A SURVEY OF ECONOMIC MODELS OF CRIMINAL BEHAVIOR

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• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP07-01280R000400470001-0
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• Document Creation Date: December 27, 2016
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• Publication Date: October 1, 1987
• Content Type: REPORT

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l~_~ _ EXl3,-C,~ .
A SURVEY OF ECONOMIC MODELS
OF CRIMINAL BEHAVIOR:
PERSONNEL SECURITY
RESEARCH AND EDUCATION CENTER
99 PadfC Stmt. Building 455
Montwsy. California 93940-2481
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A SURVEY OF ECONOMIC MODELS OF CRIMINAL BEHAVIOR
PERSONAL AUTHOR(S)
Haga, William James
.3j r'PE OF REPORT
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Criminal behavior, economic models
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Economic theories of criminal behavior premise the criminal as rational actor engaged
i
n n a calculus of incentives and disincentives. The fundamental model assumes the
actor allocates time between legitimate and illegitimate activities, with time alloca-
tion affected by the deterrent effects of conviction probability and punishment severity.
This paper presents the economic model of criminal behavior developed by Becker and
refined by Ehrlich, Block, Heineke, and others.
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PERS-TR-87-004 October 1987
A SURVEY OF ECONOMIC MODELS OF CRIMINAL BEHAVIOR
Prepared by
William J. Haga
Reviewed by
Nancy Nieboer Turpin
Released by
Carson Eoyang
Director
The work contained in this report was sponsored by
Office of Naval Research under work order N62271-86-M-0257-
Personnel Security Research and Education Center
Monterey, California 93940-2481
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The premise of economic theories of criminal behavior is
that criminals, like everyone else, behave rationally.
Economists contend that people are drawn to criminal activities
because they expect to be better off from engaging in them
than not.
The economic approach implies that criminals are no
different from the general population when it comes to reacting
to incentives. This approach supports the concept of deterrence
by which economists contend that crime will be reduced by
raising the expected costs of illegal activities to potential
criminals.
The bedrock economic model of criminal behavior, developed
by Gary Becker (1968), is the allocation of time between
illegitimate and legitimate activities. The work of Ehrlich,
Block, Heineke and others who have followed Becker are
refinements or tests of the time allocation model.
A product of the time allocation model is the estimation
of the deterrent effects of two variables: the probability of
conviction and the severity of punishment.
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Page
SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . .
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . .
BECKER . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Optimal Level of Crime in Society . . . . . . . . . . 2
Harm to Society . . . . . . . . . . . . . . . . . . . 3
Cost of Apprehension and Conviction . . . . . . . . . 3
Supply of Offenses . . . . . . . . . . . . . . . . . 3
Deterrence . . . . . . . . . . . . . . . . . . . . . 4
Summary of Becker' s Model . . . . . . . . . . . . . . 5
CRITICISM OF BECKER -- STIGLER . . . . . . . . . . . . . . 6
Doubtful Value of "Social Value" . . . . . . . . 6
Supply of Offenses . . . . . . . . . . . . . . . . 6
Enforcement Agencies . . . . . . . . . . . . . . . . 7
EHRLICH . . . . . . . . . . . . . . . . . . . . . . . . . 8
The Economic Perspective on Crime . . . . . . . . . . 8
Supply of Offenses . . . . . . . . . . . . . . . . . 9
Demand for Offenses . . . . . . . . . . . . . . . . . 9.
Crime and Punishment at the Margin . . . . . . . . . 10
BLOCK AND HEINEKE . . . . . . . . . . . . . . . . . . . . 12
OPTIMAL INCOME TAX EVASION -- ALLINGHAM AND SANDMO . . . . 13
MARKET EQUILIBRIUM MODEL . . . . . . . . . . . . . . . . . 14
EMPIRICAL STUDIES OF ECONOMIC MODELS OF CRIME . . . . . . 14
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . 17
APPENDIX A: MAJOR FEATURES OF SELECTED ECONOMIC MODELS
OF CRIME DEALING WITH PROPERTY OFFENSES . . . . . . A-1
APPENDIX B: RESULTS AND ADVANCES OF SELECTED ECONOMIC
MODELS OF CRIME DEALING WITH PROPERTY OFFENSES . . B-1
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"It is otherwise with the injuries to property.
The benefit of the person who does the injury is
often equal to the loss of him who suffers it.
-- Adam Smith 1776
The economic modeling of criminal behavior is a rather
new application of microeconomics. It arose in the United
States in response to the growth of crime which began in the
1960's and continued through the 1970's. The psychological
approach (criminals are sick) and the sociological approach
(society is sick) that were the conventional wisdom in
criminology were found wanting. By the late 1960's, the
proportions of the crime problem drew the attention and labors
of economists. That is not the same as saying they were invited
into the debate. They were not.
Economists bring to the study of criminal behavior their
usual microeconomic tools: income, costs, elasticity, trade-
offs, returns to input factors, supply schedules, demand
schedules and equilibrium levels. Not novel in themselves,
they were novel when applied to the matter of illegitimate
behavior.
