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Racial Bias in Motor Vehicle Searches:

Theory and Evidence

John Knowles, Nicola Persico and Petra Todd1

CARESS WORKING PAPER #99-06

August 19, 1999

1Knowles, Persico and Todd are Assistant Professors in the Economics De-

partment of the University of Pennsylvania. We thank George Mailath and Ken

Wolpin for helpful discussions. We thank the Maryland ACLU for providing us

with data and information. Please direct correspondence to any of the authors

at 3718 Locust Walk, Philadelphia, PA 19104 or to jknowles@econ.sas.upenn.edu,

persico@econ.sas.upenn.edu, or petra@athena.sas.upenn.edu.

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Abstract

African American motorists in the United States are more likely than white

motorists to have their cars searched by police checking for illegal drugs and

other contraband. The courts are faced with the task of deciding on the basis

of tra¢c-stop data whether police are basing their decisions to stop cars on

the race of the driver. We develop a model of law enforcement for a popula-

tion with two racial types who also di¤er along other dimensions relevant to

criminal behavior. We discuss why a simple test commonly applied by the

courts is inadequate when the econometrician observes only a subset of the

characteristics observed by the policemen. Next, we show how to construct

a test for whether di¤erential treatment is motivated purely out of e¢ciency

grounds, i.e. to maximize the number of arrests, or re‡ects racial prejudice.

The test is valid even when the set of characteristics observed by the police-

men are only partially observable by the econometrician. We apply the tests

for discrimination to tra¢c stop data from Maryland. Finally, we present a

simple analysis of the tradeo¤ between e¢ciency and fairness.

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1 Introduction

African American motorists in the United States are more likely than white

motorists to have their cars searched by police checking for illegal drugs

and other contraband. In the state of Maryland, for example, 80% of mo-

torists searched by state police on the I-95 highway between January 1995

and September 1996 were African-American, although only 18% of motorists

on this road were African American.1While it is conceivable that African

American motorists are more likely to commit the types of tra¢c o¤enses

that police use as pretexts for vehicle checks, tra¢c studies and police testi-

mony suggest that blacks and whites are not distinguishable by their driving

habits. An alternative explanation for the racial disparity in tra¢c stops is

racial discrimination: police o¢cers make their decision to stop cars partly

on the basis of race. This explanation, known as “racial pro…ling,” is the

basis of several recent lawsuits against state governments. The issue has also

attracted attention in political spheres, forcing the resignation of the New

Jersey chief of police and provoking the U.S. President to describe racial

pro…ling as a “morally indefensible, deeply corrosive practice.”2

Evidence of racial pro…ling is often interpreted as an indication of racist

preferences on the part of the police. The task of deciding whether racism

is a factor in police tra¢c stops falls on the courts, which consider various

pieces of statistical evidence in reaching a decision. The case for discrimina-

tion rests largely on the observation that the proportion of African-Americans

among the drivers stopped by police far exceeds the proportion in the general

population of drivers. This simple comparison is the basis of expert witness

testimonies in various legal cases.3A re…ned version of the test performs

1This information comes from Lamberth (1996), a study commissioned by the Maryland

ACLU.

2“Clinton Order Targets Racial Pro…ling”, Associated Press, June 9, 1999.

3In the 1993 case of Maryland v. Wilkins, a statistician testi…ed that “The disparities

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the same comparison after conditioning on other observable characteristics

of drivers thought to be related to criminal propensities. If race has no ad-

ditional explanatory power in a regression after introducing the conditioning

variables, then this is taken as evidence of no discrimination.4

The drawback to this approach to testing for discrimination is that it

requires the analyst to have data on the full set of characteristics that a

policeman uses in deciding whether to stop a motorist.5If some characteris-

tics are unobserved, then race may have explanatory power due to omitted

variable bias. Another drawback of the test is that even if race has no ex-

planatory power, there is still the possibility that police target individuals

with certain characteristics because those characteristics are correlated with

race and not because they are good predictors of criminality. Thus, the va-

lidity of the test hinges crucially on judgements about what constitutes a set

of admissible conditioning variables and on whether the analyst has access

to the full set of variables.

Even if regression-based tests conclude in favor discrimination, they are

not informative about the motivation for discrimination. Police may use race

as a criterion in tra¢c stops for e¢ciency reasons (because they are trying to

maximize arrests and race helps predict criminality) or because they prefer

stopping one racial group over another. We call discrimination for e¢ciency

reasons statistical discrimination, using the terminology of Arrow (1973). In

contrast, we say that an o¢cer is prejudiced (or racist) if, cæteris paribus,

he has a preference for searching motorists of a particular race. We model

are su¢ciently great that, taken as a whole, they are consistent with and strongly sup-

port the assertion that the Maryland State Police are targeting the community of black

motorists for stop, detention and investigation...”.

4See Donohue (1999).

5A training manual issued by the Illinois State Police highlights some indicators of

criminal activity. These include tinted windows, religious paraphernalia used to divert

suspicion, and attorney’s business cards. We report the complete list in the Appendix.

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prejudice as a taste for discrimination, following Becker (1957). Prejudice is

a property of the o¢cer’s utility function, while statistical discrimination is

a property of equilibrium. An equilibrium exhibits statistical discrimination

if, conditional on all other observables available to non-racist policemen, one

race is searched more often than another.

In this paper, we propose a test for distinguishing between statistical

discrimination and racist preferences, which is derived from a simple model

of law enforcement via police searches. A key advantage of the test is that

it is feasible even when only a subset of the variables used by the policeman

in deciding whether to search a motorist are available. In fact, while more

variables allow for a more powerful test, the test can be carried out when

race is the only characteristic observed.

Our model belongs to the literature on optimal auditing. Early models,

such as Becker (1968) and Stigler (1970) examined citizens’ incentives to

misbehave under an exogenous probability of being audited. More recent lit-

erature, mainly dealing with income reporting and tax evasion, assumes that

both parties, the auditing and the auditee, behave strategically (see Rein-

ganum and Wilde (1986), Border and Sobel (1987), and Scotchmer (1987)).

To the best of our knowledge, ours is the …rst paper that attempts an em-

pirical test of an optimal auditing model.

Our model assumes that the police force maximizes the number of arrests

net of costs of searching motorists. Police take into account observable infor-

mation about the driver that may or may not include race, while motorists

take into account the probability of being searched in deciding whether to

carry contraband in their car. Prejudice is introduced into the model as a

di¤erence in the perceived cost of searching di¤erent drivers. In equilibrium,

police are most likely to search those motorists whose visible characteristics

are most closely linked to crime, and the minimum level of suspicion that

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results in a search may vary across racial groups. However, a key implica-

tion of the equilibrium model is that if a police o¢cer has the same tastes

for searching two subgroups of the population, such as two di¤erent racial

groups, then the probability that a stopped driver is carrying contraband

should be identical across those subgroups.

