Robust Counterfactual Analysis for Nonlinear Panel Data Models
Abstract:
This paper studies robust counterfactual analysis in a wide variety of nonlinear panel data models. I focus on counterfactual predictions of the behavior of an outcome variable under exogenous manipulations of endogenous explanatory variables. I avoid parametric distributional assumptions and only impose time homogeneity on the distribution of unobserved heterogeneity. I derive the sharp identified set for the distribution of the counterfactual outcome, noting that point identification is impossible in general. I provide tractable implementation procedures for popular nonlinear models, including binary choice, ordered choice, censored regression, and multinomial choice, by exploiting an index separability condition. I propose inference for sharp bounds on counterfactual probabilities based on aggregate intersection bounds and Bonferroniadjusted confidence intervals. As empirical illustrations, I apply my approach to actual data to predict female labor force participation rates under counterfactual fertility scenarios, as well as market shares of different saltine cracker brands under counterfactual pricing schemes.