GARP Among Thieves

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An experimental test of criminal behavior among juveniles andyoung adults: GARP among thieves

Michael S. VisserUniversity of Oregon

Eugene, OR [email protected]

Bill HarbaughUniversity of Oregon and NBER

Eugene, OR [email protected]

Naci MocanUniversity of Colorado at Denver and NBER

Campus Box 181, P.O. Box 173364Denver CO 80217-3364

[email protected]

October, 2004(draft, please do not cite)

JEL classifications: K42, D10, C90

Abstract: Gary Becker's (1968) model of rational criminal behavior forms the basis ofhow economists think about crime. In this paper we report results from economicexperiments that provide a direct test of the primary hypothesis of this model: thatcriminal behavior responds rationally to changes in the possible rewards and in theprobability and severity of punishment. We find that the data are generally consistentwith revealed preference axioms, monotonic choice, and the law of demand. These

results strengthen the argument that criminal behavior, and the response of criminals tochanges in enforcement and penalties, can be accounted for by economic models.

Acknowledgements: We would like to thank the students, teachers, and administratorsof South Eugene High School for their assistance, without which this research wouldnot have been possible. This research was supported by a grant from the NSF.


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An experimental test of criminal behavior among juveniles andyoung adults: GARP among thieves

I. Introduction

Since the seminal paper of Becker (1968), which created the foundation for the

economic analysis of criminal behavior, economists have extended the basic theoretical

framework (e.g. Ehrlich 1973, Block and Heineke 1975, Schmidt and Witte 1984, Flinn

1986, Lochner 2004, Mocan et al., forthcoming). The original framework, as well as its

more recent variants, postulate that participation in crime is the result of an optimizing

individuals response to incentives such as the expected payoffs from criminal activity,

and costs such as the probability of apprehension and the severity of punishment.

Although early empirical research reported evidence suggesting that enhanced

deterrence reduces crime (Ehrlich 1975, Witte 1980, Layson 1985), other papers found no

significant evidence of deterrence (Myers 1983, Cornwell and Trumbull 1994). The

main challenge in empirical analysis has been to tackle the simultaneity between

criminal activity and deterrence. Specifically, an increase in criminal activity is

expected to prompt an increase in the certainty and severity of punishment (e.g. an

increase in the arrest rate and/or police effort), which makes it difficult to identify the

causal impact of deterrence on crime. Three types of strategies have been used to

overcome the simultaneity problem. The first solution is to find a good instrument

which is correlated with deterrence measures but uncorrelated with crime. Examples


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are Levitt (1997) which uses electoral cycles as an instrument for police hiring and

Levitt (2002) which uses the number of per capita municipal firefighters as an

instrument for police effort. The second strategy is to use high-frequency time-series

data. For example, in monthly data, an increase in police effort in a given month will

affect criminal activity in the same month, but an increase in crime is much less likely to

alter the size of the police force in that same month, because of the much longer lag

between a policy decision to increase the ranks and the actual deployment of police

officers on the street. This identification strategy has been employed by Corman and

Mocan (forthcoming) and Corman and Mocan (2000). The third strategy is to find a

natural experiment which generates a truly exogenous variation in deterrence, as in Di

Tella and Schargrodsky (2004) who use the increase in police protection around Jewish

institutions in Buenos Aires after a terrorist attack to identify the impact of police

presence on car thefts.

Although these empirical strategies have permitted researchers to refine and

improve upon earlier estimates, a convincing natural experiment is very difficult to

find. The validity of any instrumental variable can always be questioned, and one can

argue that if policy makers have perfect foresight about future crime, monthly data

would also suffer from simultaneity. One can also argue that unobservable effort by the

existing complement of police officers might respond quickly to changes in crime rates

even if hiring does not.

One application of Beckers model that has received a great deal of attention

concerns tax compliance. By noting that tax compliance is a problem of law


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enforcement, we can see that the regulatory agency is faced with a tradeoff between

compliance and costly enforcement. Beckers model can aid these regulatory agencies

in optimally solving this problem by informing decision makers about the different

deterrent effects associated with penalties and the probability of detection.

Theoretical models of tax compliance and enforcement follow Becker (1968) and

model agents as expected utility maximizers. Early examples include Allingham and

Sandmo (1972) and Srinivisan (1973). A central prediction of these models is a negative

correlation between tax rates and compliance, and a positive correlation between

income and compliance.

Empirical tests of these predictions, however, have been sparse and somewhat

inconclusive, since any data clearly suffers from the same general simultaneity problem

outlined above. Feinstein (1991) pools data from the 1982 and 1985 IRS Taxpayer

Compliance Measurement Program in an effort to better identify the effects of tax rate

changes and income on compliance. However, the results from the pooled study

suggest a positive relationship between tax rates and compliance and no relationship

between income and compliance.

A battery of laboratory experiments have also been applied to the problem of tax

compliance. Generally speaking, experimental studies find that greater tax rates are

associated with lower compliance levels (see for example Friedland, Maital, and

Rutenberg 1978; Alm, Jackson, and McKee 1992; and Baldry 1987). Clark, Friesen, and

Muller (2004) design an experiment to analyze the tradeoffs between two different

conditional audit rules and the simple random audit rule. As expected, they find that


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the simple audit rule maximizes compliance relative to the conditional audit rules, but

is also the most costly to implement of the three audit rules. Boylan and Sprinkle (2001)

conduct an experiment designed to determine whether the manner in which income is

obtained affects the relation between tax rates and taxpayer compliance. They find that

when income is earned (versus endowed), compliance rates increase when agents face a

tax rate increase, and that the opposite is true when income is endowed. They conclude

that income is not a fungible commodity, meaning that money earned is valued

differently than is money endowed.

