Debiased Inference for Dynamic Nonlinear Panels with Multi-dimensional Heterogeneities

We introduce a generic class of dynamic nonlinear heterogeneous parameter models that incorporate individual and time effects in both the intercept and slope. To address the incidental parameter problem inherent in this class of models, we develop an analytical bias correction procedure to construct a bias-corrected likelihood. The resulting maximum likelihood estimators are automatically bias-corrected. Moreover, likelihood-based tests statistics -- including likelihood-ratio, Lagrange-multiplier, and Wald tests -- follow the limiting chi-square 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.