Job market paper
An Improved Inference for IV Regressions
Revise and resubmit, Quantitative Economics
Abstract
Empirical applications of instrumental variables (IV) regressions often involve both low-dimensional and high-dimensional sets of instruments. In Angrist and Krueger (1991), the quarter-of-birth instruments generate a much larger set that includes many interaction-based technical instruments; in shift-share designs considered in Goldsmith-Pinkham, Sorkin, and Swift (2020), a single IV aggregates many underlying base instruments. To improve inference in such settings, this paper proposes a combination test that integrates low- and high-dimensional IV specifications. The test linearly combines a cluster-robust Wald statistic based on low-dimensional IVs with leave-cluster-out Lagrange multiplier (LM) and Anderson-Rubin (AR) statistics constructed from the many IVs. We establish the joint asymptotic normality of these statistics and show that the proposed test is asymptotically optimal within a broad class of tests. The procedure yields costless efficiency improvements, automatically adapts to weak identification of the many instruments, and provides a practical rule of thumb for assessing these gains.