Transcript How Much Crime Reduction Does the Marginal Prisoner Buy?

How Much Crime Reduction Does
the Marginal Prisoner Buy?
Rucker Johnson
Goldman School of Public Policy
UC Berkeley
Steven Raphael
Goldman School of Public Policy
UC Berkeley
Prisoners in State or Federal Prison per 100,000 U.S. Residents, 1925 to 2004
600
500
Prisoners per 100,000
400
300
200
100
0
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
Deriving long-run equilibrium in
incarceration rates as a function of
observed transition probabilities
Define the vector Pt as

P ' t  P1t
P 2t

P 3 t , where

j
P
t 1
j
and where the index values indicate the three potential states of not in prison/not on
parole (j=1), in prison (j=2), and on parole (j=3). Define the matrix Tt as
T 11t T 12 t T 13 t 
 21
22
23 
Tt  T t T t T t , where 0  T ij t  1, i, j and
T 31t T 32 t T 33 t 


T
j
ij
t
 1, j.
For a given transition probability matrix, Tt, the equilibrium population distribution
across the three states (defined by the vector P*) satisfies the equation
P *'  P *' Tt .
Simulated Equilibrium Incarceration Rates Based on A Markov Process Compared to Actual
Incarceration Rates
600.00000
500.00000
400.00000
implied equilibrium incarceration rate per
100,000
300.00000
Actual Incarceration Rate
200.00000
100.00000
0.00000
1975
1980
1985
1990
1995
2000
2005
Alternative simulation of the evolution of U.S. incarceration
rates based on 1980 starting values and observed transition
probabilities
For each year, we observe actual values of Tt. Thus, the distribution of the population
across the three states can be written as a function of the starting values in 1980 and the
transition probability matrices according to the recursive equations
P1981  P1980 T1980 .
'
'
P1982 '  P1981 ' T1981  P1980 ' T1980 T1981
P1983 '  P1982 ' T1982  P1981 ' T1981T1982  P1980 ' T1980 T1981T1982
Pt '  P1980 ' i 1980 Ti
t
Actual Incarceration Rates and Simulated Incarceration Rate using 1980 Starting Values and
Empirical Transition Probabilities
600.00000
Incarcerated per 100,000
500.00000
400.00000
Simulated Incarceration Rate
300.00000
Actual Incarceration Rate
200.00000
100.00000
0.00000
1975
1980
1985
1990
1995
2000
2005
Simulated Incarceration Rates: Base Simulation and Holding Prison Entry Probabilities to
1980 Levels
600
500
Prisoners per 100,000
400
Base Simulation
Holding Parole Returns to 1980 level
300
Holding new commitments rate to 1980 level
Holding new commitment and parole return
rates to 1980 levels
200
100
0
1975
1980
1985
1990
1995
2000
2005
Simulated Incarceration Rates: Base Simulations and Holding Exit Probabilities to 1980 Levels
600
500
Prisoners per 100,000
400
Holding prison exit probabilities to 1980 levels
300
Base Simulation
200
100
0
1975
1980
1985
1990
1995
2000
2005
A simple non-behavioral model of the incapacitation
effects of prison on crime
Define the vector S '  [S1 S 2 ] , where S1 is the proportion not incarcerated and S2 is the
proportion incarcerated. Assume



The probability of committing a crime is c for all non-incarcerated and 0 for the
incarcerated.
Probability of being apprehended and sent to prison is p for all who commit crime
and 0 for all who do not
The likelihood of being released from prison is the constant θ for all incarcerated
For any period t the population distribution across these two states is determined by the
equation
St '  St 1 'T
Where the transition matrix is defined in accordance with the probabilities defined above
as
1  cp cp 
T 
1   

For a constant T, equilibrium is defined by the equation
S * '  S * 'T
Which gives the two equations
S *1  (1  cp ) S *1  S * 2
S
*
2
 cpS
*
1
 (1   ) S
*
.
2
When combined with the constraint, S1,t  S 2,t  1, t , the three equations imply
equilibrium values that are a function of the transition probabilities alone,
S *1 
S *2

cp  
.
cp

cp  
Given the equilibrium population shares, the equilibrium crime rate is given by
Crim e*  cS *1  c(1  S * 2 ) 
c
.
cp  
dS * 2
,
dc
dCrim e*
 0
dc
Basic identification problem
highlighted in the existing literature



