Abstract

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. In contrast to Crudu, Mellace and Sándor (2021) and Mikusheva and Sun (2021) who proposed jackknife Anderson-Rubin tests that are also robust to (i)-(iii), we modify a score statistic by jackknifing and construct its heteroskedasticity robust variance estimator. Compared to the Lagrange multiplier tests by Kleibergen (2002) and Moreira (2001) and their modification for many instruments by Hansen, Hausman and Newey (2008), our JLM test is robust to heteroskedastic errors and may circumvent a possible decrease in the power function. Simulation results illustrate the desirable size and power properties of the proposed method. This is a joint work with Taisuke Otsu (LSE).