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Econometrics Paper
Jackknife Lagrange multiplier test with many weak instruments
Yukitoshi Matsushita and Taisuke Otsu
August 2020
Paper No' EM 613:
Full Paper (pdf)

JEL Classification: C12; C26

Tags: many instruments; weak instruments; lagrange multiplier test; jackknife

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.