  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.
