How Much Crime How Much Crime Reduction Does the Reduction Does the

Marginal Prisoner Buy?Marginal Prisoner Buy?Rucker JohnsonRucker Johnson

Goldman School of Public PolicyGoldman School of Public PolicyUC BerkeleyUC Berkeley

Steven RaphaelSteven RaphaelGoldman School of Public PolicyGoldman School of Public Policy

UC BerkeleyUC Berkeley

Prisoners in State or Federal Prison per 100,000 U.S. Residents, 1925 to 2004

0

100

200

300

400

500

600

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Pri

son

ers

per

100

,000

Deriving long-run equilibrium Deriving long-run equilibrium in incarceration rates as a in incarceration rates as a

function of observed transition function of observed transition probabilitiesprobabilities

Define the vector Pt as

j

tj

tttt PwherePPPP 1,321'

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

.,1,,10,333231

232221

131211

jTandjiTwhere

TTT

TTT

TTT

Tj

tij

tij

ttt

ttt

ttt

t

For a given transition probability matrix, Tt, the equilibrium population distribution across the three states (defined by the vector P*) satisfies the equation

.** ''tTPP

Simulated Equilibrium Incarceration Rates Based on A Markov Process Compared to Actual Incarceration Rates

0.00000

100.00000

200.00000

300.00000

400.00000

500.00000

600.00000

1975 1980 1985 1990 1995 2000 2005

implied equilibrium incarceration rate per100,000

Actual Incarceration Rate

Alternative simulation of the evolution of U.S. Alternative simulation of the evolution of U.S. incarceration rates based on 1980 starting incarceration rates based on 1980 starting values and observed transition probabilitiesvalues 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

t

i it TPP

TTTPTTPTPP

TTPTPP

TPP

19801980

1982198119801980198219811981198219821983

198119801980198119811982

1980'

1980'

1981

''

''''

'''

.

Actual Incarceration Rates and Simulated Incarceration Rate using 1980 Starting Values and Empirical Transition Probabilities

0.00000

100.00000

200.00000

300.00000

400.00000

500.00000

600.00000

1975 1980 1985 1990 1995 2000 2005

Inca

rcer

ated

per

100

,000

Simulated Incarceration Rate

Actual Incarceration Rate

Simulated Incarceration Rates: Base Simulation and Holding Prison Entry Probabilities to 1980 Levels

0

100

200

300

400

500

600

1975 1980 1985 1990 1995 2000 2005

Pri

son

ers

per

100

,000 Base Simulation

Holding Parole Returns to 1980 level

Holding new commitments rate to 1980 level

Holding new commitment and parole returnrates to 1980 levels

Simulated Incarceration Rates: Base Simulations and Holding Exit Probabilities to 1980 Levels

0

100

200

300

400

500

600

1975 1980 1985 1990 1995 2000 2005

Pri

son

ers

per

100

,000

Holding prison exit probabilities to 1980 levels

Base Simulation

A simple non-behavioral model of the A simple non-behavioral model of the incapacitation effects of prison on incapacitation effects of prison on

crimecrimeDefine the vector ][' 21 SSS , 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

TSS tt '' 1

Where the transition matrix is defined in accordance with the probabilities defined above as

1

1 cpcpT

For a constant T, equilibrium is defined by the equation

TSS '' ** Which gives the two equations

2*

1*

2*

2*

1*

1*

)1(

)1(

ScpSS

SScpS

.

When combined with the constraint, tSS tt ,1,2,1 , the three equations imply

equilibrium values that are a function of the transition probabilities alone,

cp

cpS

cpS

2*

1*

.

Given the equilibrium population shares, the equilibrium crime rate is given by

cp

cSccSCrime )1( 2

*1

** .

Basic identification Basic identification problem highlighted in the problem highlighted in the

existing literatureexisting literature Based on the derivation above, it’s Based on the derivation above, it’s

easy to show that dSeasy to show that dS**22/dc, dCrime/dc, dCrime**/dc /dc

>0>0 Shocks to underlying criminality will Shocks to underlying criminality will

induce positive covariance between induce positive covariance between crime rates and incarceration rates crime rates and incarceration rates operating through the criminality operating through the criminality parameter c.parameter c.