We apply this test to data on drug-related highway searches gathered

by the Maryland State Police on the Maryland stretch of the I-95 highway.

In our data, cars of African American motorists are searched much more

frequently than those of white motorists. However, we cannot reject the

hypothesis that this is due purely to e¢ciency considerations, i.e. statistical

discrimination.6

In other words, it is possible to explain the black-white

racial disparities observed in the Maryland tra¢c stop data without recourse

to racist preferences. Of course, e¢ciency is not the only relevant criterion

in evaluating economic outcomes. At the end of our paper, we consider the

costs imposed by statistical discrimination and discuss the trade-o¤s between

racial fairness and e¤ectiveness of drug interdiction.

2 The Model

This section describes the model of police and motorist behavior that gener-

ates the implications that we will later test. Our model assumes that there

are a continuum of policemen and motorists. Let r 2 fA;Wg denote the

race of the motorist, which we assume is observable by the policeman. Let c

denote all observable characteristics other than race that are potentially used

by the policeman in searching cars. The variable c may be unobserved or only

partially observed by the econometrician. Although c is a multidimensional

6Although limitations in our data do not allow us to carry out a test of whether statisti-

cal discrimination is present, we are currently attempting to address this issue by enriching

our data set.

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variable, for expositional ease we treat it as a one dimensional variable. All

the results in this section extend straightforwardly to the multidimensional

case. Let F (cjW) and F(cjA) denotes the distribution of c in the white and

African American populations, respectively.

Policemen search motorists, and we assume that each policeman can

choose from an in…nite supply of motorists of any type c;r. The police-

man maximizes the total number of convictions minus a cost of searching

cars. The marginal cost of searching a motorist of race r is tr. We assume

tW;tA2 (0;1). Let G denote the event where the motorist searched is found

guilty. (In our data, G corresponds to being found with drugs in the car).

We assume that motorists consider the probability of being searched in

deciding whether to carry contraband.7

If they do not carry contraband

their payo¤ is zero whether or not the car is searched. Suppose they carry

contraband; if they are searched their payo¤ is ¡j (c;r), while if they are

not searched the payo¤ is u(c;r). We can interpret u(c;r) as the expected

propensity to carry drugs, and j (c;r) as the expected cost of being con-

victed for a motorist with characteristics c and race r. We assume that

j (c;r);u(c;r) > 0.

Denote by ° (c;r) the probability that the policeman searches a motorist

of type c;r. The expected payo¤ to a motorist of type c;r from carrying

contraband is

° (c;r)[¡j (c;r)] + [1 ¡ ° (c;r)]u(c;r):

(1)

The motorist decides to carry contraband if this expression is greater than

zero. When the expression is zero the motorist is willing to randomize be-

tween carrying and not carrying. We denote the probability that a motorist

of type c;r carries contraband by P (Gjc;r).

7An alternative assumption is that motorists do not react to the probability of being

searched. In the Appendix we present that model, and present a testable implication

allowing to distinguish between the two models.

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The policeman’s problem is to choose the probability of searching each

motorist as a function of the observable characteristics, ° (c;r). The police-

man solves

max

°(c;W);°(c;A)

X

r=W;A

Z

[P (Gjc;r) ¡ tr]° (c;r)f (cjr)dc:

If P (Gjc;r)¡tr> 0 then optimizing behavior implies ° (c;r) = 1, i.e. always

search motorists of type c and r. If P (Gjc;r) = trthen the policeman is

willing to randomize over whether or not to search type c;r.8

Next, we introduce two de…nitions pertaining to racial bias in motor vehi-

cle searchers. First, a policeman is de…ned to be racist if his utility function

exhibits a preference for stopping one race. In our model, this is captured as

a di¤erence in the cost of searching motorists.

De…nition 1 We say that the policeman is prejudiced, or has a taste for

discrimination, if tA6= tW.

Next, we say that an equilibrium exhibits statistical discrimination if,

conditional on all characteristics observable by policemen with no tastes for

discrimination, the probability of searching di¤ers by race.

De…nition 2 We say that the equilibrium exhibits statistical discrimination

if tA= tW and ° (c;W) 6= ° (c;A) for some c.

It is important to observe that, while racism is de…ned as a characteristic

of the policeman, statistical discrimination is a property of equilibrium that

does not depend in any way on the policeman’s characteristics. Also, the

de…nition of statistical discrimination depends on what is observable. As

we show below, the equilibrium may exhibit statistical discrimination if the

8Our model does not allow for police to have heterogeneous tastes for discrimination

depending on the race of the policeman or for the possibility of false arrests. Donohue and

Levitt (1998 ) incorporate such features into their model in a di¤erent context.

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things on which the policeman can condition his search decision are not

su¢ciently detailed.

2.1 Equilibrium

We showthat there is an equilibriumwhere motorists randomize over whether

to carry contraband and policemen randomize over whether to search them.9

For a motorist of type c;r to be willing to randomize it must be that ex-

pression (1) equals zero.10Solving for° yields ° (c;r) = u(c;r)=[u(c;r) + j (c;r)].

This determines the policeman’s searching intensity. Notice that ° (c;r) 2

(0;1), so at equilibrium the policeman randomizes over whether to search

each type c;r.

For a policeman to be willing to randomize it must be that P (Gjc;r) = tr

for all c;r.

9At the equilibrium, both the policemen and the motorists randomize. This may look

unrealistic, since it requires agents to be indi¤erent across actions. There is a simple

interepretation of these mixed strategies that does not require agents to actually ‡ip

coins. This interpretation goes under the name of “puri…cation” of mixed strategies, and

is presented in the Appendix.

10In our model, the probability that a motorist carries contraband is never one. The

reason that this probability can never be one for any group c;r is that otherwise policemen

would search these motorists always. In a more realistic model, it may not be possible to

achieve such deterrence. To see this, consider a model where a …nite number of policemen

are spaced along a highway. Suppose that stopping and searching a vehicle takes a certain

time, during which a policeman cannot stop other cars. In that case, even if it is common

knowledge that motorist c;r carries contraband with probability one, there is a positive

probability that he will not be stopped simply because all policemen along the highway

are busy searching other motorists. Now, by making group c;r su¢ciently rare in the

population (so that policemen do not …nd it worth their while to wait for a member of

that group to pass by) and by making u(c;r) su¢ciently high, one can manufacture the

result that some group carry contraband with probability one at equilibrium.

