Nicola Persico and Petra E. Todd
“Passenger Profiling, Imperfect Screening, and Airport Security ”
PIER Working Paper 05-005
Penn Institute for Economic Research
Department of Economics
University of Pennsylvania
3718 Locust Walk
Philadelphia, PA 19104-6297
Passenger Pro…ling, Imperfect Screening, and
Nicola Persico* and Petra E. Todd*
January 12, 2005
We present a theoretical model of airport searches. The model ex-
tends previous work in the area in that detection conditional on search
is imperfect. The hit rates tests for racial bias developed in Knowles,
Persico, and Todd (2001) is shown to apply even in the presence of
imperfections in monitoring. We then study two channels for improv-
ing airport security: better targeting and better detection. We show
that better targeting does not necessarily decrease the overall crime
rate, although it will decrease crime in the group that is targeted. Im-
proved detection rates unambiguously decrease crime. Group-speci…c
improvements in detection do not necessarily increase the number of
searches for those groups. The analysis is extended to allow for the
possibility that criminal passengers disguise themselves as members of
JEL Numbers: J70, K42
Keywords: Racial Pro…ling, Crime, Police, Airport, Terrorism.
The need for greater airport security has recently led to major changes in
passenger screening procedures. One important change is the development
of a Computer Assisted Passenger Pre-Screening System (CAPPS II), a tool
to select passengers for screening which is currently being considered for im-
plementation. When boarding cards are issued, CAPPS con…rms passengers’
identities, performs criminal and credit checks, and retrieves additional in-
formation, such as residence, home ownership, income, and patterns of travel
and purchases, used to construct a predicted threat rating.1Passengers with
elevated ratings are subject to searches and baggage inspections and may be
questioned. Some other passengers are searched at random. Such pro…ling
measures have been challenged in lawsuits alleging unlawful discrimination.2
A second change in airport security has been an e¤ort to select higher ability
screeners and to improve their training (see e.g. U.S. General Accounting
We analyze the implications of these changes for search rates and crime
rates within an extended version of a model of police and criminal behavior
previously introduced in John Knowles et al. (2001) (henceforth KPT). In
KPT, police decide which vehicles to search and motorists decide whether
to carry contraband. Absent racial bias, o¢cers maximize the number of
successful searches, de…ned as uncovering contraband such as drugs or illegal
weapons. Racial bias is modeled as a reduction in the perceived cost of
searching vehicles of certain types of drivers. An implication of biased
monitoring is that the equilibrium rate at which contraband is seized (the
hit rate) is lower for the groups subject to bias.
The KPT model is not directly applicable due to several di¤erences be-
tween the airport screening process and the motor vehicle search process.
First, the model assumes that screeners know the guilty rates of di¤erent
identi…able groups when allocating their searches.This assumption may
be inappropriate when screeners rarely apprehend violators, and so may not
learn the groups’ guilty rates. CAPPS can be viewed as a way of aggre-
gating information across airports to facilitate learning. A related problem
occurs when screeners cannot easily identify distinct groups of passengers.
CAPPS reveals information that screeners may otherwise not discern. How-
ever, CAPPS does not does not completely obviate the need for screener
ability, because characteristics such as nervousness, or hidden contraband,
are only detected by a perceptive screener. In fact, searches do not always
detect violations; there is reportedly a 24% error rate in detecting weapons
in baggage screening (see Attkisson 2002).
We extend the KPT model to incorporate the screeners’ limited ability
to discern groups and to detect violations. We show that the “hit rates”
test for racial bias developed in KPT extends to this more realistic case. We
then analyze two channels through which airport security might be improved.
The …rst is better targeting of searches through improved capacity to distin-
guish groups. The second is an increase in the detection rate conditional on
targeting. Additionally, we consider monitoring strategies when passengers
can disguise themselves as other types.
