Binarization for panel models with fixed effects - Irene Botosaru; Chris Muris (Centre for Microdata Methods and Practice (cemmap), 2017)
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 mono- tone 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 counter- factual 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 Í n rate of convergence.
Keywords: C14; C23; C41; 330; panel data; fixed effects; incidental parameter; time-varying transformation model; partial effects; random coefficients; nonlinear difference-in-differences