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The model implies that for all c,

P (Gjc;A) = tA

P (Gjc;W) = tW

° (c;A) =

u(c;A)

[u(c;A) + j (c;A)]

u(c;W)

[u(c;W) + j (c;W)]

(2)

° (c;W) =

(3)

Suppose that tA= tW = t, i.e. policemen have no taste for discrimination.

Then, for all c it must be

P (Gjc;A) = t = P (Gjc;W):

(4)

Notice that this does not imply that ° (c;W) = ° (c;A). In other words,

given c, the search intensity ° may be higher for African Americans even

in the absence of prejudice. This happens if

u(c;W)

[u(c;W)+j(c;W)]<

u(c;A)

[u(c;A)+j(c;A)],

i.e. if the expected propensity to carry drugs is higher or the cost of being

convicted is lower, for African American motorists after conditioning on all

the observables c. This property may indicate that race proxies for some

variable that is unobservable by the policeman and is correlated with both

race and crime. Such an unobservable could be educational attainment.

2.2 Testing for Prejudice

It is easy to test for relationship (4) even in the absence of data on c and on °.

It su¢ces to have data on the posterior frequency of guilt by race,conditional

on being searched,

D(r) =

Z

P (Gjc;r)

° (c;r)f (cjr)

R° (s;r)f (sjr)dsdc:

Indeed, using (4) to substitute for P (Gjc;r) into D(r) we get

D(W) = t = D(A);

(5)

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which is the implication that will be tested with the data below.

Notice that there is nothing special about the characteristic “race” in

the model. An implication analogous to (5) holds for male and female, and

indeed the equality of posterior frequencies of guilty should hold true across

any characteristic on which the policeman conditions his searching decision.

Thus, in the empirical section of the paper we will test condition (5) using

both race and sex.

3 Empirical Results

3.1 Data Description

The data we analyze were collected as part of the settlement of a federal

lawsuit …led in February 1993 by the ACLU, challenging as unconstitutional

the Maryland State Police’s alleged use of a “racial pro…le” as a basis for

stopping, detaining and searching motorists. In the settlement, the state

agreed to maintain detailed records of motorist stops, and to …le quarterly

reports with the Court and the ACLU. In November, 1996 the Maryland

ACLU asked a federal court in Baltimore to hold the Maryland State Police

agency in contempt of court and to impose a $250,000 penalty, based upon

evidence showing that state police violated a 1995 court decree by continuing

a pattern of race discrimination in drug interdiction activities carried out

along the Interstate 95 corridor. Because the data on tra¢c stops by race

are only available for the time period after the intiation of the …rst ACLU

lawsuit, the estimates we report cannot be construed as decribing police

behavior prior to the legal interventions.

Our dataset consists of 1590 observations on car searches on I-95 in Mary-

land from January, 1995 through January, 1999.11The data provide infor-

11The searches were conducted in Baltimore, Cecil, Harford, Howard, and Prince

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mation on the race and sex of the motorist as well as on the year, make

and model of the vehicle, and the date, time and location of the search. We

also know whether the policeman requested consent to search the car and, if

consent to search was not requested, the probable cause that the policeman

invoked to search the car. The probable-cause information provides insight

into what types of characteristics are considered as grounds for initiating

searches.12We also know whether canine units were used in the search and

whether contraband (typically illegal drugs) was recovered. If any was re-

covered, we know what type, how much (in grams) and where it was found.

There is also information on whether currency was recovered, how much and

its location inside the car. Finally, the dataset includes the name of the

o¢cer.

It is important to recognize that our data does not pertain to the stopping

decision, but rather to the decision to stop and search the car. We do not have

dataon motorists whowere stopped, say because they were speeding, but who

were not searched. While the decision to stop could depend on di¤erences in

driving habits between di¤erent race groups, the decision to search is more

up to the policeman’s discretion. The car searches at the heart of the racial

pro…ling controversy are ones where the motorist involved has committed a

minor tra¢c violation, such as changing lanes without signalling or exceeding

the speed limit by less than 5 miles per hour. Highway studies show that

the vast majority of drivers commit such violations.13State troopers are not

required to stop motorists for these kinds of infractions, so these stops are

often used as a pretext to stop and search the motorist, other occupants and

George’s Counties.

12For example, ‘third-party-vehicle’ (a vehicle not owned by the driver) is often listed

as a grounds for requesting consent to search. The appendix lists other observables that

police sometimes use in tra¢c stops.

13According to a study designed by John Lamberth, 98.1% of all cars on a stretch of the

New Jersey Turnpike were clearly exceeding speed limits. See New Jersey v. Soto, 1996.

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the vehicle.14The decision to search is probably based on a great number of

characteristics (nervous behavior, dress code, etc.), some of which we have no

hope of getting reliable data on. Thus, our dataset a¤ords a good application

of the tests described above that are implementable with a partial set of

observed characteristics.

Table 1 summarizes the means and variances of the subset of variables

used in the empirical work. Of the 1590 total searches, 1007 or 63.4% were

performed on African-Americans, 466 or 29.3% on Whites, 97 or 6.1% on

Hispanics, and the remaining (1.3%) was performed on other race/ethnic

groups. Female motorists were rarely searched: a total of 117 female mo-

torists appear in the data, compared to 1473 men. Marijuana was the drug

most commonly found during the searches (23% of the time). It is not un-

common for drivers to be carrying up to three di¤erent types of drugs as well

as drug-related paraphernalia. Searches tend to be much more common at

night: 43% of searches were performed during the hours of midnight-6am.

Figure 1 plots the proportion of drivers searched who are African Amer-

ican, white or female against time. The circle size is proportional to the

inverse of the standard deviation of the estimates, with the smaller circles

having the larger standard deviations. The …gure reveals a downward trend

14In 1986 for instance, the Drug Enforcement Agency trained 27,000 police o¢cers in

48 states in the use of pretext stops to …nd drugs in vehicles. According to the ACLU,

the training materials in these and similar programs “implicitly” encourage the targeting

of minority motorists. The practice of using discretionary stops as pretexts in this way

was supported by the Supreme Court in Whren and Brown vs. US in 1996, which held

that any tra¢c violation was a legal basis for stopping a motorist. The ACLU, arguing

against the legality of pretextual stops, maintained that the tra¢c code is so detailed that

every driver is in violation of at least one provision at any point in time, and so pretextual

stops give police the right to stop anyone arbitrarily, and in particular would justify racist

police practices. The court statement cites without comment the ACLU statement that

in the decision to stop a motorist, race is a “decidely impermissable factor”.