I. The Model. Below, we present an extension of the KPT model that
incorporates imperfections in monitoring. There are two groups of passen-
gers, groups 1 and 2, with equal mass of 1. There is a measure S of screeners,
each of whom only searches one passenger. Screeners can distinguish whether
a passenger belongs to group 1 or 2, but cannot distinguish passengers within
A member of group i derives value v from committing a crime (regardless
of whether he is found out), which is private information and passenger-
speci…c; v is distributed according to a cdf Fi; with a density fi that is
bounded above zero on its support.
A passenger who commits a crime and is searched is detected with prob-
ability di. High values of dimean that, in their searches, screeners are good
at detecting criminals. This feature extends the KPT model, which assumed
di= 1 for all i.
A criminal is apprehended only when he is searched and detected, in
which case he incurs a loss li. The expected bene…t from not committing a
crime is zero. Passengers su¤er a cost kifrom being searched.
Each screener chooses which group to search to maximize his/her ex-
pected utility from searching. Screeners receive a utility of ? ? 1 from
apprehending a member of group 1, and of 1 from apprehending a member
of group 2. When the parameter ? exceeds 1, we say that the screeners are
biased against group 1. The assumption of hit rates maximization agrees
with the behavior described in Anderson v. Cornejo. Jan Eeckhout et al.
(2004) investigate di¤erent objective functions.
II. Analysis. A passenger of group i with value v has an expected utility
of committing a crime equal to
v ? si(dili+ ki);
where sidenotes the mass of searches devoted to group i: The passenger will
commit a crime whenever this quantity exceeds the expected utility of not
committing a crime, which is ?siki. Thus, the fraction of criminals in group
i is 1?Fi(sidili): The hit rate, i.e., the probability that a search of a member
of group i is successful, is
Hi(si;di) = di[1 ? Fi(sidili)]:
The hit rate in group 1 is a decreasing function of s1, while the hit rate in
group 2 is a decreasing function of s2= S?s1. Figure 1 depicts the hit rates
as functions of s1.
INSERT FIGURE HERE
In equilibrium, screeners must receive the same expected utility from
searching either group. Otherwise, screeners would only search the group in
which that probability is highest, which cannot be an equilibrium because
then all passengers of the other group would commit a crime. Denoting equi-
librium search intensities with a superscript ?, if both groups are searched it
S ? s?
If ? = 1, i.e., there is no bias, the equilibrium is achieved at s?
1. If ? > 1 the
equilibrium is achieved at the point s?
1further to the right. The disparity
between the equilibrium hit rates, depicted by the dashed thick line, re‡ects
the size of the bias. Thus, we have the …rst proposition.
Proposition 1 There is bias against group 1 if and only if the hit rate is
lower in group 1 than in group 2.
This proposition demonstrates the applicability of the KPT “hit rates”
test to infer bias to an environment with imperfect detectability.3Inferring
bias is key to establishing racial discrimination in airport screening. This is
because, unlike employment cases which usually fall under Title VII of the
Civil Rights act, policing situations are typically covered under Title VI or
under the Fourteenth Amendment, whereby plainti¤s must show not only
disparate impact but also intent to discriminate. Judge Easterbrook follows
a “hit rates” analysis in Anderson (See David A. Castleman and Persico
In what follows we will assume, to …x ideas, that s?
1> S=2 > s?
that group 1 is searched disproportionately more in equilibrium.
III. E¤ect of CAPPS.
Systems like CAPPS channel background
information to the screener than he/she cannot otherwise see. To the ex-
tent that the statistical model that underlies CAPSS can predict criminal-
ity, the CAPSS system allows the targeting of searches towards groups with
higher levels of criminality. The trade-o¤s entailed by such a program can
be seen in Figure 1. Suppose that, absent a system like CAPPS, screen-
ers cannot distinguish between passengers in groups 1 and 2 and so search
both groups with the same intensity S=2: Then, the aggregate crime rate
2[H1(S=2;d1) + H2(S=2;d2)], a level indicated by the dash in Figure 1.
