Identification and Estimation of Partial Effects in Nonlinear Semiparametric Panel Models

Average partial effects (APEs) are often not point identified in panel models with unrestricted unobserved heterogeneity, such as binary response panel model with fixed effects and logistic errors. This lack of point-identification occurs despite the identification of these models' common coefficients. We provide a unified framework to establish the point identification of various partial effects in a wide class of nonlinear semiparametric models under an index sufficiency assumption on the unobserved heterogeneity, even when the error distribution is unspecified and non-stationary. This assumption does not impose parametric restrictions on the unobserved heterogeneity and idiosyncratic errors. We also present partial identification results when the support condition fails. We then propose three-step semiparametric estimators for the APE, the average structural function, and average marginal effects, and show their consistency and asymptotic normality. Finally, we illustrate our approach in a study of determinants of married women's labor supply.