large dispersion of the wealth data and their trend to depend mainly on the husbandís labor market activity.

6 Regime changes

After recovering the underlying parameters of the model and assessing their success in replicating the data, we perform three regime changes: worsening each household memberís labor markets, relaxing borrowing constraints, and increasing unemployment transfers. The Örst change aims to assess the e§ect of an asymmetric downturn on a workerís labor market outcomes and, more precisely, evaluate whether the spouse increases his or her labor market activity once the partner becomes unemployed i.e., the ìadded worker e§ectî. This change is attained by increasing layo§ rates by 1 percent. The second change consists of increasing the debt limit by doubling the tightness of the borrowing constraint. Thereby we evaluate the e§ect of access to credit in family job search. The third regime change is increasing unemployment transfers of each spouse by $100 at a time and then increasing both transfers by $50 at the same time. We assess these changes by recomputing all moments from the same starting point in time but with the new regime. We are comparing two di§erent economies rather than comparing an economy before and after a policy change.

In Table 8, we report the e§ects of these regime changes on several selected observables. Worsening a spouseís labor market increases his or her unemployment but decreases it for the partner. This can be seen in the Örst two columns for joint employment status. When there is a downturn for the husband by a higher layo§ rate, there is an increase of both joint unemployment and unemployment only for the husband, associated with a decrease of joint employment and unemployment only for the wife. This evidently translates into a higher total unemployment for the husband but less evidently into a lower unemployment for the wife. The same happens when the downturn is experienced in the wifeís labor market because of a lower arrival rate: joint unemployment and unemployment only for the wife increase but joint employment and unemployment only for the husband decrease. Hence, the unemployment rate for the wife increases, while the unemployment rate for the husband declines. There is a clear ìadded worker e§ectî: an agent becomes more active in the labor market when labor market conditions worsen for the partner. Underlying these changes in outcomes are the household membersíreservation wage variations. An economic downturn increases an agentís unemployment and thereby undermines the support for the partnerís reservation wage, who becomes more likely to accept a job. On their turn, average wages of both spouses and common wealth holdings tend to decrease when the husbandís or the wifeís layo§ rate increase.

The second regime change, increasing the debt limit, decreases both household members unemployment rates, with a greater impact on the wifeís unemployment rate. The wife transitions from not working when the husband works to working while the husband keeps his job. That is, relaxing borrowing constraints implies mainly an increase in joint employment and a reduction in the wifeís unemployment rate, which brings more equality in labor market activity into the household. This regime change has negligible wage e§ects, and, as expected, it results in a decline in wealth holdings.

The third regime change is reported in the last three columns of Table 8. Increases in unemployment transfers increase unemployment and wages of the bene-Öciary spouse but decreases unemployment and wages of the spouse who does not receive them. That is, increasing unemployment transfers have the usual e§ect in the labor market of an individual but have the opposite e§ect on his or her partner (i.e., its cross-e§ect is negative). This is consistent with the mechanism explained in Section 2. Splitting individual unemployment transfers in half and increasing both spousesíunemployment transfers has similar e§ects as increasing only the husbandís unemployment transfers but quantitatively more weakly. The husbandís unemployment increases and the wifeís unemployment decreases, but in lower amounts, with both partnersís wages declining. Increasing unemployment transfers also make wealth holdings fall, on the one hand because the higher income permanently undermines the need for a bu§er stock for future unemployment spells and on the other hand because it increases the debt limit.

These regime changes corroborate, thus, i) the increased job Önding of a worker as a response to the spouseís increased job separation (i.e., the ìadded worker e§ectî), ii) that more access to credit results essentially in higher joint employment in the household, and iii) that increasing a workerís unemployment transfers lowers the spouseís unemployment rate.

