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Causal inference and racial bias in policing: New estimands and the importance of mobility data
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Abstract
Studying racial bias in policing is a critically important problem, but one that comes with a number of inherent difficulties due to the nature of the available data. In this manuscript we tackle multiple key issues in the causal analysis of racial bias in policing. First, we formalize race and place policing, the idea that individuals of one race are policed differently when they are in neighborhoods primarily made up of individuals of other races. We develop an estimand to study this question rigorously, show the assumptions necessary for causal identification, and develop sensitivity analyses to assess robustness to violations of key assumptions. Additionally, we investigate difficulties with existing estimands targeting racial bias in policing. We show for these estimands, and the estimands developed in this manuscript, that estimation can benefit from incorporating mobility data into analyses. We apply these ideas to a study in New York City, where we find a large amount of racial bias, as well as race and place policing, and that these findings are robust to large violations of untestable assumptions. We additionally show that mobility data can make substantial impacts on the resulting estimates, suggesting it should be used whenever possible in subsequent studies.
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In studies of discrimination, researchers often seek to estimate a causal effect of race or gender on outcomes. For example, in the criminal justice context, one might ask whether arrested individuals would have been subsequently charged or convicted had they been a different race. It has long been known that such counterfactual questions face measurement challenges related to omitted-variable bias, and conceptual challenges related to the definition of causal estimands for largely immutable characteristics. Another concern, which has been the subject of recent debates, is post-treatment bias: many studies of discrimination condition on apparently intermediate outcomes, like being arrested, that themselves may be the product of discrimination, potentially corrupting statistical estimates. There is, however, reason to be optimistic. By carefully defining the estimand—and by considering the precise timing of events—we show that a primary causal quantity of interest in discrimination studies can be estimated under an ignorability condition that may hold approximately in some observational settings. We illustrate these ideas by analyzing both simulated data and the charging decisions of a prosecutor’s office in a large county in the United States.
Significance
Racial segregation shapes key aspects of a healthy society, including educational development, psychological well-being, and economic mobility. As such, a large literature has formed to measure segregation. Estimates of racial segregation often rely on assumptions of uniform interaction within some fixed time and geographic space despite the dynamic nature of urban environments. We leverage Global Positioning System data to estimate a measure of segregation that relaxes these strict assumptions. Experienced segregation according to our measure is substantially lower than standard measures would suggest. By decomposing segregation by functions of a city, like entertainment, restaurants, and retail, we facilitate targeted policy making where segregation matters most.
It is commonly argued that Black people may be more likely to be stopped by the police in majority White neighborhoods due to a natural tendency to first observe and then scrutinize that which seems out of the ordinary. Anecdotal evidence of police officers appearing equally drawn to White people in predominantly Black neighborhoods is sometimes presented to suggest that the phenomenon is race neutral. Motivated by such narratives, we examine the extent to which Black versus White racial categorization encourages police scrutiny in out-of-place and in-place contexts. Applying the veil-of-darkness and vehicle search threshold tests, we find that in place or out of place, being seen as White is always an advantage in Philadelphia.
We extend the omitted variable bias framework with a suite of tools for sensitivity analysis in regression models that does not require assumptions on the functional form of the treatment assignment mechanism nor on the distribution of the unobserved confounders, naturally handles multiple confounders, possibly acting non‐linearly, exploits expert knowledge to bound sensitivity parameters and can be easily computed by using only standard regression results. In particular, we introduce two novel sensitivity measures suited for routine reporting. The robustness value describes the minimum strength of association that unobserved confounding would need to have, both with the treatment and with the outcome, to change the research conclusions. The partial R2 of the treatment with the outcome shows how strongly confounders explaining all the residual outcome variation would have to be associated with the treatment to eliminate the estimated effect. Next, we offer graphical tools for elaborating on problematic confounders, examining the sensitivity of point estimates and t‐values, as well as ‘extreme scenarios’. Finally, we describe problems with a common ‘benchmarking’ practice and introduce a novel procedure to bound the strength of confounders formally on the basis of a comparison with observed covariates. We apply these methods to a running example that estimates the effect of exposure to violence on attitudes toward peace.
