Prison and Crime Control: Evidence of Diminishing Returns to ScaleSteven RaphaelGoldman School of Public PolicyUniversity of California, Berkeley

The 2006 Italian Collective Clemency Bill• Passed on July 1, 2006• Reduced sentences of inmates convicted of certain felony

offenses prior to May 2, 2006 by three years.• Led to the immediate release of one-third of the prison

population on August 1, 2006.• Ineligible inmates include those convicted of offenses

involving organized crime, sexual assault, terrorism, kidnapping, and exploiting a prostitute.

• No post-released supervision.• Pardoned inmates who re-offend have their residual sentence

tagged on to any new sentence for offenses occurring within five years.

Scatter plot of monthly incarceration rates against month measured relative to August 2006

Estimated Annual Crime Effects per Prison Year Served

Crime e

ffect usin

g time s

eries

break

Crime e

ffect, 6

months

Crime e

ffect, 1

2 months

Crime e

ffect , 1

8 months

Crime e

ffect, 2

4 months

0

5

10

15

20

25

30

35

40

45

50

17.9

46.8

36.829.8

24.7

Per I

nmat

e Im

pact

on

Annu

al C

rimes

Re

port

ed to

the

Polic

e

Summary of Prison Overcrowding Litigation in California

• 1990: Coleman v. Brown• 2001: Plata V. Brown • 2006: Federal three-judge court established with authority

over prison growth• 2009: Three-judge court order state to immediately offer plan

to reduce prison population to 137.5 percent of capacity. State appeals to the Supreme Court.

• 2011: Supreme Court upholds the population limit order by the three-judge panel.

Provisions of Assembly Bill 109 (California Realignment)

• Non-sexual, non-violent, non-serious (triple nons) felons will serve terms in county jail rather than state prison. No post-release supervision for these inmates.

• Triple nons currently serving time are monitored post-release under the Post Release Community Supervision program administered by counties. Technical violation will result in short jail terms but not returns to state prison.

• Nearly all parole revocations are now served in county jail with a maximum of 180 days.

• Enables greater use of non-custodial alternatives for both pre-trial and convicted jail inmates (primarily electronic monitoring).

Total Weekly Admissions to the California Department of Corrections and Rehabilitation from the Beginning of October 2010 through the End of May 2013

500

1000

1500

2000

2500

3000

Wee

kly

Adm

issi

ons

to C

alifo

rnia

Sta

te P

rison

s

01 Jan 11 01 Jul 11 01 Jan 12 01 Jul 12 01 Jan 13 01 Jul 13Date

Total CDCR Weekly Population Count, January 2011 through May 2013

Octo2010

Nov2010

Dec2010

Jan2011

Feb2011

Mar2011

Apr2011

May2011

Jun2011

Jul2011

Aug2011

Sep2011

Octo2011

Nov2011

Dec2011

Jan2012

Feb2012

Mar2012

Apr2012

May2012

Jun2012

Jul2012

Aug2012

Sep2012

Octo2012

Nov2012

Dec2012

Jan2013

Feb2013

Mar2013

Apr2013

May2013

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

Priso

n Po

pula

tion

at th

e En

d of

the

Mon

th

Scatter Plot of the Annual Pre-Post Realignment Changes in Monthly Crime Rates Against the Corresponding Change in the County Incarceration Rate

-100

010

020

030

0C

hang

e in

Crim

e R

ate

-200 -100 0 100 200Change in Incarceration Rate

A. Year-over-Year Change, Violent

-100

010

020

030

040

0C

hang

e in

Crim

e R

ate

-300 -200 -100 0 100Change in Incarceration Rate

B. Diff-in-Diff, Violent

-200

-100

010

020

0C

hang

e in

Crim

e R

ate

-200 -100 0 100 200Change in Incarceration Rate

C. Year-over-Year Change, Property

-400

-200

020

040

0C

hang

e in

Crim

e R

ate

-300 -200 -100 0 100Change in Incarceration Rate

D. Diff-in-Diff, Property

Violent Crime Rate Trends in California and Synthetic California, with Synthetic Comparison Group and Weighted Identified by Matching on Violent Crime Rates for Each Year Between 2000 and 2010

2000 2002 2004 2006 2008 2010 20120

100

200

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400

500

600

700

CaliforniaComparison States

Year

Viol

ent C

rime

Rate

Property Crime Rate Trends in California and Synthetic California, with Synthetic Comparison Group and Weighted Identified by Matching on Violent Crime Rates for Each Year Between 2000 and 2010

2000 2002 2004 2006 2008 2010 20120

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

CaliforniaComparison States

Year

Prop

erty

Crim

e Ra

te

Explaining the differences

• Institution and cultural factors• Diminishing returns to scale

• Italy’s pre-pardon incarceration rate stood at 103 per 100,000

• California’s pre-pardon incarceration rate was 425 for prisoners alone. Adding the jail population of 72,000 increases the point-in-time incarceration rate to roughly 615 per 100,000 (roughly six times the incarceration rate of Italy)

