Crime, Education and Peer Pressure
Università degli Studi di Milano-Bicocca
Università degli Studi di Bergamo
We present a dynamic two-period model of individual behaviour with het-
erogeneous agents in which individuals decide how to allocate their disposable
time between education, crime and work in the legal sector. Education has a
twofold effect: it implies higher expected wages in the legal sector, increasing the
opportunity cost of committing crime and it has a sort of “civilization” effect
that makes more costly to engage in criminal activities. We model this effect by
introducing a peer pressure function.
Key words: Crime; Education; Peer Pressure
JEL Classification: I2; J24; K42
∗This paper builds on one chapter of my PhD dissertation. I would like to thank Federico Cingano,
Piergiovanna Natale, Leone Leonida and two anonymous referees for their useful comments and ad-
vices. I am solely responsible for this paper’s contents. Financial support from the University of
Milan-Bicocca is gratefully acknowledged. Email address: firstname.lastname@example.org.
Over the last three decades, a growing amount of research effort has been devoted to
study the socioeconomic determinants of criminal behaviour, partly motivated by the
remarkable increase in criminal activities in many developed countries.
The empirical evidence collected so far suggests two main stylized facts: i) criminals
tend to be less educated and from poorer and more disadvantaged backgrounds than
non criminals and ii) peer effects and social interactions are very strong in criminal
decisions. In 2001 more than 75% of the overall convicted population in Italy had not
graduated from high school and, analogously, in the US two-thirds of the incarcerated
men had not attained this level of education (Freeman, 1996).1On the other hand,
several studies (Case and Katz, 1991; Glaeser et al, 1996; Ludwig et al, 2001) find
that living in low-income and high-poverty neighbourhoods increase the probability of
engaging in crime.2
The purpose of this paper is to provide a model encompassing both the effects
of education and peer pressure on criminal behaviour. Previous theoretical works,
following Becker (1968), describe a criminal like an amoral individual, whose decision
is made on the basis of a maximization problem in which individual compares costs and
benefits of legal and illegal activities taking in account the probability of being arrested
and punished and the expected returns from crime. Instead, we consider other factors
that can affect criminal choice as education, background and peer effects. We develop
a dynamic two-period model of criminal behaviour, in which individuals decide how to
1Despite this evidence, few papers have estimated the causal relationship between education and
crime. Recently, Lochner L. (2004) and Lochner L. - Moretti E. (2004) find a significant and
robust inverse relationship between crime and high school graduation.
2For instance, Case A.C. - Katz L.F. (1991), using data from the 1989 NBER survey of youths
living in low-income Boston neighbourhoods, find that a 10 percent increase in the neighbourhood
juvenile crime rate increases the individual probability of becoming a delinquent by 2.3 percent.
Ludwig J. et al (2001), using data from a randomized housing-mobility experiment conducted on
638 families from high-poverty Baltimore neighbourhoods, estimate that relocating families from high
to low poverty neighbourhoods reduces juvenile arrest and violent criminal behaviours by teens on
the order of 30 to 50 percent.
allocate their disposable time between education, crime and work in the legal sector.
Education in our model has a multiple role: i) by investing in education agents raise
their productivity/skills and improve their labour market perspectives thus incurring
a higher opportunity cost of crime and ii) education has a “civilization” effect that
makes more costly to engage in criminal activities. We model the “civilization” effect
of education by introducing a peer pressure function, following Kandel and Lazear
(1992). In particular, introducing a peer pressure function, we are able to analyze
how individuals are affected in taking their decisions by peer group components (i.e.
parents, relatives, schoolmates, neighbours).
Our main findings suggest that a correct mix of enforcement, education subsidies
and taxation policies reduces crime. In particular, increases in law enforcement and in
education (via education subsidies) are likely to considerably affect the level of crime
and to be important components of an effective crime-fighting strategy.
Our model encompasses many of the mechanisms discussed and developed by the
relevant literature in this field.