Each of these studies describes behavior of optimizing agents responding

rationally to the incentives put before them. While this vein of research provides some

guidance for tax compliance authorities, the results have not been generalized to

accommodate other types of criminal behavior, such as auto theft, embezzlement, and

petty larceny.

In this paper, we use a laboratory experiment to collect data on responses to

unambiguously exogenous changes in the rewards and penalties pertaining to criminal

behavior. The experiments involve decisions about actions that can best be described as

petty larceny, and are done using high school students and real money. We use a

straightforward protocol for collecting choice data that can be used to test Beckers

modeldirectly. The protocol involves collecting data on (nearly) simultaneous choices

under a variety of different budget constraints. We use these to check whether peoples

choices about their criminal behavior change rationally in response to changes in the

probability of detection and changes in the size of the fine assessed.


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The data are first used to check for transitivity violations. Transitivity would

indicate that choices over the goods can be modeled as the result of constrained utility

maximization. This provides a direct test of Beckers model, which assumes rational

choice by criminals. Next, we estimate demand functions. Interestingly, Becker (1962)

points out that rational choice is not necessary for choices to satisfy the laws of demand.

More fundamentally, aggregate choices may obey the laws of demand even if some

individual choices are inconsistent with utility maximization. Therefore, we expect to

be able to provide results about these tradeoffs even if choices occasionally, or even

frequently, violate the Generalized Axiom of Revealed Preference (GARP).

Section II of this paper offers a discussion of the relevant literatures, including

Beckers model of crime and punishment, revealed preference theory, and the

experimental methods for testing it. We then describe our experiment and subjects, and

analyze our data for consistency with GARP. Next we estimate demand functions for

the amount of loot stolen. A discussion section concludes.

II. Literature

II. a. Beckers model of crime and punishment

Just as the typical consumer has preferences for food, entertainment, and leisure,

the rational criminal has preferences for stolen loot, the probability of being caught, and

the penalty associated with being caught. It is at least plausible that a criminal would

be willing to forgo some of the loot in order to reduce the probability of being caught or

the penalty associated with it. In a like manner, a criminal might be willing to take


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great risk only if the payoff is large enough. There is nothing irrational about this kind

of behavior. The agent makes a cost-benefit calculation according to her own

preferences.

While we cannot observe a criminals utility function directly, we can test

Beckers hypothesis of rationality with tests of revealed preference, using observations

of agents different choices under different budget constraints. In the next section we

review the relevant theory and some tests of it.

II. b. Revealed preference theory

The revealed preference approach to consumer behavior involves determining

what restrictions on choice behavior are imposed by assuming people chose rationally.

Integrability proofs are then used to show that choice data which are consistent with the

these restrictions are also consistent with maximization of a well-behaved classical

utility function, and vice versa.

Paul Samuelson (1938a,b) provided the first empirically useful characterization

of consumer behavior based on the observation of consumer choices. This redirection

of consumer theory advanced the view that, since preferences are unobservable, utility

theory was not falsifiable. (Samuelson, 1938a; p. 61):

The discrediting of utility as a psychological concept robbed it of its onlypossible virtue as an explanation of human behaviour in other than a circularsense, revealing its emptiness as even a construction.


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Samuelson proposed an alternative view of consumer behavior, treating

consumer choice, as fundamental, instead of relying on innately unobservable

assumptions about preferences. The behavioral restrictions that Samuelson proposed

are now known as theWeak Axiom of Revealed Preference (WARP). Using the

notation of Varian (1992), these restrictions can be stated as follows:

.tDsstsDt xRxthatcasethenotisitthen,xtonot equalisxandxRxIf

Where st xx and are consumption vectors, and DR is read is directly revealed preferred

to. In words, WARP says that if bundle tx is selected when both tx and sx are

available, then sx cannot be selected when both tx and sx are available. This does not

rule out the case where the consumer does not optimize nor does it rule out the case of

indifference, but it is no more restrictive than the conventional utility maximizing

hypothesis. In addition, it provides economists with an empirically tractable way to test

the rationality postulate without needing to know the structure of the underlying

preferences.

It is important to note that WARP is only applicable to directly revealed

preferences; that is, transitivity of preferences cannot be extended to bundles not

directly compared to each other by the consumer. For example, if A is directly revealed

preferred to B when A and B are available, and also B is directly revealed preferred to C

when B and C are available, one cannot conclude simply by relying on WARP that A

will be revealed preferred to C when only A and C are available.


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Samuelson (1948) contains a proof showing that, by varying the relative price

and income values that a consumer faces, and applying WARP, we can map out an

indifference curve that would be generated by the constrained maximization of the

consumers utility function: utility maximization implies the satisfaction of WARP.

xRxxuxuDtt

)()(

This effectively keeps utility theory from being obsolete. However, it is still possible to

find consumer choice data which satisfy WARP, but are not capable of being generated

by a rational preference relation.

H. S. Houthakker (1950) strengthened WARP to account for indirectly revealed

preferences. His Strong Axiom of Revealed Preference (SARP) requires transitivity of

preference, and is stated as follows:

.Rxxthatcasethenotisitthen,xtonot equalisxandRxxIftsstst

R is the transitive closure of DR , and is read is revealed preferred to. SARP implies

WARP.

Houthakker is also responsible for showing that choice data satisfying SARP

necessarily imply the existence of a well-behaved utility function, and that these data

can be generated by structurally derived demand functions corresponding to that utility

function. When combined with Samuelson (1948), produces the following result:

)()( xuxuxRxRxx tDtt .


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This was an important insight, but still only a necessary condition for choice data

to be consistent with utility maximization. Houthakker also takes pains to point out in

his discussion that Samuelsons revealed preference approach was originally conceived

as a substitute for utility theory, but that it has instead evolved to be rather

complementary.1

Sidney N. Afriat (1967) presented a theorem proving the sufficiency of SARP for

utility maximization, thus completing the ingredients need for a solution to the

integrability problem. Now we have an empirically useful and coherent description of

consumer behavior, which can be linked to the existence of a well-behaved utility

function. In other words, we can observe consumer choice, and as long as it is

consistent with SARP, we know that there exists some well-behaved utility function

that, when maximized, could have generated the choices we observe.