The easiest challenge to the economic approach comes in
the matter of violent crimes, crimes of passion or acts that
are essentially spontaneous responses to targets of opportunity.
Conversely, the easiest application of the economic model is to
those crimes where the motive is itself largely economic,
involving calculation and planning, e.g. embezzlement,
professional cargo hijacking, confidence rackets, tax evasion
and espionage.
Does an economic theory of criminal behavior have anything
to say to the policy and practice of personnel security? It does
in that it provides a way of thinking about criminal behavior
that departs from the prevailing psychological and sociological
approaches.
A psychological approach regards criminal behavior as an
aspect of deficient personality. A sociological approach regards
criminal behavior as a' special case of deviance from social
norms within a context of social sanctions and rewards. An
economic theory of crime regards the criminal as a rational
actor, maximizing profit within a matrix of costs and
opportunities.
As an aside, I noted that, with the exception of Ehrlich
and to some extent Heineke, economists who have applied economic
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theory to criminal behavior have not pursued it as a career
interest. Rather, economic theories of criminal behavior have
been by-products of searches for something else. The major
theorist, Becker, developed his model of the criminal as a
rational actor as a set of footnotes while developing a
production function of investment in law enforcement activities.
Block dropped his work in the economics of crime to pursue anti-
trust policy although he is currently serving as a Commissioner
on the United States Sentencing Commission.
Optimal Level of Crime in Society
Becker asks how many resources and how much punishment
should be used to enforce different kinds of laws? How many
offenses should be permitted and how many offenders should go
unpunished? The numbers will not be zero.
In Becker's model, the optimal quantity of enforcement is
a function of:
1. Costs of catching and convicting.
2. Nature of punishments (Fines or incarceration?
Recompense?)
3. Response of offenders to changes in enforcement.
He incorporates the following as elements of costs:
1. Enforcement agency costs.
2. Losses by victims.
3. Costs of preventive measures (including unseen costs
such as flight to suburbs and attendant metropolitan
development sprawl, reliance on autos, avoidance of
public transport, avoidance of urban downtown areas
after dark).
4. Costs of prosecution and defense.
5. Insurance costs.
6. Corrections system costs.
7. Social costs of enforcement (searches, delays, wrongful
arrests, invasion of privacy, administrative reporting).
Out of these elements, Becker examines five relationships:
1.
Number
of
offenses and the cost of
offenses.
2.
Number
of
offenses and punishments
levied.
3.
Number
of
offenses, arrests, convictions
and public
expenditures on courts and police.
4. Number of convictions and the costs of imprisonment
and other kinds of punishment.
5. Number of offenses and private expenditures on
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protection.
Harm to Society
As a group, offenders usually receive diminishing marginal
gains from pursuit of crime while causing increasing marginal
harm. As the number of offenses rises, criminals encounter
decreasing gains while society suffers increasing harm.
Cost of Apprehension and Conviction
The more funds spent on police, courts and equipment, the
easier it is to discover offenses and convict offenders. The
lower the costs of police, courts and juries and the more that
specialized equipment is used to offset labor intensive
activities, the more enforcement activity society can afford.
Supply of Offenses
Becker proposes that an increase in the probability of
conviction, and an increase in the severity of punishment if
convicted, would decrease (perhaps a lot, perhaps a little) the
number of offenses committed. People with judicial experience
agree with the generalization that a change in the probability
of punishment has a greater deterrent effect than a change in
the severity of the punishment.
Becker's model assumes that if people commit offenses their
expected utility exceeds the utility they would get by using
their time and other resources in alternative activities. Some
people become criminals not because their motivations are
different from those of other people but because their costs and
benefits differ. An economic analysis of criminal behavior,
Becker contends, does not need ad hoc concepts of differential
association, anomie, etc. Nor does it assume perfect knowledge,
lightening fast calculation or the other caricatures of economic
theory.
Therefore the gain in expected utility from choosing to
undertake illegal activity is:
EU = pU(Y - f) + (1 - p)U(Y)
where EU = Expected utility
p = Probability of conviction
f = Severity of punishment (specifically a fine)
Y = Gain from committing an offense
U = Decision maker's utility index
If EU is positive, Becker's model predicts that a decision
maker will choose to engage in illegal activity. If it is
negative, he or she will not. EU will be negative if the
severity of punishment > gained from an offense and the
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probability of conviction is sufficiently high. The model
assumes that a convicted criminal loses the monetary gain from
an offense as well as paying fines.
The number of offenses that will be committed by any
particular person is a function of the probability of
conviction, the severity of punishment if convicted, the
income available to that person through legitimate means,
income available through other illegal activities, and other
lesser factors such as frequency of nuisance arrests that a
person suffers. Becker also includes, as a variable, a
particular person's willingness to commit an illegal act. This
is surely the case; yet it strikes the casual reader as an
error-term loophole.