As previously mentioned, education affects the decision to engage in criminal ac-
tivities in several ways. First, higher levels of educational attainment are associated
with higher wage rate, increasing the opportunity cost of criminal behaviour. Second,
education may alter personal preferences so to affect decisions to engage in crime. In
particular, Fajnzylber et al (2002) suggest that, by incorporating a civic component,
education may increase the individual’s moral stance, and then affects the individu-
als’ perception of crime. Similarly, Usher (1997) stresses that education “perpetuates
the values of society, enculturates people to serve their communities, and promotes the
virtues of hard work and honesty” (p. 386). Third, independently of the level of educa-
tional attainment, school attendance alone, reduces the time available for participating
in criminal activities (Witte and Tauchen, 1994). Hence, education appears to be an
important variable in determining crime rate both for its direct economic implications
and for its non market effects.
Other important aspects of criminal behaviour relates to the social structure and
networks and in particular to the role of peer group in influencing individual behaviour.
Calvo-Armengol and Zenou (2003) stress the role of social structure and network in fa-
cilitating delinquent behaviour. Criminal activity may be contagious in high-crime and
disadvantaged areas both because the probability of apprehension and the punishment
associated to the criminal action may be lower than in other neighbourhoods (Sah,
1991), and since it is easier to get in touch with criminals and acquiring the know-how
for crime. Neighbour and peer pressure may also affect the actual or perceived returns
to education and legal work by influencing access to schools, that may turn out in a
lower opportunity cost of crime. Case and Katz (1991) find that there exists an im-
portant link between the behaviour of older family members and youth in relation to
criminal activity, drug and alcohol use and that youth behaviour is substantially af-
fected by neighbourhood peers. Disadvantaged youths, living in suburb or high-crime
areas, are more likely to imitate bad attitudes of their parents and neighbours (i.e.
crime participation, abuse of drug and alcohol, school drop out). Individuals are more
likely to think that illegal behaviours are legitimate if they observe their neighbours
not to respect law.
The remainder of the paper is structured as follows. In Section 2 we present in
detail the model and the equilibrium. Section 3 discusses the results and Section 4
2 The Model
We develop a dynamic two-period model of individual behaviour with heterogeneous
agents in which adolescents and adults3decide how to allocate their disposable time
between education, crime and work in the legal sector. Level of ability and endowments
achieved in primary school are taken as given. We analyze the impact of education
subsidies, taxes, law enforcement (i.e. probability of apprehension), victimization rate,
peer pressure and level of wages on criminal behaviour. Below we describe the various
components of our framework.
3As we discuss later in the subsection 2.7, individuals in the second period do not invest in education
due that they live the last period of their life.
The economy is populated by a large number of individuals who are ex-ante hetero-
geneous with respect to their learning abilities (εi). Each individual maximizes the
present value of her lifetime utility with respect to the time allocated to education in
the first period (si,1) and the time allocated to criminal activities in the first (di,1) and
in the second period (di,2) :
1 + ρUi,2
The utility function is defined as
Ui,t= ci,t− γ(si,t−1)(di,t−
where ci,t: consumption of individual i in period t,
N − 1
: average time
spent committing crime by others belonging to the same peer group, γ(si,t−1)(di,t−
peer pressure function, ρ : intertemporal discount factor. The share of type-i individual
in the population is given by the fraction χi,
χi= 1, where I is the number of ability
The individual’s utility depends on her consumption and on her disutility, com-
parable with consumption, coming from her decision about crime. The peer pressure
function implies that individuals get disutility from committing more crimes than their
peer group components. The magnitude of this effect is caught by γ(si,t−1) and depends
2.2 Occupational Opportunities
Denoting with wtthe wage rate in period t, with li,tthe time spent working in the legal
sector and with τ the tax rate, disposable income from legitimate activities of a type-i
individual is given by
yi,t= (1 − τ)wthi,tli,t
= (1 − τ)wthi,t[1 − si,t− di,t]
where hi,trepresents the level of ability of individual i at time t.