7 Family job search without wealth and savings

How important are wealth and savings to understand family job search? To answer this question, we reestimate our model excluding wealth and savings both in the model and in the data, that is, assuming that all household income is consumed at every period, as in Dey and Flinn (2008), Flabbi and Mabli (2010), Ek and Holmlund (2010), and Guler, Guvenen, and Violante (2012). This is the exercise performed by Blundell et al. (2016) in their analysis of female labor supply. The results of this estimation are presented in Table 9.

\[[ \mathrm{Table9here} ]\]

This exercise has a similar e§ect as excluding a relevant variable in any other estimation: it implies a biased estimation of the remaining parameters. In our model, the omission of savings reduces the estimated coe¢ cient of risk aversion, which accounts for the labor market interdependence between household members. This parameter declines in half, from 1.447 to 0.718. This result is in line with earlier structural estimations of this parameter in the absence of wealth data, which also Önd lower estimates. Dey and Flinn (2008), using full-time data, part-time data, and employerprovided health insurance data from the 1996-1999 panel of SIPP estimate this coe¢ cient at a low value: 0.474. Flabbi and Mabli (2010) use full-time and part-time data from the 2001-2003 panel of SIPP and estimate this coe¢ cient at a higher value, 0.9744.

This omission also blurs the identiÖcation of the leisure parameters, as it is not possible to distinguish between monetary áows and nonpecuniary incentives to stay unemployed. Despite the nonlinear utility function, without using indicators of hours of work there is no possible distinction between the value of leisure and unemployment monetary transfers in a model without savings. Accordingly, we exclude the leisure parameters from the estimation with the consequence that the estimated unemployment transfers increase substantially. However, other parameters of the model (e.g., wage o§er distributions and the arrival rates) do not present large variations, as they are well identiÖed from the observed employment transitions and wages.

[Table 10 here]

Table 10 shows the main predicted statistics for employment status and wages. This constrained model exhibits a similar Öt of employment status statistics but a less accurate account of conditional wages, especially for wives, which presents less dependence on the husbandís employment status than in the unconstrained model and in the data. This may happen because, unlike in the unconstrained estimated model where wives practically do not receive unemployment transfers, in the constrained model wives receive higher unemployment transfers, which results in less dependency on their husbandsíwages.

[Table 11 here]

Table 11 presents the e§ects of regime changes in the constrained model. Certainly, there are no e§ects of wealth accumulation and access to credit on labor market outcomes. Yet, it is possible to assess the e§ect of an economic downturn and of increasing unemployment transfers. A downturn a§ects both spouses more evenly, increasing their unemployment rate so that there is no ìadded worker effectî as in the unconstrained model in which the unemployment rate of the spouse declines. On its turn, increasing unemployment transfers mainly increases the wifeís unemployment rate, regardless of which household member is the beneÖciary. The cross-e§ect, however, is still negative when the beneÖciary is the wife; that is, the husbandís unemployment rate declines. Consequently, omitting wealth and savings conducts to neglecting the ìadded worker e§ectîand the opposite e§ect of increasing unemployment transfers for individual household members. This omission can thus result in serious miscalculations of the e§ects of unemployment policy.

Thus, wealth data, even if they present a large dispersion, contribute to a correct estimation of the labor market parameters of a family job search model. Omitting wealth in an estimation implies that the estimated coe¢ cient of risk aversion will biased downward, which will understate the interdependence between household membersí job search. Moreover, wealth data enable the identiÖcation of leisure parameters, whose omission implies an upward bias in the estimated unemployment transfers, which will distort the assessment of unemployment policies by neglecting the ìadded worker e§ectî and the negative cross-e§ect of increasing unemployment transfers.

8 Family job search with more children

What is the e§ect on family job search of having more children? We can answer this question reestimating our model using a sample of similar characteristics to the one we use in this paper, but with two or more children. This sample contains 34,989 observations on 1,058 married couples.

[Table 12 here]

Table 12 provides the main actual and predicted statistics of this sample. Very clearly, unemployment rates are higher and wages and wealth levels are generally lower than in the sample with at most one child. But most importantly, di§erences in unemployment rates and wages by the spouseís employment status are much less pronounced than in the sample with one child or none. This suggests that the presence of more children erodes the interdependency of the individual job search processes within the household. And, as it happens in our main sample, the dispersion of wealth is very high.

