Identification and Estimation of Partial Effects in Nonlinear Semiparametric Panel Models

TL;DR

This paper develops a unified framework for identifying and estimating average partial effects in nonlinear semiparametric panel models with unobserved heterogeneity, applicable even with unspecified error distributions.

Contribution

It introduces a new index sufficiency assumption for point identification of partial effects and proposes consistent, asymptotically normal estimators in complex panel models.

Findings

Established point identification under index sufficiency.

Proposed three-step semiparametric estimators with proven consistency.

Applied method to study determinants of married women's labor supply.

Abstract

Average partial effects (APEs) are often not point identified in panel models with unrestricted unobserved individual heterogeneity, such as a binary response panel model with fixed effects and logistic errors as a special case. 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.