Arizona State University Game Theory Article Summary
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Economics of Crime
Homework #6: Game Theory & Public Policy
Game Theory
1. How does the Mafias code of silence, which promises r3etribution against family members of
Mafia members who rat on other Mafia members, work to prevent the prisoners dilemma?
What must the government do to counter this?
2. You and a stranger witness a person bleeding to death. You both know the other person has
seen it as well. Design a static (simultaneous) game that models whether you call 911.
3. The United States tries to get other countries to follow its lead in the war against drugs using
trade sanctions. This policy does not consider the rights of foreign governments to set their
own policies. The government of Jamaica, knowing that legalization of marijuana would be
beneficial from a public policy standpoint, if all other things remained the same, would like to
change its laws so that marijuana possession and production are allowed. The payoffs to both
countries are presented in the game below. Determine all Nash equilibria for this game.
USA
Jamaica
Grow Marijuana
Criminalize
Impose Sanctions
(0, -50)
(-100, 50)
Free Trade
(200, -25)
(0, 0)
Public Policy
4. Describe the difference between statistical discrimination and preference-based discrimination.
How can hit rates be used to determine the difference?
5. What is the incapacitation effect discussed in the lecture? What are the policy implications of
the research findings related to the incapacitation effect?
6. Imagine you are a judge presiding over a racial discrimination case. The plaintiff is a man of
Middle Eastern descent accusing the United States Customs Service of discriminatory
practices in their non-routine searches (x-ray and/or strip searches) at John Wayne Airport. He
claims that the airport employees were biased in their selection of him and other people that
appear to be Middle Eastern. You have the most recent annual data on non-routine searches
conducted at John Wayne airport in the table below as supporting evidence. Based on the
data, what do you conclude?
White men
Black men
Hispanic men
Middle Eastern men
Asian men
# of successful searches
10,000
27,000
13,200
15,600
5,700
Total # of searches
50,000
90,000
60,000
120,000
30,000
Racial bias, Social Conditions, and Public Policy Options
Crime and Race
We have briefly discussed racial discrimination in applying the death penalty, which is one of
the most prevalent topics when discussing crime and race, but there are other aspects of race
and crime in the criminal justice system with topics such as racial profiling, discrimination in
sentencing convicted criminals, discrimination in setting bail, how criminal background checks
affect the employment opportunities of minorities, and even spatial discrimination of certain
laws. We will only discuss racial profiling in this lecture.
Racial Profiling
This is a term that most of us are familiar with, but probably has not been clearly understood. It
is an empirical fact that when police stop motorists to determine if they are carrying illegal
drugs, African-Americans are far more likely to be searched than are White motorists. For
example, in a study done in Maryland over the last half of the 1990s African-Americans made
up 63% of police searches but only accounted for 18% of motorists on the road. At first glance
this appears to be very troubling and shows support of racial bias on the part of the police, but
there may be an alternative explanation at play here.
If the objective of the police is to maximize successful searches, and if race can be used as a
predictor of criminal behavior because it is correlated with other more difficult to observe
predictors (which would be what? Namely, education and income levels, which lead to lower
opportunity costs of crime), then racial profiling by police may be an efficient tactic used by
police. In the economics literature, racial profiling used to predict criminal behavior is referred
to as statistical discrimination, while racial profiling that is motivated by prejudice is referred to
as preference-based discrimination. The question becomes, is there a way to distinguish
between the two?
The Basics of the Economic Model of Racial Profiling
Setup: Consider two groups of people Group A and Group B that can be distinguished by
some easily observable characteristic, such as race. In both groups, a certain percentage of
individuals carry illegal drugs. The objective of police is to maximize the number of successful
searches, commonly referred to as hits, while taking into account the cost of searching. Here
we are assuming that both criminals and police are rational, meaning they weigh the costs and
benefits.
Lets begin with assuming the police are equally likely to search both groups. In that case the
group with the higher percentage of individuals who carry illegal drugs (lets say group A) will
yield more successful searches. Equally likely searches then, can yield different hit rates.
