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

Author

Listed:
  • Brigham R. Frandsen
  • Lars J. Lefgren
  • Emily C. Leslie
  • Samuel P. McIntyre

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.

Suggested Citation

  • Brigham R. Frandsen & Lars J. Lefgren & Emily C. Leslie & Samuel P. McIntyre, 2026. "The Incredible Shrinking Instruments: Using Empirical Bayes to Increase Efficiency in IV Designs with Many Instruments," NBER Working Papers 34634, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:34634
    Note: LS TWP
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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • K14 - Law and Economics - - Basic Areas of Law - - - Criminal Law

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