The Economic Crime Model
Crime Choice, deterrence and crime
determinants
International Economic Policy
Scienze della Cooperazione Internazionale e dello Sviluppo- Finance&Development (LM-81),
a.a. 2015-2016
Prof. Emanuele Ragusi
Are Economics of Crime and Economic Crime
synonymous?
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Which is the relationship between crime and
economics?
1
Economics is a social science
2
Crime’s got a negative effect on
perfect allocation of resources
Crime affects the accumulation of
production factors
4
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3
Crime undermines the production of
public goods like “Security”
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The economic approaches to crime
Two
Micro approach
(Deviant behavior)
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Macro approach
Crime rate
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Microeconomic perspective
The microeconomic perspective focuses on behavior
of social actor and on his/her choices
Why do people
commit a
crime?
For personal
disadvantages
(psychic or psychiatric)
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To maximize his/her
social welfare ( it’s a
rational calculation)
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Rational Choice Theory
Human actions are the final product of a rational (logic) analysis of
costs&benefits to maximize the individual ultility
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Rational Choice Model
Two
approach
CERTAINTY
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UNCERTAINTY
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Rational Choice Model under certainty
SCARCITY: analyze the disposable resources
(time, money, energy)
IDENTIFY:
-CONSTRAINTS : what you can do
-PREFERENCES: what you want
MAXIMIZE THE WELFARE: what it’s better for
the actor
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Scarcity: the Budget Constraint
The Budget Constraint represents all combination of goods, services
and time that a consumer may purchaise given the current prices and
given his/her disposable income
𝒑𝟏 𝒙𝟏 + 𝒑𝟐 𝒙𝟐 ≤ 𝑹
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Budget
Constraint’s
Equation
Pagina 9
The Budget line
𝒙𝟐 = 𝑹 𝒑𝟐 − (𝒑𝟏 𝒑𝟐 ) 𝒙𝟏
𝒙𝟐
𝑹
Impossible
bundles
𝒑𝟐
All the
bundles
Opportunity
cost
− (𝒑𝟏 𝒑𝟐 )
Possible
bundles
𝑹
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𝒑𝟏
𝒙𝟏
This equation explains
how many units of good 2
can be consumed, given
the good 1’s consumption,
to exhaust the disposable
income
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Pagina 10
Shifts of Budget line
1.
2.
𝒙𝟐
𝑹
𝒙𝟐
𝒑𝟐
𝑹
𝑹
Shift s due to
variations ofR
L’Economia del Crimine
𝒑𝟏
Shift s due to
variations of p2
𝒑𝟐
𝒙𝟏
𝑹
𝒑𝟏
𝒙𝟏
Shift s due to
variations of p1
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Pagina 11
Consumer’s Preference Map
Don’t judge the preferences
Optimal
combination of
purchasing
goods
Preferences
The consumer can order his preferences in relation to
his degree of happiness, satisfaction and desiderability
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The hierarchy of consumer’s preferences
Consider two goods X and Y, the consumer’s preferences can be ordered in the
following way
•
𝑥1 , 𝑥2 ≻ 𝑦1 , 𝑦2 : il paniere
𝑋è strettamente
preferitoto
al Ypaniere
The X bundle
is stricly preferred
bundle𝑌;
•
The X
is indifferent
to Y𝑌;bundle
𝑥1 , 𝑥2 ∼ 𝑦1 , 𝑦2 : il paniere
𝑋èbundle
indifferente
al paniere
•
X bundle
is weakly preferred
topaniere
Y bundle
𝑥1 , 𝑥2 ≽ 𝑦1 , 𝑦2 : il The
paniere
𝑋è debolmente
preferito al
𝑌.
The preference properties
• Complete: The consumer has ranked all available alternative combinations
of commodities in terms of the satisfaction they provide him;
• Reflexive: if both bundles are identical in all respects, the consumer in
indifferent to compare both;
• Transitive: Given 3 bundles of good (X; Y and Z) and assumed that the
bundles are identical in all, if the bundle X is indifferent to Y and Y is
indifferent to Z for the consumer, it means that the bundle X is indifferent to
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Pagina 13
Z.
The indifference curves
𝑥1 , 𝑥2 ∼ 𝑦1 , 𝑦2
𝑥1 , 𝑥2 ≻ 𝑦1 , 𝑦2
𝑥1 , 𝑥2 ≽ 𝑦1 , 𝑦2
Figure estratte dal documento online Preferenze
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Other properties of indifference curves
• Strong Monocity: «more is better», if two bandles have the same quantity of one
good, but the fistr bundle’s got more of the other, it implies that the first bundle is
𝒙𝟐
preferred to the second. In this case the indifference
Best
curves have a negative slope.
bundle
• Preferences are continuos: if a bundle A is
preferred to B and C is sufficiently close to B then
A is preferred to C
• Strictly convex preferences:
consumers are willing to substitute
his abundant good in favor of his
scarce good
L’Economia del Crimine
Δ𝑥2
Δ𝑥1
A
Worst
bundle
Ipotesi di non sazietà e SMS
• Marginal Rate of Substitution
(MRS): Consumers are willing to
give up or trade-off some of one
good to get more of another.