[Table 13 here]

In Table 13 we report the estimated parameters that generate the predicted statistics of Table 12. Compared to the estimated parameters for the sample of no more than one child, in this sample the coe¢ cient of risk aversion is lower, the husbandís unemployment transfers are higher, his value of leisure is lower, and the wifeís value of leisure is higher, and the negative common value of leisure is much higher in absolute value. This is in line with the reduced ináuence of the spouseís employment status as already mentioned. The tightness of the borrowing constraint is the same as in the previous sample, but labor market parameters are clearly di§erent. The logwage o§er distribution exhibits higher means and standard deviations for both spouses; however, arrival rates for the wife are worse than in the previous sample: both arrival rates, when unemployed and employed, are lower while the layo§ rate is higher. For the husband, the arrival rate is lower when unemployed but higher when employed, while his layo§ rate is lower. That is, the husbandís labor market is generally better than in the previous sample, but his higher unemployment transfers suggest that he is also more selective in accepting wage o§ers. For the wife, both the labor market, worse than in the previous sample, and her higher value of leisure explain her higher unemployment rates.

[Table 14 here]

In Table 14, we repeat the three regime changes for the sample of two or more children. Increasing layo§ rates has a weaker e§ect on increasing unemployment of a worker but a higher e§ect on reducing the partnerís unemployment than in the previous sample. This is suggestive that the ìadded worker e§ectîincreases with the number of children. Job loss of one partner has to be compensated by job Önding of the partner. Relaxing borrowing constraints reduces household wealth holdings as in the previous sample but has an opposite e§ect on household employment. Unlike in the previous sample, with two or more children relaxing borrowing constraints reduces joint employment and joint unemployment, thereby increasing unemployment rates for both spouses but mainly for the wife. With a higher value of leisure for the wife, more access to credit allows the couple to consume more leisure, possibly spending more time with their children. The third regime change, increasing unemployment transfers, has a higher e§ect on increasing unemployment rates of the beneÖciary spouse, however, with a clear asymmetry. If the husband is the beneÖciary, both unemployment rates increase, but if the wife is the beneÖciary, her unemployment rates increase and the husbandís declines. Splitting the increase in these transfers in half between spouses implies increases in unemployment rates for both, a higher impact than the increase in the sample with at most one child. This regime change suggests that the opposite reaction of the spouse to increasing unemployment transfers in the couple with two or more children only exist if the wife is the beneÖciary. If the husband receives the increased unemployment transfers, the wife will also increase her unemployment rate, most likely to spend time with the children, captured in her higher value of leisure.

This analysis suggests that with more children in the household the ìadded worker e§ectî is stronger. However, with more children the opposite e§ect of increased unemployment transfers on individual unemployment is more asymmetric within the household. As the wife has a higher value of leisure, reáective of her taking care of the children, increased husbandís unemployment transfers act as a disincentive for her to seek employment. However, the opposite e§ect still exists for the husband: if the wife is the individual beneÖciary of increased unemployment transfers, the husbandís job Önding increases, which reverses the usually desired e§ect of this policy.

9 Conclusions

In this paper, we have developed and estimated a model of family job search and wealth accumulation. Earlier research on family job search did not consider householdsísavings decisions. We have shown that omitting wealth and savings from an analysis implies an underestimation of the household risk aversion, hence understating the interdependence between household membersíemployment transitions and wages.

We have documented that increasing job separations, particularly during economic downturns, triggers increased job Önding by his or her partner, which constitutes the ìadded worker e§ect.î We have proposed a search-theoretic mechanism for this e§ect: increased job separations of one agent undermines the unemployed partnerís job selectivity and thus decreases the partnerís reservation wage. Consequently, the partner is more likely to accept job o§ers and thus accelerates his or her transition from unemployment to employment.

A policy implication of this analysis is that increasing unemployment transfers has the classical e§ect of increasing unemployment and wages but at the same time decreases his or her partnerís unemployment and wages, implying that its cross-e§ect is negative. E§ects of unemployment transfers that are valid in an individual-agent job search framework are partly undone by the partnerís behavior in a two-agent job search context. Given that the desired e§ect of unemployment insurance is to support job search and thereby improve the quality of the resulting wage match for the whole labor force, this purpose may not be accomplished e¢ ciently for married couples. An optimal unemployment insurance has to be reassessed, departing from the individual-agent setup to consider the household as an economic decision unit.

Our results also establish that both the ìadded worker e§ectî and the negative cross-e§ect of unemployment transfers disappear and thus would be overlooked if wealth data are excluded in the model and the estimation.

We also have shown that more children in the household strengthens the ìadded worker e§ect.î Moreover, increasing the number of children implies a positive e§ect of the husbandís unemployment transfers on the wifeís unemployment rate. However, the presence of more children in the household does not change that increasing the wifeís unemployment transfers decreases the husbandís unemployment rate.

