Bootstraps for Dynamic Panel Threshold Models

TL;DR

This paper introduces new bootstrap methods for inference in dynamic panel threshold models, addressing inconsistencies of standard approaches and providing valid confidence intervals for thresholds and coefficients.

Contribution

It develops grid and residual bootstrap techniques that are valid for both continuous and discontinuous models, overcoming limitations of existing bootstrap methods.

Findings

Standard bootstrap is inconsistent for the first-differenced GMM estimator.

Proposed bootstrap methods are valid regardless of model continuity.

Monte Carlo experiments demonstrate the effectiveness of the new methods.

Abstract

This paper develops valid bootstrap inference methods for the dynamic short panel threshold regression. We show that the standard nonparametric bootstrap is inconsistent for the first-differenced generalized method of moments (GMM) estimator. The inconsistency arises from an $n^{1/4}$-consistent non-normal asymptotic distribution of the threshold estimator when the true parameter lies in the continuity region of the parameter space, which 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 for the threshold and a residual bootstrap to construct confidence intervals for the coefficients. They are shown to be valid regardless of the model's continuity. Moreover, we establish a uniform validity for the grid bootstrap. A set of Monte Carlo experiments compares the proposed bootstraps with the standard nonparametric bootstrap. An empirical application to a firm investment model illustrates our methods.