Varian (1982) provides a generalization of WARP and SARP. The Generalized

Axiom of Revealed Preference (GARP) can be stated as:

.xpxpimpliesRxxwords,otherIn.xPxnotimpliesRxx tssssttDsst

DP is read is strictly directly revealed preferred to. WARP and SARP each require

that the demanded bundle be unique, while GARP allows for more than one demanded

1 Samuelsons treatment of traditional utility theory in his Foundations (1947) can be taken as evidence ofhis acceptance of this reconciliation.


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bundle. The following restatement of Afriats theorem in terms of GARP is given in

Varian (1992), p. 133-4.

Afriats theorem. Let ( )tt xp , for Tt ,...,1= be a finite number of observationsof price vectors and consumption bundles. Then the following conditions areequivalent.

(1) There exists a locally nonsatiated utility function that rationalizes the data;

(2) The data satisfy GARP;

(3) There exist positive numbers ( ) Ttu tt ,...,1for, = that satisfy the Afriatinequalities:

( ) s;t,allforxxpuu tsttts +

(4) There exists a locally nonsatiated, continuous, concave, monotonic utilityfunction that rationalizes the data.

Varian provides an algorithm for use in testing choice data for consistency with

revealed preference axioms. The results from the evolution of revealed preference

theory are significant in that they continue Samuelsons tradition of providing

empirically useful tools that can be applied to consumer theory.

Prior to revealed preference theory, utility maximization was an un-testable

assumption of neoclassical economics. Now we can search for evidence in support of

utility maximization via the axioms of revealed preference; we simply need some

empirical choice data. Once we have verified that choice data satisfy GARP, we can

estimate demand functions, which need not be structurally derived from any particular

utility function.


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II. c. Empirical tests of revealed preference theory

Finding suitable choice data for testing whether choices obey the revealed

preference axioms is not as straightforward as it would at first appear. The application

of revealed preference axioms require consistency of preferences; that is, the underlying

preferences must remain unchanged. If we observe choices over time but ignore this

consistency requirement, we might find that the data appear not to obey revealed

preference theory and conclude that our consumer is irrational. However, we cannot

rule out the possibility that preferences have simply changed over the duration of our

sampling period. Since we cannot observe the underlying preferences these two

explanations are observationally equivalent in any set of choice data that has been

collected over time. As a result of this hurdle, most empirical research applying

revealed preference axioms has consisted of either field or laboratory experiments.

Koo (1963), Mossin (1972), and Mattei (1994) are exceptions. Each of these

studies employs a household expenditure survey. Households participating in the

surveys are asked to write down their weekly purchases of consumption goods,

aggregated up into categories. In general, these data are found to be inconsistent with

the axioms of revealed preference.

However, as previously asserted, there is no reason to believe that the

preferences of these households have not evolved over time, thereby confounding the

search for evidence of revealed preference. In addition, it is possible that households

may not truthfully report their actual behavior in a survey, since there is no clear

incentive for them to do so. In fact, there is evidence that many households consistently


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underreport their purchases of consumption goods, and also that recall about price

information is incomplete.

Experiments allow researchers to directly control and observe prices and

incomes, to control the environment wherein agents interact, and to provide sufficient

incentives for agents to make choices consistent with their true preferences. These

experiments are likely to produce significantly improved choice data compared to the

surveys above. There are a small number of experiments which examine consumption

bundles for consistency with the revealed preference axioms.

Battalio, et al. (1973) observe purchases in a field experiment conducted in a

psychiatric hospital. The experimenters controlled a token economy where various

sundries and snacks were sold to patients, who paid using tokens which they earned by

performing various tasks. The experimenters imposed large price changes every few

weeks, and found that around half of the subjects made choices that violated SARP.

However, the authors point to errors in the data collection that might explain nearly all

of these inconsistencies. In a reanalysis of these data, Cox (1997) suggests that, given

the nature of the token economy, leisure is also in the consumption bundle. When

including leisure as a good, Cox finds that approximately half of the subjects have at

least one violation, even when accounting for the data collection errors. The experiment

also lacked good control, because patients had alternate sources of their goods,

including family and another store selling similar items outside the hospital, and

because preferences could change during the course of the experiment.


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Sippel (1997) is the first example of a properly controlled laboratory experiment

applying revealed preference axioms to consumption data. Subjects were asked to

spend one hour in the laboratory, one at a time. While in the laboratory, the subject

could consume only goods purchased from the experimenter, so the opportunity cost of

consumption was essentially zero. Subjects were asked to choose among several snacks

and time-passing goods, and to pay for them using an endowment of an artificial

currency. Choices were made almost simultaneously, and the strategy method was

employed, so that one choice was chosen randomly and then implemented.2 Price

vectors were structured so as not to resemble any of the real price vectors one might

face in local stores, in an attempt to avoid framing effects: a price might be interpreted

as a signal of value, and thus bias choices.

In each of two treatments nearly half or more subjects had at least one WARP,

SARP, and/or GARP violation. The number of violations per subject was quite low,

however. For example, the maximum number of GARP violations possible was 45 and

the median number of GARP violations was 1.3 The demand analysis also supports the

view that subjects do not choose randomly, and typically behave according to

neoclassical predictions.

2 The strategy method involves multiple rounds of the same game, where the experimenter will randomly

choose only one (or perhaps a strict subset) of the rounds to calculate the subjects earnings. In this case,the strategy method provides an incentive for subjects to treat each round as a single play of the game,and maximize expected utility over the entire random lottery. This may actually mitigate against theproblem of changing or evolving preferences during the experiment. The strategy method is a commonprocedure in many experimental settings.

