Yukitoshi Matsushita and Taisuke Otsu

Published 5 August 2020

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This paper proposes a jackknife Lagrange multiplier (JLM) test for instrumental variable regression models, which is robust to (i) many instruments, where the number of instruments may increase proportionally with the sample size, (ii) arbitrarily weak instruments, and (iii) heteroskedastic errors. To the best of our knowledge, currently there is no asymptotically size correct test in this setting. Our idea is to modify the score statistic by jackknifing and to construct its heteroskedasticity robust variance estimator. Compared to Hansen, Hausman and Newey's (2008) modification for many instruments on the LM test by Kleibergen (2002) and Moreira (2001), our JLM test is robust for heteroskedastic errors and may circumvent possible decrease in the power function. Simulation results illustrate the desirable size robustness and power properties of the proposed method.