1 Economic Concepts Controlling a bad. 2 Outline The Economic Paradigm The Economic Paradigm The Data: Expenditures on the Criminal Justice System The.

11

Economic ConceptsEconomic Concepts

Controlling a badControlling a bad

22

OutlineOutlineThe Economic ParadigmThe Economic ParadigmThe Data: Expenditures on the Criminal The Data: Expenditures on the Criminal

Justice SystemJustice SystemThe Schematic Model: Crime Generation The Schematic Model: Crime Generation

and Controland ControlThe Crime Control TechnologyThe Crime Control Technology

33

Part One:The Economic ParadigmPart One:The Economic Paradigm

Step One: Spell out the options for choiceStep One: Spell out the options for choiceStep Two: Value the options for choiceStep Two: Value the options for choiceStep Three: Choose the best optionStep Three: Choose the best option

44

The Economic Paradigm & The The Economic Paradigm & The Criminal Justice SystemCriminal Justice System

Step Three: The Objective- Minimize the total Step Three: The Objective- Minimize the total cost, i.e. the damages to victims plus cost, i.e. the damages to victims plus expenditures on the criminal justice systemexpenditures on the criminal justice system We want to find the We want to find the bestbest level of expenditures on the level of expenditures on the

criminal justice system, i.e. the level that will minimize criminal justice system, i.e. the level that will minimize the total costthe total cost

Min. TC($) = r*OF + E,Min. TC($) = r*OF + E, Where TC is total cost in dollars, r is the loss rate per Where TC is total cost in dollars, r is the loss rate per

offense, OF is the number of offenses, and E is expenditure offense, OF is the number of offenses, and E is expenditure on the criminal justice system in dollarson the criminal justice system in dollars

55

Example of Optimization from Example of Optimization from Lecture One ( Introduction)Lecture One ( Introduction)

Step One: Total Cost Versus Expenditure Step One: Total Cost Versus Expenditure on the Criminal Justice System (CJS), on the Criminal Justice System (CJS), the the yellow line in the next graphyellow line in the next graph

Step Three: Choosing the lowest total cost Step Three: Choosing the lowest total cost expenditure level, expenditure level, indicated by the red line indicated by the red line in the next graphin the next graph

66

The Graphics of Total Cost, TCThe Graphics of Total Cost, TCTC = r*OF + ETC = r*OF + E

66

$

E on CJS

Total Cost (E)

Minimum Cost

Optimal Expenditure

Economic Paradigm1. Choose objective

e. g. minimize sum ofdamages to victims plus expenditures, E, on CJS

2. Describe states of the world (options for choice)

Total cost curve (E)

3. Choose the best option

77

Step One: Listing the options for Step One: Listing the options for choicechoice

Show how expenditures on the criminal Show how expenditures on the criminal justice system varies with expenditures on justice system varies with expenditures on the criminal justice systemthe criminal justice system

88

Graphics: expenditure on CJS is easyGraphics: expenditure on CJS is easy

88

$

Expenditure on criminal justice system, E on CJS, $

45 degrees

Square: all four sidesAre equal in length

99

Step One Continued: Listing the Step One Continued: Listing the options for choiceoptions for choice

Show how offenses decreases with Show how offenses decreases with expenditures on the criminal justice expenditures on the criminal justice systemsystem

1010

The Graphics of Crime Control, The Graphics of Crime Control, if Crime Is Controllableif Crime Is Controllable

1010

Offenses, OF

E on CJS

OF(E)

1111

Step Two: Valuing the options for Step Two: Valuing the options for choicechoice

The loss rate, r, is the dollar cost per The loss rate, r, is the dollar cost per offense to victims, so r*OF, the losss rate offense to victims, so r*OF, the losss rate times the number of offenses is the total times the number of offenses is the total damages to victims in dollars damages to victims in dollars

1212

The Graphics of Damages to The Graphics of Damages to Victims, if Crime Is ControllableVictims, if Crime Is Controllable

1212

$

E on CJS

r*OF(E)

1313

Step Two: Finishing the options for Step Two: Finishing the options for choice choice

Add expenditure on the criminal justice Add expenditure on the criminal justice system plus damages to victims as they system plus damages to victims as they vary with expenditures on the criminal vary with expenditures on the criminal justice systemjustice system

1414

The Graphics of Damages to The Graphics of Damages to Victims Plus Expenditures on CJSVictims Plus Expenditures on CJS

1414

$

E on CJS

r*OF(E)

45 degrees

1515

Part Two: Expenditures on the Criminal Part Two: Expenditures on the Criminal Justice SystemJustice System