Based on the derivation above, it’s easy to show
that dS*2/dc, dCrime*/dc >0
Shocks to underlying criminality will induce
positive covariance between crime rates and
incarceration rates operating through the
criminality parameter c.
Criminality is unobservable
Basic identification strategy: isolate variation in incarceration
along the dynamics adjustment path between equilibrium in
response to shocks to the transition probability parameters
Suppose that we are initially in equilibrium with a value for the criminality parameter
equal to c0 at time t=0. The system then experiences an increase in underlying
criminality operationalized by an increase in the criminality parameter at t=1 from c0 to
c1. For any period t > 0, the proportion incarcerated is given by
S2,t  S1,t 1c1 p  S2,t 1 (1  )
Which can be rewritten as
S2,t  S2,t 1 (c1 p   1)  c1 p
Which is in the form of a simple linear difference equation. To solve, we make use of the
c0 p
fact that the incarceration rate at t=0 is the equilibrium rate S * 2,t 0 
, to derive
c0 p  
the expression for the path that incarceration will follow in response to the shock
 c p
c p 
c1 p
t
S 2 ,t   o
 1
1  c1 p    
c1 p  
 co p   c1 p   
Or


S2,t  S *2,t 0  S *2,t 0 1  c1 p     S *2,t 0
t
Incarceration rate
S*, t>0
S*, t=0
t=0
t=1
Time since shock
We can derive a similar equilibrium
adjustment path for crime
Crimet  ct (1  S2,t )
Substituting for the incarceration rate and rearranging gives
Crimet  ct (S *2,t 0  S *2,t 0 )(1  cp  )t  ct (1  S *2,t 0 )
•Note, the first term in crime adjustment path is positive yet diminishing in
time, t.
•The second term is equal to the equilibrium crime rate for t>0.
•Together, the two components indicate that an increase in c causes a
discrete increase in crime above the new long-term equilibrium and then
adjusts to the new equilibrium from above.
Crime rate
Crime*, t>0
Crime*, t=0
t=0
t=1
Time since shock
Incarceration rate
Crime rate
S*, t>0
C*, t>0
S*, t=0
C*, t=0
t=0
t=1
Time since shock

Change from t=0 to t=1 for both crime and
incarceration are positive.


Crime rate reflects positive effects of change in criminality as
well as the negative effect of increased incarceration.
Change from t>0 to t+1 will be negative for crime and
positive for incarceration

Decline in crime rate is driven by an increasing incapacitation
effect alone. Increase in incarceration is driven by the system
catching up to the new equilibrium value with a lag (the key
to our identification strategy
Deriving explicit expressions for the periodic changes in
incarceration and crime for t=0 and t=1 where ΔSt=St+1-St
Changes in the incarceration rate
S 2, 0  ( S * 2,t 0  S * 2,t 0 )(c1 p   )
S 2,1  ( S * 2,t 0  S * 2,t 0 )(c1 p   )(1  c1 p   )
S 2 , t  ( S
*
2 ,t  0
S
*
2 ,t  0
)(c1 p   )(1  c1 p   )
t
Simulated Equilibrium Incarceration Rates Based on A Markov Process Compared to Actual
Incarceration Rates
600.00000
500.00000
400.00000
implied equilibrium incarceration rate per
100,000
300.00000
Actual Incarceration Rate
200.00000
100.00000
0.00000
1975
1980
1985
1990
1995
2000
2005
Expression for change in crime from t=0 to t=1
Crimeo  c1S2,0  (c1  c0 )(1  S *2,t 0 )
Partial incapacitation effect
associated with contemporaneous
increase in incarceration in
response to criminality shock
Increases in crime caused by
increased criminality holding
incarceration to the previous
equilibrium level
•We observe the change in crime and the contemporaneous change in
incarceration and wish to estimate the incapacitation effect, c1.
•We do not observe the second term however, and thus in a regression of the
change in crime on the change in incarceration, it will be swept into the error.
•Change in incarceration will be positively correlated with the error term
Expression for change in crime from t=1 to t=2
Crime1  c1S 2,1
•Change in crime for this period driven only by the increase in
incarceration rate associated with the incarceration rate
adjusting upwards to it’s new equilibrium in response to last
period’s shock.
•This suggests the following identification strategy: use last
period’s shock to predict how the incarceration rate will change
between now and next period. Instrument the actual change in
incarceration rate with the predicted change, thus isolating
variation in incarceration associated with the dynamic lagged
adjustment
Deriving explicit expressions for the periodic changes in
incarceration and crime for t=0 and t=1 where ΔSt=St+1-St
Changes in the incarceration rate
S 2, 0  ( S * 2,t 0  S * 2,t 0 )(c1 p   )
S 2,1  ( S * 2,t 0  S * 2,t 0 )(c1 p   )(1  c1 p   )
S 2 , t  ( S
*
2 ,t  0
S
*
2 ,t  0
)(c1 p   )(1  c1 p   )
t
Data

State level panel covering the period 1978 to 1998.