The individual ability is defined as:
0 < α < 1
Individual ability is an increasing function of the level of education acquired in the
previous period by agents and of εi, learning ability different across individuals. We
exogenously assume hi,0, that represents the level of ability acquired during compulsory
2.3 Criminal Opportunities
During their lives agents optimally choose whether to engaged or not in criminal activ-
ities. If an agent engages in criminal activities, she obtains with probability (1 − πa) a
return R(di,t,hi,t), function of the time devoted to crime and individual ability. Returns
from crime are supposed to be increasing at a decreasing rate in individual ability and
in time devoted to crime. With probability πaa criminal is apprehended and punished.
An apprehended criminal goes to jail for the entire period in which she is apprehended.4
Each individual faces an equal probability πvof being victim of a crime, where πvis
equal to the endogenous fraction of criminals in the population.5If victimized, an
individual loses a fraction δ of her disposable income from legitimate activities.
2.5 Peer Pressure Function
“The peer pressure function is an attempt to formalize the discussion of taste” (Kandel
and Lazear, 1992: p. 804). Following Kandel and Lazear (1992), we try and model
4Our analysis is general and will not change allowing that an apprehended criminal goes to jail for
a fraction of her disposable time.
5By using the Law of Large Numbers we can consider πv to be the same both for criminals and
criminal preferences. Usher (1997) states that “education promotes good citizenship.
Education does more than teach skills to enhance one’s capacity to earn income. It
perpetuates the values of society, enculturates people to serve their communities, and
promotes the virtues of hard work and honesty” (p. 368). Education affects individuals’
preferences and modifies their perception of phenomena like crime, corruption and other
illegal attitudes. In this sense education may alter individuals’ behaviours and may be
particularly helpful in reducing or enhancing the influence of peer group components.
In other words, if education promotes the virtues of hard work and honesty it is likely
that an individual living in a “bad” neighbourhood will be affected in her decision and
will act differently with respect to her peer group components; on the other hand if an
individual lives in a context where honesty is a shared value it is likely that education
enhances her adherence to the prevalent social rules.
Individuals are affected in their decisions by peer group components (i.e. relatives,
parents, schoolmates, neighbours). In this sense the role of socioeconomic background
is relevant in affecting individuals’ decisions, but we think that the role of education
may be important in modifying some “bad” attitudes coming from the peer group.
We define the peer pressure function in the following way:
where γ(si,t−1) is an increasing function of the education level attained in the previ-
ous period and (di,t−
crime and average time spent committing crime by others belonging to the same peer
dt) is the difference between individual’s time spent committing
group. We can identify γ(si,t−1) as a “socialization” or moralization effect of education,
while the component (di,t−
average behaviour of components of respective peer group.6Socialization component
dt) represents the effect on utility by deviating from the
of the peer pressure function is supposed to be increasing at a decreasing rate in time
devoted to education.
The effect of the peer pressure function on utility is negative if the individual will
commit more crime than her peer group average and is positive if she will commit
6We consider linear deviation from average behaviour.
less crime than her group average. The magnitude of this effect is given by the first
component γ(si,t−1). In particular, more educated people tend to suffer more disutility,
while less educated tend to underestimate this effect.
It is worth to notice that if an individual behaves as her peers the effect of peer
group on individual’s utility tend to be null. In other words, if an agent acts in line
with the prevalent social norms, because the norms are strict, she is forced to do it or
she is not able to break the rule, this would imply a null effect on the utility. Only
deviations from the average behaviour or the prevalent social norms affect individual’s
Disposable time is allocated among each activity: school, work in the legal sector and
crime. Individual time endowment is: li,t+ si,t+ di,t = 1 and li,t,si,t,di,t ≥ 0. If
apprehended, individual will go to jail for the entire length of the model period. In
the second period schooling is equal to 0, namely individuals can choose only between
work in the legal sector and crime.
