RANK TESTS FOR INSTRUMENTAL VARIABLES REGRESSION WITH WEAK INSTRUMENTS

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Abstract
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).Andrews gratefully acknowledges the research support of the National Science Foundation via grant SES-0417911.