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. Copyright © 2015 John Wiley & Sons, Ltd.