Data on crime (7 part 1 felony offenses) from from the
Uniform Crime Reports
Prison totals, total admissions, and total releases by state and
year come from the Bureau of Justice National Prisoner
Statistics program.
Population totals come from the Census bureau as do a
number of state-level demographic measures.
Regional economic indicators come from either the Bureau
of Labor Statistics or the Bureau of Economic Analysis.
Constructing the instrument
Table 1
Illustration of the Calculation of the Predicted Change in Incarceration Rates for New
York Between 1980 and 1982
1979
1980
1981
1982
118.39
125.33
147.30
161.39
Current incarceration rate ( S 2,t )
Admission rate (cp)
-
0.00059
0.00071
0.00072
Release rate (θ)
-
0.432
0.329
0.360
Equilibrium Incarceration rate
based on current transition
probabilities
cp
( S 2*,t 0 
*100,000)
cp  
-
135.87
215.61
199.97
Incarceration rate at t = 0 ( S 2, 0 )
Predicted change in incarceration
rate, t=1 to t=2
(S2*,t 0  S2,0 ) * (1  cp   )(cp   )
-
118.39
125.33
147.30
-
4.29
19.94
12.15
Actual change in incarceration
rate, t=1 to t=2
-
21.97
14.09
13.64
Scatter Plot of the Actual One-Year Change in State Level Incarceration Rates Against the
Predicted Change Based on Prior Period Shocks
400
300
200
Actual Change
100
0
-100
-50
0
50
100
-100
Actual Change = 7.08 + 0.73*Predicted Change, R2=0.101
standard error (1.18) (0.07)
-200
-300
-400
Predicted Change
150
200
Population-Weighted Scatter Plot of the Actual One-Year Change in State-Level Incarceration
Rates Against the Predicted Change Based on Prior Period Shocks
400
300
200
Actual Change
100
0
-100
-50
0
50
100
150
-100
Actual Change = 7.67 +0.71*Predicted Change, R2=0.152
standard errors (0.88) (0.05)
-200
-300
-400
Predicted Change
200
Table 2
First Stage Effect of the Predicted Change in Incarceration Rates Based on Last
Period Shock on the Current Change in Incarceration Rates
Dependent Variable=ΔIncarceration Rate
(1)
(2)
(3)
(4)
Predicted Δ
0.708
0.678
0.686
0.578
Incarceration
(0.051)
(0.055)
(0.055)
(0.061)
Δ% in
276.03
222.58
-364.60
popul. 0 to 17
(585.54)
(613.28)
(675.31)
Δ% in
539.90
620.86
259.31
popul. 18 to 24
(659.97)
(720.32)
(784.72)
Δ% in
-977.15
77.88
-7.08
popul. 25 to 44
(620.33)
(662.17)
(709.78)
Δ% in
-699.49
-842.13
-2053.59
popul. 45 to 64
(641.42)
(800.01)
(1010.93)
Δunemployment
-0.682
-0.037
-0.228
rate
(0.682)
(1.013)
(1.018)
Δpoverty rate
43.29
55.81
69.99
(425.05)
(42.95)
(43.64)
Δ% black
-54.63
-60.43
-51.23
(45.05)
(45.53)
(45.74)
Δ per capita
0.003
-0.003
-0.002
income
(0.002)
(0.003)
(0.003)
Year Effects
No
No
Yes
Yes
State Effects
No
No
No
Yes
2
R
0.152
0.176
0.256
0.295
N
1,070
1,070
1,070
1,070
F-statistic*
191.74
154.13
154.52
88.94
(P-value)
(<0.0001)
(<0.0001)
(<0.0001)
(<0.0001)
Table 3
Descriptive Statistics for Crime and Incarceration Rates for the Overall Sample Period and
Sub-Periods
Average
Standard Deviation
Within-State Standard
Deviation
Panel A: 1978 to 1998
Violent Crime
630.21
272.09
102.88
Murder
8.61
4.17
1.99
Rape
37.24
12.16
6.22
Robbery
225.71
137.82
48.14
Assault
358.65
158.31
74.27
Property Crime
4,795.07
1,147.98
585.73
Burglary
1,245.76
419.86
292.18
Larceny
3,015.02
691.24
315.99
Motor Veh. Theft
534.29
233.39
123.17
Incarceration Rate
255.29
137.65
107.84
Panel B: 1978 to 1984
Violent Crime
555.09
243.67
50.72
Murder
9.13
3.96
1.25
Rape
34.57
12.20
3.46
Robbery
226.38
150.65
36.44
Assault
285.02
112.09
21.12
Property Crime
4,917.04
1,138.91
398.92
Burglary
1,479.70
415.20
184.28
Larceny
2,970.79
669.11
209.06
Motor Veh. Theft
466.55
202.11
52.48
Incarceration Rate
