Identification of time-varying counterfactual parameters in nonlinear panel models

We present identiﬁcation results for counterfactual parameters in a class of nonlinear semiparametric panel models with ﬁxed eﬀects and time eﬀects. This class accommodates both discrete and continuous outcomes and discrete and continuous regressors, and includes the binary choice model with two-way ﬁxed eﬀects, the ordered choice model with time-varying thresholds, the censored regression model with time-varying censoring, and various transformation models for continuous dependent variables. 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). Our main results focus on static models, with a set of results applying to models without any exogeneity conditions. Our results do not require parametric assumptions on the distribution of the error terms and do not require time-homogeneity on the outcome equation. . 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 ﬁxed eﬀects, time eﬀects, and non-logistic errors.