This paper considers tests in an instrumental variables (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 (2006a). 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). We also introduce a rank test that is analogous to the Lagrange multiplier test of Kleibergen (2002) and Moreira (2001).
Andrews, Donald W.K. and Soares, Gustavo, "Rank Tests for Instrumental Variables Regression with Weak Instruments" (2006). Cowles Foundation Discussion Papers. 1854.