Irene Botosaru, University of Bristol Chris Murris, University of Bristol
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 structural function and for partial effects in a 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 impose no parametric distributional assumptions. First, we provide a systematic solution to the incidental parameter problem in FELT. Second, we identify the distribution of counterfactual outcomes and a menu of time-varying partial effects without any assumptions on the distribution of unobserved heterogeneity. Third, we obtain new results for nonlinear difference-in-differences that accomodate both discrete and censored outcomes, and for FELT with random coefficients. Finally, we propose rank- and likelihood-based estimators that achieve a root-n rate of convergence.