2.7 Honest and Criminal Consumption level
Given the assumptions made in the previous subsections, the consumption level of an
individual who chooses not to be a criminal is given by
where T represents the direct cost of education (i.e. tuition fees paid by agents
(1 − δ)yi,t− si,tT
(1 − πv)
minus education subsidy obtained by the government T = F − S). Similarly, the
consumption level of an individual who chooses to be a criminal is:
yi,t+ R(di,t,hi,t) − si,tT
(1 − δ)yi,t+ R(di,t,hi,t) − si,tT
(1 − πv)(1 − πa)
πv(1 − πa)
where c is the level of consumption of a convicted criminal.7
2.8 Agent’s Decision
Given the tax rate (τ), the wage rate in the first and in the second period (w1and w2),
the tuition fee (F), the education subsidy (S), the learning ability (εi) and the initial
level of ability (hi,0) individuals choose how to allocate their disposable time between
education, work in the legal sector and crime by solving the following maximization
1 + ρUi,2
subject to (6), (7) and the time constraints.
The problem faced by an individual can be written as:
where φ = (1 − τ)(1 − πa)(1 − δπv) and θ = (1 − τ)(1 − δπv).
Because agents are heterogeneous with respect to their learning ability, there will
si,1θw1h1(si,0)(1 − si,1) − si,1T − γ(si,0)(di,1−
θw2h2(si,1) − γ(si,1)(di,2−
si,1,di,1,di,2φw1h1(si,0)(1 − si,1− di,1)+
πac − si,1T + (1 − πa)R(di,1,hi,1) − γ(si,0)(di,1−
πac + (1 − πa)R(d∗
φw2h2(si,1)(1 − d∗
i,2,hi,2) − γ(si,1)(d∗
be a level of learning ability ˆ ε such that for εi> ˆ ε agents will be honest and for εi< ˆ ε
agents will engage in criminal activities.8
7As in Imrohoroglu A. et al (2000) we assume that apprehended criminals cannot work or
access their assets to finance their consumption while in jail.
8As long as education increases the marginal return to work more than crime (wth
t(st−1)), crime is decreasing in education. We argue that for unskilled property crimes, edu-
cation is likely to have little effect on criminal returns. Thus, this implies that an agent will be honest
above a certain level of ability and she will engage in criminal activities below.
Then, the problem of an individual who chooses to be engaged in criminal activities
φw1h1(si,0)(1 − si,1− di,1) + πac − si,1T+
(1 − πa)R(di,1,hi,1) − γ(si,0)(di,1−
(1 − πa)R(d∗
φw2h2(si,1)(1 − d∗
i,2,hi,2) − γ(si,1)(d∗
i,2) + πac+
The first order conditions with respect to si,1, di,1and di,2for an interior solution are:
di,1: φw1h1(si,0) = (1 − πa)Rd1(di,1,hi,1) − γ(si,0)
si,1: (1 + ρ)[φw1h1(si,0) + T] =
+(1 − πa)Rh2h0
di,2: φw2h2(si,1) = (1 − πa)Rd(di,2,hi,2) − γ(si,1)
2(si,1)(1 − d∗
2i(si,1) − γ0(si,1)(d∗
The FOCs allow us to study individual behaviour and in particular how agents
allocate their disposable time between school, work in the legal sector and crime.
Equations (11) and (13) show that individuals spend time in committing crime
up to the point in which the expected marginal return from crime equals the expected
marginal return fromlegal activities after taxes plus the marginal effect of peer pressure.
The inclusion of peer pressure implies that return from illegal activities is lower than
it would be without considering peer pressure. If, as we have supposed, the internal
pressure function is increasing in the level of education, then more educated individuals
will find more costly to commit crime because they get disutility from crime.
