Robustness of Bootstrap in Instrumental Variable Regression

This paper studies robustness of bootstrap inference methods for instrumental variable regression models. In particular, we compare the uniform weight and implied probability bootstrap approximations for parameter hypothesis test statistics by applying the breakdown point theory, which focuses on behaviors of the bootstrap quantiles when outliers take arbitrarily large values. The implied probabilities are derived from an information theoretic projection from the empirical distribution to a set of distributions satisfying orthogonality conditions for instruments. Our breakdown point analysis considers separately the effects of outliers in dependent variables, endogenous regressors, and instruments, and clarifies the situations where the implied probability bootstrap can be more robust than the uniform weight bootstrap against outliers. Effects of tail trimming introduced by Hill and Renault (2010) are also analyzed. Several simulation studies illustrate our theoretical findings.