Bootstrapping Anderson-Rubin Statistic and J Statistic in Linear IV Models with Many Instruments

Abstract

A bootstrap method is proposed for the Anderson-Rubin test and the J test for overidentifying restrictions in linear instrumental variable models with many instruments. We show the bootstrap validity of these test statistics when the number of instruments increases at the same rate as the sample size. Moreover, since it has been shown in the literature to be valid when the number of instruments is small, the bootstrap technique is practically robust to the numerosity of the moment conditions. A small-scale Monte Carlo experiment shows that our procedure has outstanding small sample performance compared with some existing asymptotic procedures.