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A Sharp Test for the Judge Leniency Design

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Listed:
  • Mohamed Coulibaly
  • Yu-Chin Hsu
  • Ismael Mourifi'e
  • Yuanyuan Wan

Abstract

We propose sharp testable implications and tests to jointly assess the random assignment, exclusion, and monotonicity assumptions in judge leniency designs. Our procedures accommodate various data scenarios in which the number of defendants handled by a judge may be either small or large, and allow for discrete or continuous instrumental variables. When the validity of the design is rejected, a variant of the marginal treatment effect can be identified under weaker assumptions. We apply our test to the Philadelphia court data studied by Stevenson (2018) and demonstrate that it outperforms non-sharp joint tests by significant margins in simulation studies

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2405.06156
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    References listed on IDEAS

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    1. Hsu, Yu-Chin & Liu, Chu-An & Shi, Xiaoxia, 2019. "Testing Generalized Regression Monotonicity," Econometric Theory, Cambridge University Press, vol. 35(6), pages 1146-1200, December.
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    6. Martin Huber & Giovanni Mellace, 2015. "Testing Instrument Validity for LATE Identification Based on Inequality Moment Constraints," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 398-411, May.
    7. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    8. Amanda E. Kowalski, 2016. "Doing More When You're Running LATE: Applying Marginal Treatment Effect Methods to Examine Treatment Effect Heterogeneity in Experiments for the Young and Privately Insured"," Cowles Foundation Discussion Papers 2045, Cowles Foundation for Research in Economics, Yale University.
    9. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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