Sources of diminishing returns to scale

• Criminogenic heterogeneity among those who criminally offend

• Expansion of the use of prison along the extensive margin• Net less serious offenders for less serious offenses

• Expansion of the use of prison along the intensive margin• More likely to incarcerate offenders beyond the age of desistance

Proportion of Inmates Serving an Entire Review Period in a California State Prison in 2008 That Acquire a Rules Violation Report between Classification Hearings

A1A2 BCD EF Any rules violation0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

1.86%

11.99%

14.38%

24.93%

Prop

ortio

n of

inm

ates

with

a ru

les v

iola

tion

The Relationship between the Likelihood of Acquiring a Rules Violation and Age within California State Prisons, 2008

0.1

.2.3

.4P

ropo

rtion

any

vio

latio

n

20 40 60 80Age

-.010

.01.

02.0

3.04

Pro

porti

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1A2

viol

atio

n

20 40 60 80Age

0.0

5.1

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.2P

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BC

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20 40 60 80Age

0.0

5.1

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.2.2

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EF

viol

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20 40 60 80Age

Diminishing Returns Sets in at Surprisingly Low Incarceration Levels

• Cross-province differences in the effects of the Italian pardon• The effects of a targeted and highly selective sentence

enhancement in the Netherlands.• Effects of exogenous increase in jail incarceration in Israel• Estimates of the average effect of a prison year served on

crime rates in the United States at different points in time

Estimates of the Annual Effects of a Pardoned Inmate on Province Level Crime Totals

0

10

20

30

40

15

36

4

Per I

nmat

e Im

pact

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rimes

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rted

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e

Estimated Impact of a Pardoned Inmate on Local Crime by Key Percentiles of the Per-Pardon Incarceration Rate

10th 25th 50th 75th 90th0

50

100

150

200

250

32.5

58.9

100.1

160.1

191.9

32.6 27.6 19.98.6 2.6

Incarceration RateAnnual Incapacitation Effect

Percentile of the Cross-Province Distribution of Pre-Pardon Incarceration Rates

Inca

rcer

ation

Rat

e or

Ann

ual I

ncap

acita

tion

Estim

ate

Analysis of Habitual Offender Sentence Enhancement in Holland 2001 (Study by Ben Vollard in the Economic Journal, 2012)• The Dutch pass a sentence enhancement in 2001 targeted at

offenders with 10 or more prior felony offenses.• Increases sentence for theft from two months to two years.• Limited initially to 10 largest cities, but later (2004) expanded

nationwide.• Ability to apply the sentence limited through a centralized rationing

process of available prison space.• Resulted in cross-area differences in the extent to which localities

were able to apply the sentence enhancement to their population of usual suspects.

• Based on police records, Vollard estimates that there were roughly three to four thousands offenders whose criminal history made them eligible for the sentence enhancement.

• Dutch incarceration rate at the time low by U.S. standards (124 per 100,000)

Relationship between recorded offenses in years preceding the policy change among those receiving the sentence enhancement and the proportion of eligible offenders sentenced under the new law

Ann

ual N

umbe

r of O

ffen

ses

on O

ffen

ce H

isto

ry

8

6

4

2

0 0 0.1 0.2 0.3 0.4 0 .5

Incapacitation R a tio

Vollard results• Large average annual incapacitation effects on the order of 50

to 60 offenses prevented per year served.• Moving from the 25th to the 75th percentile of the

incapacitation ratio results in a 25 percent reduction in the incapacitation effect.

Realignment in Israel (Ater, Givati, and Rigbi 2013)• Responsibility for housing arrestees transferred from police

department to the Israeli Prison Authority. • Before reform arrestees housed at police stations or local jails,

managed by police stations and paid for out of the police budget

• After reform, responsibility and budget transferred to state agency.

• Israeli incarceration rate inclusive of pre-trial population (about 35 percent of total) stood at 225 per 100,000 in 2013

• Individuals arrested after the reform were 20 percentage points less likely to be charged. Authors interpret this as a reduction in the probable-cause threshold implemented by police officers once responsibilities were realigned

• Individuals arrested after the reform faced maximum sentences that were on average 60 percent lower than individuals arrested before the reform

• Increase in arrests driven almost entirely by increased arrests for public order and property crime rather than violent crime.

• Increase in arrests and incarcerated arrestees reduced property and public order crime but had no impact on violent crime (elasticity of roughly 0.4).