Endogenous selection bias is a central problem for causal inference. Recognizing the problem, however, can be difficult in practice. This article introduces a purely graphical way of characterizing endogenous selection bias and of understanding its consequences (Hernan et al. 2004). We use causal graphs (direct acyclic graphs, or DAGs) to highlight that endogenous selection bias stems from conditioning (e.g., controlling, stratifying, or selecting) on a so-called collider variable, i.e., a variable that is itself caused by two other variables, one that is (or is associated with) the treatment and another that is (or is associated with) the outcome. Endogenous selection bias can result from direct conditioning on the outcome variable, a post-outcome variable, a post-treatment variable, and even a pre-treatment variable. We highlight the difference between endogenous selection bias, common-cause confounding, and overcontrol bias and discuss numerous examples from social stratification, cultural sociology, social network analysis, political sociology, social demography, and the sociology of education.
Racial bias in traffic enforcement has become a popular line of inquiry, but examinations into explanations for the disparity have been scant. The current research integrates theoretical insights from the racial threat hypothesis with inferences drawn from the empirical analyses of the factors that stimulate officer suspicion. The most intriguing finding from this beat-level examination of the structural predictors of several traffic stop outcome measures concerns the conditional effect of the racial composition of the beat on search rates. The analyses reveal that the search rate increases in areas where the proportion of Black residents is higher; however, this finding is observed only for White motorists. This finding is interpreted as indicating that structural characteristics of an area can provide cues to officers regarding who belongs in that environment. As a result, social control increases among groups whose racial characteristics are inconsistent with the neighborhood racial composition.
We propose an ecological dimension to racial profiling by comparing the distribution of drivers on the roadways with officers' proactive surveillance and stop behavior in a predominantly white suburban community bordering a predominantly African American community. African Americans are subject to significant racial profiling, as reflected in disproportionate surveillance and stopping by the police when driving through whiter areas. Officers' behavior is not explained by African Americans' criminality because the “hit rates” for African American drivers are lower in white areas. Profiling is sensitive to race and place and manifests itself organizationally, reflecting community patterns of residential segregation.
In medical studies, there are many situations where the final outcomes are truncated by death, in which patients die before outcomes of interest are measured. In this article we consider identifiability and estimation of causal effects by principal stratification when some outcomes are truncated by death. Previous studies mostly focused on large sample bounds, Bayesian analysis, sensitivity analysis. In this article, we propose a new method for identifying the causal parameter of interest under a nonparametric and semiparametric model. We show that the causal parameter of interest is identifiable under some regularity assumptions and the assumption that there exists a pretreatment covariate whose conditional distributions among two principal strata are not the same, but our approach does not need the assumption of a mixture normal distribution for outcomes as required by Zhang, Rubin, and Mealli (2009). Hence, the proposed method is applicable not only to a continuous outcome but also to a binary outcome. When some of the assumptions are violated, we discuss biases of estimators and propose methods to reduce these biases. We conduct several simulation studies to evaluate the finite-sample performance of the proposed approach. Finally, we apply the proposed approach to a real dataset from a Southwest Oncology Group (SWOG) clinical trial.
Presents a discussion of matching, randomization, random sampling, and other methods of controlling extraneous variation. The objective was to specify the benefits of randomization in estimating causal effects of treatments. It is concluded that randomization should be employed whenever possible but that the use of carefully controlled nonrandomized data to estimate causal effects is a reasonable and necessary procedure in many cases. (15 ref) (PsycINFO Database Record (c) 2006 APA, all rights reserved).
In cluster randomized experiments, individuals are often recruited after the cluster treatment assignment, and data are typically only available for the recruited sample. Post-randomization recruitment can lead to selection bias, inducing systematic differences between the overall and the recruited populations and between the recruited intervention and control arms. In this setting, we define causal estimands for the overall and the recruited populations. We prove, under the assumption of ignorable recruitment, that the average treatment effect on the recruited population can be consistently estimated from the recruited sample using inverse probability weighting. Generally, we cannot identify the average treatment effect on the overall population. Nonetheless, we show, via a principal stratification formulation, that one can use weighting of the recruited sample to identify treatment effects on two meaningful subpopulations of the overall population: Individuals who would be recruited into the study regardless of the assignment, and individuals who would be recruited into the study under treatment but not under control. We develop an estimation strategy and a sensitivity analysis approach for checking the ignorable recruitment assumption, which we implement in the publicly available CRTrecruit R package. The proposed methods are applied to the ARTEMIS cluster randomized trial, where removing co-payment barriers increases the persistence of P2Y inhibitor among the always-recruited population.
