Non-parametric identification and estimation of partial effects with endogeneity and selection

This study investigates the identification and estimation of heterogeneous partial effects using a non-parametric model. The model encompasses a univariate discrete regressor and encounters sample selection challenges due to partial outcome observations. The identification process involves transforming the original model into a generalized partial linear model. Therefore, we propose a flexible three-step estimator. The first two steps entail estimating propensity scores to address the endogeneity of the discrete regressor and sample selection issues, whereas the final step employs a pairwise difference estimation strategy to partial out the non-linear term. We show this estimator to be asymptotically normal. We obtain a consistent estimator of the asymptotic covariance matrix using weighted bootstrap. Monte Carlo simulation results show that this estimator performs well in finite samples. To illustrate, we apply our model to estimate women’s return to education with data from the Chinese Household Income Project, and find that the effect varies with work experience. Specifically, the return to education initially increases but decreases as work experience accumulates, reflecting the diminishing impact of education relative to job skills over time.