3 This is the number of violations reported in Sippel (1997). As noted previously, it is impossible to haveexactly one revealed preference violation, so it must be the case that Sippel (1997) counts the number ofviolations differently than we do.


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Harbaugh, Krause, and Berry (2001) apply the revealed preference test in a series

of consumption games on children of varied ages (about 7 and 11 years old) and on

undergraduates (about 21 years old). Children and undergraduates were offered

choices among eleven different choice sets, each bundle consisting of a number of small

bags of chips and boxes of juice. Choice sets were constructed using implicit price and

income vectors which form overlapping budget sets. GARP typically assumes that

preferences are locally non-satiated, but since subjects in this experiment made discrete

choices this requirement must be strengthened to one of strongly monotone preferences

to maintain the validity of the transitivity test. The strategy method was employed.

Harbaugh et al. found that nearly half to three quarters of subjects exhibited at

least one violation, though the average number of violations again tended to be

relatively small. On average, even for the youngest children, there were significantly

fewer (4.3) transitivity violations than would be expected under random choice

(uniform 8.91, bootstrapping 8.29). Under the uniform random choice, each bundle was

randomly selected with equal probability. Under the bootstrap random choice, each

bundle was given a weight proportional to its frequency in the actual choices made by

the experiment subjects. The average number of violations decreased in older children

(2.1), but there as no significant difference between 11 year olds and undergraduates

(2.0). While the authors discouraged generalization from their experiment, it does

provide persuasive evidence that even children may be rational utility maximizers, at

least with respect to relatively familiar consumption goods.


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Harbaugh et al. also looked at whether children with different assessed levels of

mathematical ability are better at choosing. They acquired student scores for a required

standardized test on the 11 year olds in their sample (administered when these students

were 10 year olds). Using the choice data, Harbaugh et al. also calculated Afriats

Critical Cost Efficiency Index, which measures the costliness of revealed preference

violations. One minus the index is the percentage of income that is wasted on a

violation. This gives us an idea of how much one would have to relax the budget

constraint in order to remove revealed preference violations. An index closer to one is

associated with less costly violations. They regressed the number of GARP violations

and Afriats Index on the math test score. While signs of the key slope coefficients are

as expected children with better scores show fewer and smaller violations and their

magnitudes are large, these coefficients are not statistically significant at standard

levels. However, the number of observations is relatively small (just 37), a broader

examination of this hypothesis may yield different results.

Andreoni and Miller (2002) offered subjects opportunities to share an

endowment with another anonymous partner. Implicit prices and incomes were varied

across decisions to create intersecting budget sets, allowing researchers to check for

GARP consistency. Over 98% of subjects exhibited utility maximizing choices. They

also find that a majority exhibit altruistic behavior, in varying degrees. This stands in

stark contrast to the predictions of neoclassical rationality that agents are only self-

interested in a very narrow sense; that is, they would never give up any resource

without compensation. Andreoni and Miller further estimated three classes of standard


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CES utility functions (perfect substitutes, perfect complements, perfectly selfish) and

find that almost half of the subjects exhibited behavior that was exactly consistent with

at least one of these utility functions.

Becker (1968) extends neoclassical consumer theory to criminal behavior.

Revealed preference theory provides us with an empirically useful strategy for

verifying whether the neoclassical utility model can be applied to criminal behavior. If

we find that criminal behavior is consistent with revealed preference axioms, then we

know that economic models are capable of explaining criminal behavior and advising

policy. Even if the data are not perfectly consistent with revealed preference axioms,

we can still make policy recommendations based on aggregate data, since it is still likely

to obey the laws of demand.

III. Experiment design

The complete protocol for our experiment is included in Appendix A. People are

randomly and anonymously matched with a partner, and they each start with a $5

endowment. Everyone makes decisions as if they are the criminal, and we then

randomly determine who is a criminal and who is a victim. The choice sets are

constructed from budget sets defined over three goods: stolen loot, the probability of

getting away with stealing, and the amount you keep, after repayment of the stolen loot

and the fine, if you are caught.4 We construct multiple choice sets, each consisting of a

4 Since a fine is presumably a bad, we take a base fine and subtract from it a good that might beinterpreted as a fine discount. The amount of this discount varies according to the tradeoffs imposed by


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list of bundles of these three goods. The bundles can be thought of as different crimes;

that is, some will involve taking a little money, facing a good chance of getting away

with it, and a modest fine if caught, while others will involve a higher amount of loot,

but a lesser chance of getting away with it, and so on. Taking nothing is always an

option.

The list of bundles for each choice set are constructed with different implicit

incomes and prices. These prices can be viewed as the rates of tradeoff between loot,

the probability of getting away with the theft, and the smallness of the fine if you are

caught. That is, a high implicit price for loot relative to the price of getting away with it

means that, in this choice set, choosing a crime with lots of loot will cost dearly in terms

of the chances of getting caught. Incomes can be thought of as the overall extent of

criminal opportunities available. A higher income means that, relative to a low income

choice set, there are crimes available that involve not only a lot of loot, but also a very

good chance of getting away with the crime, and small fines if caught.

The incomes and implicit prices are varied in such a way that the choice sets

overlap frequently, with the intersections of the constraints designed in such a way as to

ensure many possibilities for intransitive choices. Choice sets include both the bundles

on the frontier of the budget set, and some interior bundles to check for monotonicity.

Table 1A gives summary information on the choice sets and Table 1B gives the menu of

bundles for a representative choice set.

the implicit prices. The base fine is set sufficiently high to make sure that criminals who are caught arenot paid for committing a crime.


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Bronars (1987) discusses the power of revealed preference tests in a two-good

setting. He finds that power is maximized when two-good budgets bisect each other at

arbitrarily small angles (that is, they nearly coincide). The three-good analog is that

budget planes intersect each other such that the area on either side of the intersection is

equal in both budgets, and that they intersect at arbitrarily small angles.