This article presents a theoretical and methodological framework for comparative urban studies grounded in the proposition that a neighborhood depends not only on its own conditions, as typically conceived, but also the conditions of the neighborhoods to which its residents are connected, through networks of everyday urban mobility. Based on this framework, we highlight three arguments and associated applications based on the analyses of networks of movement throughout large American cities. The first is that even though residents of disadvantaged neighborhoods travel far and wide, their relative isolation and segregation persist. Second, mobility-based socioeconomic disadvantage, or what has been termed triple neighborhood disadvantage, explains neighborhood well-being independent of residential-based disadvantage. Third, a city’s level of social connectedness depends on how uneven and concentrated networks of everyday mobility are among its neighborhoods, which in turn are hypothesized to predict social behavior across cities beyond that expected by their residential-based segregation. The results offer a new way of thinking about neighborhood effects, the dynamics of everyday urban mobility, spatial inequality, and social segregation that can be studied in a comparative framework in cities anywhere.
Neighborhood racial composition contributes to racial disparities in arrests, but prior research has almost exclusively focused on the magnitude of a minority population with somewhat mixed findings. We investigate whether racial disparities in arrests perpetuate when the racial composition reaches a particular threshold to assess whether the accumulation of race matters, and to what degree. To expand upon prior research, we include a range of part 2 crimes—public drunkenness, drug offenses, and disorderly conduct—“lower level” crimes which may allow for greater police discretion. We conduct negative binomial regression analyses using arrest data from a mid-sized city in the South between 2010 and 2015. Results show evidence of a threshold effect, but this pattern differs across race and crime type. There is no evidence that Whites are more likely to be arrested in Black neighborhoods. This suggests that race-specific arrest rates may be driven by offense type and neighborhood racial composition.
Background:
In cluster randomized trials, patients are typically recruited after clusters are randomized, and the recruiters and patients may not be blinded to the assignment. This often leads to differential recruitment and consequently systematic differences in baseline characteristics of the recruited patients between intervention and control arms, inducing post-randomization selection bias. We aim to rigorously define causal estimands in the presence of selection bias. We elucidate the conditions under which standard covariate adjustment methods can validly estimate these estimands. We further discuss the additional data and assumptions necessary for estimating causal effects when such conditions are not met.
Methods:
Adopting the principal stratification framework in causal inference, we clarify there are two average treatment effect (ATE) estimands in cluster randomized trials: one for the overall population and one for the recruited population. We derive analytical formula of the two estimands in terms of principal-stratum-specific causal effects. Furthermore, using simulation studies, we assess the empirical performance of the multivariable regression adjustment method under different data generating processes leading to selection bias.
Results:
When treatment effects are heterogeneous across principal strata, the average treatment effect on the overall population generally differs from the average treatment effect on the recruited population. A naïve intention-to-treat analysis of the recruited sample leads to biased estimates of both average treatment effects. In the presence of post-randomization selection and without additional data on the non-recruited subjects, the average treatment effect on the recruited population is estimable only when the treatment effects are homogeneous between principal strata, and the average treatment effect on the overall population is generally not estimable. The extent to which covariate adjustment can remove selection bias depends on the degree of effect heterogeneity across principal strata.
Conclusion:
There is a need and opportunity to improve the analysis of cluster randomized trials that are subject to post-randomization selection bias. For studies prone to selection bias, it is important to explicitly specify the target population that the causal estimands are defined on and adopt design and estimation strategies accordingly. To draw valid inferences about treatment effects, investigators should (1) assess the possibility of heterogeneous treatment effects, and (2) consider collecting data on covariates that are predictive of the recruitment process, and on the non-recruited population from external sources such as electronic health records.
Racial conflict theories suggest that racialized policing should wane in areas where people of colour are the majority and Whites, the minority. This article examines community-level predictors of racial/ethnic differences in drug arrests from 2011 to 2016 across 86 census tracts in Newark, NJ, a city where most officers and residents are persons of colour. We examine whether racial conflict indicators predict Black, White and Hispanic drug arrests, accounting for other factors. Findings indicate that racialized policing prevails within this majority–minority context. Officers tend to arrest Blacks in communities with greater White and Hispanic residents and Whites in predominantly Black areas. In contrast, Hispanic arrests are not attributable to racialized policing. We conclude with recommendations for future theoretical redevelopment.
Researchers often lack the necessary data to credibly estimate racial discrimination in policing. In particular, police administrative records lack information on civilians police observe but do not investigate. In this article, we show that if police racially discriminate when choosing whom to investigate, analyses using administrative records to estimate racial discrimination in police behavior are statistically biased, and many quantities of interest are unidentified—even among investigated individuals—absent strong and untestable assumptions. Using principal stratification in a causal mediation framework, we derive the exact form of the statistical bias that results from traditional estimation. We develop a bias-correction procedure and nonparametric sharp bounds for race effects, replicate published findings, and show the traditional estimator can severely underestimate levels of racially biased policing or mask discrimination entirely. We conclude by outlining a general and feasible design for future studies that is robust to this inferential snare.