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Pagina 15
𝒙𝟏
Optimal Choice
Budget
Constraint
Indifference
Curves
𝒙𝟐
E
𝒙𝟏
Optimum
Point E represents the maximum utility of a consumer
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Pagina 16
Utility functions
Utility is a measure (number) of consumer’s preferences over a set
of goods and services.
Two
main properties
Due
Principali
proprietà:
• 𝑈 𝐴 = 𝑈 𝐵 𝑠𝑒 𝑒 𝑠𝑜𝑙𝑜
iff 𝑠𝑒 𝐴~𝐵;
• 𝑈 𝐴 > 𝑈 𝐵 𝑠𝑒 𝑒 𝑠𝑜𝑙𝑜
iff 𝑠𝑒 𝐴 ≻ 𝐵
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Uncertain microeconomic approach
Considering this specific approach, it’s important to pay attention to the
slope of utility curve to explain the agent’s risk propensity
Aversion
Risk-taking
concave
𝑓 𝑐𝑜𝑛𝑐𝑎𝑣𝑎:
𝑓 ′ > 0 𝑒 𝑓′′ ≤ 0
𝑓 𝑐𝑜𝑛𝑣𝑒𝑠𝑠𝑎:
convex
𝑓 ′ > 0 𝑒 𝑓′′ ≥ 0
indifferent
linear
𝑓 𝑙𝑖𝑛𝑒𝑎𝑟𝑒:
𝑓 ′ = 0 𝑒 𝑓 ′′ = 0
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Pagina 18
Economic Crime Model
The first economic framework to crime studis was
conducted by the Nobel prize G.S. Becker (1968)
L’Economia del Crimine
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Pagina 19
Crime behavior modeling
Becker considers the combination of gains and
losses related to a crime. He doesn’t take in account
the social and psychological conditions of the agent
Social agent decides to commit or not a
crime
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The Becker’s model
EU= pU(Y-f)+ (1-p)U(Y+g)
EU: expected utility of a person;
Y: income’s agent
U: utility function
f: monetary equivalent of the punishment
g: gains from crime
p: probability of convinction
(1-p): probability of success (not be imprisoned)
When does an agent offend?
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Pagina 21
offend or not … that is the question!
If EU> U(
U(Y)
Se EU>
𝑊0 )
L’Economia del Crimine
If EU<U(
U(Y)
Se EU<
𝑊0 )
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Pagina 22
To be “innovative” or not?
If Y is a certain gain, how
does an agent take in account
the possibility of risk?
Analysis of L, G and p
Personal risk propensity
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Pagina 23
Gary Becker model
p=0
U
b
U(𝑊0 + 𝐺)
c
U(𝑊0 )
U(𝑊0 − 𝐿)
a
d
e
p=1
(𝑊0 − 𝐿)
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𝑊0
W*
𝑊0
(𝑊0 + 𝐺)
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Pagina 24
Gary Becker model’ assumption
An agent commits a crime in function of the value that he gives to the
probability of convinction, to the gains from offens and to the losses
2 main
considerations
The preferences are
omogenius and continous :
crimes are in function of the
opportunity cost of an offens. If
the crime cost increases, we
assist to a contraction of crime
supply
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Both criminals and justice
are rational.
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Pagina 25
Exogenous factors of Becker’s model
What happens to EU if exogenous variables change?
•p: probability of conviction;
•f: monetary value of punishment.
U’(Y)>0
(∂EU/∂p)= U(Y-f)-U(Y+g)<0
(∂EU/∂f)= -pU’(Y-f)<0
So an increase of exogenous factor, reduce the
expected utility and, as consequence, reduce the
number of crime
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Offens Supply Market
O= O(p; f; u)
•Dependent variable
O: number of crime committed by a person;
•Deterrence variable: p and f
•Covariates
v: gains from legal activities and propensity to respect
law.
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Isaac Ehrlich’s Model
Main
1. Legal-illegal 2. The participation to illegal activity is
considered a kind of job
Mix activities
=
Optimal time
allocation
LEGAL
Titolo Presentazione
ILLEGAL
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Pagina 28
Ehrlich’s hypothesis
1. Only 2 activities: Legal and Illegal => the transiction to one of the two state
doen’t pay costs
2. The returns of both activities are an increasing function of time
𝑾𝒍 𝒕𝒍 : under certainty
𝑾𝒊 𝒕𝒊 : under uncertainty in function of p (probability of conviction) e (1-p)
(probability of success)
3. The time amount is predetermined ∆𝒕𝒍
success
unsuccess
= −∆𝒕𝒊
𝑊𝑠 = 𝑊0 + 𝑊𝑙 𝑡𝑙 + 𝑊𝑖 (𝑡𝑖 )
Sanction
𝑊𝑢 = 𝑊0 + 𝑊𝑙 𝑡𝑙 + 𝑊𝑖 𝑡𝑖 − 𝐹𝑖 (𝑡𝑖 )
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How does agent allocate time?