145.53
62.76
25.63
Panel C: 1985 to 1991
Violent Crime
654.53
285.81
82.52
Murder
8.72
4.22
1.58
Rape
38.84
12.22
3.68
Robbery
233.19
143.09
33.96
Assault
373.77
157.11
55.09
Property Crime
4,972.12
1,225.08
293.81
Burglary
1,290.24
403.34
114.29
Larceny
3,105.04
732.39
183.82
Motor Veh. Theft
576.83
260.04
99.78
Incarceration Rate
235.57
94.62
42.04
Panel D: 1992 to 1998
Violent Crime
682.91
275.04
89.96
Murder
8.25
4.41
1.62
Rape
38.57
11.92
4.12
Robbery
224.72
126.30
48.33
Assault
411.35
170.15
44.59
Property Crime
4,598.19
1,051.30
390.55
Burglary
1,031.62
307.38
124.08
Larceny
3,000.57
666.60
197.39
Motor Veh. Theft
566.00
229.18
96.41
Incarceration Rate
356.13
135.87
52.47
Table 4
OLS and IV Estimates of the Effect of Changes in Incarceration Rates on Changes in Violent Crime Rates Using the
Entire State-Level Panel (Dependent Variable=ΔViolent Crime Rate)
Specification (1)
Specification (2)
Specification (3)
Specification (4)
OLS
IV
OLS
IV
OLS
IV
OLS
IV
ΔIncarceratio
n rate
-0.149
(0.063)
-0.698
(0.166)
-0.029
(0.060)
-0.346
(0.173)
-0.006
(0.050)
-0.216
(0.140)
-0.017
(0.053)
-0.358
(0.189)
Controls
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Year Effects
No
No
No
No
Yes
Yes
Yes
Yes
State Effects
No
No
No
No
No
No
Yes
Yes
R2
0.005
0.016
0.127
0.127
0.474
0.471
0.491
0.481
N
1,071
1,071
1,071
1,071
1,071
1,071
1,071
1,071
Implied
elasticity at
the mean
-0.06
-0.28
-0.01
-0.14
-0.002
-0.09
-0.01
-0.15
Table 5
OLS and IV Estimates of the Effect of Changes in Incarceration Rates on Changes in Property Crime Rates Using the
Entire State-Level Panel (Dependent Variable=ΔProperty Crime Rate)
Specification (1)
Specification (2)
Specification (3)
Specification (4)
OLS
IV
OLS
IV
OLS
IV
OLS
IV
ΔIncarceratio
n rate
-1.608
(0.338)
-6.271
(0.941)
-0.949
(0.335)
-5.318
(1.015)
-1.043
(0.259)
-4.879
(0.794)
-1.137
(0.271)
-7.317
(1.165)
Controls
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Year Effects
No
No
No
No
Yes
Yes
Yes
Yes
State Effects
No
No
No
No
No
No
Yes
Yes
R2
0.021
0.040
0.094
0.098
0.519
0.478
0.552
-0.455
N
1,071
1,071
1,071
1,071
1,071
1,071
1,071
1,071
Implied
elasticity at
the mean
-0.09
-0.33
-0.05
-0.28
-0.06
-0.26
-0.06
-0.39
Table 6
OLS and IV Estimates of the Effect of Changes in Incarceration Rates on Changes in Individual Part 1 Felony Offenses
Specification (1)
Specification (2)
Specification (3)
Specification (4)
Dependent
Variable
OLS
IV
OLS
IV
OLS
IV
OLS
IV
Δ Murder
-0.002
(0.001)
-0.010
(0.004)
-0.001
(0.001)
-0.004
(0.003)
-0.002
(0.001)
-0.002
(0.004)
-0.001
(0.001)
-0.001
(0.005)
Δ Rape
-0.019
(0.004)
-0.062
(0.011)
-0.015
(0.004)
-0.058
(0.012)
-0.010
(0.004)
-0.034
(0.010)
-0.009
(0.004)
-0.042
(0.014)
Δ Robbery
-0.082
(0.033)
-0.399
(0.090)
-0.028
(0.033)
-0.255
(0.095)
-0.036
(0.029)
-0.173
(0.082)
-0.037
(0.030)
-0.243
(0.110)
Δ Assault
-0.046
(0.037)
-0.227
(0.098)
0.016
(0.037)
-0.029
(0.104)
0.041
(0.033)
-0.007
(0.093)
0.029
(0.035)
-0.072
(0.124)
Δ Burglary
-0.435
(0.125)
-2.497
(0.358)
-0.132
(0.127)
-2.520
(0.405)
-0.324
(0.095)
-1.662
(0.288)
-0.322
(0.099)
-2.276
(0.409)
Δ Larceny
-1.005
(0.200)
-2.856
(0.532)
-0.595
(0.197)
-2.157
(0.570)
-0.640
(0.161)
-2.415
(0.472)
-0.711
(0.168)
-3.640
(0.669)
Δ Motor
Vehicle Theft
-0.167
(0.067)
-0.917
(0.182)
-0.042
(0.065)
-0.641
(0.192)
-0.077
(0.059)
-0.801
(0.178)
-0.105
(0.062)
-1.401
(0.262)
Control
Variables
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Year Effects
No
No
No
No
Yes
Yes
Yes
Yes
State Effects
No
No
No
No
No
No
Yes
Yes
Comparison of these results to those from
previous research