Criminality is unobservableCriminality is unobservable

0*

,2

*

dc

dCrime

dc

dS0

*,

2*

dc

dCrime

dc

dS0

*,

2*

dc

dCrime

dc

dS

Basic identification strategy: isolate variation Basic identification strategy: isolate variation in incarceration along the dynamics in incarceration along the dynamics

adjustment path between equilibrium in adjustment path between equilibrium in response to shocks to the transition response to shocks to the transition

probability parametersprobability parametersSuppose 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

)1(1,211,1,2 ttt SpcSS

Which can be rewritten as

pcpcSS tt 111,2,2 )1(

Which is in the form of a simple linear difference equation. To solve, we make use of the

fact that the incarceration rate at t=0 is the equilibrium rate

pc

pcS t

0

00,2

* , to derive

the expression for the path that incarceration will follow in response to the shock

pc

pcpc

pc

pc

pc

pcS t

o

ot

1

11

1

1,2 1

Or

0,2*

10,2*

0,2*

,2 1 tt

ttt SpcSSS

t=0 t=1

S*, t=0

S*, t>0

Incarceration rate

Time since shock

We can derive a similar We can derive a similar equilibrium adjustment path for equilibrium adjustment path for

crimecrime)1( ,2 ttt ScCrime

Substituting for the incarceration rate and rearranging gives

)1()1)(( 0,2*

0,2*

0,2*

ttt

tttt SccpSScCrime

•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.

t=0 t=1

Crime*, t=0

Crime*, t>0

Crime rate

Time since shock

t=0 t=1

S*, t=0

S*, t>0

Incarceration rate

Time since shock

Crime rate

C*, t=0

C*, t>0

Change from t=0 to t=1 for both crime and Change from t=0 to t=1 for both crime and incarceration are positive. incarceration are positive. Crime rate reflects positive effects of change in Crime rate reflects positive effects of change in

criminality as well as the negative effect of criminality as well as the negative effect of increased incarceration.increased incarceration.

Change from t>0 to t+1 will be negative for Change from t>0 to t+1 will be negative for crime and positive for incarcerationcrime and positive for incarceration Decline in crime rate is driven by an increasing Decline in crime rate is driven by an increasing

incapacitation effect alone. Increase in incapacitation effect alone. Increase in incarceration is driven by the system catching up incarceration is driven by the system catching up to the new equilibrium value with a lag (the key to to the new equilibrium value with a lag (the key to our identification strategyour identification strategy

Deriving explicit expressions for the periodic Deriving explicit expressions for the periodic changes in incarceration and crime for t=0 changes in incarceration and crime for t=0

and t=1 where and t=1 where ΔΔSStt=S=St+1t+1-S-Stt

Changes in the incarceration rateChanges in the incarceration rate

tttt

tt

tt

pcpcSSS

pcpcSSS

pcSSS

)1)()((

)1)()((

))((

110,2*

0,2*

,2

110,2*

0,2*

1,2

10,2*

0,2*

0,2

Simulated Equilibrium Incarceration Rates Based on A Markov Process Compared to Actual Incarceration Rates

0.00000

100.00000

200.00000

300.00000

400.00000

500.00000

600.00000

1975 1980 1985 1990 1995 2000 2005

implied equilibrium incarceration rate per100,000

Actual Incarceration Rate

Expression for change in crime from Expression for change in crime from t=0 to t=1t=0 to t=1

)1)(( 0,2*

010,21 to SccScCrime

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 Expression for change in crime from t=1 to t=2t=1 to t=2

1,211 ScCrime

•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 Deriving explicit expressions for the periodic changes in incarceration and crime for t=0 changes in incarceration and crime for t=0

and t=1 where and t=1 where ΔΔSStt=S=St+1t+1-S-Stt

Changes in the incarceration rateChanges in the incarceration rate

tttt

tt

tt

pcpcSSS

pcpcSSS

pcSSS

)1)()((

)1)()((

))((

110,2*

0,2*

,2

110,2*

0,2*

1,2

10,2*

0,2*

0,2

Data Data

State level panel covering the period 1978 to State level panel covering the period 1978 to 1998.1998. Data on crime (7 part 1 felony offenses) from from Data on crime (7 part 1 felony offenses) from from

the Uniform Crime Reports the Uniform Crime Reports Prison totals, total admissions, and total releases Prison totals, total admissions, and total releases

by state and year come from the Bureau of Justice by state and year come from the Bureau of Justice National Prisoner Statistics program.National Prisoner Statistics program.

