detect invalid instruments, in the presence of heterogeneous treatment effects and endogeneity. We also provide a formal …

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 …) under homoskedasticity, and has much lower bias and dispersion under heteroskedasticity, in nearly all cases considered. …

regressions with multiple endogenous regressors to be robust to heteroskedasticity and autocorrelation. Equivalently, we extend …