Equation (12) allows us to study the costs and returns of education. On the one
hand, a higher level of education implies higher returns from both legal activities and
criminal activities. This depends on the fact that education affects both ability in
the legal sector and in the criminal sector. On the other hand, an individual with
a high level of education if apprehended and convicted experiences greater losses in
earnings. As stressed by Fajnzylber et al (2002) “we can conjecture, however, that
if legal economic activities are more skill or education intensive than illegal activities,
then it is more likely that education will induce individuals not to commit crimes”.
2.10Specific Functional Forms
In order to find an explicit solution for the model we suppose that the functions pre-
sented in the previous sections have the following functional forms displaying the func-
tions’ properties discussed above:
hi,t(si,t−1) = εisα
i,t−1 with 0 < α < 1
γi,t(si,t−1) = sβ
with 0 < β < 1
R(di,t,hi,t) = dη
with 0 < η < 1
Hence, by using these functional forms we can rewrite the FOCs for an interior solution
si,1: (1 + ρ)£φw1εisα
i,0= (1 − πa)ηdη−1
i,1(1 − d∗
(1 − πa)(1 − η)d∗η
i,1 − βsβ−1
i,1= (1 − πa)ηεidη−1
By solving the FOCs we can obtain an explicit function for time devoted to criminal
(1 − τ)(1 − δπv)wtsαη
(1 − πa)εiη
We know that −1 <
In this section we briefly present the effects of policy variables, we will discuss in
η−1< 0 and (1 − πa)η > 0.
detail the implications of the model in the following sections. An increase in education
received at t − 1, also compulsory primary schooling, will lead to a reduction in the
level of crime in the following period. Moreover, an increase in taxes and an increase
in δπv, which determines the incentive to work of agents,9will have a positive effect
9δπvdetermines the incentive to work of agents. In fact, δπvdetermines the expected net (post-
tax) income that a worker will spend for consumption considering that she will be victimized with
on time devoted to crime. Finally, both an increase in wages and in the probability of
apprehension (πa) have a negative effect on time spent committing crime.
We are interested in an explicit solution for si,1. By using (18) representing the
FOC with respect to si,1, we can define:
δεi(1 − πa)£(1 − τ)(1 − δπv)w2sα−1
i,1(1 − d∗
i,2) + (1 − η)d∗η
d2) = (1 + ρ)£(1 − τ)(1 − πa)(1 − απv)w1εisα
(1 − τ)(1 − δπv)w2sαη
(1 − πa)εiη
Rearranging and defining
(1 − πa)(1 − η) = μ
(1 + ρ)£φw1εisα
i,1(1 − d∗
i,2) + μεid∗η
which represents an implicit function in si,t. By simulating and calibrating this
equation for different values of the parameters we observe that the left hand side of
equation (23) is decreasing in si,1, then we can determine the effects of policy para-
meters on education. An increase in income tax (τ) and in δπvleads to a reduction
in education, while a reduction in T, obtained either by an increase in education sub-
sidy or a reduction in tuition fees paid by agents, will raise time spent in education.
probability πvand a fraction δ of her income will be subtracted. If we consider very unsafe society (i.e.
with high levels of both the fraction of net salary stolen (δ) and the probability of being victimized
(πv)) the expected net income from work of a worker is very low and it does not compensate her
disutility from work. In other words, if with high probability a big fraction of salary will be stolen an
agent will prefer not to work. Then in very insecure society agents will work less or, even if it is not
considered in our model, will spend part of their income for private security in order to be safe from
Furthermore, an increase in second period wage rate will lead to an increase in educa-
tion in the first period, while an increase in first period wage will reduce time spent
in school.10Finally, the effects of learning ability and probability of apprehension on
time spent in education are ambiguous.