Population totals come from the Census bureau as Population totals come from the Census bureau as do a number of state-level demographic measures.do a number of state-level demographic measures.

Regional economic indicators come from either the Regional economic indicators come from either the Bureau of Labor Statistics or the Bureau of Bureau of Labor Statistics or the Bureau of Economic Analysis. Economic Analysis.

Constructing the instrumentConstructing the instrumentTable 1 Illustration of the Calculation of the Predicted Change in Incarceration Rates for New York Between 1980 and 1982 1979 1980 1981 1982 Current incarceration rate ( tS ,2 )

118.39 125.33 147.30 161.39

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

cpS t

*0,2 *100,000)

- 135.87 215.61 199.97

Incarceration rate at t = 0 ( 0,2S ) - 118.39 125.33 147.30

Predicted change in incarceration rate, t=1 to t=2

))(1(*)( 0,2*

0,2 cpcpSS t

- 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

-100

0

100

200

300

400

-100 -50 0 50 100 150 200

Predicted Change

Act

ual

Ch

ang

e

Actual Change = 7.08 + 0.73*Predicted Change, R2=0.101 standard error (1.18) (0.07)

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

-100

0

100

200

300

400

-100 -50 0 50 100 150 200

Predicted Change

Act

ual

Ch

ang

e

Actual Change = 7.67 +0.71*Predicted Change, R2=0.152 standard errors (0.88) (0.05)

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 Incarceration

0.708 (0.051)

0.678 (0.055)

0.686 (0.055)

0.578 (0.061)

Δ% in popul. 0 to 17

- 276.03 (585.54)

222.58 (613.28)

-364.60 (675.31)

Δ% in popul. 18 to 24

- 539.90 (659.97)

620.86 (720.32)

259.31 (784.72)

Δ% in popul. 25 to 44

- -977.15 (620.33)

77.88 (662.17)

-7.08 (709.78)

Δ% in popul. 45 to 64

- -699.49 (641.42)

-842.13 (800.01)

-2053.59 (1010.93)

Δunemployment rate

- -0.682 (0.682)

-0.037 (1.013)

-0.228 (1.018)

Δpoverty rate - 43.29 (425.05)

55.81 (42.95)

69.99 (43.64)

Δ% black - -54.63 (45.05)

-60.43 (45.53)

-51.23 (45.74)

Δ per capita income

- 0.003 (0.002)

-0.003 (0.003)

-0.002 (0.003)

Year Effects No No Yes Yes State Effects No No No Yes R2 0.152 0.176 0.256 0.295 N 1,070 1,070 1,070 1,070 F-statistic* (P-value)

191.74 (<0.0001)

154.13 (<0.0001)

154.52 (<0.0001)

88.94 (<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 Rape Robbery Assault

8.61 37.24

225.71 358.65

4.17 12.16

137.82 158.31

1.99 6.22

48.14 74.27

Property Crime Burglary Larceny Motor Veh. Theft

4,795.07 1,245.76 3,015.02

534.29

1,147.98 419.86 691.24 233.39

585.73 292.18 315.99 123.17

Incarceration Rate 255.29 137.65 107.84 Panel B: 1978 to 1984 Violent Crime 555.09 243.67 50.72 Murder Rape Robbery Assault

9.13 34.57

226.38 285.02

3.96 12.20

150.65 112.09

1.25 3.46

36.44 21.12

Property Crime Burglary Larceny Motor Veh. Theft

4,917.04 1,479.70 2,970.79

466.55

1,138.91 415.20 669.11 202.11

398.92 184.28 209.06 52.48

Incarceration Rate 145.53 62.76 25.63 Panel C: 1985 to 1991 Violent Crime 654.53 285.81 82.52 Murder Rape Robbery Assault

8.72 38.84

233.19 373.77

4.22 12.22

143.09 157.11

1.58 3.68

33.96 55.09

Property Crime Burglary Larceny Motor Veh. Theft

4,972.12 1,290.24 3,105.04

576.83

1,225.08 403.34 732.39 260.04

293.81 114.29 183.82 99.78

Incarceration Rate 235.57 94.62 42.04 Panel D: 1992 to 1998 Violent Crime 682.91 275.04 89.96 Murder Rape Robbery Assault