1616

0

40,000

80,000

120,000

160,000

200,000

240,000

1950 1960 1970 1980 1990 2000 2010

TOTALCJSDIRECT

Expenditures by Federal, State & Local Governments On the Criminal Justice System ($millions, nominal) 1971-2007

Federal State and Local ExpendituresFederal State and Local Expenditures

1717

Exponential Growth?Exponential Growth?Total Criminal J ustice System Expenditures, Federal, State & Local 1971-

2007

y = 5E-70e0.0858x

R2 = 0.9824

0

50000

100000

150000

200000

250000

300000

350000

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Year

1818

Exponential Growth of ExpendituresExponential Growth of ExpendituresE(t) = E(0)*eE(t) = E(0)*eg*tg*t

where E is expenditures in year t, E(0) is where E is expenditures in year t, E(0) is expenditures in year 0, e is the exponential expenditures in year 0, e is the exponential function, g is the exponential rate of growth function, g is the exponential rate of growth per year, and t is year tper year, and t is year t

The natural logarithm, ln, linearizes this The natural logarithm, ln, linearizes this relationshiprelationshipLn[E(t)] = ln[E(0)*eLn[E(t)] = ln[E(0)*eg*tg*t] = ln[E(0)] + g*t] = ln[E(0)] + g*t If you plot expenditures on a logarithmic scale If you plot expenditures on a logarithmic scale

against t (year), then g is the slopeagainst t (year), then g is the slopeSee graph on the next slideSee graph on the next slide

1919

9.2

9.6

10.0

10.4

10.8

11.2

11.6

12.0

12.4

1950 1960 1970 1980 1990 2000 2010

LNTOTCJSDIR

1971-1991: !0%

1992-2002: 6.5%

2003-2007: 4.9%

Natural Logaritm of Expenditures on the Criminal Justice System Versus Year, 1971-2007

Three Eras of Growth in CJS ExpendituresThree Eras of Growth in CJS Expenditures

2020

Correcting for inflation, Using CPICorrecting for inflation, Using CPITotal Direct Criminal J ustice System Expenditures, 2007 Dollars (CPI)

y = 2E-31e0.0414x

R2 = 0.9902

0

50000

100000

150000

200000

250000

300000

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

year

2121

Real Total Direct CJS Expenditures On Real Total Direct CJS Expenditures On a Logarithmic Scalea Logarithmic Scale

10.8

11.0

11.2

11.4

11.6

11.8

12.0

12.2

12.4

45 50 55 60 65 70 75 80 85 90 95 00 05 10 15

LNTOTDIRCJS07

Real Total Direct Criminal Justice Expenditures, Federal, State & Local,2007 $

2222

Part Three: Schematic of the Criminal Part Three: Schematic of the Criminal Justice System Justice System

Crime Generation (supply of offenses)Crime Generation (supply of offenses)Crime Control, the production of the Crime Control, the production of the

certainty and severity of punishment certainty and severity of punishment (deterrence and detention)(deterrence and detention)

2323

Crime Generation

Crime Control

OffenseRate PerCapita

ExpectedCost ofPunishment

Schematic of the Criminal Justice System

Causes ?

(detention,deterrence)

Expenditures

Weak Link

2424

Schematic of the Criminal Justice Schematic of the Criminal Justice System System

Crime Generation (supply of offenses)Crime Generation (supply of offenses)Offenses varies with the certainty of Offenses varies with the certainty of

punishment, CR, the severity of punishment, punishment, CR, the severity of punishment, SV, the celerity of punishment, CY,socio-SV, the celerity of punishment, CY,socio-economic causal factors, SE, and moral economic causal factors, SE, and moral compliance, MCcompliance, MC

OF = f(CR, SV, CY, SE, MC)OF = f(CR, SV, CY, SE, MC)Crime ControlCrime Control

2525

Crime Generation

Crime Control

OffenseRate PerCapita

ExpectedCost ofPunishment

Schematic of the Criminal Justice System

Causes ?

(detention,Deterrence, Rehabilitation,And revenge)

Expenditures

Weak Link

2626

Schematic of the Criminal Justice Schematic of the Criminal Justice System System

Crime Generation (supply of offenses)Crime Generation (supply of offenses)OF = f(CR, SV, CY, SE, MC)OF = f(CR, SV, CY, SE, MC)

Crime Control, the production of the Crime Control, the production of the certainty and severity of punishment certainty and severity of punishment (deterrence and detention)(deterrence and detention)Clearance ratio, CR, varies with the level of Clearance ratio, CR, varies with the level of

offenses, OF, and labor resources, Loffenses, OF, and labor resources, LCR = g(OF, L)CR = g(OF, L)

2727

Crime Generation

Crime Control

OffenseRate PerCapita

ExpectedCost ofPunishment

Schematic of the Criminal Justice System: Simultaneity

Causes ?