Hit Rate = # of successful searches / total # searches for that group
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If the police are NOT racially biased, a more efficient use of resources would be to search group
A more intensively relative to group B to increase the number of hits. But how will the criminals
in each group respond to the change in search rates?
Since we assume criminals are rational, as the police intensify the search of group A there will
be a greater deterrent effect and less criminal activity in that group (Why? expected
punishment costs increase since probability of being caught increased for group A), but a
smaller deterrent effect and more criminal activity in group B (decreased exp. punishment
costs). As the hit rate in group A begins to decline and the hit rate in group B continues to rise,
eventually these two hit rates will become equal. If not, the police will continue to have an
incentive to move more resources to searching the group with the higher hit rate. Thus, if
criminals respond to the changes in deterrence, equal hit rates between the two groups are an
indication that the police are NOT racially biased, even if the search rates between the two
groups are different. If the police ARE racially biased, however, we can expect to see a lower hit
rate associated with the group that suffers the prejudice. In other words, the lower hit rate
indicates that police are inefficiently over-deterring that group, suggesting that an additional
explanation such as racial bias is partly motivating the searches.
**Hence, the numerator in the hit rate formula does not determine bias this measures
efficiency in police doing their job. The denominator is the indicator of racial prejudice since if
police are over searching a particular group relative to the expected criminality of the group
and/or other groups this will cause the hit rate to be lower.
A real world example may help solidify this theoretical model. In the late 1990s a case was
brought against the United States Customs Service and some of its employees for allegations of
discriminatory practices at OHara airport. It was filed by a group of black women who were
subjected to non-routine searches, such as x-rays and strip searches, yet no contraband was
found on them. The claim was that the employees acted biasedly against black women
compared to other groups including white women, white men, and black men when conducting
these searches. To support their claim they presented the following sample of national data on
the searching of airline passengers: 6.4% of black women were subjected to x-rays, compared
to only 0.73% of white women, 0.53% of white men, and 4.6% of black men. Based solely on
the search rates, black women were searched more than the other groups (substantially higher
compared to whites). Is this evidence of racial bias? We cannot tell with this data alone! We
need to look at the hit rates. For the same sample, contraband was found on 27.6% of black
women, 19.5% of white women, 25.1% of white men, and 61.6% of black men (these are the hit
rates). What do you gather from this? The plaintiffs claimed that the substantially higher search
rates of black women were not matched by higher hit rates, implying the excessive searching
was ineffective and biased. What do you think? Were they right?
Based on our model, the similar hit rates between black women, white women, and white men
actually suggest a lack of bias between these three groups. If it was biased we would see a
lower hit rate for black women, since bias would be causing a large number of innocent people
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to be ineffectively searched. Actually, based on the hit rates it suggests that black women,
white women, and white men are being biased against in comparison to black men and that
with such high hit rates, a more efficient use of resources should be to intensify searching this
group and reduce the intensity of the combined three groups. Recall that differentially low hit
rates imply bias, and in this case it is white women with the lowest hit rate, which may imply
they are the group suffering the most bias.
Some studies have challenged the theoretical model that assumes if hit rates are equal then no
bias is present. Meaning it is possible to have equal hit rates, but still have racial bias present.
One study that looked at this looked at the race of both the individuals searched and of the
police. If police are not racially biased then a white and black cop should approach racial
profiling in similar ways, meaning if there is an efficient but unequal search rate among groups
of people the cops should employ the same technique (statistical discrimination). However, if
the race of the officer affects the search, then racial bias may be present. They are looking to
find if white officers excessively search black individuals? And/or do black officers excessively
search white individuals? One study that looked at this concluded that if the race of the officer
differed from the race of the individual, there is a higher probability they will be searched. This
was true for both white cops searching blacks and black cops searching whites. Overall, there is
racial profiling that occurs but what is important that economics tells us is that the search
rates, even when substantially different for different groups, is not indicative of racial bias.
Some studies conclude that racial profiling is an efficient police technique using statistical
discrimination while others conclude that it is racial bias from preference-based discrimination,
it may very well be both of these types of discrimination occurring at the same time. Policy
officials then face the difficult task of determining if the benefits of racial profiling as an
effective police search and deterrent technique outweighs the costs associated with racially
biased police behavior.
