Economics 160
Lecture 5
Professor Votey
Law Enforcement Effectiveness:
Productivity
Votey 2, Notes: pp. 30-18
The Science of Decisionmaking
Methodology: The Economic Paradigm
Recall 3 Steps (Notes, pp 3,4)
1. Specification:
Specify the Alternative States of the World
2. Valuation:
Establish a Value System, e.g. Prices
3. Optimization:
Picking the “Best” Solution
Profit Maximization, Cost Minimization
Minimizing the Net Social Costs of Crime:
An Application of Economic Decisionmaking
The Tool: Some Form of Cost/Benefit Analysis
Costs
Social Costs of Crime
(SC)
Costs to Victims
(VC)
Control Costs
(CC)
Notes, p. 4
OF*
Minimum Social Cost of Crime
Offenses
(Crime Level)
Minimizing the Net Social Costs of Crime:
An Application of Economic Decision-making
The Tool: Some Form of Cost/Benefit Analysis
We referred to: E. J. Mishan, Cost-Benefit Analysis, Ch. 3,
in REFERENCES (RBR)*
Costs
Social Costs of Crime
(SC)
VC
Costs to Victims
Control Costs
(CC)
OF*
Minimum Social Cost of Crime
Offenses
(Crime Level)
*Ed Mishan, an English economist is a well known figure to
the older members of the Econ Department, having been
an academic visitor here on at least two occasions (the two
during my time here which began in Fall 1966). He is one
of the internationally known economists who played a role
in developing the economic science behind the huge
infrastructure investments made during the Great
Depression that created such enormous projects as the
Hoover Dam on the Colorado River.
That same science would form the basis for any public
projects today that might be undertaken to create jobs and
repair U. S. infrastructure as has been recently proposed.
Since those days, there has been much criticism of such
investments, mostly by individuals who believe that any
investments by society should be limited to the private
sector since they believe only markets can lead to efficient
outcomes. Interestingly, the Hoover Dam, arguably the largest
public project undertaken by any country up to that time, was
completed under budget and ahead of schedule.
There have been many criticisms of such fiscal policy
stimulants as originally advocated by the British economist
John Maynard Keynes. They do take time to work and only
seem to work markedly on a massive scale.
Our economy did not fully recover during the 1930’s, but
the policy was certainly vindicated by our participation in WW II,
when we put 16,000,000 people to work in the military while
going from a third rate to the greatest military establishment in
the world with a two ocean navy and an air force second to
none, both of which we continued to maintain following the war,
while simultaneously paying for the rebuilding of the economies
of both our allies and enemies with Marshall Plan Aid, and while
paying off our own debt that we undertook to fight the war.
Minimizing the Costs of Crime
Minimizing the Costs of Crime
Objective: Min SC = VC + CC
Notes, p 5
Minimizing the Costs of Crime
Objective: Min SC = VC + CC
The Logic:
The minimum social cost of crime is the smallest sum
We could realize, of victim costs plus the costs of crime control.
If we minimize the costs of a “BAD”, we have more
of our resources left to spend on “GOODS”.
Recall from Lecture 1 the circular flow diagram that
represented the interacting system of Crime Generation
and Control
OFFENSES
Output
Crime
Generation
Input
Deterrence
Detention
Rehabilitation
(Retribution)
Resources
Input
Crime
Control
(Social Defense)
Output
Text Reference: Economics of Crime Control, Chapter 9 and in Notes, p13
Economic Notions of Productivity
Consider A Steel Mill – an example from heavy
industry
Resources:
Raw Materials: Iron Ore, Coal, Limestone
Labor: Variety of Skills
Capital: Blast Furnace, Oxygen Furnace
Rolling Mills, Plating Mills
Technology:
Means of Linking Inputs
Output:
Iron, Finished Steel
 How does one make a Reasonable Analogy between a typical
production process and the Criminal Justice System?
Next: Conceiving of Outputs
The Criminal Justice System
Theory
1. Basis for Defining/Identifying Outputs
A Schematic
1. Functions
2. Stages of Operation
3. Operating Entities
2. Basis for Evaluating Effectiveness
Empirical Evidence
Notes, p 14, Figure 2.2
Criminal Justice System:
The Real World Process
Input
OF
Law Enforcement
POLICE FORCE
Produces
ARRESTS
Function
Operating Entity
Prosecution
Stage 2
DA
COMPLAINTS
COMPLAINTS
Adjudication
INDICTMENTS
COURTS
INPUTS/
OUTPUTS
?
