Estimating the Likelihood of Arrest from Police Records in Presence of Unreported Crimes

TL;DR

This paper develops a statistical framework to estimate arrest likelihood from police records by adjusting for unreported crimes using victimization survey data, revealing significant decreases in arrest probabilities and nuanced racial disparities.

Contribution

Introduces a two-step regression method integrating survey data to accurately estimate arrest likelihood accounting for unreported crimes and racial disparities.

Findings

Adjusted arrest likelihood decreases significantly after accounting for unreported crimes.

Racial disparities in arrests are smaller when considering crime characteristics and reporting rates.

Methodology improves accuracy of arrest probability estimates from police data.

Abstract

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.