Debiased Inference for Dynamic Nonlinear Panels with Multi-dimensional Heterogeneities

Abstract: We introduce a generic class of dynamic nonlinear heterogeneous parameter models that incorporate individual and time fixed effects in both the intercept and slope. These models are subject to the incidental parameter problem, in that the limiting distribution of the point estimator is not centered at zero, and that test statistics do not follow their standard asymptotic distributions as in the absence of the fixed effects. To address the problem, we develop an analytical bias correction procedure to construct a bias-corrected likelihood. The resulting estimator follows an asymptotic normal distribution with mean zero. Moreover, likelihood-based tests statistics -- including likelihood-ratio, Lagrange-multiplier, and Wald tests -- follow the limiting chi-squared distribution under the null hypothesis. Simulations demonstrate the effectiveness of the proposed correction method, and an empirical application on the labor force participation of single mothers underscores its practical importance.