Generalizing the Hit Rates Test for Racial Bias in Law Enforcement, With an Application to Vehicle Searches in Wichita1

This paper considers the use of outcomes-based tests for detecting racial bias in the context of police searches of motor vehicles. We characterize the police and motorist decision problems in a game theoretic framework, where police encounter motorists and decide whether to search them and motorists decide whether to carry contraband. Our modeling framework generalizes that of Knowles, Persico and Todd (2001) (KPT) by allowing for police heterogeneity in costs of search and in tastes for discrimination and for motorist heterogeneity in the costs and bene…ts from crime. We also consider the possibility that drivers’characteristics are endogenously determined in that drivers can alter their characteristics to reduce the probability of being monitored. We establish the properties of the equilibrium in these more general settings and show that the outcomes-based test proposed in KPT can still be applied. After developing the theory, we apply the tests to data on police searches of motor vehicles gathered by the Wichita police department. The empirical …ndings are consistent with the notion that police in Wichita choose their search strategies to maximize successful searches. We also summarize evidence on these tests when applied to other police datasets. JEL Numbers: J70, K42 Keywords: Racial Pro…ling, Crime, Police, Wichita In his …rst address to Congress, President George W. Bush reported directing his Attorney General "to develop speci…c recommendations to end racial pro…ling. It’s wrong, and we will end it in America."1 By the term “racial pro…ling,”he was referring to a presumed unlawful use of race or ethnicity in police interdiction. Over the last ten years, numerous lawsuits have been brought against US city police departments alleging racially biased law enforcement practices.2 Partly in response to this litigation, many police departments now routinely collect information on the demographic characteristics of the individuals that they subject to stops and searches and on the outcomes of these encounters. A common pattern found in police datasets is that blacks and Hispanics tend to be overrepresented in police tra¢ c stops and searches. This pattern raises concerns as to whether the disparities re‡ect police bias or whether they are the byproduct of goal-oriented enforcement by unbiased police. Various tests have been proposed in the literature to assess whether police behavior is racially biased. The simplest tests are so-called benchmarking tests, which compare the racial/ethnic composition of the population monitored by the police against population benchmarks, for example, the racial composition of the general population in a given area. A more sophisticated version of the benchmark test examines whether race/ethnicity predicts whether an individual is subject to monitoring, after taking account other characteristics that the police are permitted to use as potential indicators of criminality. One drawback of this type of test is that the result usually depends on the