Stage 1
CONVICTION
(guilty)
DISMISSAL
(not guilty)
Stage 3
Stage 4
Corrections
or Punishment
JAILS,PRISON,PROBATION
RELEASE
(PAROLE)
How Good is the output analogy in cases of
non-market decision making?
Consider other Public Service Industries:
Education - What is the output?
 Number of Students ? - or are these inputs?
 Number of Graduates?
Hospitals - What is the Output?
 Number of Patients ?
Again, this is an input
 Lives Saved?
For how long?
 What determines hospitals’ rankings?
An Aside - about the past
Physical Outputs in a Command
Economy –
How are they measured?
A story from? George Karcz
 Or maybe Doug Morgan
About Light Fixtures
What did we decide was the proper social
objective with respect to CRIME?
Minimizing the Social Cost
Minimizing the Social Cost

What does this mean in terms of productivity?
Minimizing the Social Cost
 What does this mean in terms of productivity?
 Reducing Crime Numbers or Seriousness (or both)
Minimizing the Social Cost
Notes, p.5
 Recall: Social Cost Minimization implies:
Min SC = VC + CC i.e., Victim Costs + Control Costs
 Irrespective of the values we place on individual offenses, as
long as they are positive, Social Cost Minimization requires
Reducing Crime Numbers or Seriousness
Minimizing the Social Cost
 Recall: Social Cost Minimization implies:
 Min SC = VC + CC i.e., Victim Costs + Control Costs
 Irrespective of the values we place on individual offenses, as
long as they are positive, Social Cost Minimization requires
Reducing Crime Numbers or Seriousness or Reducing
Control Costs
Minimizing the Social Cost
 Recall: Social Cost Minimization implies:
Min SC = VC + CC i.e., Victim Costs + Control Costs
 Irrespective of the values we place on individual offenses, as
long as they are positive, Social Cost Minimization requires
Reducing Crime Numbers or Seriousness or Reducing Control
Costs
 Consider the Circular Flow Process: (again)
Minimizing the Social Cost
 Irrespective of the values we place on individual offenses, as
long as they are positive, Social Cost Minimization requires
Reducing Crime Numbers or Seriousness (or control costs)
 Recall: Social Cost Minimization implies:
Min SC = VC + CC i.e., Victim Costs + Control Costs
 Consider the Circular Flow Process: (again)
OFFENSES
Output
Crime
Generation
Input
Notes, p. 5
Deterrence
Detention
Rehabilitation
(Retribution)
Resources
Input
Crime
Control
(Social Defense)
Output
Minimizing the Social Cost
 Recall: Social Cost Minimization implies:
Min SC = VC + CC i.e., Victim Costs + Control Costs
 on individual offenses, as long as they are positive, Social Cost
Minimization requires Reducing Crime Numbers or Seriousness
(or both)
 Consider the Circular Flow Process: (again) Irrespective of the
values we place
OFFENSES
Output
Crime
Generation
Input
Deterrence
Detention
Rehabilitation
(Retribution)
Victim Costs + Resources
Input
Crime
Control
(Social Defense)
Output
Looking at the Circular Flow Process, One observes
that Arrests and Offenses seem to move together
Separating the Effects
Resort to the Economic Paradigm and
Economic Decision Theory
Appeal to the approach of
The Utilitarians
Jeremy Bentham - the father of . . .
Modern Economic Decision Theory
Evaluating Results Based on Expected Net
Benefits
What we are trying to do at this point?
Find out what works to control crime.
But we want to find out the BEST way,
optimization, i.e. determining Best Policy
It is great to have a theory
It is better to have a theory that we know works.
With appropriate research a theoretical model
becomes a policy model
This work facilitates the implementation of the
Economic Paradigm
Economic Decision Theory in a Nutshell
Expected Net Benefits (of any action):
 Expected Net Benefits = Expected Benefits - Expected
Costs
E(NB)
=
E(B)
E(C)
 In terms of value:
the Value of the Expectation = $B x P(B) - $C x P(C)
 The Basis for:
 The decision from the potential criminal’s point of view?
And
 The logical counter policy from Society’s point of view?