Theoretically, this crime rate may be higher or lower relative to the level that
obtains when screeners can distinguish between the two groups. Whether it
is higher or lower depends on the shape of the curves H1 and H2. If the
curve H1is very ‡at, for example, eliminating a CAPPS-like system will not
appreciably increase crime in group 1. That is, removing the capability of
distinguishing groups can in fact decrease aggregate crime. (On this perhaps
surprising point, see Persico, 2000, and Bernard E. Harcourt, 2004).
With regard to airport searches, we conjecture that dispensing with CAPPS
would increase the crime rate because, at least in customs searches, random
searches appear much less likely than directed searches to uncover contraband
(about six times less likely: see Table 7 in U.S. General Accounting O¢ce
2000). It seems improbable that the deterrent e¤ect of searching groups that
are so much less likely to commit a crime at a higher rate would more than
make up for the decreased deterrence in high-crime groups.
IV. Group-Speci…c Improvements in Detection Ability. Consider
a situation in which a search constitutes a cursory pat-down and a few ques-
tions. Suppose that in this process, a criminal passenger of group i gives
o¤ a signal which the screener is able to detect with probability di. If the
signal is detected, the screener engages in a more extensive investigation and
discovers that the individual is guilty. If the signal is not detected, either
because the screener missed it or because the individual is innocent and so
did not emit the signal, the individual is waved through.
Within this simple model, di captures the screener’s ability to pick up
subtle clues. We are interested in the e¤ect of increasing d1on the equilib-
rium search intensity of group 1. The latter decreases if the curve H1shifts
downward (refer to Figure 1). That curve shifts downwards if
= ? ? [1 ? F1(s1d1l1) ? s1d1l1f1(s1d1l1)]
is negative. The sign of this expression depends on two countervailing e¤ects.
On the one hand, searches of passengers of group 1 become more successful
and, therefore, the hit rate on group 1 increases. On the other hand, potential
criminals learn that screeners are better at detecting them and are therefore
deterred. The latter e¤ect reduces the hit rate. The …rst e¤ect is negligible
when 1?F1is close to zero, that is, when almost everyone is honest. In that
case, expression (2) is negative (recall that fiis bounded above zero). This
proves the following result.
Proposition 2 Suppose a su¢ciently large fraction of the population is hon-
est. Then, regardless of bias, an increase in the screener’s ability to detect
criminals in group 1 results in fewer searches of that group and increased
expected utility for honest members of that group.
V. Group-Neutral Improvements in Detection Ability. Consider
a situation in which a search represents the cursory examination of hand
luggage. Let d be the probability that the screener detects any weapons or
other contraband. In this setting, it is natural to assume that d1? d2? d,
that is, detection ability is group-neutral. A high d screener is very competent
in screening all luggage.
The equilibrium condition is given by equation (1). We are interested in
the e¤ect of an increase in d on the proportion of group 1 passengers searched.
A marginal increase in d shifts down both curves H1and H2. The proportion
of group 1 passengers searched increases if and only if
>@H2((S ? s1);d)
The left hand side of this equation is expressed in equation (2); there is
an analogous expression for the right hand side. Whether the inequality is
satis…ed depends on details of the model, such as the functions fiand the
values of li, which are unlikely to be observable. In the absence of such
information, we cannot tell whether the inequality is satis…ed and, therefore,
whether an increase in d increases the proportion of members of group 1 who
are searched. We conclude that there is no reason to believe that increasing
the general competence of screeners in the sense described above would result
in fewer searches of group 1 members.
VI. Extension: Endogenous Characteristics. A group 1 passenger
bent on committing a crime may …nd it expedient to disguise himself as, or
delegate the crime to, a member of another group which is apprehended with
a lower probability. We augment the model by allowing members of group
1 to, at a cost ?, hire an agent in group 2 to whom the crime is delegated.
