Binary Choice With Binary Endogenous Regressors in Panel Data

This article considers the estimation of the causal effect of fertility on female-labor-force participation equations. My main concern is to examine two considerations, the endogeneity of fertility and the impact of controlling for unobserved heterogeneity and for predetermined existing children. Using PSID data, a switching binary panel-data model that accounts for selectivity bias as well as for other forms of time-invariant unobserved heterogeneity is estimated. Individual effects are allowed to be correlated with the explanatory variables, which can be predetermined as opposed to strictly exogenous. Family sex composition is used as an instrument for exogenous fertility movements. The results indicate that exogeneity assumptions of children variables induce a downward bias in absolute value in the estimated negative effect of fertility on participation, although the failure to account for unobserved heterogeneity overstates this effect. Moreover, stronger effects of fertility are found when existing children are treated as predetermined but not strictly exogenous variables.