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. We find that the estimator is asymptotically as efficient as
the limited-information maximum likelihood (LIML) estimator under many weak
instruments. In Monte Carlo experiments, we find that the estimator performs as
well as LIML or Fuller (1977) under homoskedasticity, and has much lower bias
and dispersion under heteroskedasticity, in nearly all cases considered.

Keywords. Instrumental variables, heteroskedasticity, many instruments, jackknife.
JEL classification. C12, C13, C23.