3 Predictions of the Model
In presenting the results and the implications of the model we focus our attention
on interior solutions. This is mainly due to the fact that available data and several
empirical studies stress that between 60% and 80% of individuals who decide to commit
crimes are engaged at the same time in the legal sector or school (Imrohoroglu et al
, 2001; Lochner, 2004). Then, it appears more relevant to focus on interior solutions
rather than to study boundary ones in which individuals either not commit crimes or
spend the whole amount of their disposable time in criminal activities.
3.1 Crime and Education
Our model clarifies the conditions under which education may reduce criminal activity.
Indeed, from the explicit solution for di,t(20), we observe that an increase in the time
spent in investing in education tends to reduce crime unambiguously. On the one
hand, a higher education implies higher returns both from work and crime; on the
other hand, an individual with a high level of education if apprehended and convicted
experiences a greater earnings loss. Thus, more time invested in education in the first
period is associated with higher expected returns in the legal sector in the second
period, this corresponds to a higher opportunity cost of crime and then to a lower level
of crime in the second period. Moreover, a compulsory attendance, that in our model is
represented by si,0reduces available disposable time, then the merely fact of attending
school is a deterrent for crime by reducing available time for criminal activities.
10In particular, note that increasing the level of the first period wage implies that education is more
costly in terms of foregone income. Moreover, ceteris paribus, the increase in adolescence wage will
reduce the time spent in criminal activities.
Our model also predicts that education has an indirect effect (“socialization effect”)
that influences the overall individuals decision of engaging in criminal activities. In
fact, the socialization effect makes criminal decision more costly in psychological terms
(internal pressure), while the overall effect of the peer pressure depends on average peer
group behaviour. More educated individuals will commit less property crimes than
others. The peer-group effect enhances and reinforces the market effect of education
representing an additional and complementary channel through which education affects
It is important to consider whether and how individual learning ability (εi) influ-
ences the decisions about investment and crime. Individuals more able (i.e. with a
higher learning ability) will usually spend more time for schooling since their returns
from education are higher and this implies a higher wage during adulthood. Thus
more capable individuals will invest more in education and will commit less crime
during both adolescence and adulthood than less able individuals.
The results described above hold as long as education increases the marginal returns
to work more than marginal returns to crime (wth
i,t(si,t−1) > Rhi,th
while education is likely to have a small effect on the returns of unskilled property
crimes, this need not to be true for white collar crimes. It could be the case that for
skilled crimes the inverse applies: education may increase marginal returns to crime
more than to legal work (wth
i,t(si,t−1) < Rhi,th
t(si,t−1)). In other words, because the
difference between marginal returns from legal activity and marginal returns from crime
cannot be unambiguosly signed, the relationship between education and crime can
present non-linearities. Such a non-linearity is conditional on the level of education
itself: when education is low, education reduces criminal activity; when education is
high, it may be the case that education increases criminal activity for certain crimes
(e.g. fraud). But, we need to account for the peer-group effect. In fact, on the one
hand for white collar crimes it may be likely that an increase of education leads to
an increase of crime through its market effect, but on the other hand the increase of
education in our model implies a negative increasing effect on crime through the peer-
group effect. These two effects have opposite signs and then it may be the case than
even in presence of marginal criminal returns from education higher than marginal
legal returns from education, individuals do not engage in crime because of peer-group
This finding is particularly important; it suggests that the criminal return does
not represent the only variable considered by individuals, in fact agents are influenced
in taking their decisions about criminal behaviour by psychological effects, such as
internal pressure and prevalent neighbours behaviour. In particular, individuals are also
influenced by the behaviour of others, in two senses. First, the greater the proportion
of agents in any given population who are already criminals, the more likely it is
that any other individual will convert into becoming a criminal. Second, the greater
the proportion of the population who are wholly disinterested in being criminals, the
greater the pressure on those who are criminals to become law-abiding.
Then, our model allows us to decribes both the conditions under which education
reduces crime, and when these conditions are likely to be violated, suggesting the
possibility of a non-linear relationship between education and crime.
