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

47 Pages Posted: 24 Mar 2020

See all articles by Joseph Cooprider

Joseph Cooprider

Boston College - Department of Economics

Stefan Hoderlein

Boston College

Alexander Meister

University of Rostock

Date Written: February 27, 2020

Abstract

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.

Keywords: Heterogeneity, Nonparametric, Identification, Random Coefficients

Suggested Citation

Cooprider, Joseph and Hoderlein, Stefan and Meister, Alexander, 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 (February 27, 2020). Available at SSRN: https://ssrn.com/abstract=3545485 or http://dx.doi.org/10.2139/ssrn.3545485

Joseph Cooprider (Contact Author)

Boston College - Department of Economics ( email )

140 Commonwealth Avenue
Chestnut Hill, MA 02467
United States

Stefan Hoderlein

Boston College ( email )

140 Commonwealth Avenue
Chestnut Hill, MA 02467
United States

Alexander Meister

University of Rostock ( email )

Postfach 10 08 88
Rostock, 18055
Germany

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