Joint estimation of sequential labor force participation and fertility decisions using Markov chain Monte Carlo techniques

Three basic mechanisms are behind the statistical relationship between fertility decisions and labor force participation decisions. 1) Causal direct effect: the time spent in child-care reduces the labor market effort leading to a temporary drop in post-birth labor force participation. 2) Causal indirect effect: the time spent out of labor market while on maternity leave alters women’s participation experience and, thus, indirectly affect both pre- and post-birth participation behavior. In the post-birth period, the indirect effect will compound the direct effect. The sign of the indirect effect in the pre-birth period is ambiguous. 3) Unobserved heterogeneity: Differences in tastes for work and family structure may induce a correlation between participation and fertility decisions throughout lifetime. They may further induce differences in pre-market human capital investments and, thus, affect labor market outcomes. This paper proposes a model that disentangles these three mechanisms and evaluates their relative importance. Sequential participation and fertility decisions are jointly modeled. Participation decisions on a three-state space - employed full-time, employed part-time, not employed – and dichotomous fertility decisions are represented by a multivariate probit model with a general correlation structure. The model allows for a high degree of flexibility in modeling the correlation between labor force participation and fertility decisions and the dependence of sequential decisions. We estimate this model using data from the 1979 National Longitudinal Survey of Youth. The estimation is performed using Markov chain Monte Carlo methods.