We assume that the agent would not have otherwise committed the crime,
and that ? is su¢ciently large to induce the agent to commit the crime. A
group 2 agent is searched with intensity s2and detected with probability d2.
However, if the agent is detected, the principal su¤ers l1. A criminal group
1 passenger delegates only if the expected utility from doing so exceeds that
of committing the crime himself, i.e., if
v ? s1d1l1< v ? s2d2l1? ?:
Clearly, there is delegation in equilibrium only if ? is su¢ciently small.
We assume that ? is distributed in the population according to a cdf G
independent of v. For each value of s1and s2, then, the fraction of group 1
members who commit a crime and do not delegate is
[1 ? F1(s1d1l1)] ? [1 ? G(l1(s1d1? s2d2))];
and the fraction of group 2 members who commit a crime (delegated or not)
[1 ? F2(s2d2l2)] + G(l1(s1d1? s2d2)) ? [1 ? F1(s2d2l1)]:
Based on these crime rates, the hit rates in the groups 1 and 2 are, respec-
H1(s1;s2;d1;d2) = H1(s1;d1) ? [1 ? G(l1(s1d1? s2d2))]
H2(s1;s2;d1;d2) = H2(s2;d2) + d2? G(l1(s1d1? s2d2)) ? [1 ? F1(s2d2l1)]:
It can be veri…ed that Hi is decreasing in si and increasing in sj. Thus,
plotting the two curves as a function of s1yields a similar picture to Figure
1. When the crime rates in the two groups are small, then
@d1H1(s1;s2;d1;d2) ? ?s1d1l1f1(s1d1l1) ? [1 ? G(l1(s1d1? s2d2))]
@d1H2(s1;s2;d1;d2) ? 0:
In equilibrium, [1 ? G(l1(s1d1? s2d2))] cannot be smaller than d2=(?d1), for
otherwise the expected utility from searching group 2 would exceed that from
group 1, which cannot happen in equilibrium. This implies that
0. Thus, as we increase d1by a small amount, the curve H1shifts down while
the curve H2does not shift, as a …rst approximation. Therefore, Proposition
2 continues to hold in the case where characteristics are endogenous.
VII. Implications for Improving Airport Security. In this paper,
we study two channels for improving airport security: better targeting and
better detection. Better targeting does not necessarily decrease the overall
crime rate, although it will decrease crime in the group that is targeted.
Targeting systems such as CAPPS have been controversial from a civil lib-
erties perspective. This paper shows that hit rates tests for racial bias can
be applied even in the presence of imperfections in monitoring. Such tests
can serve as a check on whether, e¤ectively, CAPPS introduces racial/ethnic
bias in searching.
We also found that improved detection rates unambiguously decrease
crime. In exploring this second channel, we showed that group-speci…c im-
provements in detection do not necessarily increase the number of searches for
those groups. This suggests that improving cultural sensitivity of screeners
should help not only in improving detection but also in reducing the burden
of searches on innocent members of high crime groups.
* Nicola Persico and Petra E. Todd are Associate Professors of Eco-
nomics at the University of Pennsylvania. Their address is 3718 Locust
Walk, Philadelphia, PA 19104. Partial support from the NSF is gratefully
1. CAPPS II was authorized by Congress in 2004 as part of the Trans-
portation Safety Administration (TSA) Enabling Act. The precise al-
gorithms and criteria used to calculate threat levels are classi…ed.
2. See Green v. TSA, Case No. C04-763 Z, (W.D. Wash., …led 2004); see
also Anderson v. Cornejo, 355 F.3d 1021 (7th Cir. 2004).
3. The result generalizes to the case of n > 2 groups. Knowles and Ruben
Hernandez-Murillo (2004), and Nicola Persico and Petra Todd (2004),
apply the hit rates test to other environments. Shamena Anwar and
Hanming Fang (2004) develop a di¤erent test.
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