Social Conditions and Reforms
Though the core body of economic research on crime focuses on the costs and benefits of
traditional deterrence policies affecting the certainty or severity of punishment, there is
growing focus on other policy options to reduce the crime rate these include things like labor
market conditions, education, juvenile behavior, family background, and so on. Since each
dollar spent on one of these programs is a dollar less on the others it is important to know all
the pros and cons of each when distributing our resources.
Unemployment and Crime
Since we know criminals behave rationally, they are making calculated choices about
participating in the illegal market as well as the legal markets. Based on this, it would seem
right to assume that during times of high UE we would see high crime rates (since fewer legal
options available) and during times of low UE we would see lower crime rates. If this is true,
policy then should focus on improving job opportunities to reduce crime. Do you think this
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positive relationship holds for UE and crime? No, it is far more complex than that, just like we
discussed with the macroeconomic effects of economic growth. For example, there is some
evidence to suggest that alcohol, drugs, and gun consumption decreases during higher levels of
UE. What can explain this? The income effect which causes the purchase of these goods to
decrease when our income decreases and vice versa. So here UE and crime may be inversely
related, furthermore when income levels decline there may be less attractive items for
criminals to steal as well and vice versa.
Another difficulty is determining causation which may be simultaneous in both directions. We
often are quick to conclude that unemployment leads to more crime, but crime may lead to
more unemployment. Why would this be? Because of criminal background checks, and
criminals having a hard time finding employment. Also, businesses might not want to locate in
areas with higher crime rate, reducing job opportunities in that area.
Another complication is that participating in crime or in a legitimate job may not be mutually
exclusive, meaning some people do both. It is common for drug dealers to also hold a valid job,
which even may provide a market of clients for them. Also, for white collar crimes like
embezzlement of stealing from employers it requires the criminal to be hired in a legitimate
firm.
Many studies have tried to tease out the effects of UE on crime with mixed results. They do
seem to find it has more of an impact on property crimes and not much on violent crimes.
However, what does seem to be true is that since UE is a short-term issue (due to its cyclical
nature) it has a much smaller effect or impact on crime compared to wages. Wages may be a
better measure of labor market conditions to explain the crime rate because a decline in wages
tends to have a longer-lasting impact on individuals. One study found that a 20% decline in the
wages of unskilled men between 1979-1997 (since unskilled men are most likely to participate
in criminal behavior, better than taking whole population which washes out the results), led to
property crime increasing by 20% and violent crime increasing by 35% over this same period
and approximately 50% of that change they attributed to the change in wage. The conclusion
here then is that to help deter long-term crime trends improvements in the wages paid to
unskilled workers are likely to be more effective than improvements in employment
opportunities. *Note this must be a sustained change/increase in wage and not just a one-time
payment like we often see during recessionary times, which does not change criminal behavior.
Juvenile Crime
One undisputed fact of criminal behavior is that young individuals, particularly young makes,
commit a disproportionate amount of crime. For example, in 1997 individuals aged 15-19
accounted for over 30% of property crime arrests but made up only 7% of the population.
Similar numbers hold for violent crime arrests. The most common juvenile crime (in a
proportional sense) is arson with juveniles making up 49% of all arrests.
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When applying our economic model of crime to juveniles, it may be the case that there is a
strong deterrent effect of punishment for young criminals, but actual punishment levels are too
low to greatly affect their behavior meaning they are acting rationally based on knowing that
they get a less harsh sentence because they are under 18. One study found that the average
rate of return for a single property crime to juveniles is $200 per day and that the average
number of days incarcerated per crime is 0.6 days. In other words, a juvenile considering
committing a property crime is facing a half-day prison sentence for a $200 gain. The same
sentence for an adult under this scenario would face an average sentence of 2.6 days in jail.
Therefore, a juvenile may find that committing a typical property crime yields a decent rate of
return compared to other crimes and compared to an adult offender.