In the present paper, we have centered our attention on employment transitions and wage variations. We have made the case that wealth data are important even if the purpose of the analysis is restricted to these labor market features. However, the inclusion of wealth data opens the doors to analyzing other important issues, such as consumption smoothing in the presence of uncertain household incomes and limited access to credit. Our model also has implications for these issues. In our model, a household combines wealth holdings and individualsí job acceptance decisions to maintain a stable level of consumption over time. We have left the analysis of these issues for future research.

A limitation of our analysis is the assumption that existing observed couples and their number of children are exogenous. A valuable extension of the current framework would be to analyze how our results change when couple formation and dissolution as well as fertility decisions are allowed. This extension would also imply departing from the unitary job search model to allow for a collective framework that considers bargaining and cooperation within the household.

When better data become available, another important improvement would be to distinguish between unemployment and being out of the labor force. A further and challenging extension would be an equilibrium framework that improves the assessment of regime changes by considering Örmsíreactions to increased reservation wages caused by increased unemployment beneÖts.

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Appendix: Numerical solution of the model

Continuous and discrete variables

In the numerical solution of the model, wealth is a continuous variable, only discretized to support the computation of any value on its domain, while wages are discretized. Table gives further details of this discretization.

Table A1. Discretization of Variables

The lower bound on wealth is set at a fraction of the natural borrowing limit, so that a household can borrow up to some fraction of the present discounted value of their lowest possible income. We also deÖne w and w

Wage o§er distribution

For each discretized wage, , and for each agent, , we compute discrete probabilities integrating the wage interval deÖned by the grid:

\[g \left(j, l\right) = \frac {\Phi \left(\frac {\ln w _ {j} + \Delta_ {w} / 2 - \mu_ {l}}{\sigma_ {l}}\right) - \Phi \left(\frac {\ln w _ {j} - \Delta_ {w} / 2 - \mu_ {l}}{\sigma_ {l}}\right)}{\Phi \left(\frac {\ln \overline {{w}} - \mu_ {l}}{\sigma_ {l}}\right) - \Phi \left(\frac {\ln \underline {{w}} - \mu_ {l}}{\sigma_ {l}}\right)}.\]

Value function, policy rules, and expected value function

These are approximated by:

\[\begin{array}{r c l} V (A _ {t}, w _ {1}, w _ {2}) & = & V [ i, j, k ], \\ A _ {t + 1} (A _ {t}, w _ {1}, w _ {2}) & = & A [ i, j, k ], \\ E V (A _ {t + 1}, w _ {1}, w _ {2}) & = & E V [ i ^ {\prime}, j, k ]. \end{array}\]

Solution to the dynamic problem

The following steps are done for each and

1. Initialization. We initialize the value function at the deterministic value of consuming all wealth and income forever with the instantaneous value of leisure, which admits an explicit expression:

\[V [ i, j, k ] = c _ {1} \frac {(A [ i ] + (1 + \frac {1}{r}) (w [ j ] + w [ k ])) ^ {1 - \gamma}}{1 - \gamma} - \frac {1}{1 - \gamma} \frac {1}{1 - \beta} + \vartheta [ j, k ],\]

\[\text { where } c _ {1} = \left(1 - \beta^ {\frac {1}{\gamma}} (1 + r) ^ {\frac {1 - \gamma}{\gamma}}\right) ^ {- \gamma}, \text { and } \vartheta [ j, k ] = \vartheta_ {1} I (j = 0) + \vartheta_ {2} I (k = 0) + \vartheta_ {3} I (j = 0) I (k = 0).\]

2. Integration. For each combination integrate over all admissible values of and k. For instance, for we calculate the following three summations:

\[E V _ {1 1} \left[ i ^ {\prime}, 0, 0 \right] = \sum_ {j = 1} ^ {N _ {w}} \sum_ {k = 1} ^ {N _ {w}} \max \left[ V \left[ i ^ {\prime}, j, k \right], V \left[ i ^ {\prime}, j, 0 \right], V \left[ i ^ {\prime}, 0, k \right], V \left[ i ^ {\prime}, 0, 0 \right] \right] g (j, 1) g (k, 2),\]

\[E V _ {1 0} \left[ i ^ {\prime}, 0, 0 \right] = \sum_ {j = 1} ^ {N _ {w}} \max \left[ V \left[ i ^ {\prime}, j, 0 \right], V \left[ i ^ {\prime}, 0, 0 \right] \right] g (j, 1),\]

\[E V _ {0 1} \left[ i ^ {\prime}, 0, 0 \right] = \sum_ {k = 1} ^ {N _ {w}} \max \left[ V \left[ i ^ {\prime}, 0, k \right], V \left[ i ^ {\prime}, 0, 0 \right] \right] g (k, 2).\]