(detention,Deterrence, Rehabilitation,And revenge)

Expenditures

Weak Link

OF = f(CR, SV, CY, SE, MC)OF = f(CR, SV, CY, SE, MC)

CR = g(OF, L)CR = g(OF, L)

Part Four: Crime Control Technology Part Four: Crime Control Technology

Combine crime generation with the Combine crime generation with the production function using a 4-way diagramproduction function using a 4-way diagramOF = f( CR, SV, CY, SE, MC)OF = f( CR, SV, CY, SE, MC)CR = h(E)CR = h(E)

2828

Production Function for the Criminal Justice System (CJS)1. Variation in clearance ratio with criminal justice system expenditure per capita

Clearance Ratio

Criminal Justice System expenditures per capita

production function

CR = h($E)

2929

per capita expenditures on CJS

offense rate per capita

Clearance ratio

Crime Generation

Four-Way Diagram: Crime Generation & Crime Control

3030

per capita expenditures on CJS

offense rate per capita

expected cost of punishment

Crime Generation

Four-Way Diagram: Crime Generation & Crime Control

per capita expenditures on CJS

ProductionFunction

3131

per capita expenditures on CJS

offense rate per capita

Clearance ratio

Crime Generation

Four-Way Diagram: Crime Generation & Crime Control

per capita expenditures on CJS

ProductionFunction

square

450

3232

per capita expenditures on CJS

offense rate per capita

Clearance ratio

Crime Generation

Four-Way Diagram: Crime Generation & Crime Control

per capita expenditures on CJS

ProductionFunction

square

4501

1

3333

per capita expenditures on CJS

offense rate per capita

Clearance ratio

Crime Generation

Four-Way Diagram: Crime Generation & Crime Control

per capita expenditures on CJS

ProductionFunction

square

4501

1

3434

per capita expenditures on CJS

offense rate per capita

Clearance ratio

Crime Generation

Four-Way Diagram: Crime Generation & Crime Control

per capita expenditures on CJS

ProductionFunction

square

4501

1

3535

per capita expenditures on CJS

offense rate per capita

Clearance ratio

Crime Generation

Four-Way Diagram: Crime Generation & Crime Control

per capita expenditures on CJS

ProductionFunction

square

4501

1

2

2

3636

per capita expenditures on CJS

offense rate per capita

expected cost of punishment

Crime Generation

Four-Way Diagram: Crime Generation & Crime Control

per capita expenditures on CJS

ProductionFunction

square

4501

1

2

2

3

3737

per capita expenditures on CJS

offense rate per capita

Four-Way Diagram: Crime Generation & Crime Control

1

2

3

3838

Test the Theory with the DataTest the Theory with the Data

Report to the Nation On Crime and Report to the Nation On Crime and Justice, Second editionJustice, Second editionP. 122P. 122

3939

Source: Report to the Nation on Crime and Justice 4040

Source: Report to the Nation on Crime and Justice

Expect

Get

4141

per capita expenditures on CJS

offense rate per capita

Clearance ratiot

Crime GenerationOF=f( CR, SV, CY, SE, MC)

Four-Way Diagram: Crime Generation & Crime Control

per capita expenditures on CJS

ProductionFunction

square

4501

1

2

2

3

4242

Source: Report to the Nation on Crime and Justice

Causal conditions account for more variation than control

4343

Crime Generation

Crime Control

OffenseRate PerCapita

ExpectedCost ofPunishment

Schematic of the Criminal Justice System

Causes ?

(detention,deterrence)

Expenditures

Weak Link

4444

Part Five; Class Survey Fall 2011 Vs. Winter 2011

Scoring Ten BehaviorsScoring Ten Behaviors48 responses Fall 201148 responses Fall 201186 responses in Winter 201186 responses in Winter 2011

SERIOUSNESS SURVEY

RATE THE SERIOUSNESS OF EACH OF THE FOLLOWING BEHAVIORS ON A SCALE FROM ZERO( LEAST SERIOUS) TO TEN( MOST SERIOUS):

MEDIAN W11 F111. HOMICIDE _10 10__2. MASS POISONING ( e.g. TYLENOL) _ 9 9__ 3. FORCIBLE RAPE _ 9 _10_4. ARSON: SET FIRE TO A GARAGE _ 7 __75. SELLING HEROIN _ 7 _7_6. AUTO THEFT _ 6 _6_7. EMBEZZLEMENT OF $1,000 _ 5 __58. PROSTITUTE IN A HOUSE OF PROSTITUTION _ 4 __39. POSSESSION OF MARIJUANA _ 2 __110. SNIFFING GLUE _ 2 __1