Thus, applying differential punishments for adult and juvenile offenders may be an important
contributing factor in explaining youth crime. What is the policy implication here? It is simple
enforce harsher punishments for juveniles. However, another explanation is that it may be the
case that the deterrent effect is just really weak for young criminals. Meaning it is not the low
severity of punishment accounting for juvenile crime but the inability of any punishment to
change juvenile behavior. Thus, if the deterrent effect does not exist then we need alternate
methods besides jail or fines to reduce juvenile crime. So we really need to have information on
if the deterrent effect exists for juveniles meaning do they actually fit the rational crime
model and weigh out the benefits and costs including the probabilities and severity of
punishment when deciding to commit a crime or not?
One study attempted to answer this by looking at survey data in 1995 from 15,000 individuals
ages 13-17 with several control variables for individual and family characteristics: age, race,
ethnicity, religion, parents education level, etc. as well as county variables like population
density, unemployment rate, poverty measure, and racial compositions. They used a change in
the arrest rates for violent crime to measure deterrence effects and found that increased
arrests did lead to less juvenile crime for males selling drugs and committing assaults and for
females selling drugs and stealing. There were other factors that influenced the crime rate of
juveniles. They found that as UE rate increases so do some types of juvenile crime. Other
factors that affect juvenile crime were parents education level, religious beliefs, and family
structure (single or double parent household).
Another study looking at the severity of punishment as a person transitions from juvenile to
adult found a sharp decline in crime rates for individuals aging out of the juvenile system, which
shows that juveniles are at least as responsive to changes in severity of punishment as adults
are. There are other considerations as well, such as from a cost standpoint it is more expensive
to incapacitate/house juveniles in detention centers than adults. Also, even though there does
seem to be a deterrent effect present there may be public sympathy involved that encourages
policy officials to be less effective in deterring juvenile crime. Based on these issues, perhaps
the best social policy to implement is to reduce the likelihood that juveniles become criminals
in the first place.
5
Education as a Crime Deterrent
Providing educational opportunities to inmates is not the only way to reduce the crime rate.
Improving education of youth, especially high school students, may lead to reduced future
criminal behavior. The relationship between education reduced crime is straightforward,
increased education leads to an increase of legitimate job opportunities and higher wages
which reduces the financial attraction to criminal activities (opportunity cost of crime is
increased, so education is indirectly linked to severity of punishment). Also, being imprisoned
has a social stigma to it and acts as an additional deterrent. This stigma is likely to be greater for
more educated individuals. Also, increased education may lead to individuals risk preferences
and be cause them to be less near-sighted in their decisions (more consideration for their
future) and led them to be less prone to carry risk, reducing likelihood of criminal behavior.
Calculating the effect of education on crime is challenging because of reverse causation issues
between education and criminal behavior. We usually predict that less educated people will
commit more crime, but it may also be the case that people with a greater propensity to
commit crime are less likely to stay in school. So, is it less education that is accounting more for
crime? Or is it criminal behavior that is accounting for less education? Also, it may not always
be the case that less education leads to more crime, specifically for white collar crime which is
usually done by educated individuals in positions of power.
One study that has focused on finding out if the causal link is as predicted that less education
leads to more crime- found that more education does reduce the crime rate, and an additional
year in high school significantly reduces the probability of arrest and incarceration. This finding
is likely best explained with the improved job and wage opportunities of educated individuals.
Furthermore, the study finds that an increase in high school graduation rates not only has
private benefits for the individual but also social benefits from reduced social costs of crime.
They find that a 1% increase in the male H.S. graduation rate leads to a $1.4 billion dollar per
year savings in the social costs of crime.
School and the Incapacitation effect
In addition to providing increased job and wage opportunities to deter crime, schooling may
provide another avenue to reduce crime and that is through incapacitation. Though students
are not in school 24 hours like people in prison are, they are required to be in school for a
certain number of hours five days a week in which during this time they are less able to commit
crimes. This suggests a potential policy option for reducing juvenile crime may be to increase
the duration of the school day. There are two studies that try to address the school
incapacitation effect to see if school attendance reduces juvenile crime. What do you guys think
the results were?
