Robustness of Bootstrap in Instrumental Variable Regression

Abstract

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, 2009), 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) study on the effect of openness of countries to inflation rates is presented. Several extensions including the analysis for the residual bootstrap are provided.