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A Sharp Test for the Judge Leniency Design

Author

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

Abstract

We propose a new specification test to assess the validity of the judge leniency design. We characterize a set of sharp testable implications, which exploit all the relevant information in the observed data distribution to detect violations of the judge leniency design assumptions. The proposed sharp test is asymptotically valid and consistent and will not make discordant recommendations. When the judge's leniency design assumptions are rejected, we propose a way to salvage the model using partial monotonicity and exclusion assumptions, under which a variant of the Local Instrumental Variable (LIV) estimand can recover the Marginal Treatment Effect. Simulation studies show our test outperforms existing non-sharp tests by significant margins. We apply our test to assess the validity of the judge leniency design using data from Stevenson (2018), and it rejects the validity for three crime categories: robbery, drug selling, and drug possession.

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.
    • Handle: RePEc:arx:papers:2405.06156
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    File URL: http://arxiv.org/pdf/2405.06156
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    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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