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.
Estimation of Dynamic Panel Threshold Model using Stata
我们开发了一个Stata命令xthenreg来实现Seo和Shin（2016，Journal of Econometrics 195：169-186）提出的动态面板阈值模型的一阶差分GMM估计。进一步，我们给出了动态门限模型的扭折约束GMM估计的渐近方差公式，并给出了估计算法。我们还提出了一种快速的自举算法来实现线性检验的自举。通过蒙特卡罗模拟和经济应用说明了该命令的使用。
Threshold Regression for Fixed-T Panel Data with Interactive Fixed Effects
Free University of Bozen-Bolzanno（博尔扎诺自由大学）；Brunel University of London（伦敦布鲁内尔大学）；University of Birmingham（伯明翰大学）；Lund University（隆德大学）；Deakin University（迪肯大学）
Asymptotic Variance Theory for Trimmed Least Squares and Trimmed Least Absolute Deviations in Censored Panel Models with Fixed Effects
University of California, Los Angeles（加州大学洛杉矶分校）；University of Copenhagen（哥本哈根大学）；Aarhus Center for Econometrics (ACE)（奥胡斯计量经济学中心）；Princeton University（普林斯顿大学）
