A Panel Data Estimator for the Distribution and Quantiles of Marginal Effects in Nonlinear Structural Models with an Application to the Demand for Junk Food

In this paper, we propose a framework to estimate the distribution of marginal effects in a general class of structural models that allow for arbitrary smooth nonlinearities, high dimensional heterogeneity, and unrestricted correlation between the persistent components of this heterogeneity and all covariates. The main idea is to form a derivative dependent variable using two periods of the panel, and use differences in outcome variables of nearby subpopulations to obtain the distribution of marginal effects. We establish constructive nonparametric identification for the population of ``stayers" (Chamberlain (1982)), and show generic non-identification for the ``movers". We propose natural semiparametric sample counterparts estimators, and establish that they achieve the optimal (minimax) rate. Moreover, we analyze their behavior through a Monte-Carlo study, and showcase the importance of allowing for nonlinearities and correlated heterogeneity through an application to demand for junk food. In this application, we establish profound differences in marginal income effects between poor and wealthy households, which may partially explain health issues faced by the less privileged population