An Improved Inference for IV Regressions

Abstract

Empirical instrumental variables (IV) studies often report separate results based on low-dimensional instruments and many base instruments. This paper proposes a combination test that integrates these commonly reported statistics. The test linearly combines a cluster-robust Wald statistic based on low-dimensional IVs with leave-one-cluster-out Lagrangian Multiplier (LM) and Anderson-Rubin (AR) statistics constructed from many IVs. We establish joint asymptotic normality and asymptotic optimality of the proposed test. The procedure yields costless efficiency improvements, automatically adapts to weak identification of many instruments, and is accompanied by a practical rule of thumb for assessing efficiency gains.