With them we build the integral

\[\begin{array}{r c l} E V \left[ i ^ {\prime}, 0, 0 \right] & = & \lambda_ {1} \lambda_ {2} E V _ {1 1} \left[ i ^ {\prime}, 0, 0 \right] + \lambda_ {1} \left(1 - \lambda_ {2}\right) E V _ {1 0} \left[ i ^ {\prime}, 0, 0 \right] \\ & & + \left(1 - \lambda_ {1}\right) \lambda_ {2} E V _ {0 1} \left[ i ^ {\prime}, 0, 0 \right] + \left(1 - \lambda_ {1}\right) \left(1 - \lambda_ {2}\right) V \left[ i ^ {\prime}, 0, 0 \right]. \end{array}\]

We repeat this process for the expected value functions of the other three joint employment status.

3. Di§erentiation. Compute the derivative of this object over wealth using a cubic interpolation:

\[\begin{array}{l l l} E V _ {A} \left[ i ^ {\prime}, j, k \right] & = & \frac {- E V \left[ i ^ {\prime} + 2 , j , k \right] + 4 E V \left[ i ^ {\prime} + 1 , j , k \right] - 3 E V \left[ i ^ {\prime} , j , k \right]}{A \left[ i ^ {\prime} + 2 \right] - A \left[ i ^ {\prime} \right]}, i f i ^ {\prime} = 1; \\ & = & \frac {E V \left[ i ^ {\prime} + 1 , j , k \right] - E V \left[ i ^ {\prime} - 1 , j , k \right]}{A \left[ i ^ {\prime} + 1 \right] - A \left[ i ^ {\prime} - 1 \right]}, i f N _ {A} > i ^ {\prime} > 1; \\ & = & \frac {3 E V \left[ i ^ {\prime} , j , k \right] - 4 E V \left[ i ^ {\prime} - 1 , j , k \right] + E V \left[ i ^ {\prime} - 2 , j , k \right]}{A \left[ i ^ {\prime} \right] - A \left[ i ^ {\prime} - 2 \right]}, i f i ^ {\prime} = N _ {A}. \end{array}\]

4. Policy rule inversion. We use the endogenous gridpoints method as in Carroll (2006). For each and optimal consumption found:

\[C \left[ i ^ {\prime}, j, k \right] = \left(\beta (1 + r) E V _ {A} \left[ i ^ {\prime}, j, k \right]\right) ^ {- \frac {1}{\gamma}}.\]

5. Smoothing. Conditional on , regress on ). Whenever there are nonmonotonicities in over , use predicted consumption instead of actual consumption:

\[\widehat {C} \left[ i ^ {\prime}, j, k \right] = \widehat {b} _ {0} + \widehat {b} _ {1} A \left[ i ^ {\prime} \right] + \widehat {b} _ {2} \left[ A \left[ i ^ {\prime} \right] \right] ^ {2}.\]

6. Inverse solution. Find wealth at time t as a function of and denoted by for each

\[\widetilde {A} \left[ i ^ {\prime}, j, k \right] = \widehat {C} \left[ i ^ {\prime}, j, k \right] - w [ j ] - w [ k ] - \frac {A \left[ i ^ {\prime} \right]}{1 + r}.\]

7. Conditional solution. Reposition current liquid wealth to Önd the solution. Interior solution. For each i locate i such that

then compute the linear interpolations

\[\begin{array}{r c l} A ^ {\prime} \left[ i, j, k \right] & = & a A \left[ (i ^ {\prime} \right] + (1 - a) A \left[ i ^ {\prime} + 1 \right], \\ E V ^ {*} & = & a E V \left[ i ^ {\prime}, j, k \right] + (1 - a) E V \left[ i ^ {\prime} + 1, j, k \right], \end{array}\]

where

Corner solutions. If , then let ; if , then

\[\begin{array}{r c l} A ^ {\prime} \left[ i, j, k \right] & = & A \left[ i ^ {*} \right] \\ E V ^ {*} & = & E V \left[ i ^ {*}, j, k \right]. \end{array}\]