First, since students have ample time outside of school hours (evenings, weekends, holidays,
etc.) it is important for this kind of study to look at juvenile crime committed when they should
have been in school but were not. Second, it is important to know if crime is actually reduced
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from being in school or is it just displaced to other times when not in school. This way policy
makers will know if extending the school day doesnt prevent crimes and instead only changes
the occurrence of crimes to the evening hours. The two studies attempted to do this in
different ways. One compared the juvenile crime rate on school days compared to in-service
days, which are paid days off for k-12 educators to have professional development and
planning time away from the students. The other study used teacher strike days instead for the
reason students are not in school. Using strike days is a bit better since there is usually no
forewarning about a strike compared to in-service days, which are typically planned and
announced well in advance and gives parents more time to plan for child supervision.
The studies had similar and mixed results. First, they found that being in school does provide a
significant incapacitation effect for property crimes. Not only was there less property crime on
days where school was in session, but also there did not appear to be a displacement effect
across other days meaning that school attendance actually reduces total crime and not just
displaces it. The total property crime rate was reduced between 15-30%. However, this was not
the only finding. They also found that violent crimes between juveniles increase with school
attendance, by an amount between 30-37%. Here it tells us that when juveniles are forced to
spend more time with each other violent crimes between them are more likely to occur. With
these opposing results, it is difficult to evaluate the effectiveness of policies meant to increase
school attendance. The main take away seems to be to that one way to reduce juvenile crime is
to provide adequate distractions for them, but in a setting where you are not placing a large
amount of juveniles together at one time. After-school enrichment programs like YMCAs, gang
intervention programs, career development programs, etc. would be good solutions to this.
Crime in the City
It is a fact that crime rates in cities, especially large metropolitan areas, are larger than crime
rates in rural areas. There are three main reasons for this. The first is that there are higher
monetary returns to criminals in dense urban areas than in smaller suburbs or rural cities. This
can be explained by greater access to wealthy individuals in large cities as well as a greater
density of potential victims. The second reason is that criminals face a lower probability of
arrest in a large city, this is because for many crimes here the police are going to confront a
much larger suspect pool making it harder to apprehend the criminal. The last and most
significant reason is that the greater the percentage of female-headed households, the greater
the crime rate. Why? This is likely due to less supervision of youth, more financial hardship in
the household, and lack of a strong male role model. Unfortunately, it is hard to say whether
single-female headed households are attracted to large urban areas to live or if being in a large
urban area creates more female headed households. Either way we can conclude that family
structure is an important determinant to the crime rate in large urban areas. This suggests the
importance of other policies beyond the traditional deterrence policies affecting certainty or
severity of punishment are important. What type programs may be needed to help reduce the
7
incidence of female-headed households or to reduce the propensity for members in such
households to commit crime is still an open and difficult question.
Prison verses Social Programs
With most social issues there are several policy options that can be implemented to resolve
whatever problems are at hand. In deterring crime, there are two such policies are 1) to devote
more resources towards apprehending, convicting, and punishing criminals or 2) devote
resources towards social programs, especially aimed at the young to discourage future criminal
behavior. This leads to an obvious economic question: what is the optimal trade-off between
devoting resources to each of these deterrence options?
Based on economic theory, when do we know we have optimized the distribution of resources
to each? The answer is to devote resources to each one until the last dollar spent on each
policy option brings the same return in deterrence benefits gives us the same bang for our
buck. Conversely, if one more dollar spent on either policy would bring us a reduction in crime
then we are not at the optimal allocation of resources. This all sounds very simple, and is in
theory, but doing this in the real world is very difficult mainly because it is extremely difficult
to calculate the marginal value of a dollar in different settings.
There was one study that attempted to measure the trade-off between allocating resources
toward increasing the prison population verses expanding social programs in the U.S. They
claim, based on their results that by cutting spending on prisons and reallocating those savings
to social programs that crime can be reduced. Meaning that without increasing the current
amount spent on policies, crime can be reduced which implies that currently too many
resources are being spent on prison as a crime deterrent. Their conclusion relies on many
assumptions in their study, so we can take this with a grain of salt in whether it is actually true
or not, but their method to going about this is important to understand how economists
attempt to measure difficult trade-offs.