So far, presenting our results we have not consider the existence of multiple equi-
libria, while this represents an important feature of our model. The equilibrium multi-
plicity stems from the heterogeneity in individual’s learning ability and the peer-group
As previously discussed, individuals with a higher learning ability will spend more
time for education and commit less crime when adults. In particular, a society charac-
terized by a large majority of individuals with little learning abilities will have a level
of criminal activity higher than a society in which the overall share of the population
has a high learning ability.
Furthermore, the existence of peer-group effect on crime leads to multiple equilibria
even if individual have the same learning ability. This outcome is amenable to the fact
that the internal pressure may vary among individuals.11
11In fact, even if not explicitly consider in our model, the internal pressure may be different among
individuals, since some individuals may be more “socializing” than others. In particular, it could be
that β is different across individuals, then the “internal” peer pressure would be γi,t(si,t−1) = sβi
3.2 Crime, Wages and Taxes
Since wages and taxes enter the agent’s decision in the same way (even if in opposite
direction), we focus our analysis on the effect of an increase of wage, that corresponds
to a flat tax reduction.12It is important to distinguish between the effect of a wage
increase in adolescence and in adulthood. In adulthood, an increase in wages unam-
biguously reduces the time spent in criminal activities increasing the opportunity cost
of criminal behaviour for adults. The effect of a change in the wage rate for adolescent
is not straigthforward and it has to be carefully analyzed. In fact, a higher wage for
adolescents implies that they will spend more time working in the legal sector reducing
time spent for criminal activities. Moreover, this also reduces time spent for schooling
and then it will lead to a lower level of education when adults. An increase of wage rate
during adolescent affecting only labour market returns implies a decrease in adolescent
crime rate in the short-run, but conversely leaving unaffected education returns and
reducing time for schooling during adolescence leads to an increase in adult crime rate.
On the one hand, a higher wage during adolescence implies that education is costly in
terms of foregone income, then individuals will prefer to allocate more time to legal
work than to education. This will also imply that, by having attained a lower level of
education, individuals will have a lower wage in the second period, then their oppor-
tunity cost of being criminal will be lower. On the other hand, a higher wage during
adulthood implies that more skilled workers will benefit from it, and then individuals
are prone to study more during adolescence in order to exploit higher wages when
adults. So far, we have not consider which it could be the effect of a change in wage
rate on peer-group effect. Increasing the adolescent wage rate leads to a reduction of
12In our model we consider a flat tax reduction, while Chiu W.H. and Madden P. (1998) consider
income tax progressivity. In their model they “show how the level of crime may be higher under
regressive taxation” (p. 136) and “in particular, a poll tax would induce a higher crime rate than a
proportional tax, which would in turn induce a higher crime rate than a progressive tax” (p. 135).
We need to distinguish between relative and absolute inequality. In our model we simply care about
disposable resources of individuals, but we do not consider relative inequality as in Chiu W.H. and
Madden P. (1998).
time spent for schooling and then to a lower level of education in the following period.
Less education implies a reduced effect of peer-group effect since γ will be lower. In our
model a reduction of schooling in the first period determined by a higher wage during
adolescence generates an increase of crime higher than it would have been without
3.3 Crime and Law Enforcement
An important determinant of criminal activities is represented by law enforcement and
deterrence. In our model, law enforcement is proxied by the probability of apprehen-
sion (πa). As expected, we observe that an increase in the probability of apprehension
reduces the level of time spent in committing crime. In fact, increasing the proba-
bility of apprehension corresponds to a reduction of the expected return from illegal
activities, in other words this implies a higher opportunity cost of criminal activity.