In studies of race disparities in policing, scholars generally employ quantitative methodologies with the goal of determining whether race disparities exist or, in fewer instances, of ruling out correlates. Yet, lacking from theoretical and empirical efforts is an elucidation of how and why on‐the‐ground policing produces race disparities that are justified in legal, race‐neutral terms. To address this knowledge gap, I analyze officers’ self‐reported accounts of their enforcement activities, justifications, and decision‐making in a representative sample of 300 official reports of drug arrests made in St. Louis from 2009 to 2013. These accounts are analyzed across neighborhood racial contexts and arrestee race, revealing important differences that help illuminate the race disparity problem. Unlike drug arrests in White neighborhoods or of White citizens that primarily stem from reactive policing, drug arrests in Black and racially mixed neighborhoods and of Black citizens result from officers’ greater use of discretionary stops based on neighborhood conditions, suspicion of ambiguous demeanor, or minor infractions. During such stops, officers’ discovery of drug possession often results from discretionary Terry frisks or searches incident to arrests for outstanding bench warrants. These findings fill important theoretical and empirical gaps and have implications for reforms toward racially just policing.
This paper explores racial differences in police use of force. On non-lethal uses of force, blacks and Hispanics are more than 50 percent more likely to experience some form of force in interactions with police. Adding controls that account for important context and civilian behavior reduces, but cannot fully explain, these disparities. On the most extreme use of force—officer-involved shootings—we find no racial differences either in the raw data or when contextual factors are taken into account. We argue that the patterns in the data are consistent with a model in which police officers are utility maximizers, a fraction of whom have a preference for discrimination, who incur relatively high expected costs of officer-involved shootings.
A large body of empirical research exists that attempts to determine whether or not police discriminate on the basis of race. We investigate whether the methods used typically produce valid inferences. We find that they often most likely do not and that results may diverge from reality in either direction, indicating discrimination when it is not present or alternatively indicating a lack of discrimination when it is in fact present. The reason for this is that tests make assumptions about police behavior that are often implausible. Because of this, the simplest forms of benchmark and outcome tests should not be used, although the problem is more general. We discuss several possible ways to improve inferences about the absence or presence of discrimination, such as employing matching or weighting techniques and using novel, computationally intensive methods. Expected final online publication date for the Annual Review of Criminology Volume 2 is January 13, 2019. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
This research investigates the source of Black–White differences in drug arrests by conducting a neighborhood-level test of the differential police scrutiny and racially discriminatory policing hypotheses. The study examines drug arrests made across 78 neighborhoods in St. Louis between 2009 and 2013. Results from the negative binomial regression analyses lend the greatest support to the racially discriminatory policing perspective. Neighborhood racial composition significantly shapes drug law enforcement practices, net of neighborhood-level violent and property crime rates, drug-related calls for service by citizens, and socioeconomic disadvantage. Specifically, findings suggest that officers engage in “out-of-place” racial profiling in drug law enforcement, as they tend to target suspects whose race is incongruent with the neighborhood racial context. Implications of the study findings are discussed.
Non-manipulable factors, such as gender or race have posed conceptual and practical challenges to causal analysts. On the one hand these factors do have consequences, and on the other hand, they do not fit into the experimentalist conception of causation. This paper addresses this challenge in the context of public debates over the health cost of obesity, and offers a new perspective, based on the theory of Structural Causal Models (SCM).
Cambridge Core - American Government, Politics and Policy - Suspect Citizens - by Frank R. Baumgartner
Recent studies have examined racial disparities in stop-and-frisk, a widely employed but controversial policing tactic. The statistical evidence, however, has been limited and contradictory. We investigate by analyzing three million stops in New York City over five years, focusing on cases where officers suspected the stopped individual of criminal possession of a weapon (CPW). For each CPW stop, we estimate the ex ante probability that the detained suspect has a weapon. We find that in more than 40% of cases, the likelihood of finding a weapon (typically a knife) was less than 1%, raising concerns that the legal requirement of “reasonable suspicion” was often not met. We further find that blacks and Hispanics were disproportionately stopped in these low hit rate contexts, a phenomenon that we trace to two factors: (1) lower thresholds for stopping individuals — regardless of race — in high-crime, predominately minority areas, particularly public housing; and (2) lower thresholds for stopping minorities relative to similarly situated whites. Finally, we demonstrate that by conducting only the 6% of stops that are statistically most likely to result in weapons seizure, one can both recover the majority of weapons and mitigate racial disparities in who is stopped. We show that this statistically informed stopping strategy can be approximated by simple, easily implemented heuristics with little loss in efficiency.
