Identification and Estimation of Nonseparable Panel Data Models

In this study, we explore the identification and estimation of nonseparable panel data models with endogeneity. We show that the structural function is nonparametrically identified when it is strictly increasing in a scalar unobservable variable, the conditional distributions of unobservable variables are the same over time, and the joint support of explanatory variables satisfies weak assumptions. To identify the target parameters, many nonseparable panel data models impose the following two assumptions: (1) the structural function does not change over time and (2) there exist stayers, namely individuals with the same regressor values in two time periods. Our approach allows the structural function to depend on the time period in an arbitrary way and there are no stayers. We extend our identification results to the discrete outcome case, and show that the structural function is partially identified. Although the identification result is nonparametric, in estimation part of the paper, we consider parametric models and develop an estimator that implements our identification results. We then show the consistency and asymptotic normality of our estimator. A Monte-Carlo study indicates that our estimator performs well in finite samples.