The Incredible Shrinking Instruments: Using Empirical Bayes to Increase Efficiency in IV Designs with Many Instruments

Brigham R. Frandsen, Lars Lefgren, Emily C. Leslie and Samuel P. McIntyre

No 34634, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: In instrumental variables (IV) estimation with many instruments, such as judge fixed effects designs, the precision of jackknife-estimated first-stage fitted values can vary widely across observations. We propose a Shrunken JIVE estimator (SJIVE) that shrinks leave-one-out first-stage predictions toward overall or conditional means, with the degree of shrinkage depending on first-stage precision. We derive the variance-minimizing shrinkage rule and show that SJIVE has weakly lower asymptotic variance than JIVE. Under exclusion and monotonicity conditions, SJIVE identifies a proper weighted average of individual treatment effects. We illustrate the method in an application studying the effect of patent approval on the follow-on innovation of startup firms, where SJIVE produces substantially smaller standard errors than UJIVE.

JEL-codes: C1 C11 C21 K14 (search for similar items in EconPapers)
Date: 2026-01
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