COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1796 Robustness of Bootstrap in Instrumental Variable Regression Lorenzo Camponovo and Taisuke Otsu April 2011 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. |