The number of offenses committed in a society is a function
of (p, f, u), where:
p = Probability of conviction.
f = Severity of punishment.
u = Portmanteau variable representing other
influences.
An increase in either the probability of conviction, or the
severity of punishment, reduces the utility of criminal activity
and thus drives down the number of offenses committed.
An increase in the probability of conviction with an
equal % reduction in the severity of punishment would not
change the expected income from offenses. But it would change
the expected utility because the level of risk would drop. An
increase in the probability of conviction would reduce the
utility of offenses and thus reduce the number of offenses
committed.
Whether crime pays is, at root, a matter of an individual
offender's preferences for risk and is not directly related to
the efficiency of the enforcement agencies or the funds spent
on combatting crime. If risks were preferred at some
combinations of values of probability of conviction and severity
of punishment and disliked at others, policy could influence
whether crime pays by mixing probability of conviction and
severity of punishment.
The more serious the offense, the higher the probability
of imprisonment if convicted. About 58% of murder/manslaughter
offenders are apprehended, tried and found guilty. Nearly 40%
go to prison. Compare that to burglary (Becker 1968, Table 2):
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Murder
Burglary
% found guilty of estimated number of offenses:
58%
13%
% entered prison of estimated number of offenses:
40%
3%
Summary of Becker's Model
Becker's work establishes that optimal policies to combat
illegal behavior are part of an optimal allocation of resources
to law enforcement functions. He notes that important
contributors to criminology in the eighteenth and nineteenth
centuries, Beccaria and Bentham, explicitly applied an economic
framework. Becker sees his work as re-establishing the role of
economics in the analysis of criminal behavior. Specifically,
his economic model of crime supports theories of deterrence:
increases in the probability or conviction and in the severity
of punishment reduce the number of offenses committed in a
society. What his theory does not tell us is the magnitudes of
these deterring variables or even which is larger. ,
Becker's chief contribution is to reassert the economic
approaches as an alternative to the psychological and
sociological models of aberration and deviance in the literature
of criminology. If society has defined certain activities as
criminal, Becker contends, then society ought to choose from
criminal justice policies that combine probability of conviction
with severity of punishment to minimize the social losses to
crime. Pyle (1983) notes in his criticism of Becker, that the
suggestion that the optimal level of criminal activity in a
society would be greater than zero is more useful than it
appears at first reading. Clearly, society must tolerate some
level of criminal activities and losses to crime.
Society cannot afford the cost of "complete" enforcement
of its rules. Instead society provides law enforcement agencies
with a budget that dictates a level of enforcement that is
considerably lower than "complete."
A potential offender is deterred from committing a crime
by the expected punishment, which is (at first approximation)
the probability of punishment times the severity of punishment,
e.g: $100 if the probability of conviction is 10% and the fine
is $1000. Hence, increasing the severity punishment would seem
as likely to have a deterrent effect as increasing the
probability of conviction. Capital punishment is cheaper than
long term imprisonment; seizure of an offender's property may
not be much more expensive than collecting a moderate fine.
Becker argues that the imposition of fines is superior to
other forms of punishment, chiefly because it consumes so few
enforcement and criminal justice resources. He proposes that the
revenue generated by fines be used to compensate the victims of
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crime. This suggestion compels a measurement of the harm done
by crime. At first glance, this seems sure to make the
application of criminal law even more complicated and lengthy
than it already is. Yet, such issues are determined regularly
in civil proceedings.
CRITICISM OF BECKER -- STIGLER
Doubtful Value of "Social Value"
Stigler notes that Becker avoids concluding that harsh
punishments are a deterrent by introducing a concept called
"social value of the gain to offenders." Stigler finds this
concept of little value and lacking any empirical base. What,
he asks, is the positive social value upon the utility derived
from a murder?
Instead, Stigler offers his own explanation of limited
deterrent effect of severe punishment. A potential criminal,
like everyone else, makes decisions at the margin. The marginal
deterrence of heavy punishments could be very small or even
negative. If a thief will have his hand cut off for taking $5,
he might as well take $5000. If an offender is as likely to be
executed for a minor assault as for murder, capital punishment
inappropriately applied is not a deterrence to murder (and
perhaps even an incentive).
A limit on law enforcement is society's avoidance of over-
enforcement: the charging and convicting of many innocent people
in order to apprehend most of the guilty ones. The conviction
of innocent people encourages crime (They're going to punish you
anyway whether you do it or not. Therefore, you might as well
do it.)
Supply of Offenses
Illegal activity can be'either an act of production for
income (theft, embezzlement, espionage) or an act of consumption
(speeding for thrills). The professional criminal seeks income,
reckoning on the present value of the expected returns and the
costs of criminal activity, comparing their difference with the
net returns of other criminal activity and legitimate
activities. The details of occupational choice are not different
from those encountered in legitimate occupations:
1. One must choose location of operations.
2. One must decide between frequent, small operations and
occasional, large operations.
3. One must consider periods of involuntary unemployment
(incarceration).
