A JACKKNIFE LAGRANGE MULTIPLIER TEST WITH MANY WEAK INSTRUMENTS

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 sample size, (ii) arbitrarily weak and (iii) heteroskedastic errors. In contrast Crudu, Mellace, Sándor (2021, Econometric Theory 37, 281–310) Mikusheva Sun Review Economic Studies 89, 2663–2686), who proposed Anderson–Rubin tests that are also (i)–(iii), we modify score statistic by jackknifing construct its heteroskedasticity variance estimator. Compared Kleibergen (2002, Econometrica 70, 1781–1803) Moreira (2001, Tests Correct Size when Instruments Can Be Arbitrarily Weak , Working paper) their modification Hansen, Hausman, Newey (2008, Journal Business & Statistics 26, 398–422), our JLM errors circumvent possible decrease in power function. Simulation results illustrate desirable size properties method.