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in the proportion of African American drivers searched and an upward trend

in the proportion of white drivers searched.15There is no clear trend for

the proportion of female motorists. If there is variation over time in police

practices, at least two issues arise: …rst whether the model’s predictions hold

in all the subperiods of the data, and second, whether the model can help

elucidate the cause of this variation. These issues are discussed later in the

paper.

3.2 Test Results

To implement our test for detecting tastes for discrimination, we need to

de…ne what it means to be guilty. We classify as guilty anyone found carrying

any amount of drugs of the following types: marijuana, heroine, cocaine,

crack, PCP, LSD, and methadone. A small number of individuals were found

in possession of barbituates (such as valium); these we did not classify as

guilty.

Figure 2 plots the proportion of African American and white drivers found

to be carrying drugs.16As discussed above, our test for prejudice compares

the probability of being found guilty conditional on a subset of observed

characteristics. The model has a strong implication; namely, that no mat-

ter what the set of observable conditioning characteristics, the probability of

being guilty should be the same across the groups de…ned by those charac-

teristics.

We …rst describe test results obtained when we condition on character-

istics nonparametrically through cell means. Then we will consider ways of

carrying out the same test in a parametric setting.

15These trends are statistically signi…cant in regressions of the proportions on a linear

time trend.

16We only present the plots for white and black because sample sizes for the other groups

are too small to disaggregate by month.

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3.2.1 Nonparametric Tests

Tables 2a-2c compare the probability of being found guilty of carrying drugs,

across cells, de…ned by race, sex and race*sex. Although African American

motorists are much more likely to be searched by police, the proportion found

guilty among whites and African Americans is nearly identical. This …nding is

consistent in our model with pure statistical discrimination. It is inconsistent

with racial prejudice. Among Hispanics, though, the proportion found guilty

is lower than among African-Americans or whites. Table 3 reports p-values

from a Pearson chi-squared test of association between guilty and race. It

rejects the null hypothesis of no association at conventional signi…cance levels

when all race groups are used in the test, but does not reject when the sample

is restricted to African Americans and whites.

In Table 3b, we compare the probability of being found guilty for men

and women. Again, the conditional probabilities are similar and a Pearson

chi-squared test does not reject the null hypothesis of no association with

sex. (See p-values in Table 4). Table 3c conditions more …nely, this time on

both sex and race. Again, the joint test rejects the null of no association if

Hispanic males are included, but not when they are excluded.17

Thus, for the african-american sample our …ndings are consistent with no

prejudice. At the same time, existing research suggest thatR° (c;A)dF (cjA) >

R° (c;W)dF (cjW), i.e. African American are searched proportionately more

often than whites. The disparity in the search intensity between blacks and

whites may be due to statistical discrimination, i.e. ° (c;A) 6= ° (c;W).

Alternatively, the disparity may simply be evidence of a di¤erent distri-

bution of characteristics c among races. In other words, it may be that

° (c;A) = ° (c;W) but F (cjW) 6= F (cjA), hence any di¤erence in the search

intensity between the two races is due to the distribution of observables c in

17There are no Hispanic women in our data, so the rejection is due to Hispanic males.

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the two populations. However, for the Hispanic sample the lower probabil-

ities of being guilty would imply under our model tastes for discrimination

against Hispanics.18

Our data were collected during three distinct time periods, the …rst when

the police were being audited as part of the law suit, the second when the

audit period was over but the police were still gathering data as part of the

settlement agreement, and the third after a second lawsuit alleging that the

police were still discriminating had been …led. These distinct periods can be

clearly seen in Figure 3, which gives a histogram of how many observations

were collected in di¤erent time periods. During the audit period and after

the …ling of the second lawsuit, data collection was more intense.

We were concerned that police behavior could have been changing over

these three time periods and that the tests of equality of guilt probabilities,

which combine all time periods, mask variation over time. To address this

concern, we perform the identical tests after disaggregating the data by the

three time periods: prior to May, 1996, in between June, 1996 and December,

1998, and after December 1998. The tests performed on the disaggregated

data yield the same conclusions as those performed on the full sample. They

do not reject equality of the probabilities within each of the time periods when

Hispanic males are excluded from the sample, but do reject when Hispanics

are included. These results are reported in Appendix B. (See p-values in

Table B.2)

3.2.2 Parametric Tests

As discussed in the introduction, a common approach to testing for discrimi-

nation is to ask whether race has a signi…cant coe¢cient in a regression after

18However, a caveat is in order: when Hispanics are found with drugs, they appear to be

found with very large quantities relative to other races. Unfortunately, because we have

so few guilty Hispanics in our data, this feature is not statistically signi…cant.

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including other covariates. One such test compares

Pr(G = 1jr;c) = Pr(G = 1jc)

where c is a particular set of characteristics considered to be valid condition-

ing variables and r is the race indicator variable. The probability can be

estimated using a parametric procedure such as probit or logistic regression.

Under a probit assumption,

G = 1(c° ¡ v > 0)

where v is normally distributed.

A drawback of a parametric approach is that the test is only valid if the

systematic component and the error component of the model are correctly

speci…ed.19

Accumulated Monte Carlo evidence suggests that probit esti-

mates are relatively robust to misspeci…cation in terms of the distribution

of the error component, but can be quite sensitive to misspeci…cation in the

systematic component of the model.20With a small number of binary covari-

ates, one can minimize the possibility of misspeci…cation in the systematic

component of the model by including all possible interactions between the

elements of c: In practice, however, many covariates are often introduced in

a linear fashion without higher order interactions, so a parametric test for

the signi…cance of coe¢cient on the race indicator variable can be highly

sensitive to functional form misspeci…cation.

Our theoretical model has a much stronger prediction. If the probit model

is correctly speci…ed, then the coe¢cients associated with all the conditioning

19An exception is the case where the error terms are misspeci…ed but the regressors are

all normally distributed.

20Intuitively, this robustness is partly due to the fact that a normal error distribution

has some properties in common to all cdf’s, namely that Fv(¡1) = 0 and Fv(1) = 1. If

the true error distribution is symmetric, the normally distribution also gets the midpoint

right, Fv(0) = 0:5: See discussion in Todd (1996).