4. Earnings can be expected to rise for a while on a
learning curve of experience.
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The probability of apprehension is an increasing function
of the frequency of the commission of offenses. The probability
of detection rises after each commission because the enforcement
agency is learning an offender's habits. This is an incentive
for a strategy of infrequent attempts to get large sums. This,
however, is countered by the fact that large targets are better
protected. A liquor store is more accessible than Fort Knox.
Rational law enforcement will have these properties:
1. Expected penalties increase with expected gains so there
is no marginal net gain from larger offenses. Let the
criminal commit in a given year S crimes of size Q
(monetary value to the criminal of success in the
crime). p is the probability of the successful
completion of one crime (the % of crimes completed
successfully). p is a decreasing function of the
expenditure (E) undertaken by society to prevent and
punish the crime.
Hence: p = p(E, Q, S).
2. Expenditures on prevention and enforcement should yield
a diminution in offenses, at the margin, equal to the
return upon the investment of these resources in other
areas. An increment of expenditures yields a decrement
in offenses.
Enforcement Agencies
A deficiency in the design of enforcement agencies is the
use of inappropriate methods to determine the extent of
enforcement. The annual report of an enforcement agency is a
justification of previous year's expenditures and a plea for
enlarged budgets.
Set the scale of enforcement where MR = MC (MR is marginal
return, not marginal revenue). If the scale of enforcement is
correct, society is not spending two dollars to save itself one
dollar of damage or failing to spend one dollar where it will
save two dollars.
Guide the selection of cases so that the agency will not
seek numerous easy cases (a la FBI pursuit of auto thieves) to
boost the record of performance. In 1967, the Secret Service
spent roughly half of its $17 million budget ($8 1/2 million)
to save the public from the loss of $1.6 million in counterfeit
money. The public reviews public policy through to means:
(1) appropriations to enforcement agencies.
(2) verdicts by juries.
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These reveal the desire of the public not to enforce
certain laws.
The Economic Perspective on Crime
The conventional wisdom in the criminology literature is
that participation in crime is guided by a predisposition that
crime is a deviant behavior; its causes must be sought in
deviant circumstances determining behavior. Offenders have a
presumed unique motivation that must be traced to a unique inner
psychological structure, e.g. the impact of exceptional social
or family circumstances.
Reliance on a motivation unique to the offender as the
major explanation of actual crime prevents predictions about the
outcomes of objective circumstances. There is no persuasive
empirical support for this approach.
Even if offenders do differ systematically from non-
offenders, both respond to incentives.
Ehrlich looks at measurable opportunities in terms of costs
and rewards for both legal and illegal activities. He proposes
this as an alternative focus of research interest to looking at
the cost of punishments alone. This approach links crime rates,
on one hand, to income inequalities and level of enforcement
activity on the other. It sees participation in illegal activity
as a particular case of occupational choice: an offender's
decision to engage in crime approximates an optimal allocation
of resources, under uncertainty, to competing activities.
In violating the law, one can increase one's wealth. In
violating the law, one risks one's wealth and well-being. In
engaging in legal wealth-generating or consumption activities,
one is also subject to risks. The net gain in both kinds of
activities is subject to uncertainty.
Ehrlich argues that participation in illegal activity is
not an either/or decision regarding legal activity. Rather, a
person seeks an optimal mix of illegal and legal activities,
allocating time and other resources to competing activities.
Ehrlich does not suggest that offenders are the same as
non-offenders in all respects or that they respond to the same
incentives. Their responses vary with their degree of
specialization in illegitimate activities. The role of
opportunities for illegitimate or legitimate activities is
crucial in determining the extent of participation in
illegitimate activities.
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Supply of Offenses
Offenders' occupational choices involve an optimal
allocation of time among competing legitimate and illegitimate
activities that differ in mix of risks and rewards. Offenders
are maximizers of expected utility.
Factors in choice of crime as an occupation:
Probability of apprehension.
Probability of conviction.
Probability of punishment.
Marginal return to legitimate activity.
Marginal return to illegitimate activity.
Risk.
Initial wealth.
A 1% increase in probability of apprehension generates a
larger deterrent effect than a 1% increase in probability of
conviction (if caught) and probability of punishment (if
convicted).
A strong preference for risk among offenders may reverse
deterrent effects of sanctions.
Even if a severe sanction has little effect on currently
practicing offenders, it can reduce crime rate by deterring
entry of potential offenders into the occupation. (Use of a
polygraph affects perception of the probability of
apprehension).
A society can have a consumer demand for the products of
economically-motivated crimes: e.g. drugs, and stolen goods. An
explicit demand from a market exists for products of espionage.
Prices for espionage products are a result of needs by a
monopsony (one major buyer) and the seller's consideration of
risk.
Offenses to create wealth (buyer-seller market demand):
Loan sharking.
Prostitution.
Drug dealing.
Gambling.
Specialized offenses (custom-ordered by buyer):
Continuing acts of espionage.
Theft of luxury cars.
