Binarization for panel models with fixed effects

In nonlinear panel models with fixed effects and fixed-T, the incidental parameter problem poses identification difficulties for structural parameters and partial effects. Existing solutions are model-specific, likelihood-based, impose time homogeneity, or restrict the distribution of unobserved heterogeneity. We provide new identification results for the large class of Fixed Effects Linear Transformation (FELT) models with unknown, time-varying, weakly monotone transformation functions. Our results accommodate continuous and discrete outcomes and covariates, require only two time periods and no parametric distributional assumptions. First, we provide a systematic solution to the incidental parameter problem in FELT via binarization, which transforms FELT into many binary choice models. Second, we identify the distribution of counterfactual outcomes and a menu of time-varying partial effects. Third, we obtain new results for nonlinear difference-in-differences with discrete and censored outcomes, and for FELT with random coefficients. Finally, we propose rank- and likelihood-based estimators that achieve vn rate of convergence.