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Leniency Designs: An Operator’s Manual

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  • Paul Goldsmith-Pinkham
  • Peter Hull
  • Michal Kolesár

Abstract

We develop a step-by-step guide to leniency (a.k.a. judge or examiner instrument) designs, drawing on recent econometric literatures. The unbiased jackknife instrumental variables estimator (UJIVE) is purpose-built for leveraging exogenous leniency variation, avoiding subtle biases even in the presence of many decision-makers or controls. We show how UJIVE can also be used to assess key assumptions underlying leniency designs, including quasi-random assignment and average first-stage monotonicity, and to probe the external validity of treatment effect estimates. We further discuss statistical inference, arguing that non-clustered standard errors are often appropriate. A reanalysis of Farre-Mensa et al. (2020), using quasi-random examiner assignment to estimate the value of patents to startups, illustrates our checklist.

Suggested Citation

  • Paul Goldsmith-Pinkham & Peter Hull & Michal Kolesár, 2025. "Leniency Designs: An Operator’s Manual," NBER Working Papers 34473, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:34473
    Note: CF LE LS PE PR
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    References listed on IDEAS

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    1. Angrist, Joshua & Kolesár, Michal, 2024. "One instrument to rule them all: The bias and coverage of just-ID IV," Journal of Econometrics, Elsevier, vol. 240(2).
    2. Mohamed Coulibaly & Yu-Chin Hsu & Ismael Mourifi'e & Yuanyuan Wan, 2024. "A Sharp Test for the Judge Leniency Design," Papers 2405.06156, arXiv.org, revised Nov 2025.
    3. Clément de Chaisemartin, 2017. "Tolerating defiance? Local average treatment effects without monotonicity," Quantitative Economics, Econometric Society, vol. 8(2), pages 367-396, July.
    4. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    5. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    6. David C Chan & Matthew Gentzkow & Chuan Yu, 2022. "Selection with Variation in Diagnostic Skill: Evidence from Radiologists [The Determinants of Productivity in Medical Testing: Intensity and Allocation of Care]," The Quarterly Journal of Economics, Oxford University Press, vol. 137(2), pages 729-783.
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    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • G0 - Financial Economics - - General
    • H0 - Public Economics - - General
    • J0 - Labor and Demographic Economics - - General
    • K0 - Law and Economics - - General

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