Bootstraps for Dynamic Panel Threshold Models

This paper develops valid bootstrap inference methods for the dynamic short panel threshold regression. We demonstrate that the standard nonparametric bootstrap is inconsistent for the first-differenced generalized method of moments (GMM) estimator. The inconsistency is due to an $n^{1/4}$-consistent non-normal asymptotic distribution for the threshold estimate when the parameter resides within the continuity region of the parameter space. It stems from the rank deficiency of the approximate Jacobian of the sample moment conditions on the continuity region. To address this, we propose a grid bootstrap to construct confidence intervals of the threshold, a residual bootstrap to construct confidence intervals of the coefficients, and a bootstrap for testing continuity. They are shown to be valid under uncertain continuity, while the grid bootstrap is additionally shown to be uniformly valid. A set of Monte Carlo experiments demonstrate that the proposed bootstraps perform well in the finite samples and improve upon the standard nonparametric bootstrap.