8. Then compute the value function using

\[\begin{array}{r c l} C ^ {*} [ i, j, k ] & = & A [ i ] + w [ j ] + w [ k ] - \frac {A ^ {\prime} [ i , j , k ]}{1 + r}, \\ V [ i, j, k ] & = & U (C ^ {*} [ i, j, k ]) - \vartheta [ j, k ] + \beta E V ^ {*} + \vartheta [ j, k ]. \end{array}\]

9. Evaluate convergence. , stop; otherwise go back to step 2, and repeat the process.

Table 1. Employment, Wages, and Wealth by Household Employment Status

Table 2. Unemployment Rate and Average Wage by Spouseís Wage Segment

Table 3. Household Employment Transitions, as a Percentage of All Transitions

Table 4. Household Employment Transitions, Conditional on Current Household Employment Status

Table 5. Employment Transitions, Wage, and Wealth Variations by Spouseís Employment Transitions (standard deviations in smaller fonts)

Table 6. Parameter Values and Asymptotic Standard Errors

Table 7. Previous Employment Status by Employment Status Spell in Percentage (each column adds up to 100%) Table 8. E§ects on Employment, Wages and Wealth of Three Regime Changes:

i. An Economic Downturn, ii. Relaxing Borrowing Constraints, and iii. Increasing Unemployment Transfers

* if the spouse is employed. if both are employed.

Table 9. Parameter Values and Asymptotic Standard Errors Family Job Search Without Wealth

Table 10. Employment and Wages by Spouseís Employment Status Family Job Search Without Wealth Table 11. E§ects on Employment and Wages of two regime changes: i. An Economic Downturn, ii. Increasing Unemployment Transfers

Family Job Search Without Wealth

* if the spouse is employed.

Table 12. Employment, Wages and Wealth by Household Employment Status Two or More Children

Table 13. Parameter Values and Asymptotic Standard Errors Two or More Children

Table 14. E§ects on Employment, Wages and Wealth of three regime changes: i. An Economic Downturn, ii. Relaxing Borrowing Constraints, and iii. Increasing Unemployment Transfers. Two or More Children

* if the spouse is employed. if both are employed.

Figure 1. Joint employment status by wages of husband and wife, conditional on wealth level A Figure 2. Reservation wages of the wife when the husband is unemployed as a function of wealth

Figure 3. Four reservation wage levels of the husband as a function of wealth and wages of the wife

Figure 4. Change in joint employment status from increasing husbandís unemployment transfers

Figure 5. Hazard rate by joint employment status

Figure 6. Proportion of transitions from a given joint employment status

References

1. 2016-10: “Family Job Search and Wealth: The Added Worker Effect Revisited”, J. Ignacio García-Pérez y Sílvio Rendon.

References

1. 2016-09: “Evolución del Gasto Público por Funciones durante la crisis (2007-2014): España vs UE”, José Ignacio Conde-Ruiz, Manuel Díaz , Carmen Marín y Juan F. Rubio-Ramírez.

References

1. 2016-08: “Thinking of Incentivizing Care? The Effect of Demand Subsidies on Informal Caregiving and Intergenerational Transfers”, Joan Costa-Font, Sergi Jiménez-Martín y Cristina Vilaplana-Prieto.

References

1. 2016-07: “The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications”, Martin M. Andreasen, Jesús Fernández-Villaverde y Juan F. Rubio-Ramírez.

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1. 2016-06: “The effects of non-adherence on health care utilisation: panel data evidence on uncontrolled diabetes”, Joan Gil, Antonio Sicras-Mainar y Eugenio Zucchelli.

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1. 2016-05: “Does Long-Term Care Subsidisation Reduce Unnecessary Hospitalisations?”, Joan Costa-Font, Sergi Jiménez-Martín y Cristina Vilaplana-Prieto

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1. 2016-04: ““Cultural Persistence” of Health Capital: Evidence from European Migrants”, Joan Costa-Font y Azusa Sato.