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variables should equal zero (since the conditional probability should be equal

across all groups). Three versions of this test are shown in Table B.3 of the

Appendix. The results for each model show that our conclusions from the

non-parametric tests remain valid under the probit speci…cation: only the

indicator for Hispanic seems to have a statistically signi…cant e¤ect on the

guilty rate, even when the model allows e¤ects to vary over time.

The nonparametric test results presented above are not subject to the

criticism that the probability model could be misspeci…ed. However, a prob-

lem often encountered in using nonparametric conditioning methods is that

the cell sizes become small as the number of covariates increases.21Fortu-

nately, our test requires only that a subset of the covariates be used, making a

nonparametric test viable. But if additional covariates were available and the

sample size were very large, a more powerful test for racial prejudice could be

constructed by combining results from tests on multiple sets of conditioning

variables.

3.3 Testing for statistical discrimination

If we had data on the entire vector c and we had a complete record of those

motorists who are stopped but not searched, we would be able to recover the

search intensity:

° (c;r) =# of motorists with characteristics c;r that are searched

# of motorists with characteristics c;r that are stopped:

Using expressions (2) and (3), we can recover u(c;r)=[u(c;r) + j (c;r)] from

° (c;r). This allows us to test whether for some (or all) c it is true that

simultaneously u(c;W) = u(c;A) and j (c;W) = j (c;A). Remember that

u(c;r) and j (c;r) capture a motorist’s expected propensity to carry drugs,

given his characteristics c and race r. If for all c we have that u(c;r) or j (c;r)

21This is a version of the curse of dimensionality problem.

16

Page 19

is not invariant to r for some c, then upon seeing that c the policeman expects

di¤erent races to have di¤erent propensities to carry contraband. This may

be because race is correlated with some trait that a¤ects the propensity to

carry drugs (say, education level) which the policeman cannot observe.

4 E¢ciency vs. Fairness

If we take the viewpoint that the bene…t of law enforcement is crime deter-

rence and that its cost is the cost of policing, then a non-prejudiced police

force would implement the e¢cient search behavior given the behavior of

motorists. This is because each police o¢cer trades o¤ the probability of ar-

resting against the cost of performing searches. The fact that the equilibrium

exhibits statistical discrimination is implied by e¤…ciency in crime reduction,

which according to this simple viewpoint, is not a¤ected by considerations

of racial disparities.

This outcome may be considered less than satisfactory in terms of fairness.

Assume that a person who does not carry contraband su¤ers a cost when

searched. Assume further that one race has a higher average propensity to

carry contraband. According to our model, persons from this race will be

searched more frequently, and will therefore su¤er a higher expected cost of

being searched.

We say that an outcome is fair when individuals of di¤erent races with

the same observables other than race, c; experience the same expected cost

of being stopped.

De…nition 3 An outcome is fair if for all c we have ° (c;W) = ° (c;A).

Under this de…nition, statistical discrimination is unfair. One way of

implementing the fair outcome is simply to constrain the police force to stop

17

Page 20

both races at the same rate, conditional on c.22

To explore the tradeo¤

between fairness and e¢ciency, it is useful to consider a stylized version of

our model, which allows us to derive a simple expression for the ine¢ciency

associated with the “fair” outcome.23

Consider a simpli…ed version of our model where tA= tWand c is absent,

so the only observable that the police can condition on is race. Assume

further that the propensity to carry drugs is higher for African Americans

than for whites, i.e.

u(c;W)

[u(c;W)+j(c;W)]<

u(c;A)

[u(c;A)+j(c;A)]. According to the previous

analysis, African Americans and whites will be stopped at rates °¤(A) and

°¤(W), with °¤(A) > °¤(W). The bene…t of law enforcement is t, the

probability that any motorist carries contraband at equilibrium. The cost is

t[°¤(A)'(A) + °¤(W)'(W)]

where '(r) represents the fraction of people with race r in the entire popu-

lation.

Consider now the behavior of police under the contraint that ° (A) =

° (W). This constraint requires that both races be stopped at the same

rate (this is as if policemen were color-blind when deciding whom to search).

Denote with ¤¤ the equilibrium of this constrained game. Assume that police

do not allow African Americans to carry drugs for sure, i.e. t < '(A).24

Then at equilibrium whites do not carry drugs, while African Americans

randomize between carrying drugs or not. To be willing to randomize it

22One might also argue, however, that several variables potentially included in c should

not be considered ‘fair’ conditioning variables. For example, age is a such a characteristic.

It is known to be correlated with criminal behavior, which would lead to younger drivers

being searched more frequently.

23If monetary transfers are possible, then a straightforward way of recovering fairness

without compromising e¢ciency is to avoid putting any constraint on police behavior, and

o¤er side payments to members of the race that is searched more often.

24If they carry drugs for sure, the expected probability of the average motorist being

guilty conditional on being stopped is at least '(A).

18

Page 21

must be that °¤¤(A) = °¤(A). For the police to be willing to randomize

it must be that t = P¤¤(GjA)'(A). The bene…t of law enforcement is

the average probability that a motorist carries contraband at equilibrium,

P¤¤(GjA)'(A) = t. The cost is

t[°¤(A)'(A) + °¤(A)'(W)]:

Comparing the two equilibria we notice that the bene…t is the same,

but the number of searches necessary to achieve that bene…t di¤ers. It is

t[°¤(A)'(A) + °¤(W)'(W)] in the unconstrained equilibrium, and t[°¤(A)'(A) + °¤(A)'(W)

in the fair equilibrium. Thus, the e¢ciency cost of fairness is

t'(W)[°¤(A) ¡ °¤(W)]:

The quantities in this expression could in principle be measured: in order to

compute the cost of fairness, we need only the proportion of motorists found

guilty and the probabilities that police will stop motorists of di¤erent races

at the unconstrained optimum, and the racial proportions of the population.

These numbers would give us a rough estimate, based on the key simplifying

assumption, which is that police use only race to decide whether to stop

motorists.

The above e¢ciency analysis reduces the bene…ts of drug interdiction to

the reduction of contraband on the road, and the cost of stopping to the cost

of policing. In practice, the bene…ts and costs of drug interdiction are much

more complex and some aspects may be di¢cult to quantify even abstracting

from considerations of fairness. A realistic measure of the e¢ciency cost

of fairness must then be confronted with the expected bene…ts of the fair

outcome, which we do not attempt here.

