Factor based identification-robust inference in IV regressions

Abstract

Robust methods for instrumental variable inference have received considerable attention recently. Their analysis has raised a variety of problematic issues such as size/power trade-offs resulting from weak or many instruments. We show that information reduction methods provide a useful and practical solution to this and related problems. Formally, we propose factor-based modifications to three popular weak-instrument-robust statistics, and illustrate their validity asymptotically and in finite samples. Results are derived using asymptotic settings that are commonly used in both the factor and weak-instrument literature. For the Anderson–Rubin statistic, we also provide analytical finite-sample results that do not require any underlying factor structure. An illustrative Monte Carlo study reveals the following. Factor-based tests control size regardless of instruments and factor quality. All factor-based tests are systematically more powerful than standard counterparts. With informative instruments and in contrast to standard tests: (i) power of factor-based tests is not affected by k even when large; and (ii) weak factor structure does not cost power. An empirical study on a New Keynesian macroeconomic model suggests that our factor-based methods can bridge a number of gaps between structural and statistical modeling.