Abstract

This paper proposes a valid inference procedure for many instruments that is robust to heteroskedasticity, the number of instruments being proportional to sample size, weak instrument asymptotics, and heterogeneous treatment effects. The procedure targets a JIVE estimand and proceeds by calculating a normalized LM statistic and comparing it with critical values from a standard normal distribution. To establish the validity of this procedure, this paper shows that the LM statistic is asymptotically normal and a novel variance estimator is consistent.