Average U.S. State Incarceration Rates for Three Sub-Periods Analyzed

1977 through 1988 1989 through 1999 2000 through 20100

50

100

150

200

250

300

350

400

450

500

171

349

449

Aver

age

Stat

e In

carc

erati

on R

ate

(Pris

oner

s pe

r 100

,000

)

Table 7.3Estimates of the Effect of a One-Person Increase in the Prison Incarceration Rate on Violent Crime for Different Time Periods  Specification  No controls Controlling for state

demographicsControlling for state demographics and year effects

Violent Crime       1977 through 1988 1989 through 1999 2000 through 2010

-2.110 (1.079)c

0.061 (0.388)-0.012 (0.304)

-2.262 (1.044)b

0.106 (0.288)-0.069 (0.256)

-1.298 (0.724)c

0.034 (0.177)-0.177 (0.309)

       Murder       1977 through 1988 1989 through 1999 2000 through 2010

-0.022 (0.037)-0.011 (0.005)c

-0.009 (0.007)

-0.021 (0.036)-0.012 (0.004)a

-0.009 (0.007)

-0.006 (0.037)-0.010 (0.004)b

-0.009 (0.008)       Rape       1977 through 1988 1989 through 1999 2000 through 2010

-0.158 (0.059)a

-0.016 (0.015)0.001 (0.021)

-0.151 (0.053)a

-0.017 (0.012)0.003 (0.019)

-0.104 (0.038)a

-0.019 (0.010)c

-0.004 (0.026)       Robbery       1977 through 1988 1989 through 1999 2000 through 2010

-1.811 (0.784)b

-0.014 (0.166)-0.012 (0.149)

-1.814 (0.758)b

-0.001 (0.124)-0.034 (0.129)

-1.171 (0.545)b

-0.048 (0.087)-0.151 (0.145)

        Assault       1977 through 1988 1989 through 1999 2000 through 2010

-0.119 (0.337)0.102 (0.235)0.008 (0.171)

-0.276 (0.288)0.135 (0.197)-0.030 (0.147)

-0.016 (0.271)0.112 (0.155)-0.020 (0.194)

Table 7.4Estimates of the Effect of a One-Person Increase in the Prison Incarceration Rate on Property Crime for Different Time Periods

  Specification  No controls Controlling for state

demographicsControlling for state demographics and year effects

Property Crime       1977 through 1988 1989 through 1999 2000 through 2010

-18.096 (8.087)b

0.319 (0.943)-2.822 (1.696)

-19.267 (7.968)b

-0.245 (0.680)-2.134 (1.414)

-8.640 (4.777)c

-1.289 (0.654)c

-2.049 (1.527)

       Burglary       1977 through 1988 1989 through 1999 2000 through 2010

-8.694 (3.606)b

-0.277 (0.195)-0.390 (0.419)

-9.176 (3.572)b

-0.409 (0.284)-0.241 (0.387)

-4.437 (2.076)b

-0.477 (0.253)c

-0.342 (0.462)

       Larceny       1977 through 1988 1989 through 1999 2000 through 2010

-8.701 (4.182)b

0.678 (0.629)-1.726 (0.994)c

-8.954 (4.161)b

0.302 (0.424)-1.108 (0.822)

-3.278 (2.437)-0.526 (0.401)-1.178 (0.925)

       Motor Vehicle Theft       1977 through 1988 1989 through 1999 2000 through 2010 

-0.702 (0.815)-0.081 (0.318)-0.703 (0.489)

-1.137 (0.747)-0.139 (0.262)-0.785 (0.428)c

-0.924 (0.926)-0.284 (0.202)-0.526 (0.444)

Further evidence from the U.S. (Liedke, Piehl and Useem 2006)

• Assess how the crime-prison elasticity varies with the scale of incarceration using state-level panel data.• Allowing for higher-order polynomial regressions and spline

functions with incarceration level notches• Find substantial prison-crime effects at low incarceration rates• Effects decline rapidly with incarceration growth• Somewhere between an incarceration rate of 325 and 425 per

100,000, elasticity falls to zero or turns slightly positive.

Concluding thoughts• Much more room for selective incapacitation, especially in the

United States where the incarceration rate is so high.• While a sizable share of U.S. prison growth is attributable to

changes in drug sentencing policy (roughly one-fifth) the lion’s share in state prisons is attributable to longer sentences for violent offenders (roughly one half of growth). • Many violent offenders are often thought to be low-risk of

recidivism. Creates tension between utilitarian and just-desert objectives of corrections.

• We are likely way beyond the point where benefits in terms of crime control outweigh the budgetary and social costs of current incarceration levels.

Studies discussed in this presentation

• Buonanno, Paolo and Steven Raphael (2013), “Incarceration and Incapacitation: Evidence from the 2006 Italian Collective Pardon,” American Economic Review, 103(6): 2437-2465.

• Itai, Ater; Givati, Yehonatan; and Oren Rigbi (2013), “Organizational Structure, Police Activity, and Crime,” Available at SSRN: http://ssrn.com/abstract=2326928 or http://dx.doi.org/10.2139/ssrn.2326928

• Liedke, Raymond; Piehl, Anne Morrison and Bert Useem (2006), “The Crime Control Effect of Incarceration: Does Scale Matter?” Criminology and Public Policy, 5: 245-275.

• Lofstrom, Magnus and Steven Raphael (2013), Public Safety Realignment and Crime Rates in California, Public Policy Institute of California, San Francisco, CA.

• Raphael, Steven and Michael Stoll, Why Are So Many Americans in Prison?, Russell Sage Foundation, New York, NY (2013).

• Vollard, Ben (2013), “Preventing Crime Through Selective Incapacitation,” The Economic Journal, 123 (567): 262-284.