Prevention and effective law enforcement policies will allow to reduce the overall crime
rate. Moreover, we need to pay attention to the other effects that law enforcement
may have on the equilibrium. In fact, by reducing the time spent in committing crime,
an increase in πa implies that individuals will spend more of their disposable time
in schooling or work, when they are adolescent. More time spent for schooling when
adolescents implies a higher level of educational attainment and this leads to a higher
wage in the second period, thus the individual opportunity cost of crime is higher. In
other words, stricter law enforcement apart from reducing expected returns from crime
leads to a new equilibrium characterized by lower crime and higher schooling during
adolescence and by lower crime and higher employment when adults. Once again, we
need to stress that the “pure” market effect of education is reinforced and enhanced
by the peer-group effect. This implies that the reduction in crime in the second period
will be higher than it would have been without considering peer-group effect.
Finally, we need to analyze the role of victimization rate on the crime rate. Unsafe
societies are characterized by a higher level of victimization rate than others. It is
reasonable to expect that in this kind of societies the probability of being victim of
a crime will affect individual decision. From equation (20), we observe that a joint
increase in the probability of victimization (πv) and in the fraction of disposable income
stolen if victimized (δ) has a positive effect on crime. In fact, we can consider the joint
effect of δπvas the incentive to work for individuals. The more likely they will be stolen
of a fraction δ of their income the less they work. This outcome suggests that unsafe
societies (or societies characterized by a high victimization rate) present a higher crime
rate during both adolescence and adulthood than safe society, this in turn will imply
a lower level of education.
3.4 Crime and Education Subsidies
Education subsidies may represent an important instrument to raise education invest-
ment and then to reduce the crime rate. By simulating equation (23), we observe that
an increase in the education subsidy or otherwise a reduction in tuition fees will raise
time spent in education by adolescents. On the one hand, this implies that during ado-
lescence individuals will spend less time committing crime, but we need to distinguish
between working and not working adolescents. In fact, working adolescents are not
affected by education subsidies, because the amount of time spent committing crime
is only determined by their potential wage. Non-working adolescents will spend more
time in school and thus reduces their criminal activities in response to higher education
subsidies. On the other hand, a higher level of education during adolescence means
a lower level of crime during adulthood, as previously discussed in paragraph 3.1. In
general, a higher education subsidy leads to an equilibrium with more education and
less crime during adolescence and less crime during adulthood.
This result is an important finding of our model. Education subsidy may represent
a relevant policy to achieve crime reduction and it could be particularly useful for
those individuals coming from poor or disadvantaged families, which could not afford
the costs of education.
4 Conclusions and Policy Remarks
The model presented in this paper incorporates both the effects of education and
peer pressure on criminal behaviour. We introduce a peer pressure function, following
Kandel and Lazear (1992), to a standard Becker’s optimization model of crime in order
to analyze how peer effects influences criminal decisions.
Our findings show that criminal return does not represent the only variable consid-
ered by individuals, agents are influenced in taking their decisions by other components,
such as internal pressure and prevalent neighbours behaviour.
The model highlights both the condition under which education reduces crime rate,
and when these conditions are likely to be violated (i.e. case of white collar crime).
Our analysis suggests that a correct mix of enforcement, education subsidies and
taxation policies reduces crime. In particular, increases in law enforcement and in
education (via education subsidies) are likely to considerably affect the level of crime
and to be important components of an effective crime-fighting strategy.
Policy implications stemming from our work indicate that education represents an
important channel through which reduce the crime rate, thus policies aiming at reduc-
ing drop-out rate and increasing compulsory attendance may be particularly useful.
Impatient societies, with a higher intertemporal discount rate, will be more prone to
undertake policies aiming at increasing the probability of apprehension, while more
patient societies will prefer to adopt measures that allow for a persistent reduction of
crime in the long run, as by increasing the education level.
Furthemore, it is important to implement socioeconomic policies complementary to
educational policies. In fact, the effect of education on crime may be limited in presence
of a prevaling disadvantaged social context. In this case, it is necessary to implement
a policy that combines interventions aimed at increasing the level of education of the
population together with interventions acting on the extra-scholastic situation aimed
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