Estimating a Fractional Response Model with a count endogenous regressor and an application to female labor supply

This chapter proposes M-estimators of a fractional response model with an endogenous count variable under the presence of time-constant unobserved heterogeneity. To address the endogeneity of the right-hand-side count variable, I use instrumental variables and a two-step procedure estimation approach. Two methods of estimation are employed: quasi-maximum likelihood (QML) and nonlinear least squares (NLS). Using these methods, I estimate the average partial effects, which are shown to be comparable across linear and nonlinear models. Monte Carlo simulations verify that the QML and NLS estimators perform better than other standard estimators. For illustration, these estimators are used in a model of female labor supply with an endogenous number of children. The results show that the marginal reduction in women's working hours per week is less as women have one additional kid. In addition, the effect of the number of children on the fraction of hours that a woman spends working per week is statistically significant and more significant than the estimates in all other linear and nonlinear models considered in the chapter.