IDENTIFICATION-ROBUST TWO-STAGE BOOTSTRAP TESTS WITH PRETESTING FOR EXOGENEITY
针对工具变量分析中常见的外生性预检验导致第二阶段检验严重扭曲的问题，提出一种识别稳健的两阶段检验统计量，并开发了尺寸调整的野生自助法，在弱识别下仍能保持正确渐近尺寸且具有更高功效。
Pretesting for exogeneity has become routine in many empirical applications involving instrumental variables (IVs) to decide whether the ordinary least squares or IV-based method is appropriate. Guggenberger (2010a, Econometric Theory , 26, 369–382) shows that the second-stage test – based on the outcome of a Durbin-Wu-Hausman-type pretest in the first stage – exhibits extreme size distortion, with asymptotic size equal to 1 when the standard critical values are used. In this paper, we first show that both conditional and unconditional on the data, standard wild bootstrap procedures are invalid for two-stage testing. Second, we propose an identification-robust two-stage test statistic that switches between OLS-based and weak-IV-robust statistics. Third, we develop a size-adjusted wild bootstrap approach for our two-stage test that integrates specific wild bootstrap critical values with an appropriate size-adjustment method. We establish uniform validity of this procedure under conditional heteroskedasticity or clustering in the sense that the resulting tests achieve correct asymptotic size, regardless of whether the identification is strong or weak. Our procedure is especially valuable for empirical researchers facing potential weak identification. In such settings, its power advantage is notable: whereas weak-IV-robust methods maintain correct size but often suffer from relatively low power, our approach achieves better performance.