 These are two sides of the same coin
Working within the framework of the
Criminal Justice System
Bentham’s focus: “Pain” - the institutional counterpart:
Punishment via the system of Corrections
Enlarging the Expectation: Increase the likelihood of
pain
We call this combination of activities Deterrence
The Criminal Justice System: is involved at every
stage
Raising the expected cost implies:
$C x P(C) = P(Arrest) x P(Conv|Arrest) x
P(Jail|Conv) x $Jail
Each Stage contributes to the reduction in CRIME
Criminal Justice System
Measures of Output
Quantity Measures
A. The number of Arrests
 Made on basis of probable cause
B. Arrest Ratio(a relative measure)
 = AR = Arrests / Offenses
 Was declining in 1960’s and ‘70’s for U.S. and California
Q. Do Arrests deter crime?
 Sjoquist, American Economic Review (1973) – in
References
 San Diego
 Problem: Arrests may not be best measure
Criminal Justice System
Measures of Output (-cont.)
Quality Measures
A. Clearances (an absolute measure)
 crimes cleared by arrest = CL
 The last burglar - an example
B. Clearance Ratio (a relative measure)
 = CR = Clearances / Offenses
 Problems with the Clearance Ratio
System Quality
A. Convictions (an absolute measure)
 Outcome determined in a court of law
Criminal Justice System
Measures of Output (-cont.)
B. Conviction Ratio (a relative measure)
 CR = Felony Convictions / Offenses (sometimes
CR)
Other Measures
A. Police Ratio
 = Complaints (filed in courts) / Offenses
 measures combined quality of Police & DA efforts
B. Complaints Ratio
 = Complaints (filed w/DA) / Arrests
 measures quality of Police efforts by DA
Output Measures Compared for Homicide in
California
What was happening to felony offense rates in
California and the U. S. ?
Text, p 65
The Decline of Criminal Justice Effectiveness
The Effect of Increasing Expenditures for
Law Enforcement in California and the U. S.
How Do We Use Output Measures to Evaluate
the System? Economic Production Theory
Output
Case of:
Constant Returns
to Scale
Fixed Proportions
Inputs
Notes, Fig.2.3, p.16
Economic Production Theory
Applied to Law Enforcement
Case of:
Varying Proportions
CL
CL
Production: CL = f( OF, L)
OFFENSES
(load on the System)
RESOURCES
(labor)
Assumes the load
on the System
(offenses) is held
fixed
An example of Diminishing Returns
L
What if we hold Resources Fixed and Increase Offenses?
Notes, Fig. 2.5, p 17
Economic Production Theory
Applied to Law Enforcement
Case of:
Varying Proportions
CL
CL
Production: CL = f( OF, L)
OFFENSES
(load on the System)
Assumes System
Resources are held
fixed while offenses
vary
RESOURCES
(labor)
OF
Notes, Fig. 2.5, p.17
Economic Production Theory
Applied to Law Enforcement
Case of:
Varying Proportions
CL
CL
Production: CL = f( OF, L)
OFFENSES
(load on the System)
Assumes System
Resources are held
fixed while offenses
vary
RESOURCES
(labor)
OF
So much for Productivity, What does this imply about
Police Effectiveness?
Determining Police Effectiveness
CL
CL1
0
A
OF1
Notes Fig. 2.6, p.17
OF
Determining Police Effectiveness
CL
A
CL1
How do we
measure
Police
Effectiveness?
Notes Fig. 2.6, p.17
a
0
OF1
As Slope of 0A = tan a = OF to A = CL1
0 to OF1
OF1
OF
Determining Police Effectiveness
CL
A
CL1
How do we
measure
Police
Effectiveness?
Notes Fig. 2.6, p.17
a
0
OF1
As Slope of 0A = tan a = OF1 A = CL1
0 OF1
OF1
OF
Does anyone
recall what this is?
Determining Police Effectiveness
CL
A
CL1
Notes Fig. 2.6, p.17
a
0
OF1
OF
tan a = OF1 A = CL1 = CR1 The CLEARANCE RATIO
0 OF1
OF1
To plot the Clearance Ratio for various Offense Levels
CL
B
CL2
A
CL1
a
0
Notes Fig. 2.6, p.17
OF1
OF2
OF
To plot the Clearance Ratio for various Offense Levels
CL
B
CL2
A
CL1
Notes Fig. 2.6, p.17
a
0
OF1
OF2
OF
Plot points A and B in space showing the Clearance
Ratio relative to Offense levels
Plotting points A and B in CR - OF space
CR
Note that CR1 = CL1 > CR2 = CL2
OF1
OF2
and
CR1
A
B
CR2
0
line AB is drawn holding L constant
(CR,OF|L0)
OF1
OF2
OF
What happens to Police Effectiveness with an increase
in Police Resources?