Center of the Scores Distribution

Mode: most likelyMode: most likelyMedian: middle personMedian: middle personAverage: sum of scores divided by total Average: sum of scores divided by total

number of peoplenumber of people

Density Function for the Standardized Normal Variate

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-5 -4 -3 -2 -1 0 1 2 3 4 5

Standard Deviations

Den

sity

2]1/)0[(2/1*]2/1[)( zezf

2.5%2.5%mean

Median seriousness Scores Fall 2011 and Winter 2011

7

1

Forcible rape

homicide

Poisoning

Arson, Selling heroin

Auto Theft

embezzlement

Prostitute

, Pot Possession, Sniff ing glue

y = 0.8367x + 1.1633

R2 = 0.9882

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10 12

Fall 2011

Win

ter

2011

Consistency from year to year

ConclusionsConsistency from year to yearTriage is possible: we can separate the

more serious behaviors from the less serious behaviors

Distribution of Homicide Scores in F 2011Histogram

0 0 0 0 0 0 0 2 03

43

0

10

20

30

40

50

0 1 2 3 4 5 6 7 8 9 10

Seriousness score

Fre

qu

en

cy

ConclusionsConsistency from year to yearTriage is possible: we can separate the

more serious behaviors from the less serious behaviors

For serious behaviors, a clear majority viewFor example, for homicide 43 out of 48 score it

a 10, while 3 out of 43 score it a 9 and 2 out of 48 score it a 7.

Distribution of Forcible Rape Scores F 2011

Histogram

25

12

7

1210

5

10

15

20

25

30

Bin 0 1 2 3 4 5 6 7 8 9 10

Seriousness scores

Fre

qu

en

cy

Over half the class score forcible rape a 10, 44 out of 48 score it 8 or above.

Three ? Views on Pot, Fall 2011

Score: 0-2, 35Score: 3-5, 11Score: 6&7, 224, a score of 1, would carry a majority vote, 32, a score of 2, would carry a 2/3 vote

Histogram

7

20

85

3 31 1 0 0 0

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10

Seriousness Scores

Fre

qu

en

cy

ConclusionsConsistency from year to yearTriage is possible: we can separate the

more serious behaviors from the less serious behaviors

For serious behaviors, a clear majority viewFor example, for homicide 43 out of 48

score it a 10, while 3 out of 43 score it a 9 and 2 out of 48 score it a 7.

The less serious behaviors are more controversial!

QuestionSince a 2/3 majority view pot

possession as not very serious, a score of 2, why doesn’t pot get decriminalized?

Dispersion of Scores Distribution

Measures of dispersionMeasures of dispersionStandard deviationStandard deviation Inter-quartile rangeInter-quartile rangeRange: Maximum - MinimumRange: Maximum - Minimum

Density Function for the Standardized Normal Variate

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-5 -4 -3 -2 -1 0 1 2 3 4 5

Standard Deviations

Den

sity

2]1/)0[(2/1*]2/1[)( zezf

2.5%2.5%mean

The more serious the behavior, the less disagreement about policy. Fall

2011

Mass Poisoning

Embezzlement

Arson

Auto Thef t

Prostitute

Pot Possession

Selling Heroin

Sniffi ng Glue

Forcible rape

Homicide

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 2 4 6 8 10 12

Seriousness Score

Bureau of Justice Statistics,Report to the Nation

The Alternativep.170

One more step: converting seriousness scores to a metric (years of sentence or Loss rate of $)

The Economics of Crime Control, Ch. 4

Source: $ 1.54 Million (1990), Orley Ashenfelter, Princeton,Based on highway safety

Homicide

Embezzlement of $1000

y = 0.6494e1.4679x

R2 = 1

1

10

100

1000

10000

100000

1000000

10000000

0 2 4 6 8 10 12

Ser iousness Socre

Calibrating $ values for Seriousness

Behavior Seriousness

Loss Rate, $ NIJ Cohen

Homicide 10 $1,540,001 $1,191,000

Poisoning 9 $354,830

Rape 10 $1,540,001 $87,000

arson 7 $18,837 $38,000

Selling heroin 7 $18,837

Auto theft 6 $4,340 $4,000

embezzlement 5 $1,000.04

prostitute 3 $53

Pot possession

1 $2.82Miller, Cohen, Wiersema: Victim Costs & Consequences (NIJ)

Months Served in California Vs. Fall 2011 Seriousness

Possession Vehicle Theft

Arsont

Rape

Homicide

y = 9.445e0.1906x

R2 = 0.693

0

20

40

60

80

100

120

0 2 4 6 8 10 12

Seriousness Scores

Mo

nth

s S

erv

ed

Months Served in CA Prison Vs. F ’11 Seriousness Scores

Summary