June 2024 Estimating the likelihood of arrest from police records in presence of unreported crimes
Riccardo Fogliato, Arun Kumar Kuchibhotla, Zachary Lipton, Daniel Nagin, Alice Xiang, Alexandra Chouldechova
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Ann. Appl. Stat. 18(2): 1253-1274 (June 2024). DOI: 10.1214/23-AOAS1833


Many important policy decisions concerning policing hinge on our understanding of how likely various criminal offenses are to result in arrests. Since many crimes are never reported to law enforcement, estimates based on police records alone must be adjusted to account for the likelihood that each crime would have been reported to the police. In this paper we present a methodological framework for estimating the likelihood of arrest from police data that incorporates estimates of crime reporting rates computed from a victimization survey. We propose a parametric regression-based two-step estimator that: (i) estimates the likelihood of crime reporting using logistic regression with survey weights and then (ii) applies a second regression step to model the likelihood of arrest. Our empirical analysis focuses on racial disparities in arrests for violent crimes (sex offenses, robbery, aggravated and simple assaults) from 2006–2015 police records from the National Incident Based Reporting System (NIBRS), with estimates of crime reporting obtained using 2003–2020 data from the National Crime Victimization Survey (NCVS). We find that, after adjusting for unreported crimes, the likelihood of arrest computed from police records decreases significantly. We also find that, while incidents with white offenders, on average, result in arrests more often than those with black offenders, the disparities tend to be small after accounting for crime characteristics and unreported crimes.


Riccardo Fogliato conducted this work as a Ph.D. student at Carnegie Mellon University. The authors thank Richard Berk for valuable feedback and suggestions and David Buil-Gil for helpful discussions. We also thank reviewers, Associate Editor, and Editor for their insightful comments.


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Riccardo Fogliato. Arun Kumar Kuchibhotla. Zachary Lipton. Daniel Nagin. Alice Xiang. Alexandra Chouldechova. "Estimating the likelihood of arrest from police records in presence of unreported crimes." Ann. Appl. Stat. 18 (2) 1253 - 1274, June 2024. https://doi.org/10.1214/23-AOAS1833


Received: 1 June 2022; Revised: 1 September 2023; Published: June 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.1214/23-AOAS1833

Keywords: Likelihood of arrest , NCVS , NIBRS , racial disparities , unreported crime

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 2 • June 2024
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