Identification and estimation of partial effects in nonlinear semiparametric panel models
Journal of Econometrics, 105860
Laura Liu, Alexandre Poirier, Ji-Liang Shiu
Abstract
Average partial effects (APEs) are often not point identified in panel models with unrestricted unobserved individual heterogeneity, as in binary response panel models with fixed effects and logistic errors for example. 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 APEs, average structural functions, 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.