Our violent crime-prison elasticity estimates range from -0.09 to -0.15 and
property crime estimates range from -0.28 to -0.39.
Levitt (1996) estimates range from -0.38 to -0.42 for violent crime and 0.26 to -0.32 for property crime.
Murder
Rape
Robbery
Assault
Burglary
Larceny
Motor Vehicle Theft
Our estimates of crimes
averted
0.001
0.042
0.243
0.072
2.276
3.642
1.401
Estimates from Marvell
and Moody (1994)
Not significant
0.02
0.25
Not signficant
2.281
2.77
0.56
Estimating the Monetary Value of an Additional Prisoner in 1993
Levitt Point Estimates of
Levitt Estimates Adjusted for
Crimes Avoided
Under-reporting
Money Damages per Crime Quality of Life Costs
Total Savings
Murder
-0.004
-0.004
17,000
2,700,000
$10,868
Rape
-0.031
-0.053
9,800
40,800
$2,682
Robbery
-0.55
-1.1
2,900
14,900
$19,580
Assault
-0.55
-1.2
1,800
10,200
$14,400
Burglary
-1.3
-2.6
1,200
400
$4,160
Larceny
-2.6
-9.2
200
0
$1,840
Motor Vehicle theft
-0.5
-0.7
4,000
0
$2,800
Total
-5.535
Our Overall Point Estimates
Murder
-0.001
Rape
-0.042
Robbery
-0.243
Assault
-0.072
Burglary
-2.276
Larceny
-3.640
Motor Vehicle theft
-1.401
Total
-7.675
-14.857
$56,330
Our Point Estimates Adjuted
for Under-Reporting
Money Damages per Crime Quality of Life Costs
Total Savings
-0.001
17,000
2,700,000
$2,717
-0.072
9,800
40,800
$3,633
-0.486
2,900
14,900
$8,651
-0.157
1,800
10,200
$1,885
-4.552
1,200
400
$7,283
-12.880
200
0
$2,576
-1.961
4,000
0
$7,846
-20.109
$34,591
Table 7
First Stage Effect of the Predicted Change in Incarceration Rates Based on Last Period
Shock on the Current Change in Incarceration Rates for Three Sub-Periods of the Panel
Dependent Variable=ΔIncarceration Rate
(1)
(2)
(3)
(4)
0.338
(0.081)
0.301
(0.082)
0.292
(0.087)
-0.050
(0.098)
17.42
(<0.0001)
13.37
(0.0003)
11.22
(0.0009)
0.26
(0.611)
0.395
(0.074)
0.371
(0.075)
0.378
(0.075)
-0.185
(0.099)
28.52
(<0.0001)
24.53
(<0.0001)
25.23
(<0.0001)
3.41
(0.065)
0.801
(0.096)
0.820
(0.113)
0.875
(0.115)
0.584
(0.153)
70.43
(<0.0001)
51.78
(<0.0001)
57.69
(<0.0001)
14.40
(0.0002)
Controls
Variables
No
Yes
Yes
Yes
Year Effects
No
No
Yes
Yes
State Effects
No
No
No
Yes
Time Period:
1978 – 1984
Predicted Δ
Incarceration
F-statistic*
(P-value)
Time Period:
1985 – 1991
Predicted Δ
Incarceration
F-statistic*
(P-value)
Time Period:
1992 – 1998
Predicted Δ
Incarceration
F-statistic*
(P-value)
Table 8
