Robust Inference for Dynamic Panel Threshold Models

This paper develops robust bootstrap inference for a dynamic panel threshold model to improve the finite sample coverage and to be applicable irrespective of the regression's continuity. When the true model becomes continuous and kinked but this restriction is not imposed in the estimation, we find that the usual rank condition for the GMM identification fails, since the Jacobian of the moment function for the GMM loses the full-column rank property. Instead, we establish the identification in a higher-order expansion and derive a slower $n^{1/4}$ convergence rate for the GMM threshold estimator. Furthermore, we show that it destroys asymptotic normality for both coefficients and threshold estimators and invalidates the standard nonparametric bootstrap. We propose two alternative bootstrap schemes that are robust to the continuity and improve the finite sample coverage of the unknown threshold. One is a grid bootstrap that imposes null values of the threshold location. The other is a robust bootstrap where a resampling scheme is adjusted by a data-driven criterion. We show that both bootstraps are consistent. Finite sample performances of proposed methods are checked through Monte Carlo experiments, and an empirical application is shown