Part F-I
The Economic Theory of Crime
and Punishment
Applying the model of rational crime
10/21/08
Crime_D
1
Objectives
- apply the predictive model of criminal behaviour
- understand the specific factors that might influence
the crime rate
- elasticities (practical importance of individual
influences)
10/21/08
Crime_D
2
Rational Crime
- aggregate crime
Recall the ‘first law of deterrence’
“As the expected punishment increase, the number of crimes
decreases” – this describes the slope of the Aggregate Crime
Curve
What might cause the Aggregate Crime Curve (ACC) to shift in
or out?
Anything that causes the expected net benefit to the
criminal to increase (decrease) will cause the ACC to shift
out (in).
Recall y(x) = x – c(x) focus shifts to c(x) the direct cost to
the criminal of committing crime
10/21/08
Crime_D
3
Rational Crime
- aggregate crime
Aggregate crime curve
Severity of
punishment
ACC2
Anything that causes the expected
net benefit to the criminal to
increase (decrease) will cause the
ACC to shift out (in) – c(x).
ACC0
ε1
ACC1
c1
10/21/08
c0
c2
Aggregate number
of crimes
Crime_D
4
Rational Crime
- Direct Costs of Committing Crime
What should be included in the costs of committing a crime
c(x)?
- out-of-pocket expenses
- tools, information, payoffs, fencing
fees, money laundering fees, etc
- opportunity cost of time and effort
- opportunity cost of future legitimate economic
opportunities (if caught)
- opportunity cost of reputation (public shame – if caught)
- guilt (private shame)
10/21/08
Crime_D
5
Rational Crime
- Direct Costs of Committing Crime
Out-of-pocket expenses
- tools, information, payoffs, fencing
fees, money laundering fees, etc
Some crimes are low cost crimes – e.g. shoplifting
Some crimes are high cost crimes – e.g. drug smuggling,
contract killing
Poorer criminals - mugging, shoplifting, selling street drugs
Richer criminals - drug smuggling, loan sharking, major frauds
All crimes can be made more, or less, expensive to the criminal
10/21/08
Crime_D
6
Rational Crime
- Direct Costs of Committing Crime
opportunity cost of time and effort
- some individuals are more productive criminals than are other
individuals (bigger, faster, more violent, more devious, etc.). For
such individuals crime is less costly – less effort. (Woody Allen
robbing a bank?)
- note criminals usually specialize in the types of crime in which
they are most productive (shoplifters, muggers, bank robbers,
counterfeiters, fraudsters, selling drugs, loan sharking, financial
fraud)
- some individuals are more productive in the legitimate labour
market (better educated, more experience, better ‘connected’
bigger, faster, etc.).
10/21/08
Crime_D
7
Rational Crime
- Direct Costs of Committing Crime
opportunity cost of time and effort
The following is most applicable to full-time or part-time criminals not
occasional or isolated crimes
- consider the expected return from ‘time and effort’ spent in
legitimate employment vs. the expected return from ‘time and effort’
spent in criminal activity
wE(H) >, = or < wcE(Hc)
w - hourly wage in labour market (productivity in
legitimate activity)
wc - hourly wage in criminal activity (productivity in
criminal activity)
E(H) - expected hours of legitimate work
E(Hc) - expected hours of criminal activity
10/21/08
Crime_D
8
Rational Crime
- Direct Costs of Committing Crime
opportunity cost of time and effort
What affects these variables?
w (productivity in legitimate activity)
- age, education, literacy, accent, appearance,
experience, place of residence, etc.
wc (productivity in criminal activity) varies with the type of
crime
- experience, training, intelligence, strength,
deviousness, bravery, etc.
10/21/08
Crime_D
9
Rational Crime
- Direct Costs of Committing Crime
opportunity cost of time and effort
What affects these variables?
E(H) (expected hours of legitimate work)
- unemployment rate, general conditions in relevant
‘local’ labour market, etc.
E(Hc) (expected hours of criminal activity)
- opportunities in the relevant criminal activity, etc.