OLS and IV Estimates of the Effect of Changes in Incarceration Rates on Changes in
Violent and Property Crime Rates by Sub Period
Dependent Variable = Δ Violent Crime Rate
Specification (1)
Specification (2)
Specification (3)
OLS
IV
OLS
IV
OLS
IV
Marginal
effect
78 to 84
-0.245
-4.334
-0.369
-2.812
-0.165
-0.686
(0.185)
(1.320)
(0.169)
(1.113)
(0.146)
(0.837)
85 to 91
0.101
0.863
0.086
1.011
0.207
0.666
(0.155)
(0.589)
(0.156)
(0.638)
(0.135)
(0.525)
92 to 98
-0.057
-0.261
-0.046
-0.269
-0.026
-0.216
(0.064)
(0.160)
(0.065)
(0.184)
(0.065)
(0.173)
Implied
Elasticity
78 to 84
-0.06
-1.14
-0.10
-0.74
-0.04
-0.18
85 to 91
0.04
0.31
0.03
0.36
0.07
0.24
92 to 98
-0.03
-0.14
-0.02
-0.14
-0.01
-0.11
Dependent Variable = Δ Property Crime Rate
Specification (1)
Specification (2)
Specification (3)
OLS
IV
OLS
IV
OLS
IV
Marginal
effect
78 to 84
-1.846
-36.117
-2.418
-30.182
-0.705
-11.706
(1.296)
(10.330)
(1.151)
(9.778)
(0.744)
(5.341)
85 to 91
-1.559
-8.351
-0.697
-7.525
-0.802
-5.763
(0.778)
(3.146)
(0.740)
(3.215)
(0.745)
(3.019)
92 to 98
-1.205
-2.798
-0.989
-2.871
-0.964
-3.967
(0.321)
(0.814)
(0.317)
(0.923)
(0.325)
(0.954)
Implied
Elasticity
78 to 84
-0.05
-1.07
-0.07
-0.89
-0.02
-0.35
85 to 91
-0.07
-0.40
-0.03
-0.36
-0.04
-0.27
92 to 98
-0.09
-0.22
-0.08
-0.22
-0.07
-0.31
Control
No
No
Yes
Yes
Yes
Yes
Variables
Year
No
No
No
No
Yes
Yes
Effects
Table 9
OLS and IV Estimates of the Effect of Changes in Incarceration Rates on Changes in Individual Part
1 Felony Offenses by Sub Period
Specification (1)
Specification (2)
Specification (3)
OLS
IV
OLS
IV
OLS
IV
Murder
78 to 84
85 to 91
92 to 98
Rape
78 to 84
85 to 91
92 to 98
Robbery
78 to 84
85 to 91
92 to 98
Assault
78 to 84
85 to 91
92 to 98
Burglary
78 to 84
85 to 91
92 to 98
Larceny
78 to 84
85 to 91
92 to 98
Motor
Vehicle Theft
78 to 84
85 to 91
92 to 98
Control
Variables
Year Effects
-0.001 (0.005)
0.009 (0.004)
-0.003 (0.002)
-0.085 (0.030)
0.040 (0.015)
-0.008 (0.004)
-0.003 (0.005)
0.007 (0.004)
-0.004 (0.002)
-0.056 (0.028)
0.044 (0.016)
-0.010 (0.004)
0.003 (0.004)
0.011 (0.004)
-0.005 (0.002)
-0.006 (0.025)
0.032 (0.014)
-0.010 (0.004)
-0.031 (0.013)
-0.035 (0.010)
-0.009 (0.005)
-0.279 (0.085)
-0.012 (0.037)
-0.035 (0.012)
-0.028 (0.012)
-0.039 (0.010)
-0.007 (0.005)
-0.125 (0.068)
-0.031 (0.039)
-0.030 (0.014)
-0.017 (0.012)
-0.029 (0.009)
-0.005 (0.005)
0.032 (0.067)
-0.049 (0.037)
