Robustness of Bootstrap in Instrumental Variable Regression
研究了工具变量回归中自助法推断方法的稳健性，比较了基于IV估计量和GMTM估计量的检验统计量，发现基于GMTM估计量的隐含概率自助法检验具有理想的稳健性，并通过模拟和实证例子验证。
This paper studies robustness of bootstrap inference methods for instrumental variable (IV) regression models. We consider test statistics for parameter hypotheses based on the IV estimator and generalized method of trimmed moments (GMTM) estimator introduced by Čížek (2008 Čížek's , P. ( 2008 ). General trimmed estimation: Robust approach to nonlinear and limited dependent variable models . Econometric Theory 24 : 1500 – 1529 .[Crossref], [Web of Science ®] , [Google Scholar], 2009 Čížek's , P. ( 2009 ). Generalized method of trimmed moments. Working paper, Tilburg University, Tilburg, Netherlands . [Google Scholar]), and compare the pairs and implied probability bootstrap approximations for these statistics by applying the finite sample breakdown point theory. In particular, we study limiting behaviors of the bootstrap quantiles when the values of outliers diverge to infinity but the sample size is held fixed. The outliers are defined as anomalous observations that can arbitrarily change the value of the statistic of interest. We analyze both just- and overidentified cases and discuss implications of the breakdown point analysis to the size and power properties of bootstrap tests. We conclude that the implied probability bootstrap test using the statistic based on the GMTM estimator shows desirable robustness properties. Simulation studies endorse this conclusion. An empirical example based on Romer's (1993 Romer , D. ( 1993 ). Openness and inflation: Theory and evidence . The Quarterly Journal of Economics 108 : 869 – 903 .[Crossref], [Web of Science ®] , [Google Scholar]) study on the effect of openness of countries to inflation rates is presented. Several extensions including the analysis for the residual bootstrap are provided.