10/21/08
Crime_D
10
Rational Crime
- Direct Costs of Committing Crime
opportunity cost of time and effort
- for a given individual
wE(H) > wcE(Hc)
10/21/08
legitimate employment
wE(H) = wcE(Hc)
indifferent – occasional criminals
wE(H) < wcE(Hc)
life of crime
Crime_D
11
Rational Crime
- Direct Costs of Committing Crime
opportunity cost of time and effort
wE(H) > wcE(Hc) legitimate employment
wE(H) = wcE(Hc) indifferent – occasional criminals
wE(H) < wcE(Hc) life of crime
Note that even for occasional criminals wc is relevant (again
Woody Allen in ‘Take the Money and Run’
Many criminals also hold regular employment
– crime is a ‘second job’ and the above would apply
Both cyclical and long-term factors enter here
- this is were ‘economic conditions’ might affect crime
10/21/08
Crime_D
12
Rational Crime
- Direct Costs of Committing Crime
opportunity cost of future legitimate economic
opportunities
Consider two 18 year olds:
Bill - High school drop out living in poor area of town, only
employed in low paying jobs very sporadically, parents have
never held regular employment (expected average annual
lifetime earnings - $15,000)
John – currently in university, lives in suburbs, has always
had a part-time job, everyone in family holds regular
employment, etc. (expected average annual lifetime
earnings - $65,000)
10/21/08
Crime_D
13
Rational Crime
- Direct Costs of Committing Crime
opportunity cost of future legitimate economic
opportunities
What do Bill and John risk by getting involved in criminal
activity as 20 year olds?
Bill - expected average annual lifetime earnings of $15,000
John - expected average annual lifetime earnings of $65,000
Socio-economic class matters – it is a determinant of your
legitimate future prospects
Discount rate – we will discuss later
10/21/08
Crime_D
14
Rational Crime
- Direct Costs of Committing Crime
opportunity cost of reputation (public shame)
Again consider Bill and John
- Potential personal shame would appear to be related to
family status in the community - a ‘good family’, a ‘good
reputation’
Again, socio-economic class would appear to matter – it is a
determinant of the social status that you put at risk
What are the relevant sociological phenomena ??
10/21/08
Crime_D
15
Rational Crime
- Direct Costs of Committing Crime
guilt (private shame)
Morality (the extent to which the individual is constrained by
guilt or morality)
- is the individual constrained by guilty or morality?
- ‘family values’, church attendance, moral instruction in
schools, etc.
Let’s face it, if everyone was always ‘constrained by guilt and
morality’ then there would be no rational crime.
10/21/08
Crime_D
16
Rational Crime
Criminal’s optimal number of crimes - review
45o
$
Expected
punishment
Δy/Δx
Expected net
benefit y(x)
Optimizing criminal
wants to maximize
this gap
Number of crimes
Δp/Δx f(x) +
p(x) Δf/Δx
10/21/08
Crime_D
17
Rational Crime
Decision to commit crime
Harm to the victim
$
Expected
punishment
Expected net
benefit y(x)
$100
Rational crime
$80
5 crimes
$50
Number of crimes
5
10/21/08
Crime_D
18
Rational Crime
Decision to commit crime
Expected
punishment
$
Expected net
benefit y(x)
No rational crime
Expected punishment
exceeds expected net
benefit for any
number of crimes
Number of crimes
10/21/08
Crime_D
19
Rational Crime
- policies that decrease incentives to commit
rational crime
$
Anything that shifts the
expected net benefit of crime
curve downwards or the
expected punishment curve
upwards
Expected punishment p(x)f(x)
Expected net
benefit
y(x) = x – c(x)
Optimizing criminal
wants to maximize
this gap
Number of crimes
10/21/08
Crime_D
20
Rational Crime
- policies that decrease incentives to commit
rational crime
1. Decrease y(x) = x – c(x), the ‘net returns’ to a given
criminal act (shifts net benefit curve downward)
- make crime more costly for the criminal to undertake
(higher fences, better lighting, more complicated alarm
systems, more secure safes, more complicate financial
reporting systems)
- in general make the criminal work harder for his/her
reward
The usual ‘crime prevention’ techniques
‘out-of-pocket expenses’
10/21/08
Crime_D
21
Rational Crime
- policies that decrease incentives to commit
rational crime
and many other factors considered as direct costs of crime
- opportunity cost of time and effort
wE(H) > = < wcE(Hc)
(education, training and other labour market policies)
- opportunity cost of future legitimate economic
opportunities (education, training and other labour
market policies)
10/21/08
Crime_D
22
Rational Crime
- policies that decrease incentives to commit
rational crime
and many other factors considered as direct costs
of crime
- opportunity cost of reputation, public shame
(community reputation enhancing strategies –
cultural movements such Black Pride
movements, etc.) (negative strategies – drunk
driving, smoking)
- guilt, morality, private shame – family values,
moral education, churches, etc.