More generally, the model of Section 2 tells us what would be the e¤ects

on the rates of guilt by race of raising the costs to police of stopping African

American motorists. Since police equate the marginal bene…t of stopping a

19

Page 22

motorist to the marginal cost, an increase in the cost of stopping African

American motorists should result in a rise in the equilibrium probabilities of

carrying drugs. We saw in Figure 1 that the proportion of motorists searched

who are African American seems to be falling over time. One may wonder

whether this trend is due to an increase in the e¤ective cost of stopping

black motorists, say due to political pressure on the police. However, Figure

2 suggests that the proportion of guilty among either African American or

white motorists searched has remained roughly constant over time, which is

inconsistent with this hypothesis. It suggests that the fall in the proportion of

African American motorists searched is due instead to other factors a¤ecting

either u(c;r) and/or j (c;r).

5 Summary and Conclusions

Given the key role of statistical testing in detecting discrimination, it is im-

portant to know what assumptions on the behavior of motorists and troopers

are needed to justify the types of tests that are being applied. In this pa-

per, we develop a simple equilibrium model of law enforcement via tra¢c

stops and consider its implications for our ability to test for the presence

and nature of discrimination. We argue that tests for whether any sort of

discrimination occurs rely crucially on what sets of variables are considered

to be valid, nondiscriminatory variables that the police can use in stopping

cars and on whether those variables are available in the data.

However, our model shows that a test for whether discrimination, if it

occurred, is motivated purely out of e¢ciency considerations (statistical dis-

crimination) or for other reasons (prejudice) is less demanding in terms of

data requirements and only requires comparing the probability of being found

guilty of carrying contraband across various subgroups of the population. In

our model one race may be searched more often than another although at

20

Page 23

equilibrium both races have the same probability of carrying drugs. This is

true even when there is no taste for discrimination, so it is ironic that equal-

ity in the proportions guilty by race has been used in court as evidence that

police are racist.25

Our model showed that the disparities observed in the Maryland data

in terms of the proportions searched by race do not necessarily imply that

Maryland state police were motivated by racism. Our empirical …nding that

the probabilities of being found with drugs are equal across the two race

groups suggests that troopers were maximizing the e¤ectiveness of their drug

interdiction campaign, and that this was consistent with statistical discrim-

ination on the basis of race. The results do not, however, imply statistical

discrimination by our de…nition, because the police may also be conditioning

their decisions on other observable motorist characteristics not in our data.

Our …ndings for Hispanic males are consistent with a taste for discrimination

against this group, although the sample size for this group is modest.

Statistical discrimination, although e¢cient from a crime-…ghting per-

spective, may be considered unfair. This is because innocent drivers experi-

ence di¤erent probabilities of being searched depending on their race. Our

estimates suggest that e¢ciency, not fairness, is currently the main consider-

ation in drug interdiction. Achieving the fair outcome entails a cost in terms

of e¢ciency. We derived a simple expression for the cost of fairness in terms

of increased criminality, which could conceivably be estimated. Interestingly,

we observe a reduction over time in the proportion of African American mo-

torists stopped, which does not appear to be associated with a reduction

25>From a memorandum prepared by ACLU lawyers: “MSP’s own data demonstrates

that this racial distortion is unnecessary to successful drug interdiction. ...[Indeed,] MSP

data shows that statewide, police …nd contraband on black and white motorists at equal

rates. Blacks were found in possession of contraband in 28.4% of searches, whereas whites

were found with contraband 28.8% of the time.” Mertens and Jeon (1996).

21

Page 24

in e¢ciency. This suggests that the observed decline is not due to political

pressure on the police.

Although in this paper we focus on tra¢c searches, our analysis applies

more broadly to some other similar settings. Consider for example the behav-

ior of security and customs agents in airports, where it is alleged that minori-

ties and foreigners are unfairly targeted in baggage and passenger searches.26

The principles of our model can also be extended to analyze other instances

of discrimination, such as in employment or college admissions, where one

would need to clearly de…ne the nature of success, in analogy to that of guilt

in the current paper.

References

[1] Arrow, K. (1973) “The Theory of Discimination.” In Discrimination in

Labor Markets, O. Ashenfelter and A. Rees, eds., Princeton University

Press, Princeton NJ.

[2] Becker, G. (1957) The economics of discrimination, Chicago University

Press.

[3] Becker, G. (1968) “Crime and Punishment: An Economic Approach”

Journal of Political Economy, 76, p. 169-217.

[4] Border, Kim C; Sobel, Joel. (1987) “Samurai Accountant: A Theory

of Auditing and Plunder” Review of Economic Studies. Vol. 54 (4). p

525-40.

[5] Donohue, John (1999) Expert witness testimony in the case Chavez v.

Illinois State Police.

26See for instance Anderson v. Cornejo,

1999 (No. 97 C 7556).

22

Page 25

[6] Donohue, John and Levitt, Steven (1998): “The Impact of Race on

Policing, Arrest Patterns, and Crime” NBER Working Paper # W6784.

[7] Lambert, John (1996) Report in connection with the case Wilkins v.

Maryland State Police, Civil Action No. CCB-93-483.

[8] Mertens William J. and Deborah A. Jeon (1996) “Memorandum in sup-

port of plainti¤’s motion for enforcement of settlement agreement and

for further relief in the United States District Court for the District of

Maryland,” Wilkins at al. v. Maryland State Police. Civil Action No.

CCB-93-468

[9] Reinganum, J. and L. Wilde (1986) “Equilibrium Veri…cation and Re-

porting Policies in a Model of Tax Compliance” International Economic

Review, 27, p. 739-760.

[10] Scotchmer, Suzanne (1987) “Audit Classes and Tax Enforcement Policy”

American Economic Review. Vol. 77 (2). p 229-33.

[11] Stigler, G (1970) “The optimum enforcement of laws” Journal of Polit-

ical Economy, 78, p. 526-536.

[12] Todd (1996) “Empirical Methods for Evaluating the Impact of Inter-

ventions in Education and Training” Ph.D. Dissertation, University of

Chicago.

23

Page 26

A Puri…cation of Mixed Strategies

In this section we explain how the model’s mixed-strategy equilibrium is

consistent with a world in which motorists do not randomize over the decision

to carry drugs. A simple example is su¢cient to illustrate the idea. Consider

an agent who randomizes between actions a and b with Pr(a) = p. Utility

maximization implies that the agent is indi¤erent between the two actions,

u(a) = u(b). To purify this mixed strategy, we can imagine that the utility

from action a is really u(a) + X, where X is a random variable with the

property that Pr(X > 0) = p.27

If this is the case, the agent chooses a

with probability p, and is never indi¤erent between actions a and b. This

perturbed model is equivalent in tems of outcomes to the mixed strategy, but

the agent is never indi¤erent between the two actions and, as a consequence,

never ‡ips a coin.