The change in Police Effectiveness with an increase
in Police Resources, holding Offense levels constant
CR
Higher Effectiveness,
Effect of New level of
Police Resources
CR1
A
(CR,OF|L1)
B
CR2
0
(CR,OF|L0)
OF1
OF2
OF
We can show this in terms of alternative levels of Resources
Police Effectiveness in terms of
alternative levels of Resources
CR
Curves illustrated assume
Economic Efficiency, i.e.,
that Resources are being
used efficiently.
Offenses are being
held constant
0
Notes, Fig. 2.8, p18
L
What if they are not ?
What if Police are not efficient, but simply “satisficing”, i.e.,
just working sufficiently hard
to maintain Clearance Ratios?
CL
B
We will not observe diminishing
returns since the police are not
working to their limit to begin with.
A
OF
What if Police are not efficient, but simply “satisficing”, i.e.,
just working sufficiently hard
to maintain Clearance Ratios?
CL
B
We will not observe diminishing
returns since the police are not
working to their limit to begin with.
A
OF
CR
Performance
standards appear to
be maintained, since
Clearance Ratios
are maintained
A
B
OF
What if Police are not efficient, but simply “satisficing”, i.e.,
just working sufficiently hard
to maintain Clearance Ratios?
CL
B
We will not observe diminishing
returns since the police are not
working to their limit to begin with.
A
OF
What would this
imply in Economic
CR
Performance
standards appear to
be maintained, since
Clearance Ratios
are maintained
A
terms
B
OF
?
Depicting Police Manpower Inefficiency
CR
efficient production
observed output level
if police only work to
maintain the Clearance
Ratio
L
Depicting Police Manpower Inefficiency
CR
efficient production
slack
observed output level
if police only work to
maintain the Clearance
Ratio
L1
As manpower is increased
slack increases , but output level
L2
L
doesn’t rise
If this were the true picture, how could we tell ?
Depicting Police Manpower Inefficiency
CR
efficient production
slack
observed output level
if police only work to
maintain the Clearance
Ratio
L1
L2
L
slack increases as manpower
increases
There would be no statistical relationship between
Police Resources and the Clearance Ratio.
Looking at the Empirical Evidence:
Looking at the Real World
A. Acquire Data
 1. Outputs: CL, CR
 2. Inputs:
Resources: EMP, OTE, L
Case Load: OF
Technological Change: systematic changes over time
not related to inputs
B. Work Out Theoretical Statistical Models
 1. Productivity: CL = f( OF, EMP, OTE, t)
 2. Effectiveness: CR = f( OF, EMP, OTE, t)
 3.
and
: CR = f( OF, L ) with other data
Based on Theory, what do we expect to find ?
Switching
 Notice that, at this point, I have switched from
discussing the theory of what we have studied to
moving toward the testing of our theoretical model.
 Recall the distinction made in the introduction to the
course between Positive and Normative economics.
 We are moving into the realm of Positive
Economics – determining how the real world of
crime and justice works
 Such work has been the focus of much of the research of
Professor Phillips and myself.
 A worthy less technical exercise in positive economics:
Freakonomics, is by Steven Levitt, who describes himself
as a “rogue economist.” Some of it is about crime. It
provides an easy description of the logic behind his work
and ours.
 Throughout the course, we shift between explaining the
theory behind our analysis, positive economics – testing
the theory, and normative economics – the discussion of
what this all implies for sound public policy.
 Next, the results of our testing of production theory as it
relates to crime and justice.
Expected Outcomes from statistical evaluation:
Economic Theory Would Predict
dCR / dOF < 0
CR
dCR / dL > 0
CR
dCR / dt > 0 (if Tech D)
CR
t2
t1
Varying:
OF|L,t
Varying:
L|OF,t
L1
L2
Varying t|OF,L
The question we would hope to be able to answer by looking at
real world data is whether these expectations are borne out.
