Instrumental Variable Estimation with Heteroskedasticity and Many Instruments”, manuscript

It is common practice in econometrics to correct for heteroskedasticity of un-known form. This paper does so for instrumental variable estimators with many instruments. We give heteroskedasticity and many instrument robust versions of the limited information maximum likelihood (LIML) and Fuller (1977, FULL) esti-mators. We also give heteroskedasticity and many instrument consistent standard errors for these estimators. The estimators are based on removing the own observa-tion terms in the numerator of the LIML variance ratio. We derive their properties under standard, many instrument, or many weak instrument asymptotics. Based on a series of Monte Carlo experiments, we find that the estimators perform as well as LIML or FULL under homoskedasticity, and have much lower bias and dispersion under heteroskedasticity, in nearly all cases considered