Prison and Crime Control:
Evidence of Diminishing
Returns to Scale
Steven Raphael
Goldman School of Public Policy
University 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
Per Inmate Impact on Annual Crimes
Reported to the Police
50
46.8
45
40
36.8
35
29.8
30
24.7
25
20
17.9
15
10
5
0
Crime effect Crime effect, 6 Crime effect,
using time
months
12 months
series break
Crime effect ,
18 months
Crime effect,
24 months
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 postrelease 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 pretrial and convicted jail inmates (primarily electronic
monitoring).
500
1000
1500
2000
2500
3000
Total Weekly Admissions to the California Department of
Corrections and Rehabilitation from the Beginning of
October 2010 through the End of May 2013
01 Jan 11
01 Jul 11
01 Jan 12
Date
01 Jul 12
01 Jan 13
01 Jul 13
May2013
Apr2013
Mar2013
Feb2013
Jan2013
Dec2012
Nov2012
Octo2012
Sep2012
Aug2012
Jul2012
Jun2012
May2012
Apr2012
Mar2012
Feb2012
Jan2012
Dec2011
Nov2011
Octo2011
Sep2011
Aug2011
Jul2011
Jun2011
May2011
Apr2011
Mar2011
Feb2011
Jan2011
Dec2010
Nov2010
Octo2010
Prison Population at the End of the Month
Total CDCR Weekly Population Count, January
2011 through May 2013
180,000
160,000
140,000
120,000
100,000
80,000
60,000
40,000
20,000
0
-100
0
100
Change in Incarceration Rate
0
-100
200
-200
-100
0
100
Change in Incarceration Rate
-200
-100
0
Change in Incarceration Rate
100
D. Diff-in-Diff, Property
0
-400 -200
-200 -100
0
Change in Crime Rate
100 200
C. Year-over-Year Change, Property
-300
200 400
-100
-200
B. Diff-in-Diff, Violent
100 200 300 400
Change in Crime Rate
A. Year-over-Year Change, Violent
0
100 200 300
Scatter Plot of the Annual Pre-Post Realignment Changes
in Monthly Crime Rates Against the Corresponding
Change in the County Incarceration Rate
200
-300
-200
-100
0
Change in Incarceration Rate
100
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
700
600
Violent Crime Rate
500
400
California
300
Comparison States
200
100
0
2000
2002
2004
2006
Year
2008
2010
2012
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
4,000
3,500
Property Crime Rate
3,000
2,500
2,000
California
Comparison States
1,500
1,000
500
0
2000
2002
2004
2006
Year
2008
2010
2012
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
30.00%
24.93%
Proportion of inmates with a rules violation
25.00%
20.00%
14.38%
15.00%
11.99%
10.00%
5.00%
1.86%
0.00%
A1A2
BCD
EF
Any rules violation
0
.01.02.03.04
-.01
.1 .2 .3 .4
0
Proportion A1A2 violation
The Relationship between the Likelihood of
Acquiring a Rules Violation and Age within
California State Prisons, 2008
20
40
60
80
20
40
20
60
80
60
80
Age
0
.05
.1
.15
.2
.25
Proportion EF violation
0
.05
.1
.15
.2
Age
40
60
Age
80
20
40
Age
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
Per Inmate Impact on Annual Crimes
Reprted to the Police
40
36
35
30
25
20
15
15
10
4
5
0
Crime effect, all
provinces pooled
Crime effect, belowmedian incarceration
provinces
Crime effect, abovemedian incarceration
provinces
Incarceration Rate or Annual Incapacitation
Estimate
Estimated Impact of a Pardoned Inmate on Local
Crime by Key Percentiles of the Per-Pardon
Incarceration Rate
250
191.9
200
160.1
150
100.1
100
Incarceration Rate
Annual Incapacitation Effect
58.9
50
32.5 32.6
27.6
19.9
8.6
2.6
0
10th
25th
50th
75th
90th
Percentile of the Cross-Province Distribution of Pre-Pardon
Incarceration Rates
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
Annual Number of Offenses
on Offence History
8
6
4
2
0
0
0.1
0.2
0.3
Incapacitation Ratio
0.4
0.5
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
Average State Incarceration Rate (Prisoners
per 100,000)
500
449
450
400
349
350
300
250
200
171
150
100
50
0
1977 through 1988
1989 through 1999
2000 through 2010
Table 7.3
Estimates 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
Controlling for state
demographics
demographics and year
effects
Violent Crime
1977 through 1988
-2.110 (1.079)c
-2.262 (1.044)b
-1.298 (0.724)c
1989 through 1999
0.061 (0.388)
0.106 (0.288)
0.034 (0.177)
2000 through 2010
-0.012 (0.304)
-0.069 (0.256)
-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 7.4
Estimates 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
demographics
Controlling 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.