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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 the jackknife-estimated first stage can vary widely across observations. When such variability exists, we show that the precision of JIVE second-stage estimates is meaningfully improved by shrinking judge propensities towards their conditional means, where the shrinkage factor depends on the precision of the first-stage fitted value. Doing so requires no further assumptions and identifies the same local average treatment effect as the usual (unshrunken) JIVE estimator. We illustrate the precision gains from using a Shrunken JIVE estimator (SJIVE) in an application from the literature studying pre-trial detention of defendants in criminal cases.

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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