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
提出一种估计非线性结构模型中边际效应分布的方法，允许高度异质性和相关性，通过垃圾食品需求应用发现贫富家庭边际收入效应存在显著差异。
In this paper, we propose a framework to estimate the distribution of marginal effects in a general class of structural models that allow for very general 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 causal marginal effects. We establish constructive nonparametric identification for the population of “stayers”, i.e., the subpopulation whose variable of interest stays constant between two time periods, 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 at least partially explain health issues faced by the less privileged population.