Theft of fine art.
Arson (torching)
Insider knowledge of securities transactions.
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Smuggling.
Alcohol/tobacco offenses.
Generic theft (fenced goods):
Electronic entertainment goods.
Jewelry.
Non-luxury autos.
Weapons.
Antiques.
Tools.
Initial act of espionage.
Offenses to create, wealth directly (no buyer):
Embezzlement
Larceny
Robbery
Offenses for consumption:
Rape
Vandalism
Arson
Auto theft
Serial murder
Crime and Punishment at the Margin
Offenders respond to incentives (negative and positive).
In Ehrlich's view it is not necessary, however, that all
offenders respond to incentives but that an important number
of potential offenders respond to marginal changes in
probability of conviction and severity of punishment.
A socially acceptable equilibrium volume of crime is
produced through interaction between offenders and enforcement
agencies. Search is for optimal probability of conviction and
severity of punishment that produce that equilibrium volume.
Because of costs of control and protection the optimum volume
of offenses is not zero. Rather, the level of offenses is set
where the marginal cost of enforcement and prevention equals the
marginal return (reduction of losses to offenses) to enforcement
activity.
To assess the benefits of criminal activity requires a
criterion of choice: Becker and Stigler chose as criterion the
maximizing of "social income". This is the same as minimizing
the social damage from offenses plus the social costs of law
enforcement.
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Result: Propositions about
1. Optimal levels of probability of conviction and severity
of punishment.
2. Optimal level and mix of expenditure on police, courts,
corrections, prevention.
In equilibrium, the deterrent effect of probability of
apprehension will exceed the deterrent effect of the
probabilities of conviction or severity of punishment. Other
criteria of choice, of course, yield different optimal mixes.
In Ehrlich's model, a decision maker can only choose one
thing, the amount of time to be spent in illegal activity (tl).
Once this choice is made, the amount of time allocated to legal
employment is immediately determined as the remainder. So, too,
is the amount of available wealth for the decision maker since
his or her wealth, in Ehrlich's model, is determined by the time
spent in either crime or legitimate work. Such variables as the
probability of conviction are not determined by the decision
maker; the only choice left to him or her is the allocation of
time.
Ehrlich's expected utility function of entering a criminal
occupation is:
EU = pU(Xa) + (1 - p)U(Xb)
where EU = Expected utility
U= Decision maker's utility index
p = Probability of conviction
Xa = Returns from legal activity
Xb = Returns from illegal activity
As a decision maker spends more time in illegal activity
(as tl increases from zero), Xa will increase and Xb will
decrease. The response of decision makers to (1) the probability
of conviction, (2) the severity of punishment and (3) the
comparative returns to crime or to legitimate work (as that
response is developed in mathematical manipulation of Ehrlich's
model) depends upon the decision maker's personal history of
criminal involvement. That is to say, a professional criminal
will be little moved by small changes in the probability of
conviction or in the severity of punishment (although this is
not present explicitly in the model). This lack of response is
entirely rational in that practicing specialists in criminal
activity will perceive greater opportunities in criminal
activity than will prospective criminals.
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In nearly every economic model of criminal activity there
are fixed probabilities for criminal justice outcomes such as
arrest and imprisonment. This is not realistic because, as an
offender engages in more acts of crime, the probability of
arrest and conviction rises. Block and Heineke present a more
realistic treatment.
Block and Heineke propose that the psychic costs of crime
and employment must be accounted for in models of decisions to
undertake illegal activities. Each individual must allocate
available time between legal activities (which they designate
as "labor") and illegal activities (which they designate as
"theft" since their analysis is restricted to property crimes
of which espionage is a particular case).
The Block and Heineke utility function for criminal
activity is:
U = U(L, T, W)
where U = Utility
L = Labor
T = Theft
W = Wealth of decision maker -
W is determined by:
W = WO + WLL +(W1 - pF)9(T)
where WO = Endowed wealth of the decision maker
WL = Rate of return from legal activity
W1 = Rate of return from illegal activity
F = Severity of punishment (specifically fine per
offense)
p = Probability of arrest/conviction
9 = Number of offenses committed by decision maker
Pyle (1983 ) points out that the. inclusion of L and T
directly in the calculation is an important departure from
Becker and from Ehrlich with significant behavioral
implications. L and T embody the psychic costs of crime and
legitimate employment (what Pyle describes as the
"disagreeability of work or of crime").
A decision maker chooses how much time to allocate to T in
order to maximize U. Like Ehrlich, Block and Heineke assume that
the amount of leisure time was fixed. Therefore leisure does
not enter the model as a third option for a decision maker.
Labor supply models, of course, commonly use leisure as the
trade-off alternative to the amount of time a decision maker
allocates to employment.
