RANK TESTS FOR INSTRUMENTAL VARIABLES REGRESSION WITH WEAK INSTRUMENTS

This paper considers tests in an instrumental variable ~IVs! regression model with IVs that may be weak+ Tests that have near-optimal asymptotic power properties with Gaussian errors for weak and strong IVs have been determined in Andrews, Moreira, and Stock ~2006, Econometrica 74, 715–752!+ In this paper, we seek tests that have near-optimal asymptotic power with Gaussian errors and improved power with non-Gaussian errors relative to existing tests+ Tests with such properties are obtained by introducing rank tests that are analogous to the conditional likelihood ratio test of Moreira ~2003, Econometrica 71, 1027–1048!+ We also introduce a rank test that is analogous to the Lagrange multiplier test of Kleibergen ~2002, Econometrica 70, 1781–1803! and Moreira ~2001, manuscript, University of California, Berkeley!+