-0.020 (0.013)
-0.031 (0.129)
-0.053 (0.076)
-0.032 (0.032)
-2.863 (0.918)
-0.127 (0.281)
-0.075 (0.078)
-0.146 (0.126)
-0.051 (0.074)
-0.033 (0.032)
-2.512 (0.929)
-0.016 (0.288)
-0.073 (0.088)
-0.117 (0.111)
-0.059 (0.069)
-0.031 (0.033)
-1.313 (0.719)
-0.364 (0.271)
-0.060 (0.086)
-0.182 (0.085)
0.180 (0.108)
-0.013 (0.044)
-1.106 (0.456)
0.961 (0.426)
-0.143 (0.110)
-0.193 (0.082)
0.168 (0.110)
-0.003 (0.045)
-0.119 (0.426)
1.014 (0.464)
-0.156 (0.128)
-0.034 (0.076)
0.285 (0.100)
0.015 (0.045)
0.601 (0.467)
1.047 (0.413)
-0.126 (0.119)
-0.250 (0.564)
-1.064 (0.305)
-0.275 (0.087)
-17.39 (4.95)
-4.228 (1.279)
-1.083 (0.239)
-0.604 (0.505)
-0.529 (0.279)
-0.232 (0.088)
-14.87 (4.77)
-3.531 (1.256)
-1.152 (0.281)
-0.409 (0.337)
-0.624 (0.286)
-0.229 (0.090)
-5.832 (2.506)
-3.159 (1.209)
-1.201 (0.274)
-1.363 (0.736)
-1.072 (0.471)
-0.730 (0.207)
-15.24 (4.81)
-3.925 (1.816)
-1.128 (0.512)
-1.695 (0.668)
-0.653 (0.452)
-0.575 (0.204)
-13.23 (4.73)
-3.429 (1.853)
-1.063 (0.569)
-0.512 (0.469)
-0.565 (0.459)
-0.545 (0.204)
-4.779 (2.930)
-2.203 (1.781)
-1.994 (0.574)
-0.233 (0.164)
0.576 (0.164)
-0.200 (0.080)
No
-3.478 (1.102)
-0.196 (0.619)
-0.592 (0.204)
No
-0.119 (0.161)
0.484 (0.161)
-0.183 (0.078)
Yes
-2.075 (1.000)
-0.565 (0.664)
-0.656 (0.229)
Yes
0.216 (0.143)
0.386 (0.157)
-0.189 (0.082)
Yes
-1.095 (0.894)
-0.401 (0.621)
-0.771 (0.231)
Yes
No
No
No
No
Yes
Yes
Estimating the Monetary Value of an Additional Prisoner Using Period-Specific Point Estimates
Murder
Rape
Robbery
Assault
Burglary
Larceny
Motor Vehicle theft
Total
Murder
Rape
Robbery
Assault
Burglary
Larceny
Motor Vehicle theft
Total
Point Estimates 1978 to 1984 Adjusted for under-reporting
Money Damages per Crime
Quality of Life Costs
Total Savings
-0.006
-0.006
17,000
2,700,000
$16,302
-0.032
-0.055
9,800
40,800
$2,768
-1.313
-2.626
2,900
14,900
$46,743
0.000
0.000
1,800
10,200
$0
-5.832
-11.664
1,200
400
$18,662
-4.779
-16.910
200
0
$3,382
-1.905
-2.667
4,000
0
$10,668
-13.867
-33.928
$98,526
Point Estimates 1992 to 1998 Adjusted for under-reporting
Money Damages per Crime
Quality of Life Costs
Total Savings
-0.010
-0.010
17,000
2,700,000
$27,170
-0.020
-0.034
9,800
40,800
$1,730
-0.060
-0.120
2,900
14,900
$2,136
-0.126
-0.275
1,800
10,200
$3,299
-1.201
-2.402
1,200
400
$3,843
-1.994
-7.056
200
0
$1,411
-0.771
-1.079
4,000
0
$4,318
-4.182
-10.976
$43,907