In the context of our model, we can imagine of a class of individuals,

all with characteristics c;r. Let i denote a generic individual in that class,

and let i’s propensity to carry contraband be u(c;r) + Xi

c;rwhere Xi

c;ris

a random variable independent across all motorists in that class. We can

imagine that motorist i in class c;r knows his realized value xi

c;r. Then, given

a certain ° (c;r) motorist i carries contraband if and only if ° (c;r)[¡1] +

[1 ¡ ° (c;r)]

to zero we …nd a cuto¤ value xc;rsuch that a motorist carries contraband

h

u(c;r) + xi

c;r

i

> 0. Equating the left hand side of this inequality

if and only if xc;r> xc;r. This cuto¤ determines the fraction of individuals

in class c;r who carry contraband. Suppose that this fraction is higher than

in class c0;r0. Then policemen will never search an individual in class c0;r0,

so that ° (c0;r0) = 0. But then the cuto¤ in that class goes down, and the

equilibrating process equalizes the probabilities of carrying contraband across

27Notice that X may have small support, so that the two models may be quite close in

terms of primitives.

24

Page 27

classes.

25

Page 28

B A Model with Exogenous Guilt

If we had data on c an interesting exercise could be carried out. In the main

body of the paper we have assumed that motorists consider the probability

of being searched in deciding whether to carry illegal substances. Thus, the

probability that a motorist is found guilty if searched has been endogenous.

An alternative modeling assumption is that the probability that the motorist

carries contraband is exogenous, in that it does not depend on the probability

of being searched. This partial equilibrium approach transforms the problem

into one of optimal sampling. Under this assumption, a policeman takes as

given P (Gjc;r), the probability that a motorist with characteristic c and

race r is found guilty if searched. If we assume that P (Gjc;r) is increasing

in c then it is optimal for the policeman to choose two cuto¤s kW and kA,

so that if c exceeds these cuto¤s a person is searched. To set the cuto¤s

optimally the policeman solves

max

kW;kA

Z1

kW[P (Gjc;W) ¡ t]f (cjW)dc +

Z1

kA

[P (Gjc;A) ¡ t]f (cjA)dc:

The …rst order conditions are

[P (GjkW;W) ¡ t]f (kWjW)dc + [P (GjkA;A) ¡ t]f (kAjA) = 0;

whence the implicit condition

P (GjkW;W) = P (GjkA;A) = t:

(6)

Knowledge of c would allow us to build the entire schedule P (Gjc;r)

for all c greater than kr. The exogenous model predicts that this schedule

should be strictly increasing in c, while the endogenous model preditcs that

this schedule should be constant in c. Thus, knowledge of c would permit us

to determine which model seems to …t the data better. Notice that condition

(6) is expressed in terms of the probability of being guilty of the marginal

26

Page 29

motorist searched. To achieve a reliable estimate of this relationship one

would need a large number of observations.

27

Page 30

C Observable Indicators of Criminal Activity

Citizen’s band radios

Cellular telephones

Pre-paid phone cards

Tinted Windows

Radar Detectors

Perfumes

Duct tape

Pagers

Screws

Handles and knobs

Inability to completely roll down windows (which may hide concealment of drugs in the doors)

Religious paraphernalia used to divert suspicion

Police materials used in attempt to show support for law enforcement

High odometer mileage, particularly on late model vehicles

Switches and buttons, which may activate electronic compartment doors

Large amounts of cash

Attorney’s business cards

Too little or too much luggage for stated length of trip

Signs of recent drug use

Hiding places

Weapons

Only one key in ignition or no trunk key

Maps from source cities or states, map turned to locations other than those mentioned by occupants

Leased vehicles: ’Leased vehicles are used frequently by drug tra¢ckers. Many times these

vehicles are rented from airports. The person(s) authorized to drive the vehicle should

be noted on the least agreement.’

Third-party vehicles: ’Question when the owner of the vehicle is not at the scene of the stop or if

28

Page 31

the occupants cannot tell you the owner’s/lessee’s name without looking at the

registration or lease agreement themselves.

Cashier’s checks

Bondo

Source: Expert witness testimony by Professor John Donohue in ACLU v. State of Illinois. List from

Valkyrie police o¢cer manual (p. 13-15).

29

Page 32

Table 1

Means and Standard Deviations of Variables used in Analysis

(standard deviations in parentheses)

All

Obs

By Race By Sex

Black Hisp.WhiteOther FemaleMale

Black

0.63

(0.01)

1.00

(0.00)

0.00

(0.00)

0.00

(0.00)

0.00

(0.00)

0.64

(0.04)

0.63

(0.01)

White

0.29

(0.01)

0.00

(0.00)

0.00

(0.00)

1.00

(0.00)

0.00

(0.00)

0.35

(0.04)

0.29

(0.02)

Hispanic

0.06

(0.01)

0.00

(0.00)

1.00

(0.00)

0.00

(0.00)

0.00

(0.00)

0.00

(0.00)

0.07

(0.01)

Female

0.07

(0.01)

0.07

(0.008)

0.00

(0.00)

0.09

(0.01)

0.22

(0.09)

1.00

(0.00)

0.00

(0.00)

Guilty

0.33

(0.01)

0.35

(0.02)

0.12

(0.03)

0.32

(0.02)

0.47

(0.11)

0.38

(0.05)

0.32

(0.01)

Cocaine

0.08

(0.01)

0.10

(0.01)

0.03

(0.02)

0.03

(0.01)

0.37

(0.11)

0.09

(0.03)

0.08

(0.007)

Marijuana

0.23

(0.01)

0.23

(0.01)

0.23

(0.01)

0.26

(0.02)

0.41

(0.11)

0.21

(0.04)

0.23

(0.01)

Crack Cocaine

0.04

(0.005)

0.05

(0.01)

0.01

(0.01)

0.01

(0.004)

0.22

(0.09)

0.06

(0.02)

0.04

(0.005)

Heroine

0.02

(0.003)

0.02

(0.004)

0.03

(0.02)

0.03

(0.01)

0.22

(0.09)

0.06

(0.02)

0.02

(0.004)

Morphine

0.001

(.001)

0.00

(0.00)

0.00

(0.00)

0.002

(0.002)

0.00

(0.00)

0.00

(0.00)

0.001

(0.001)

Other Drugs

0.01

(0.002)

0.00

(0.00)

0.00

(0.00)

0.01

(0.005)

0.00

(0.00)

0.01

(0.01)

