Identification of time-varying counterfactual parameters in nonlinear panel models

Abstract: We develop a general framework for the identification of counterfactual parameters in a class of nonlinear semiparametric panel models with fixed effects and time effects. Our method applies to models for discrete outcomes (e.g., two-way fixed effects binary choice) or continuous outcomes (e.g., censored regression), with discrete or continuous regressors. Our results do not require parametric assumptions on the error terms or time-homogeneity on the outcome equation. Our main results focus on static models, with a set of results applying to models without any exogeneity conditions. We show that the survival distribution of counterfactual outcomes is identified (point or partial) in this class of models. This parameter is a building block for most partial and marginal effects of interest in applied practice that are based on the average structural function as defined by Blundell and Powell (2003, 2004). To the best of our knowledge, ours are the first results on average partial and marginal effects for binary choice and ordered choice models with two-way fixed effects and non-logistic errors.