An Improved Inference for IV Regressions

TL;DR

This paper introduces a new combined test for IV regressions that improves efficiency and adapts to weak instruments by integrating low-dimensional and many-instrument statistics, supported by theoretical guarantees.

Contribution

It proposes a novel combination test for IV studies that unifies low-dimensional and many-instrument approaches, with proven asymptotic properties and practical efficiency gains.

Findings

The test achieves asymptotic normality and optimality.

It provides costless efficiency improvements.

Automatically adapts to weak instrument scenarios.

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.