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As with most economic models of criminal behavior, the
Block and Heineke model assumes that an individual's allocation
of time between L and T depends on his or her attitude toward
risk. But it also implies that the allocation depends upon
their preference for honesty (UL - UT). This, unhappily,
gravitates, as do so many of these models, to an elaborate
highlighting of the obvious. To wit, if the probability of
conviction is raised, severity of punishment is increased or
the attraction of legitimate employment is enhanced, then an
honest person who is averse to risk will reduce his or her
participation in illegal activities. Otherwise, the Block and
Heineke model shows that a decision maker who is risk-averse
but dishonest will not respond in the same way to the same
deterrent changes. Ethical considerations, not surprisingly,
are found to be important determinants of criminal behavior.
OPTIMAL INCOME TAX EVASION -- ALLINGHAM AND SANDMO
Allingham and Sandmo (1972) looked at income tax evasion
as a special case of a decision to engage in criminal behavior.
I have reviewed it here because of the similarity between a
decision to evade taxes and a decision to engage in espionage.
Specifically, a decision maker must decide, in a specific time
frame, (1) whether to under-report income on a tax return and
(2) then how much to under-report the income. Unlike time
allocation models of criminal behavior in which time spent in
crime is a trade-off against time spent in legitimate
activities, a decision to under-report income has no such
competitive variables. A decision to under-report requires
little investment in time.
Tax evaders are assumed to be risk-aversive.
In the Allingham and Sandmo model, a decision maker chooses
a value of declared income to maximize expected utility:
EU = (1 - p)U(W - 9 * X) + pU[W - 9 * X - ri(W - X)]
where EU = Expected utility
W = Income
X = Declared income
9 = Constant tax rate on declared income
p = Probability of being investigated by tax
authority
W - X = Undeclared income
II = Severity of penalty (specifically a fine which
is assumed to be greater than 9)
A manipulation of this model led to the conclusion that
decision makers would declare more income for taxation if II
exceeded 100%. However, if II were less than 100%, the
mathematics of the manipulation prevented Allingham and Sandmo
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from concluding how a decision maker would behave except to
propose that risk aversion, as always, would be a major
determinant.
A market equilibrium model of criminal behavior began to
emerge in the work of Ehrlich (1981) and van den Haag (1975).
This model attempts a joint determination of volume of offenses
and net return from crime.
One early result of this model: the suggestion that the
efficacy of deterring sanctions cannot be assessed by reference
to the elasticity of the aggregate supply of offenses. The
primitive renderings of this model also suggest that the
efficacy of rehabilitation and incapacitation programs cannot
be inferred solely from the impact on individual offenders. It
depends on elasticity of market supply and demand schedules
that determine the extent to which rehabilitated offenders
will be replaced by others attracted by high net returns to
crime.
Empirical analysis of the economic models of criminal
behavior have been hampered by a general lack of relevant data.
This, in turn, has been a barrier to the development of a
comprehensive economic model of criminal behavior. For example,
Ehrlich (1986) complains that few studies attempt to determine
the private demand for self-protection.
Some researchers have attempted to link models of criminal
activity to models of law enforcement activity through three
sets of structural equations (Ehrlich, 1973):
1. Supply of offenses linking rate of offenses with
deterrence variables.
2. Production functions of law enforcement activity linking
probabilities of conviction with resource inputs.
3. Demand for enforcement linking resource spending with
determinants of public intervention.
Econometric studies have been limited by methodological
problems such as the under-reporting of crime rates by the FBI
Uniform Crime Reports. Measurement errors in the estimation of
the risk of punishment have led to biased and spurious
correlations. Often, results are biased by "missing variables"
such as markets for illicit drugs or the market for handguns.
Studies of similar offenses generally report similar
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findings: the probability of conviction and the severity of
punishment are inversely related to crime rates. Crime rates
are also found to be more elastic in response to changes in
the probability of apprehension than they are to changes in
the probabilities of conviction (if caught) or the severity of
punishment.
Crime rates are often found to be directly related to
measures of income inequality and levels of community wealth
(the more wealth in a community, the greater the opportunities
and perceived returns to criminal activity). Unemployment
effects are ambiguous. These patterns seem to hold whether the
data are gathered cross-culturally, taken from FBI records or
acquired from Victimization Survey information.
Measures of police output are weakly responsive to
increases in input resources. The response varies with the
definition of output and the specification of police production
functions.
While Forst (1976) found that not all studies are
consistent with the deterrence hypothesis, his analysis has
been criticized by Wadycki and Balkin (1979).
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Allingham, M. G. and A. Sandmo (1972). Income Tax Evasion: A
Theoretical Analysis. Journal of Public Economics, vol. 1,
pp. 323-338.
Bailey, William C., Charles H. Logan and Serapio R. Zalba
(1973). Comments on the papers in seminar. In Simon Rottenberg
(editor), The Economics of Crime and Punishment. Washington:
American Enterprise Institute for Public Policy Research, 39-62.
Beccaria-Bonesana, C. (1948). In L. Radzinowicz, A History of
English Criminal Law and Its Administration from 1750. London:
Stevens & Sons.