For the answer one should refer to the text,
The Economics of Crime Control, Chapter 9
the statistical form used for estimation:
CR = k elt OFw EMPb1 OTEb2 e
the Cobb-Douglas Production Function, from
Paul Douglas, ”Are there Laws of Production”, American
Economic Review (1939)
w, b1, b2 are elasticities
w = % D CR
1% DOF
For the answer one should refer to the text,
The Economics of Crime Control, Chapter 9
the statistical form used for estimation:
CR = k elt OFw EMPb1 OTEb2 e
the Cobb-Douglas Production Function, from
Paul Douglas, ”Are there Laws of Production”, American
Economic Review (1939)
w, b1, b2 are elasticities
w = % D CR
b 1 = % D CR
1% DOF
1% D EMP
For the answer one should refer to the text,
The Economics of Crime Control, Chapter 9
the statistical form used for estimation:
CR = k elt OFw EMPb1 OTEb2 e
the Cobb-Douglas Production Function, from
Paul Douglas, ”Are there Laws of Production”, American
Economic Review (1939)
w, b1, b2 are elasticities
w = % D CR
b 1 = % D CR _
1% DOF
1% D EMP
b2 = % D CR__
1% D OTE
For the answer one should refer to the text,
The Economics of Crime Control, Chapter 9
the statistical form used for estimation:
CR = k elt OFw EMPb1 OTEb2 e
the Cobb-Douglas Production Function, from
Paul Douglas, ”Are there Laws of Production”, American
Economic Review (1939)
w, b1, b2 are elasticities
w = % D CR
b 1 = % D CR
b2 = % D CR_
1% DOF
1% D EMP
1% D OTE
l = rate of growth of output, independent of OTE, EMP, OF
Empirical Results for 4 Felony Crimes:
Burglary, Larceny(Theft), Auto Theft, Robbery
Empirical Results for 4 Felony Crimes:
Burglary, Larceny(Theft), Auto Theft, Robbery
Parameter
Variable
Prediction
Estimate Range
Empirical Results for 4 Felony Crimes:
Burglary, Larceny(Theft), Auto Theft, Robbery
Parameter
w
Variable
OF
Prediction
<0
Estimate Range
- .37 to -.88
Empirical Results for 4 Felony Crimes:
Burglary, Larceny(Theft), Auto Theft, Robbery
Parameter
w
b1
Variable
OF
EMP
Prediction
<0
>0
Estimate Range
- .37 to -.88
NS to .72
Empirical Results for 4 Felony Crimes:
Burglary, Larceny(Theft), Auto Theft, Robbery
Parameter
w
b1
b2
Variable
OF
EMP
OTE
Prediction
<0
>0
>0
Estimate Range
- .37 to -.88
NS to .72
.13 to .30
Empirical Results for 4 Felony Crimes:
Burglary, Larceny(Theft), Auto Theft, Robbery
Parameter
w
b1
b2
l
Variable
OF
EMP
OTE
Time
Prediction
<0
>0
>0
>0
Estimate Range
- .37 to -.88
NS to .72
.13 to .30
NS
Empirical Results for 4 Felony Crimes:
Burglary, Larceny(Theft), Auto Theft, Robbery
Parameter
w
b1
b2
l
Variable
OF
EMP
OTE
Time
Prediction
<0
>0
>0
>0
NS = Not statistically different from zero
Estimate Range
- .37 to -.88
NS to .72
.13 to .30
NS
Empirical Results for 4 Felony Crimes:
Burglary, Larceny(Theft), Auto Theft, Robbery
Parameter
w
b1
b2
l
Variable
OF
EMP
OTE
Time
Prediction
<0
>0
>0
>0
Estimate Range
- .37 to -.88
NS to .72
.13 to .30
NS
NS = Not statistically different from zero
Note: The formulations estimated for each of the four offenses
produced estimates of % of “explained” variance (R2)
ranging from 78 to 86.
Empirical Results for 4 Felony Crimes:
Burglary, Larceny(Theft), Auto Theft, Robbery
Parameter
w
b1
b2
l
Variable
OF
EMP
OTE
Time
Prediction
<0
>0
>0
>0
Estimate Range
- .37 to -.88
NS to .72
.13 to .30
NS
NS = Not statistically different from zero
Note: The formulations estimated for each of the four offenses
produced estimates of % of “explained” variance (R2)
ranging from 78 to 86.
These results can be displayed graphically as well.
Law Enforcement Effectiveness Estimates
for the U. S.,1952-1968
Estimation
Forecast
Text, p. 93
Patterns for the Clearance Ratio and Offense Rates for
Robbery in Comparison with Expenditures for Law
Enforcement for the United States, 1952 - 1967.
Early Trend in Law
Enforcement
Expenditures
Text, p.93
Recall the More Recent patterns of Offense Rates
for California and the U. S.
-and the Levels of Police Protection in Place, Relative
to Overall Offense Rates, over the same period
2008
Ideas to Remember
The Economic Paradigm (3 steps)
The objective in dealing with crime
Minimizing the Social Cost of Crime
Jeremy Bentham
Who was he? What did he do?
Economic Production Theory
How does it apply to the analysis of crime?
The empirical evidence
What does it tell us?
Professor Votey
Jobs and Crime:
Youth and Women
Notes, Votey 3, p. 31