In terms of experimental design, there is a clear tradeoff between Bronars power

to detect revealed preference violations and the ability to detect large violations, in the

sense of the Afriat Index. If we design our choice sets to maximize Bronars power, we

do not present any opportunities for costly mistakes, so we have little idea about

subjects likely responses to costlier mistakes. On the other hand, if we design our

choice sets to maximize the power of Afriats Index, we may not be able to detect

revealed preference violations. While we take maximization of Bronars power as our

starting point for parameter choice, we are forced to relax it to some degree in order to

accommodate the other desirable characteristics, including a balance with the Afriat

Index.

The subjects are told that they must choose one bundle from each choice set.

After they have made their choices, we randomly determined whether their choice was

to be implemented that is, whether they were the criminal or the victim. Then, one of

the criminals choice sets was randomly chosen, and whatever choice they made from

that set was implemented. We used a randomized procedure to determine if they got

away with any crime they might have chosen, or if they were instead caught and


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must return any loot to the victim and also pay the fine. The criminal and the victim

were then paid the resulting amounts in cash.

Our protocol was designed to make sure that choices are made carefully. We

gave people a chance to change their minds after thinking things over, and we included

a simple test of whether or not independence holds in this context. This test is

explained later. We also included duplicate budget sets just to see whether people were

making internally consistent choices. In Table 1A, budgets 1 and 5, 3 and 7, and 4 and 8

are the same.

For each of the choice sets, we gave the subjects 30 seconds to choose a bundle.

We told them not to go on to the next choice set until the 30 seconds were up. We call

these 10 choices their first choices. For the second choices, we had them go through

the list again, spending a further 15 seconds on each choice set, and marking any

changes they would like to make by crossing out the old and circling the new.

We test for independence by giving them another chance to change their minds,

after the uncertainty about their role and the actual choice set is resolved. After we told

them whether they are the criminal or the victim, we had them go through the choice

sheets yet again. Finally, we told them which specific choice sheet had been chosen for

implementation, and they could then change their choice on that sheet, if they wish.

Information about choices at each stage is retained for analysis. Choice sets were

ordered starting with the low income version, and going to high. The order of choices

within the choice sets was blocked, with half the participants receiving forms where the


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amount of loot to be taken in choices goes from low to high as you go down the page,

and half vice versa.

Participants were recruited from high school math classes in Eugene, OR. After

obtaining permission from the school district and the Principal, we contacted three

teachers and performed the experiments in a total of six classes. Students were matched

with other students in their class, so they know the other participants quite well,

although all interactions and payoffs are anonymous and secret. One might expect that

total strangers would have a greater propensity to steal compared to anonymous

classmates. Because school attendance rates are high, this procedure provides a fairly

representative sample of the area high school age population. However, the sample is

not nationally representative Eugene is a medium sized college town with a

population that is richer and whiter than the US as a whole. We also recruit subjects

from an upper-division undergraduate industrial organization course at the University

of Oregon. These students clearly differ from the high school students in many ways.

In particular, they have higher GPAs, more money, and are older.

IV. Revealed preference results

First, we check to see whether choices from the duplicate choice sets pairs 1 and

5, 3 and 7, and 4 and 8 are the same. For the first decision, 167 of the 342 pairs (3 pairs

for each subject) are the same. For the final decision, 196 of 342 are the same.

Consistency is slightly higher for undergraduates. A Chi-squared test rejects

independence of choices (independence predicts that 342 decision pairs are the same)


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with p-value of 0.000 for each comparison. When we regress the number of matched

choices on demographics nothing is significant, including whether the subject is a high

school student and GPA measures.

We note that about 75% of participants change at least one choice in round 2,

about 20% change in round 3, and no one changes in round 4. We take this as evidence

that choice behavior under the uncertainty, which is resolved in rounds 3 and 4,

generally obeys independence. This is important, since independence is a necessary

requirement for our protocol to generate data that can be used to test rationality.

We check for revealed preference violations using an algorithm from Varian

(1995) which we modified to handle three goods and discrete bundles. Tests of SARP

and WARP yield comparative results that are very similar to those from GARP, so only

results for GARP are reported here. Table 2 displays the average number of GARP

violations for high school subjects, college subjects, and all subjects, and provides a

comparison to random (uniform and bootstrap) choice. In the bootstrap random choice,

each bundle is weighted by its frequency in the overall choice distribution.

Each subject group exhibits significantly fewer violations than random choice or

bootstrap choice. The average number of GARP violations across all classes is 4.2.

Table 2 gives frequencies for the number of GARP violations per subject. (All of the

counts in Table 2 are for the final choices.) Note that, since a minimum of two choices is

required to check for a transitivity violation, it is impossible to have just one violation.

Overall, about 40% of the subjects have no GARP violations. The average number of


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violations in round 1 is about 4.8, so on average the choice modifications that people

make are moving them towards greater rationality.

There is no obvious standard against which to compare the number of GARP

violations. The revealed preference theorems described above require that choices obey

the axioms without exception. In practice, this standard is not met. Sippel (1997) used a

similar protocol for eight different consumption goods, using 10 different budget sets.

He found that 24 of 42 participants violated GARP at least twice. Andreoni and Miller

(2002) examined 142 college students decisions about how much money to keep for

themselves and how much to share with another, under eight different budget

constraints. They found that nine percent of the participants committed at least some

violations of the revealed preference axioms. Harbaugh et al. (2001) looked at decisions

over two consumption goods and 11 choice sets. Eleven-year-olds and college students

had similar patterns, with about 35% displaying GARP violations. The average number

of violations was about two. The task in our experiment is more difficult, in terms of

the number of goods, than that in the Andreoni or Harbaugh experiments, but simpler

than that of Sippel. On this basis, our results seem consistent with those generated by

other experiments.