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1. 2016-03: “Like Mother, Like Father? Gender Assortative Transmission Of Child Overweight”, Joan Costa-Font y Mireia Jofre-Bonet.

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1. 2016-02: “Health Capacity to Work at Older Ages: Evidence from Spain”, Pilar García-Gómez, Sergi Jimenez Martin y Judit Vall Castello.

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1. 2016-01: “Monte Carlo evidence on the estimation of AR(1) panel data sample selection models”, Sergi Jiménez-Martín y José María Labeaga.

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1. 2015-13: “On the Treatment of Foreigners and Foreign-Owned Firms in Cost–Benefit Analysis”, Per-Olov Johansson y Ginés de Rus.

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1. 2015-12: “Evaluating Options for Shifting Tax Burden to Top Income Earners”, Jorge Onrubia, Fidel Picos y María del Carmen Rodado.

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1. 2015-11: “Differences in Job De-Routinization in OECD countries: Evidence from PIAAC”, Sara De La Rica y Lucas Gortazar.

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1. 2015-10: “Bad times, slimmer children?”, Cristina Belles-Obrero, Sergi Jimenez-Martín y Judit Vall-Castello.

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1. 2015-09: “The Unintended Effects of Increasing the Legal Working Age on Family Behaviour”, Cristina Belles-Obrero, Sergi Jimenez-Martín y Judit Vall-Castello.

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1. 2015-08: “Capital Humano y Productividad”, Ángel de la Fuente.

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1. 2015-07: “The effect of changes in the statutory minimum working age on educational, labor and health outcomes”, Sergi Jiménez-Martín, Judit Vall y Elena del Rey.

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1. 2015-06: “The Effects of Employment Uncertainty, Unemployment Insurance, and Wealth Shocks on the Retirement Behavior of Older Americans”, Hugo Benítez-Silva, J. Ignacio García-Pérez y Sergi Jiménez-Martín.

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1. 2015-05: “Instruments, rules and household debt: The effects of fiscal policy”, J. Andrés, J.E. Boscá y J. Ferri.

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1. 2015-04: “Can International Macroeconomic Models Explain Low-Frequency Movements of Real Exchange Rates?”, Pau Rabanal y Juan F. Rubio-Ramírez.

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1. 2015-03: “Privatización, competencia y regulación aeroportuaria: Experiencia internacional”, Ofelia Betancor y María Paz Espinosa.

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1. 2015-02: “La experiencia internacional en alta velocidad ferroviaria“, Daniel Albalate y Germà Bel.

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1. 2015-01: “Household Debt and Fiscal Multipliers“, J. Andrés, J.E. Boscá y J. Ferri.

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1. 2014-21: “Structural Estimation of a Model of School Choices: the Boston Mechanism vs. Its Alternatives”, Caterina Calsamiglia, Chao Fu y Maia Güell.

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1. 2014-20: “Which club should I attend, Dad?: Targeted socialization and production”, Facundo Albornoz, Antonio Cabrales y Esther Hauk.

References

1. 2014-19: “The Informational Content of Surnames, the Evolution of Intergenerational Mobility and Assortative Mating”, Maia Güell, José V. Rodríguez Mora y Chris Telmer.

References

1. 2014-18: “Risk-sharing and contagion in networks”, Antonio Cabrales, Piero Gottardi y Fernando Vega-Redondo.

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1. 2014-17: “A simple model of aggregate pension expenditure”, Ángel de la Fuente.

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1. 2014-16: “The economic evaluation of infrastructure investment. Some inescapable tradeoffs”, Ginés de Rus.

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1. 2014-15: “Cross-country data on the quantity of schooling: a selective survey and some quality measures”, Ángel de la Fuente y Rafael Doménech.

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1. 2014-14: “Educational Attainmet in the OECD, 1960-2010, (version 3.1)”, Ángel de la Fuente y Rafael Doménech.

References

1. 2014-13: “The Systematic Component of Monetary Policy in SVARs: An Agnostic Identification Procedure”, Jonas E. Arias, Dario Caldara y Juan F. Rubio-Ramírez.

References

1. 2014-12: “Reforming the U.S. Social Security system accounting for employment uncertainty”, Hugo Benítez-Silva, J. Ignacio García-Pérez y Sergi Jiménez-Martín.