Family job search and consumption: the added worker effect revisited

In this paper we find out the determinants of consumption variations depending on the employment transitions experienced by household members. We set up a utility-maximizing household search model in which consumption and job search decisions are made jointly. Families determine a level of consumption, who has to work, and what is the minimum acceptable wage for each family member. This interaction implies that each member’s reservation wage is highly dependent not only on the partner’s labor market status but also on his/her wage. As in other job search models, the labor market environment of each household member is stochastic: both employed and unemployed agents receive job offers arriving randomly from a known wage offer distribution. Employed agents face the risk of being laid off from their current job. We assume that labor market environments of the household members are unconnected. However, assets and consumption are common to the household, which links the household members’ employment decisions. The household’s problem can be summarized in four value functions: both members unemployed, husband unemployed and wife employed, husband employed and wife unemployed, and, finally, both members employed. The expected discounted utility of the household differs according to the current employment states, asset holdings, and wages of its members. The solution to this model is contained in policy rules for consumption, or assets, and reservation wages for each employment status. It can be proved that consumption is increasing in assets and in wages for all employment status. Finally, reservation wages emerge from comparing the different value functions. We define two different reservation wages for each member, one when the partner is unemployed and another one when the partner is employed. In this model, not only wealth but also the employment status of the partner allows agents to be more selective and search longer. If the partner becomes unemployed, an agent cannot afford to be so selective and he/she has to accept lower wage offers. The model allows, thus, for the traditional “added worker effect†, if a household member becomes unemployed. Moreover, we show that reservation wages describe an inverted U in the partner’s wage. This effect, which we name “the new added worker effect†, is more important the higher is the wealth of the household. The intuition behind this effect is the following: when an agent is unemployed and looks for jobs, he/she is initially more selective the higher is the wage of the partner because the income effect of the partner’s wage dominates. However, when the wage of the partner is high enough, given the risk of being laid off, the household as a decision unit considers that the way to reduce the risk of losing the income necessary to maintain consumption is to have both members employed. Hence, there is a critical value where the reservation wage of the unemployed partner begins to decrease with the partner’s wage. Using the Spanish Continuous Family Expenditure Survey (ECPF) for the period 1985-1996, we estimate the behavioral parameters of the theoretical model for a sample of Spanish households. We use the policy rules of the dynamic programming problem to construct the likelihood function of our observed data. By maximizing the likelihood function, we recover those parameters that explain the relationship between consumption and employment status within the household. With the results of this estimation, we simulate some policy experiments. In particular we are interested on how the Unemployment Benefits system affects intra-household decisions.