As in Harbaugh, Krause, and Berry (2001) and Andreoni and Miller (2002), our

revealed preference test requires that preferences are strongly monotonic. Rather than

take this on faith, our experiment is designed to test this assumption by including

dominated bundles in the choice set that is, bundles with simultaneously lower loot

and/or higher probabilities of detection and fine than other options in the choice set.


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dichotomous variable to indicate if the subject is the oldest child in his or her family.5

Tenure is the number of years the subject has lived in Oregon. A larger value may be

considered as a proxy for enhanced ties to friends and community; therefore it may be

negatively correlated with the propensity to steal.

Since the data are discrete and cardinal, we estimate count data models in an

attempt to explain the number of GARP violations using the socio-demographic

variables. Table 5 presents the results negative binomial regressions, Poisson

regressions yield similar results. The first column includes the explanatory variables

age, gender, GPA, the height of the individual, whether he or she is a high school

student, oldest child, and the amount of money spent per week. The second column

displays a more flexible specification where the explanatory variables are interacted

with the High School dummy, allowing the hypothesis of differential impact of the

variables by High School vs. college status can be entertained. Being older is associated

with about 0.6 fewer GARP violations. While the interaction of Age and High School is

positive and significant, the net difference between the coefficients on this interaction

term and Age is not. This means that, among high school students, age does not

contribute to the explanation of the number of GARP violations, while among college

students, being older is associated with a decrease in the number of GARP violations.

Gender, height and being the oldest child have no additively separable impact on the

number of GARP violations. A general conclusion seems to be that the degree of

5 In case of no siblings, the subject is classified as the oldest child.


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rationality of behavior is not well explained by the available socio-demographic

variables.

Rationality requires that choices over crimes obey GARP. Although our data are

not entirely consistent with this axiom, the number of violations is in line with what

other researchers have observed for choices over general types of consumption goods.

Thus, the observed behavior is at least broadly consistent with utility maximization.

V. Crime and deterrence

In this section of the paper we estimate demand functions for stolen money.

Specifically, we investigate the determinants of the amount of loot stolen as a function

of personal characteristics of the person who steals, the price of the stolen loot, the

probability of being caught, and the amount of fine. Table 6 presents the distribution of

the number of thefts. During the 10 rounds of the experiment, each individual had the

opportunity to steal 10 times. Thus, in Table 6, zero thefts means that the individual

never stole during the experiment, and a 10 indicates that he or she stole money in

every round. There is substantial variation in the number of thefts, with 49 percent of

the subjects stealing money in each round.

If people are choosing rationally, then we would expect them to respond to the

changes in implicit prices in ways that are consistent with the laws of demand. For

example, we would expect that participants will respond to an increase in the cost of

choosing a crime with high loot by tending to move toward crimes with less loot but

also lower probabilities of detection and/or lower fines. An increase in available


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27

III contain coefficient estimates for the commodity prices, which always have the

expected sign, though the fine price is not significant. Columns II and III include

coefficients for additional demographic variables. These specifications both suggest

that older students tend to steal more. Column II suggests that taller people steal more.

Money is included in Column III, and is significant. Columns IV and V include price

interactions with the High School dummy variable. As before, the price coefficients all

have the expected sign, though only the price of loot is significant. Columns IV and V

also indicate that the coefficients of detection price and fine price are the same for

college and high school students, but suggests that these effect of the price of loot may

be smaller for high school students.

VI. Discussion and conclusion

The extent to which criminals and potential criminals respond to variations in

deterrence is an important issue, both theoretically and from a public policy

perspective. Despite significant progress in recent empirical analyses in identifying the

causal effect of deterrence on crime, objections are still raised with regard to the validity

of methods proposed to eliminate the simultaneity between crime and deterrence. In

this paper we designed an experiment where subjects are exposed to exogenous

variations in the relative tradeoffs between three important aspects of criminal

opportunities: loot, the probability of detection, and the fine. We conduct the

experiment with juveniles and young adults age groups that are frequently labeled as

irrational or unresponsive to deterrence.


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28

We find that behavior among these groups with respect to petty criminal

decisions is not entirely rational. However, behavior is approximately as consistent

with the theoretical requirements of rational choice behavior as is choice behavior over

consumption goods. Furthermore, we find that, in aggregate, responses to changes in

criminal opportunities are consistent with the laws of demand. This serves to

underscore the deterrent properties of law enforcement effort and the penalties applied

to criminal acts.

Experimental research in the tax compliance literature has alluded to as much by

describing the effects of audit rates and marginal tax rates on tax compliance. However,

this experiment generalizes the rational criminal model to a broad range of criminal

behaviors, such as auto theft, embezzlement, and petty larceny. Caveats are that the

participants in these experiments are not necessarily criminals outside the laboratory,

and that the crimes in our experiments involve small financial gains and losses. Given

these qualifications, we believe these results strengthen the argument that criminal

behavior and the response of criminals to changes in enforcement and penalties can be

accounted for by economic models.


