Instrumental Variable Estimation with Heteroskedasticity and Many Instruments

This paper gives a relatively simple, well behaved solution to the problem of many instruments in heteroskedastic data. Such settings are common in microeconometric applications where many instruments are used to improve efficiency and allowance for heteroskedasticity is generally important. The solution is a Fuller (1977) like estimator and standard errors that are robust to heteroskedasticity and many instruments. We show that the estimator has finite moments and high asymptotic efficiency in a range of cases. The standard errors are easy to compute, being like White’s (1982), with additional terms that account for many instruments. They are consistent under standard, many instrument, and many weak instrument asymptotics. Based on a series of Monte Carlo experiments, we find that the estimators perform as well as LIML or Fuller (1977) under homoskedasticity, and have much lower bias and dispersion under heteroskedasticity, in nearly all cases considered.