Robustness of bootstrap in instrumental variable regression

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 estimatorand generalized method of trimmed moments (GMTM) estimator introduced by Cížek (2008, 2009),and compare the pairs and implied probability bootstrap approximations for these statistics byapplying the finite sample breakdown point theory. In particular, we study limiting behaviors ofthe bootstrap quantiles when the values of outliers diverge to infinity but the sample size is heldfixed. The outliers are defined as anomalous observations that can arbitrarily change the value ofthe statistic of interest. We analyze both just- and over-identified cases and discuss implicationsof the breakdown point analysis to the size and power properties of bootstrap tests. We concludethat the implied probability bootstrap test using the statistic based on the GMTM estimator showsdesirable robustness properties. Simulation studies endorse this conclusion. An empirical examplebased 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.