Becker, Gary S. (1968). Crime and Punishment: An Economic
Approach. Journal of Political Economy, vol. 76 (March/April),
176-217. Reprinted in Gary S. Becker and William M. Landes
(editors), Essays in the Economics of Crime and Punishment.
New York: National Bureau of Economic Research, 1-54.
Bentham, Jeremy (1931). Theory of Legislation. New York:
Harcourt Brace.
Block, Michael K. and J. M. Heineke (1975). A Labor Theoretic
Analysis of the Criminal Choice. American Economic Review,
vol. 65, no. 3 (June), 314-325.
Cobb, William E. (1973). Theft And The Two Hypotheses. In
Simon Rottenberg (editor), The Economics of Crime and
Punishment. Washington: American Enterprise Institute for
Public Policy Research, 19-34.
Ehrlich, Isaac (1970). Participation in Illegitimate
Activities: An Economic Analysis. Unpublished Ph.D.
dissertation, Columbia University, New York.
Ehrlich, Isaac (1973). Participation in Illegitimate Activities:
An Economic Analysis, Journal of Political Economy, vol. 81,
no. 3 (May/June). Reprinted in Gary S. Becker and William M.
Landes (editors) , Essays in the Economics of Crime and
Punishment. New York: National Bureau of Economic Research
(1974), 68-134.
Ehrlich, Isaac (1981). On The Usefulness of Controlling
Individuals: An Economic Analysis of Rehabilitation,
Incapacitation and Deterrence, American Economic Review, June.
Ehrlich, Isaac (1986). Crime and Punishment, preprint of
chapter in John Eaton, Murray Milgate and Peter Newman
(editors), The New Palgrave: A Dictionary of Economic Theory
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and Doctrine. Macmillan, forthcoming.
Forst, D. E. (1976). Participation in Illegitimate Activities:
Further Empirical Findings, Policy Analysis, Summer.
Heineke, J. M. (1978a). Economic Models of Criminal Behavior:
An Overview. In J. M. Heineke (editor), Economic Models of
Criminal Behavior. Amsterdam: North Holland.
Heineke, J. M. (1978b). Substitution Among Crimes And The
Question of Deterrence: An Indirect Utility Function Approach
to The Supply of Legal And Illegal Activity. In J. M. Heineke
(editor), Economic Models of Criminal Behavior. Amsterdam:
North Holland.
Horton, Paul B. (1973). Problems in Understanding Criminal
Motives. In Simon Rottenberg (editor), The Economics of Crime
and Punishment. Washington: American Enterprise Institute for
Public Policy Research, 11-17.
Krohm, Gregory and Jack P. Gibbs (1973). Comments on the
papers in seminar. In Simon Rottenberg (editor), The Economics
of Crime and Punishment. Washington: American Enterprise
Institute for Public Policy Research, 103-116.
Leftwich, Richard H. and Ansel M. Sharp (1976). Economics of
Social Issues. Dallas: Business Publications, Inc., chapter 5.
McKenzie, Richard B. and Gordon Tullock (1975). the New World
of Economics. Homewood: Richard D. Irwin, Inc., part four.
Pyle, David J. (1983). The Economics of Crime and Law
Enforcement. London: Macmillan.
Schmidt, Peter and Ann White (1984). An Economic Analysis of
Crime and Justice. Orlando: Academic Press, pp. 166-171.
Sjoquist, D. L. (1973). Property Crime And Economic Behavior:
Some Empirical Results. American Economic Review, vol. 63, pp.
439-446.
Smith, Adam (1776). An Inquiry into the Nature and Causes of
the Wealth of Nations. New Rochelle: Arlington House, Book IV,
Part IX, Expense of Justice, 311-313.
Stigler, George (1970). The Optimum Enforcement of Laws.
Journal of Political Economy, vol. 78, no. 2 (March/April),
Reprinted in Gary S. Becker and William M. Landes (editors),
Essays in the Economics of Crime and Punishment. New York:
National Bureau of Economic Research, 55-67.
Tittle, Charles R. (1973). Punishment and Deterrence of
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Deviance. In Simon Rottenberg (editor), The Economics of Crime
and Punishment. Washington: American Enterprise Institute for
Public Policy Research, 85-102.
van den Haag, Ernest (1975). Punishing Criminals, New York:
Basic Books.
Witte, A. D. (1980). Estimating The Economic Model of Crime
with Individual Data. Quarterly Journal of Economics, vol. 94,
pp. 57-84.
Wadycki, W. J. and S. Balkin (1979). Participation in
Illegitimate Activities: Forst's Model Revisited, Journal of
Behavioral Economics, Winter.
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MAJOR FEATURES OF SELECTED ECONOMIC MODELS
OF CRIME DEALING WITH PROPERTY OFFENSES
Source: Peter Schmidt and Ann White. An Economic Analysis of
Crime and Justice. Orlando: Academic Press, 1984, 166-171.
Theorist: Becker (1968)
Concept: Expected utility.
Objective: Maximize expected utility which is
direct function only of wealth.
Allocation: Time.