In the spring and summer of 2016, seven studies that examined the impact of subject race on police use of force were announced in the media and the paraphrased headlines ranged from “there is bias in the use of force,” “there is no bias in the use of force,” and “there is bias in some types of force, but not others.” The purpose of this research note is to examine these disparate findings and the methods that might explain them, with attention to sample characteristics, the types of analyses, the number and character of agencies studied, and how concepts are operationalized. This analysis will help research consumers analyze critically the results from race-and-force studies and, hopefully, add to our understanding of this important national issue.
We outline a framework for causal inference in settings where assignment to a binary treatment is ignorable, but compliance with the assignment is not perfect so that the receipt of treatment is nonignorable. To address the problems associated with comparing subjects by the ignorable assignment - an "intention-to-treat analysis" - we make use of instrumental variables, which have long been used by economists in the context of regression models with constant treatment effects. We show that the instrumental variables (IV) estimand can be embedded within the Rubin Causal Model (RCM) and that under some simple and easily interpretable assumptions, the IV estimand is the average causal effect for a subgroup of units, the compliers. Without these assumptions, the IV estimand is simply the ratio of intention-to-treat causal estimands with no interpretation as an average causal effect. The advantages of embedding the IV approach in the RCM are that it clarifies the nature of critical assumptions needed for a causal interpretation, and moreover allows us to consider sensitivity of the results to deviations from key assumptions in a straightforward manner. We apply our analysis to estimate the effect of veteran status in the Vietnam era on mortality, using the lottery number that assigned priority for the draft as an instrument, and we use our results to investigate the sensitivity of the conclusions to critical assumptions.
A This paper proposes a regression model where the response is beta distributed using a parameterization of the beta law that is indexed by mean and dispersion parameters. The proposed model is useful for situations where the variable of interest is continuous and restricted to the interval (0, 1) and is related to other variables through a regression structure. The regression parameters of the beta regression model are interpretable in terms of the mean of the response and, when the logit link is used, of an odds ratio, unlike the parameters of a linear regression that employs a transformed response. Estimation is performed by maximum likelihood. We provide closed-form expressions for the score function, for Fisher's information matrix and its inverse. Hypothesis testing is performed using approximations obtained from the asymptotic normality of the maximum likelihood estimator. Some diagnostic measures are introduced. Finally, practical applications that employ real data are presented and discussed.
Problems involving causal inference have dogged at the heels of statistics since its earliest days. Correlation does not imply causation, and yet causal conclusions drawn from a carefully designed experiment are often valid. What can a statistical model say about causation? This question is addressed by using a particular model for causal inference (Holland and Rubin 1983; Rubin 1974) to critique the discussions of other writers on causation and causal inference. These include selected philosophers, medical researchers, statisticians, econometricians, and proponents of causal modeling.
Research on race effects in police traffic stops is theoretically underdeveloped. In this study, we derive propositions from Donald Black's theory of law to explain the interaction effects of officer and driver race on searches in traffic stops in St. Louis, Missouri. Our citywide results and those for stops in predominantly White communities are generally consistent with the theory: Searches are more likely in stops of Black drivers than in those of White drivers, especially by White officers, controlling for other characteristics of the officer, driver, and stop. In predominantly Black communities, however, stops of White drivers by White officers are most likely to result in a search. We interpret both sets of results as manifestations of racial profiling in segregated communities and suggest that Black's theory of law remains a promising theoretical framework for future research on the continuing significance of race-based policing in the United States.
Adjustments for bias in observational studies are not always confined to variables that were measured prior to treatment. Estimators that adjust for a concomitant variable that has been affected by the treatment are generally biased. The bias may be written as the sum of two easily interpreted components: one component is present only in observational studies; the other is common to both observational studies and randomized experiments. The first component of bias will be zero when the affected posttreatment concomitant variable is, in a certain sense, a surrogate for an unobserved pretreatment variable. The second component of bias can often be addressed by an appropriate sensitivity analysis.