10/21/08
Crime_D
23
Rational Crime
- policies that decrease incentives to commit
rational crime
2. Increase p(x), the probability of being caught, convicted and
punished (shifts expected punishment curve upward)
- increase the number and efficiency (equipment, training,
etc.) of police, prosecutors, courts, prisons.
- give police, courts, prosecutors more ‘political/legal’ power to
investigate and prosecute suspected criminals
- generally, devote more resources and give up some of the
personal freedoms of all citizens
10/21/08
Crime_D
24
Rational Crime
- policies that decrease incentives to commit
rational crime
3. Increase f(x), the punishment if caught (shifts
expected punishment curve upward)
- larger fines, longer sentences, etc.
- In general this requires more resources
(prisons, etc.) since fines are not enough in most
cases (poor criminals, really big crimes).
10/21/08
Crime_D
25
Rational Crime
- what is really important?
Aggregate crime is a function of
y(x) = x – c(x)
- crime prevention measures
- opportunity cost of time and effort (education, labour
market conditions)
- opportunity cost of future legitimate economic
opportunities (education, labour market conditions)
- opportunity cost of reputation, public shame (community
enhancing strategies, etc.
- guilt, morality, private shame – family status, church
attendance, etc.
10/21/08
Crime_D
26
Rational Crime
- what is really important?
and aggregate crime is a function of
p(x)
- number and efficiency (equipment, training, etc.) of
police, prosecutors, courts, prisons.
- ‘political/legal’ power to investigate and prosecute
suspected criminals
f(x)
- larger fines, longer sentences, etc.
10/21/08
Crime_D
27
Rational Crime
- what is really important?
With respect to alternative theories of criminal behaviour, the
model of rational crime is all inclusive.
On a purely theoretical level, this makes it less useful.
How do we settle debates such as ‘harsher punishment vs.
better education’
What do we tell policy makers? Just do everything - anything
that decreases y(x), increase p(x) or increase f(x)
Not very useful advice
A purely theoretical economic analysis of criminal activity
takes us only so far.
10/21/08
Crime_D
28
Rational Crime
- what is really important?
What is required at this point is empirical analysis. The various
elasticities must be quantified.
Will longer sentences deter the illegal use of guns? Yes, but be how
much?
- will a 10% increase in the prison sentence decrease gun
related crime by 25% or by 1%?
Will more police on the streets deter the illegal use of guns? Yes, but be
how much?
- will a 10% increase in police funding decrease gun related
crime by 10% or by 1%?
Will better job opportunities decrease the illegal use of guns? Yes, but be
how much?
- will a 10% increase in job opportunities decrease gun related
crime by 30% or by 1%?
10/21/08
Crime_D
29
Rational Crime
- what is really important?
There will always be debates over such issues and they can
only be settled by appeal to empirical evidence.
We will look at one of these empirical studies.
The model of rational crime is important because it is the
necessary first step in addressing empirical questions
concerning criminal activity. It provides a framework within
which to address specific questions. It tells the empiricist
what factors must be controlled for when addressing
specific questions. It brings structure to the various
debates.
10/21/08
Crime_D
30
Rational Crime
- some applications
Should a thief be allowed to give good title? In Canada if you
buy a stolen good, without knowing it is stolen, and it is
found to be stolen you must give it back. In Europe, if you
buy a stolen good, without knowing that it is stolen, and it
is found to be stolen, you need not give it back. What effect
do these alternative rules have on the expected number of
thefts?
More or fewer handguns – again has two effects on expected
crime
In response to recent terrorists attacks, governments have
tried to decrease the returns from terrorism y(x) and
increase the probability of terrorists being caught and
convicted p(x) . In what ways have you personally paid
some of the costs of these attempt to decease terrorism?
10/21/08
Crime_D
31
Rational Crime
- some applications
Does poverty ‘cause’ crime; yes and no. Poverty does not generally cause
tax fraud, price fixing or major financial frauds. Poverty (a downturn in
the level of economic activity), or inequality in the distribution of
wealth, might lead to more theft, muggings, embezzlements, etc.