First they consider two policy options 1) to increase the current prison population by 50% over
the current level or 2) maintain the current prison population and spend the saved resources
from the first policy option on potential crime-reducing social programs. To evaluate the
benefit of the first option, they rely on estimates for how sensitive crime is to changes in the
prison population, empirical studies predict doubling the prison population leads to a reduction
in crime by 10-30%. Because option 1 is to only increase the prison population by 50% they can
then estimate that crime would be reduced by half of this or 5-15%. Also, if the incarceration
rate is held constant in option 2, then they can expect crime to be 5-15% higher under this
policy compared to policy 1. This gives them an important benchmark, if additional resources
saved with option 2 can be reallocated into social programs that reduce crime by more than 515%, that reallocation can be considered efficient.
The next step is to calculate the dollar value of resources saved by not increasing the prison
population. Taking into account not only the cost to house criminals, but also their lost
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legitimate job earnings they estimate it would cost between $5.6B-$8B dollars to increase the
prison population by 50%, this is the amount of money that can be devoted to social policies
instead. These may include programs like preschool and early childhood education (i.e. Head
Start), family-based therapy, treatment programs for juvenile delinquents, job skill
enhancement programs, and so on. The last step is to calculate the deterrence benefits of
these programs. Here the data is extremely limited on the effectiveness of these programs in
reducing crime. Here they use what little evidence there is and also add a limiting assumption
that only half these benefits are achieved to be conservative, and still find that it is likely that
resources can be used more efficiently to reduce crime if reallocated away from increasing the
prison population and put towards social programs. Lastly, they point out that this is not likely
to be an attractive option for politicians. This is because we see a more immediate drop in the
crime rate from the increase in prison population than we do for investment in social programs,
which typically have large (current) upfront costs and a long time period to see it pay off (future
benefits). Most politicians tend to favor programs that they can take credit for while they are
still in office (principle-agent problem). Overall, resources are scarce and trying to carefully
think about where resources can best be used is what economic policy analysis is all about.
There is more to policy analysis than just believing one policy is better than another and even
where cost-benefit analysis is very difficult or seems impossible, it is always a good place to
start to at least identify some key trade-offs.
If there is time, discuss with each other: What did you learn this lecture? What was most
interesting to you?
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©
Urban
Crime:
Issues and
Policies
Housing Policy
Debate
Volume
7, Issue
4
Fannie Mae Foundation 1996. All Rights Reserved.
731
731
Urban Crime: Issues and Policies
Ann Dryden Witte
Florida International University, Wellesley College,
and National Bureau of Economic Research
Abstract
Research suggests that some social and criminal justice policies can affect the
crime rate. This article considers the major criminal justice and social policy
issues related to urban crime, such as drugs, domestic violence, property
values, and the underground economy.
Family disruption, drugs, limited economic opportunities, and unoccupied and
unsupervised youth are all found to be associated with urban crime. The
article concludes that major reductions in crime are likely to result only from
increased economic and social opportunities for families and youth, particularly for young males. Intensive programs directed at families and at-risk
youth are more likely to lower crime than are programs directed at people
already heavily involved in illegal activities. It costs less to keep young people
in education and training programs than to imprison them, and such programs
are more likely to produce productive and well-adjusted adults.
Keywords: Policy; Crime; Education
Introduction
Urban crime is a major issue for Americans. This is true even
though the most reliable evidence available, data from the National Crime Survey, indicates that the level of crime is lower
today than it was in the late 1970s and early 1980s. The amount
of crime is less for the most feared offenses, including rape,
aggravated assault, burglary, and larceny, as well as for less
serious offenses.1
The composition of crime has changed. While the overall murder
rate in the United States has declined since the late 1970s, the
murder rate for young males, particularly young black males,
has increased. Beginning in 1985, the murder victimization rate
for blacks ages 15 to 24 began to increase substantially. In the
late 1980s, the victimization rate for young blacks exceeded the
previous record levels of the early 1970s,