Factors controlled: Omnibus vector for factors such as "law
a bidingness."
Relationships: Number of offenses is affected by legal
alternatives, but is not determined
simultaneously with them.
Assumption about risk: Risk aversion.
Theorist:
Concept:
Objective:
Allocation:
Factors controlled:
Relationships:
Assumption about risk:
Theorist:
Concept:
Objective:
Allocation:
Factors controlled:
Relationships:
Assumption about risk:
Ehrlich (1970, 1973)
Expected utility.
Maximize expected utility which is a
direct function only of wealth.
Time.
Race, education, location and sex.
Crime function and labor supply
function are inversely related.
Risk aversion.
$joquist (1973)
Expected utility.
Maximize expected utility which is a
direct function only of wealth.
Time.
Race, population density, education,
city size.
Crime function and labor supply
function are inversely related.
Risk aversion.
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Theorist:
Concept:
Objective:
Allocation:
Factors controlled:
Relationships:
Assumption about risk:
Theorist:
Concept:
Objective:
Allocation:
Factors controlled:
Relationships:
Assumption about risk:
Theorist:
.Concept:
Objective:
Allocation:
Factors controlled:
Relationships:
Assumption about risk:
Theorist:
Concept:
Objective:
Allocation:
Factors controlled:
Relationships:
Assumption about risk:
Allingham and Sandmo (1973)
Expected utility function.
Maximize expected utility which is a
direct function only of wealth.
Wealth.
Unspecified shift parameters in illegal
gain and penalty function.
Crime is inversely related to amount
of wealth devoted to other activities.
Risk aversion.
Block and Heineke (1975)
Expected utility.
Maximize expected utility which depends
on wealth and time allocation.
Time.
Tastes for labor and theft.
Time in theft and working are
determined simultaneously.
Risk aversion.
Heineke (1978)
Expected utility.
Maximize expected utility which depends
on time allocation and level of
consumption.
Time and wealth.
Tastes for alternative time
allocations.
Time allocations and level of
consumption determined simultaneously.
None.
Witte (1980)
Utility function.
Maximize utility which depends on time
allocation and expected wealth.
Time.
Age, prior record, addiction
supervision, marital status and prior
behavior.
All time allocations are determined
simultaneously.
None.
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RESULTS AND ADVANCES OF SELECTED ECONOMIC MODELS
OF CRIME DEALING WITH PROPERTY OFFENSES
Source: Peter Schmidt and Ann White. An Economic Analysis of
Crime and Justice. Orlando: Academic Press, 1984, 166-171.
Theorist: Becker (1968)
Results: Increases in penalty or fine decrease the
number of offenses; increased fines are
relatively more effective than increased
probability of apprehension.
Advances over Resurrection of Bentham's insights.
Previous Work:
Theorist: Ehrlich (1970, 1973)
Results: Time allocated to illegal activity decreases
with increases in probability of
apprehension, severity of penalty or wage
rate; it increases with increased wealth
and illegal gains; fines are relatively
more effective for risk aversive potential
offenders.
Advances over Elaboration of Becker's insights. Introduces
Previous Work: both gains and losses in illegal activity
and gains in legal activity.
Theorist: Sjoquist (1973)
Results: Time allocated to illegal activity decreases
with increases in probability of sanctions,
wage rate and severity of punishment;
increases with returns to illegal activity.
Advances over Elaboration of Becker's insights. Introduces
Previous Work: both gains and losses in illegal activity
and gains in legal activity.
Theorist: Allingham and Sandmo (1972)
Results: Proportion of wealth allocated to illegal
activities decreases with increases in
severity of penalty or the probability of
its imposition; increases with increases
in wealth and illegal gains; increased
fines are more effective than increased
probabilities for risk aversive potential
offenders.
Advances over Combines Becker's model with portfolio
Previous Work: theory in application to tax evasion.
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Theorist: Block and Heineke (1975)
Results: No comparative static results forthcoming
under normal preference restrictions.
Advances over Introduces time allocation directly into
Previous Work: utility function; shows restrictions
needed to get comparative static results.
Theorist: Heineke (1978a)
Results: Time allocated to illegal activity decreases
with increases in severity of penalty and
the probability of imposition; increases
with increases in wealth, illegal gains,
and legal gains; increased fines are
relatively more effective than increased
probability of apprehension for the risk
aversive.
Advances over Shows that when leisure is allowed to
Previous Work: vary, legal and illegal activities are gross
complements; points up the nature of
restrictive assumptions in Ehrlich's and
Sjoquist's models.
Theorist: Heineke (1978b)
Results: No comparative static results are
forthcoming.
Advances over Models joint labor supply decision for
Previous Work: larceny, burglary, robbery and the labor
market. This allows substitution among
property offenses.
Theorist: Witte (1980)
Results: No comparative static results forthcoming.
Advances over Combines insights from Block & Heineke and
Previous Work: Ehrlich by introducing and unemployment
rate, criminal justice sanctions and time
allocation into the utility function.
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