The choice is in function of the value of 𝑡𝑖 and 𝑡𝑙 .
𝐸𝑈 = 𝑝𝑈 𝑊𝑢 + (1 − 𝑝)(𝑊𝑠 )
[𝑝(𝑑𝑈 𝑑𝑊𝑢 )]/[(1 − 𝑝)(𝑑𝑈 𝑑𝑊𝑠 )] = (𝑊′𝑖 − 𝑊′𝑙 )/(𝑊′𝑖 − 𝑊′𝑙 𝐹′𝑖 )
Marginal Rate of
Substitution
Marginal Rate of
Transformation
Exchange u with s to
maintain the EU’s value
unchanged
Titolo Presentazione
𝑊𝑢 ’s transformation rate in
𝑊𝑠 redistributing the work time
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Pagina 30
An agent commits a crime, when….?
Line of certain
allocation
𝑊𝑠
𝑊0 + 𝑊𝑖 (𝑡𝑖 )
a
𝑊𝑠 = 𝑊𝑢
= 𝑊0 + 𝑊𝑙 (𝑡)
b
𝑊0 + 𝑊𝑙 (𝑡𝑙 )
45°
𝑊0 + 𝑊𝑖 𝑡𝑖 − 𝐹𝑖 (𝑡𝑖 )
Titolo Presentazione
𝑊0 + 𝑊𝑙 (𝑡𝑙 )
𝑊𝑢
04/05/2016
The PPF’s slope (Curve
AB) must be higher than
the indifference curve
′
𝑊 𝑖 (𝑡𝑖 ) − 𝑝𝐹 ′ 𝑖 𝑡𝑖 > 𝑊′𝑙 (𝑡𝑙 )
Pagina 31
Main results of Ehrlich’s research
Inversal relationship between the time for illegal activities
and the probability of conviction.
An increase of the punishment’s severity reduces the
crime supply
An increase of the illegal returns implies a contraction of
time allocated for legal activities
From Micro to Macro
Perfect omogenity of actors
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Pagina 33
An equation to estimate the crime
𝑌𝑖𝑡 = 𝛼 + 𝛽𝑋𝑖𝑡 + 𝑢𝑖𝑡
𝑂 = 𝑂(𝑃; 𝑆; 𝐼)
𝑃 = 𝑃(𝑂; 𝑆; 𝐼)
𝑆 = 𝑆(𝑂; 𝑃; 𝐼)
Titolo Presentazione
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The crime’s determinants (Buonanno, 2003 Review)
Economic Variables
GPD,
Wage,
Employment rate
Unemployment rate
Social Variables
Population,
Social Cohesion Indicators
(family, number of divorce,
education)
Political Variables
Democracy,
Political participation,
Strike,
Social Movements
Deterrence
Probability of conviction
Severity
Police forces
ECM Reviews
Fonte
Paese
Modell
Casi
o
Periodo
Variabili
Buonanno
Fixed Province 1993-1999
Spain
et al 2008
Effects s (46)
(7 years)
Deterrence (probability of conviction and
apprehension); Male population 15-29 years;
density; % foreigners; GDP per capita; growth
rate; unemployment 15-29 years; education;
crimes
Rando
1992-2008
m
Contees
(17 years)
Effects
Crimes (violent, against property); Deterrence
(probability of conviction e severity);
Unemployment; medium wage; young male
population (15-29); Gini’s Coefficient.
Han et al.
UK
2013
Total crime; Deterrence (probability of
Kakamu et
Fixed Province 1991-2001 (11 conviction, Police agents’ numeber);
Japan
al. 2008
Effects s (47)
years)
Unemployment; GDP per capita; foreignersber
of nights in Hotel
North
Cornwell
Fixed
Caroli
Contee 7 anni
et al. 1994
Effects
na
Entorf et
al. 2000
Total crime; Deterrence (probability of
conviction and apprehension severity); medium
wage; density; young male population 15-24.
Total crime; Deterrence (probability of
Germa Fixed
1963-1996 (34
Lander
conviction and apprehension, severity, repeat
ny
Effects
years)
offenders) GDP per capita; wage differential
Grazie per l’attenzione
emanuele.ragusi@uniroma1.it
Ricevimento
Martedì 10:30-11:30
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