Recent studies by police departments and researchers confirm that police stop racial and ethnic minority citizens more often than whites, relative to their proportions in the population. However, it has been argued stop rates more accurately reflect rates of crimes committed by each ethnic group, or that stop rates reflect elevated rates in specific social areas such as neighborhoods or precincts. Most of the research on stop rates and police-citizen interactions has focused on traffic stops, and analyses of pedestrian stops are rare. In this paper, we analyze data from 175,000 pedestrian stops by the New York Police Department over a fifteen-month period. We disaggregate stops by police precinct, and compare stop rates by racial and ethnic group controlling for previous race-specific arrest rates. We use hierarchical multilevel models to adjust for precinct-level variability, thus directly addressing the question of geographic heterogeneity that arises in the analysis of pedestrian stops. We find that persons of African and Hispanic descent were stopped more frequently than whites, even after controlling for precinct variability and race-specific estimates of crime participation.
This article assesses the strengths and weaknesses of using “outcome tests” to assess racial disparities in police practices. An outcome test, for example, might assess whether the probability of finding contraband was higher for whites who are searched than for minorities who are searched.
Despite their ubiquity, observational studies to infer the causal effect of a so-called immutable characteristic, such as race or sex, have struggled for coherence, given the unavailability of a manipulation analogous to a “treatment” in a randomized experiment and the danger of posttreatment bias. We demonstrate that a shift in focus from actual traits to perceptions of them can address both of these issues while facilitating articulation of other critical concepts, particularly the timing of treatment assignment. We illustrate concepts by discussing the designs of various studies of the role of race in trial court death penalty decisions. © 2011 The President and Fellows of Harvard College and the Massachusetts Institute of Technology.
This paper provides new evidence on racial profiling using information on the race of both motorists and officers. Extending the model of Knowles, Persico, and Todd (2001), we develop a new test for distinguishing between preference-based and statistical discrimination. Our test is based on the notion that if search decisions are driven purely by statistical discrimination, then they should be independent of officer race. Our results, by contrast, demonstrate that officers are more likely to search if officer race and driver race differ. We then investigate and rule out two alternative explanations for our findings. Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.
Many scientific problems require that treatment comparisons be adjusted for posttreatment variables, but the estimands underlying standard methods are not causal effects. To address this deficiency, we propose a general framework for comparing treatments adjusting for posttreatment variables that yields principal effects based on principal stratification. Principal stratification with respect to a posttreatment variable is a cross-classification of subjects defined by the joint potential values of that posttreatment variable tinder each of the treatments being compared. Principal effects are causal effects within a principal stratum. The key property of principal strata is that they are not affected by treatment assignment and therefore can be used just as any pretreatment covariate. such as age category. As a result, the central property of our principal effects is that they are always causal effects and do not suffer from the complications of standard posttreatment-adjusted estimands. We discuss briefly that such principal causal effects are the link between three recent applications with adjustment for posttreatment variables: (i) treatment noncompliance, (ii) missing outcomes (dropout) following treatment noncompliance. and (iii) censoring by death. We then attack the problem of surrogate or biomarker endpoints, where we show, using principal causal effects, that all current definitions of surrogacy, even when perfectly true, do not generally have the desired interpretation as causal effects of treatment on outcome. We go on to forrmulate estimands based on principal stratification and principal causal effects and show their superiority.
The key problem in testing for racial profiling in traffic stops is estimating the risk set, or "benchmark," against which to compare the race distribution of stopped drivers. To date, the two most common approaches have been to employ Census-based residential population data or to conduct traffic surveys in which observers tally the race distribution of drivers at a certain location. It is widely recognized that residential population data may provide poor estimates of the population at risk of a traffic stop; at the same time, traffic surveys have limitations and may be too costly to carry out on the ongoing basis required by recent legislation and litigation. In this paper, we propose a test for racial profiling that does not require explicit, external estimates of the risk set. Rather, our approach makes use of what we refer to as the "veil of darkness" hypothesis, which asserts that at night, police cannot determine the race of a motorist until they actually make a stop. The implication is that the race distribution of drivers stopped at night should equal the race distribution of drivers at risk of being stopped at night. If we further assume that racial differences in traffic patterns, driving behavior, and exposure to law enforcement do not vary between day and night, we can test for racial profiling by comparing the race distribution of stops made during daylight to the race distribution of stops made at night. We propose a means of weakening this assumption by restricting the sample to stops made during the evening hours and controlling for clock time while estimating day/night contrasts in the race distribution of stopped drivers. We provide conditions under which our estimates are robust to a substantial non-reporting problem present in our data and in many ...
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Nonparametric bounds on treatment effects
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