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References

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Table 1A

Choice Set Characteristics

Budget parametersBudget loot_p prob_p nfine_p income

1 .25 1 1 1.2

2 1 2 1 2.9

3 .5 4 1 3.25

4 .5 2 1 2.25

5 .25 1 1 1.2

6 1 2 1 2.75

7 .5 4 1 3.25

8 .5 2 1 2.25

9 1 4 1 3.75

10 .25 2 1 1.75

Table 1BSample Bundles, from Choice Set 5

You each start with $5

Markone

choicebelow

Dollars totake fromPerson B

Your paymentincluding your

starting $5if you are not

discovered

Chance thatyou are

discovered

Dollars paidto

experimenterif discovered

Your paymentincluding your

starting $5if you are

discovered

$0 $5 --- --- ---

$1.00 $6.00 25% $1.55 $3.45

$1.00 $6.00 50% $1.30 $3.70

$1.00 $6.00 75% $1.05 $3.95

$1.00 $6.00 75% $1.25 $3.75

$2.00 $7.00 50% $1.55 $3.45

$2.00 $7.00 75% $1.30 $3.70

$3.00 $8.00 75% $1.55 $3.45


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Table 2

Frequency of GARP Violations

Number of

GARPviolations

HS UO All Bootstrap

0 37% 48% 40% 3%

1* 0% 0% 0% 0%

2 6% 0% 4% 3%

3 7% 0% 5% 5%

4 6% 0% 4% 6%

5 8% 10% 9% 10%

6 5% 6% 5% 16%

7 4% 6% 4% 20%

8 6% 6% 6% 21%

9 6% 10% 7% 14%

10 14% 13% 14% 4%

N 83 31 114 10,000

*Note that it is impossible to have exactly one violation.


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Table 3

Monotonic bundle choicesSample Bootstrap

Monotone

Choices Frequency

Running

total Frequency

Running

Total0 0% 0% 0% 0%1 7% 7% 0% 0%2 4% 11% 1% 1%3 5% 16% 3% 4%4 10% 26% 10% 14%5 5% 32% 20% 34%6 12% 44% 27% 61%7 10% 54% 22% 83%8 6% 60% 12% 95%

9 16% 76% 4% 99%10 25% 100% 1% 100%N 114 10,000


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Table 4

Descriptive Statistics

Variable Definition

High

School College All

Loot* The money stolen in each round1.23

(1.14)1.77

(1.21)1.38

(1.19)

GARP Number of GARP violations4.01

(3.84)4.00

(4.16)4.01

(3.91)

Age Age of the individual15.98

(15.98)22.01(0.96)

17.62(2.86)

Height Height of the individual in feet5.59

(0.32)5.88

(0.35)5.67

(0.35)

GPA

High school GPA if the individualis in high school; the average ofhigh school and college GPAs ifthe in college

3.12(0.54)

3.20(0.33)

3.14(0.49)

MoneyHow much money the individualspends on his/her own per week

18.34(17.93)

72.71(171.93)

33.13(94.02)

MaleDichotomous variable (=1) if theperson is male

0.51 0.71 0.56

Oldest

Child

Dichotomous variable (=1) if the

person is oldest child 0.34 0.52 0.39

TenureThe number of years the personlived in Eugene, Oregon

8.43(3.59)

5.39(4.46)

7.61(4.08)

N 83 31 114* Loot is the average of all 10 rounds


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Table 5

Negative Binomial Estimatesof the Number of GARP Violations

Variable I II

Age0.050

(0.104)-0.605**(0.298)

Age*High School--

0.764**(0.318)

Male0.115

(0.284)0.220

(0.487)

Male*High School--

-0.039(0.588)

Height-0.072(0.378)

0.993(0.792)

Height*High School--

-1.571*(0.896)

GPA-0.001(0.235)

-0.929(0.782)

GPA*High School--

1.083(0.822)

Money -0.005*(0.003)

-0.010(0.010)

Money*High School--

0.009(0.010)

Oldest Child-0.566***(0.244)

-0.303(0.465)

Oldest Child*High School--

-0.406(0.550)

High School0.075

(0.561)-10.539(6.739)

n 114 114Log Pseudo-Likelihood -277.35 -273.74

Robust standard errors in parentheses*, ** and *** indicate 10, 5, and 1% significance


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Table 6

Number ofThefts*

Number ofIndividuals

Percentage ofTotal

0 5 4%

1 2 2%

2 2 2%

3 4 4%

4 6 5%

5 2 2%

6 6 5%

7 6 5%

8 13 11%9 12 11%

10 56 49%*The number of thefts is the number of rounds where theindividual stole money. Thus, 0 indicates that theindividual did not steal money during the entireexperiment, and 10 indicates that he/she stole in everyround.


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Table 7

Participation in Crime

Probit Estimates ofDecision to Steal

Negative Binomial

Estimates of theNumber of Thefts

Variable Ia IIa III IV

Loot Price-0.004(0.416)

0.003(0.430)

--

--

Detection Price0.240

(0.184)0.251

(0.191)

--

--

Fine Price-0.141*

(0.082)

-0.145*

(0.085)

-

-

-

-

Age0.042*(0.025)

0.048**(0.023)

0.064**(0.027)

0.060**(0.028)

Male-0.066(0.073)

-0.048(0.069)

-0.069(0.101)

-0.055(0.099)

Height0.141

(0.098)0.134

(0.104)0.152

(0.126)0.152

(0.130)

Money0.001

(0.001)--

0.0002*(0.0001)

--

High School0.138

(0.185)0.130

(0.166)0.232

(0.172)0.187

(0.165)

GPA-0.023(0.057)

--

-0.020(0.069)

--

Oldest Child-0.064(0.055)

-0.072(0.057)

-0.094(0.072)

-0.091(0.072)

Tenure-0.006(0.007)

--

-0.007(0.010)

--

n 1140 1140 114 114Log-Likelihood -528.29 -533.81 -1105.91 -1106.51

Robust standard errors in parentheses*, ** and *** indicate 10, 5 and 1% significance levels respectivelya) The reported coefficients are marginal probabilities


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Table 8Demand for Loot

Variable I II III IV V

Loot Price

-3.880***

(0.866)

-3.880***

(0.868)

-3.880***

(0.869)

-6.524***

(1.394)

-6.524***

(1.397)

Loot Price*HighSchool

--

--

--

3.632**(1.748)

3.632**(1.751)

Detection Price0.987***(0.348)

0.987***(0.349)

0.987***(0.349)

0.749(0.559)

0.749(0.560)

DetectionPrice*High School

--

--

--

0.326(0.707)