0.02

(0.003)

Paraphernalia

0.01

(0.002)

0.003

(0.002)

0.010

(0.010)

0.02

(0.006)

0.00

(0.00)

0.01

(0.01)

0.01

(0.002)

Night

(12am-6am)

Number of

Observations

0.43

(0.01)

0.46

(0.02)

0.44

(0.05)

0.35

(0.02)

0.51

(0.11)

0.47

(0.05)

0.43

(0.01)

1582100297 463201171465

30

Page 33

Table 2a

Proportion of Vehicles Searched Found with Drugs

by Race/Ethnicity

Not GuiltyGuilty

African American

White

Hispanic

0.66

0.68

0.87

0.34

0.32

0.11

Table 2b

Proportion of Vehicles Searched Found with Drugs

by Sex

Not GuiltyGuilty

male

female

0.68

0.64

0.32

0.36

Table 2c

Proportion of Vehicles Searched Found with Drugs

by Race/Ethnicity and Sex

Not Guilty Guilty

maleAfrican American

White

Hispanic

Other

0.66

0.67

0.89

0.68

0.34

0.33

0.11

0.32

female African American

White

Hispanic

Other

0.56

0.78

*

100.00

0.44

0.22

*

*

31

Page 34

Table 3

P-values on Pearson Chi-Squared Tests on

Hypothesis that Proportion Guilty is Equal Across Various Groups

Groups

! ! ! !2

p-value

race (African American,

Hispanic and white)

21.59<0.001

race (African American, White)

0.97 0.33

sex (male, female)

0.820.37

sex and race (African

American, Hispanic, white and

male, female)

26.97<0.001

sex and race (African

American, white and male or

female)

6.29 0.10

32

Page 35

Table B.1a

Proportion of Vehicles Searched Found with Drugs

by Race/Ethnicity

Period 1

Not

Guilty

Period 2

Not

Guilty

Period 3

Not

Guilty

Guilty Guilty Guilty

African American

White

Hispanic

0.66

0.72

0.88

0.34

0.28

0.12

0.62

0.71

0.87

0.38

0.29

0.13

0.69

0.64

0.91

0.31

0.36

9.00

Table B.1b

Proportion of Vehicles Searched Found with Drugs

by Sex

Period 1

Not

Guilty

Period 2

Not

Guilty

Period 3

Not

Guilty

GuiltyGuilty Guilty

male

female

0.68

0.63

0.32

0.37

0.67

0.64

0.33

0.36

0.69

0.65

0.31

0.35

Table B.1c

Proportion of Vehicles Searched Found with Drugs

by Race/Ethnicity and Sex

Period 1

Not

Guilty

0.66

0.73

0.88

0.70

Period 2

Not

Guilty

0.63

0.69

0.87

0.50

Period 3

Not

Guilty

0.71

0.62

0.91

0.80

GuiltyGuilty Guilty

maleAfrican American

White

Hispanic

Other

0.34

0.27

0.12

0.30

0.37

0.31

0.13

0.50

0.29

0.38

0.09

0.20

female African American

White

Hispanic

Other

0.64

0.56

n/a

100.00

0.36

0.44

n/a

0.00

0.52

0.00

n/a

n/a

0.47

100.00

n/a

n/a

0.48

0.79

n/a

n/a

0.52

0.21

n/a

n/a

33

Page 36

Table B.2

P-values on Pearson Chi-Squared Tests on

Hypothesis that Proportion Guilty is Equal Across Various Groups

Period 1

! ! ! !2

Period 2

! ! ! !2

Period 3

! ! ! !2

Groupsp-value p-valuep-value

race (African American,

Hispanic and white)

8.68 0.01 8.900.01 9.72 0.01

race (African American, White)

2.41 0.12 2.54 0.111.18 0.28

sex (male, female)

0.72250.40 0.110.74 0.200.66

sex and race (African

American, Hispanic, white and

male, female)

9.9481 0.0413.990.007 17.00 0.002

sex and race (African

American, white and male or

female)

3.66 0.307.470.06 8.27 0.04

34

Page 37

Table B.3

Parameter Estimates for Probit Model of Conditional Probability of being ‘Guilty’

Models without Covariates

(p-values from Hypothesis Tests shown in footnote)

VariableModel (1)(a)

Model (2) (b)

Model (3) (c)

Indicator for white-0.46

(0.06)

(-0.38

(0.04)

-1.16

(0.16)

-0.66

(0.13)

-0.32

(0.07)

-1.20

(0.32)

…

Indicator for black…

Indicator for Hispanic…

Indicator for white * time… 0.007

(0.004)

-0.003

(0.004)

0.002

(0.011)

…

…

Indicator for black * time……

Indicator for Hispanic * time……

indicator for white * period 1… -0.58

(0.11)

-0.53

(0.13)

-0.34

(0.09)

-0.39

(0.05)

-0.27

(0.09)

-0.45

(0.09)

-1.17

(0.28)

-1.13

(0.29)

-1.17

(0.28)

indicator for white * period 2……

indicator for white * period 3……

indicator for black * period 1……

indicator for black * period 2……

indicator for black * period 3……

indicator for Hispanic * period 1……

indicator for Hispanic * period 2……

indicator for Hispanic * period 3……

(a) P-value from test of hypothesis white=black=Hispanic is 0.0001. P-value from test that

white=black is 0.2523.

(b) P-value from test of hypothesis black=white=Hispanic for both intercept and time trend is

0.0001. P-value from test that black=white for both intercept and time trend is 0.0530.

(c) P-value from test of hypothesis that black=white=Hispanic within all time periods is 0.0007. P-

value from test that black=white for all time periods is 0.2266.

35

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19951996 19971998 1999

0.0

0.2

0.4

0.6

0.8

1.0

Proportion of Drivers Searched who are African Americ

1995 1996 1997 19981999

0.0

0.2

0.4

0.6

0.8

1.0

Proportion of Drivers Searched who are White

19951996 19971998 1999

0.0

0.1

0.2

0.3

0.4

0.5

Proportion of Drivers Searched who are Female

Figure 1

36

Page 39

proportion

199519961997 1998 1999

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Proportion of African American Drivers Found with Dru

proportion

199519961997 1998 1999

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Proportion of White Drivers Found with Drugs

Figure 2

37

Page 40

1995:1 1995:7 1996:1 1996:7 1997:1 1997:7 1998:1 1998:7 1999:1

Month

0

20

40

60

80

Cars Searched

Number of Cars Searched by Maryland Troopers on I-95

Figure 3

38