Consideration of y(x), the net benefit that a given criminal gets from a
given crime, indicates that the opportunity cost of criminal activity
falls as legitimate economic options (current and future) deteriorate
(the relative returns from crime increase) - a group of rich people
living next to a group of poor people provide potentially profitable
crime opportunities.
Does poverty, or unemployment cause people to be ‘bad’, become less
moral? NO, but as economic conditions deteriorate (current or future),
relative prices (wages) began to change and crime becomes a
relatively more profitable activity. It causes them to do ‘bad things’.
Can wealth cause crime? Are some crimes positively related to income?
10/21/08
Crime_D
32
Rational Crime
- some applications
More police should lead to less crime but so do
more efficient courts (quicker and more certain
conviction) and longer prison sentences. What
does the above model imply about the allocation
of a fixed criminal/justice budget across police,
courts and prison?
Why is it that local police forces apparently ‘waste’
their time on public education programs
encouraging ‘crime prevention’ for breaking and
entering, theft from autos, muggings, etc. but
when one of these crimes actually occurs they
don’t ‘really do much’?
10/21/08
Crime_D
33
Rational Crime
- what about the individual’s
rate of discount?
Crime and its consequences usually represent a series of
events that occur over time
Generally:
- crime is committed today
- consequences are suffered tomorrow
- punishment, loss of future legitimate
opportunities
Criminals are often described as individuals with little ‘impulse
control’ or with ‘no thought for the future’
Economists would refer to ‘rates of discount’
10/21/08
Crime_D
34
Rational Crime
- what about the individual’s
rate of discount?
Rate of discount
A $1 today does not have the same value as a $1 tomorrow
Suppose the interest rate (r) is 10% then
$1 today is worth $1.10 is one year’s time - $1x(1.10)
$1 in one year’s time is worth $1 in one year’s time
Conversely,
$1 today is worth $1 today
$1 in one year’s time is worth $0.909 today - $1/(1.10)
10/21/08
Crime_D
35
Rational Crime
- what about the individual’s
rate of discount?
Rate of discount
The present value (today’s value) of $1 received in one year’s
time is equal to $1/(1+r)
- where r is the annual rate of discount
In general the present value (today’s value) of $x received in ‘n’
years is equal to $x/(1+r)n
Example: $1,000 received in 5 years with a 10% rate of
discount
$1,000/(1.10)10 = $1,000/2.5937 = $385.55
10/21/08
Crime_D
36
Rational Crime
- what about the individual’s
rate of discount?
What determines an individual’s personal rate of discount?
This is a matter of personal taste and preferences – ‘rate of time
preference’ – how much of a return do we want in order to
delay our gratification? (or how much are we willing to pay to
move our gratification forward in time?)
‘more jam today, or more jam tomorrow’?
Some people deny themselves small pleasures to save and earn a
3% return on their savings
Others run up credit card debts and pay an interest rate of 20%
on that debt
Most of us are somewhere in between these two examples.
10/21/08
Crime_D
37
Rational Crime
- what about the individual’s
rate of discount?
Example:
Net gain
crime
today
Punishment
in 2 years
$100
$200
$181
Punishment
in 5 years
PV of
punishment:
r=5% r=25%
r=50%
$157
$26
$100
10/21/08
$200
PV of
punishment:
r=5% r=25%
Crime_D
$128
$66
r=50%
$89
38
Rational Crime
- what about the individual’s
rate of discount?
Comments:
- The above is just one aspect to the decision to commit crime –
it does not imply that everyone who runs up VISA debt is
likely to commit crimes
- However, the higher the discount rate and the more delayed is
the punishment, the more attractive will be the net gains
from crime today (SWIFT PUNISHMENT)
- There is always the uncertainty of punishment and individuals
with high discount rates also tend to discount uncertain
future events even more (CERTAIN PUNISHMENT)
- An individual’s discount rate might vary with their mood
(manic – depressive, alcohol, drugs, etc.)
10/21/08
Crime_D
39
Rational Crime
- what about non-rational individuals?
Crimes of passion, insane, drunk, drugged
Such crimes fall outside our model
Are criminals rational amoral people? I HOPE SO!
10/21/08
Crime_D
40
10/21/08
Crime_D
41