0.326(0.708)

Fine Price0.055

(0.605)0.055

(0.188)0.055

(0.188)0.044

(0.265)0.044

(0.265)

Fine Price*HighSchool

--

--

--

0.015(0.356)

0.015(0.357)

Age--

0.144**(0.062)

0.119*(0.066)

0.129**(0.063)

0.137**(0.066)

Male--

-0.066(0.168)

-0.100(0.193)

-0.058(0.167)

-0.090(0.191)

Height--

0.426*(0.240)

0.409(0.247)

0.423*(0.240)

0.404(0.247)

Money--

--

0.002***(0.0003)

--

0.002***(0.0003)

High School--

0.458(0.422)

0.315(0.433)

-0.825(1.290)

-0.672(1.302)

GPA--

--

-0.060(0.142)

--

-0.029(0.138)

Ascending--

--

-0.066(0.123)

--

0.071(0.124)

Oldest Child--

-0.154(0.132)

-0.170(0.135)

-0.147(0.135)

-0.185(0.131)

Tenure-

-

-0.017

(0.017)

-

-

-

-

-0.016

(0.016)

Constant1.302**(0.605)

-3.758***(1.712)

-2.981(1.843)

-2.690(1.853)

-2.522(1.970)

n 1140 1140 1140 1140 1140Adjusted-R2 0.14 0.21 0.23 0.22 0.24

Robust standard errors, which are adjusted for clustering at the individual level,are in parentheses.*, ** and *** indicate 10, 5 and 1% significance levels respectively.


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40

Appendix A

Welcome:

Today we are conducting an experiment about decision-making. Your decisions are forreal money, so pay careful attention to these instructions. This money comes from aresearch foundation. How much you earn will depend on the decisions that you make,and on chance.

Secrecy:

All your decisions will be secret and we will never reveal them to anyone. We will ask

you to mark your decisions on paper forms using a black pen or pencil. If you arediscovered looking at another persons forms, or showing your form to another person,we cannot use your decisions in our study and so you will not get paid. Please do nottalk during the experiment.

Payment:

Stapled to this page is a card with a number on it. This is your claim check number.Each participant has a different number. Please tear off your card now and write yourclaim check number on the line on the first page. You are also given a packet. Write

your claim check number on top of the first page of that packet, but do not turn thepage until instructed to do so. Be sure to keep your claim check number. You willpresent this number to an assistant at the end of the experiment and you will be givenyour payment envelope.

The Experiment:

You are going to play a game today. In this game there will be two roles A and B.Everyone will be randomly assigned one role, and will be matched with another personwith the other role. You will not be told who you are paired with, and they will not betold who they are paired with, even after the experiment is over.

Person A will start with $5, and person B will also start with $5. Person A will have achance to take some of person Bs money. Taking is not without a risk. After person Amakes the decision to take or not to take, there will be a discovery phase. During thisphase there is a chance that person A will have to return the money taken from personB, and also pay some money to the experimenter. The chance that this happens, and theamount paid to the experimenter if it does, depend on the choice made by person A.


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Everyone received one packet, and each packet contains 10 different sheets stapledtogether. We will show you an example. We call these Choice Sheets.

On each Choice Sheet you will make a choice as if you are person A. You will declare

your choice of how much money to take from person B by putting a check mark next toone of the choices with a black pen or pencil.

When we play the game the amount of money you will end up with will really bedetermined by the choices you make, so you want to consider your choice verycarefully. We will give you 60 seconds on the first page and 30 seconds on eachsubsequent page. Please leave your pencil or black pen on the desk and do not markyour choice until I ask you to do so. When the time is up I will ask you to place a checkmark using a pencil next to the choice you want. It is important that you wait until thetime is up to mark your choice.

After we go over all 10 Choice Sheets and everyone has made all 10 choices, I will giveyou a chance to change your mind. This time you will have 15 seconds on each page.Please leave your pencil or black pen on the desk and do not mark your choice until Iask you to do so. To change your choice, clearly cross out (do not erase) your previouschoice, and place a check mark next to the choice you want.

Next, we randomly assign roles of A or B by flipping a coin. If it comes up heads, thenthose whose claim check number is even will be assigned the role of person A, andthose whose claim check number is odd will be assigned the role of person B. Should

the coin come up tails, then those whose claim check number is odd will be assigned therole of person A, and those whose claim check number is even will be assigned the roleof person B.

Now we have to pick which one of the 10 Choice Sheets will count. We will pick arandom number from 1 to 10, by having your teacher draw a card from a deck of 10cards. The Ace will stand for 1. The number of the card will determine which ChoiceSheet counts. We will have you turn your packet to that choice sheet.

Then we must complete the discovery phase to see if person A will have to return themoney to person B and pay some money to the experimenter. Here is how this willwork: We have 5 index cards. On each index card there is a percentage written. Theyare: 0%, 25%, 50%, 75% and 100%. We will randomly choose one of these index cards.Everybody looks at their choice on the Choice Sheet that has just been selected. If youare person A, and if the percentage written on the selected index card is less than thechance of being discovered for the choice you made on the Choice Sheet, then you arediscovered. You will have to return the money you took from person B and pay to the


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experimenter the number of money indicated in the choice. Otherwise you keep themoney.

We will collect odd numbered and even numbered packets in separate stacks. Then wewill mix up each stack , and take one from each stack to match people together. The

choice made on person As Choice Sheet will be used to determine their payments.

We will proceed through the stacks until we are done. If there is an odd number ofpeople in the room, then at the end there will be one packet left over. This packet willbe assigned the role of person A, and will be paid according to the decision on his or herchoice sheet.

Note that you dont know which of your 10 decisions will count, if any. This will bedetermined purely by chance. So the best thing for you do to is to treat every choicesheet as if it will count, and make the choice on that sheet that you most prefer.

GARP Among Thieves

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