8.25 38.57

224.72 411.35

4.41 11.92

126.30 170.15

1.62 4.12

48.33 44.59

Property Crime Burglary Larceny Motor Veh. Theft

4,598.19 1,031.62 3,000.57

566.00

1,051.30 307.38 666.60 229.18

390.55 124.08 197.39 96.41

Incarceration Rate 356.13 135.87 52.47

Table 4OLS 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

ΔIncarceration 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 5OLS 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

ΔIncarceration 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 6OLS 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 Comparison of these results to those from previous researchthose from previous research

Our violent crime-prison elasticity estimates range from -Our violent crime-prison elasticity estimates range from -0.09 to -0.15 and property crime estimates range from -0.09 to -0.15 and property crime estimates range from -0.28 to -0.39.0.28 to -0.39.

Levitt (1996) estimates range from -0.38 to -0.42 for Levitt (1996) estimates range from -0.38 to -0.42 for violent crime and -0.26 to -0.32 for property crime.violent crime and -0.26 to -0.32 for property crime.

Our estimates of crimes averted

Estimates from Marvell and Moody (1994)

Murder 0.001 Not significantRape 0.042 0.02Robbery 0.243 0.25Assault 0.072 Not signficantBurglary 2.276 2.281Larceny 3.642 2.77Motor Vehicle Theft 1.401 0.56

Estimating the Monetary Value of an Additional Prisoner in 1993Levitt Point Estimates of Crimes Avoided

Levitt Estimates Adjusted for Under-reporting Money Damages per Crime Quality of Life Costs Total Savings

Murder -0.004 -0.004 17,000 2,700,000 $10,868Rape -0.031 -0.053 9,800 40,800 $2,682Robbery -0.55 -1.1 2,900 14,900 $19,580Assault -0.55 -1.2 1,800 10,200 $14,400Burglary -1.3 -2.6 1,200 400 $4,160Larceny -2.6 -9.2 200 0 $1,840Motor Vehicle theft -0.5 -0.7 4,000 0 $2,800

Total -5.535 -14.857 $56,330

Our Overall Point EstimatesOur Point Estimates Adjuted for Under-Reporting Money Damages per Crime Quality of Life Costs Total Savings

Murder -0.001 -0.001 17,000 2,700,000 $2,717Rape -0.042 -0.072 9,800 40,800 $3,633Robbery -0.243 -0.486 2,900 14,900 $8,651Assault -0.072 -0.157 1,800 10,200 $1,885Burglary -2.276 -4.552 1,200 400 $7,283Larceny -3.640 -12.880 200 0 $2,576Motor Vehicle theft -1.401 -1.961 4,000 0 $7,846

Total -7.675 -20.109 $34,591

Table 7First 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)

Time Period: 1978 – 1984

Predicted Δ Incarceration

0.338(0.081)

0.301(0.082)

0.292(0.087)

-0.050(0.098)

F-statistic*(P-value)

17.42(<0.0001)

13.37(0.0003)

11.22(0.0009)

0.26(0.611)

Time Period: 1985 – 1991

Predicted Δ Incarceration

0.395(0.074)

0.371(0.075)

0.378(0.075)

-0.185(0.099)

F-statistic*(P-value)

28.52(<0.0001)

24.53(<0.0001)

25.23(<0.0001)

3.41(0.065)

Time Period: 1992 – 1998

Predicted Δ Incarceration

0.801(0.096)

0.820(0.113)

0.875(0.115)

0.584(0.153)

F-statistic*(P-value)

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

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 (0.185)

-4.334 (1.320)

-0.369 (0.169)

-2.812 (1.113)

-0.165 (0.146)

-0.686 (0.837)

85 to 91 0.101 (0.155)

0.863 (0.589)

0.086 (0.156)

1.011 (0.638)

0.207 (0.135)

0.666 (0.525)

92 to 98 -0.057 (0.064)

-0.261 (0.160)

-0.046 (0.065)

-0.269 (0.184)

-0.026 (0.065)

-0.216 (0.173)

Implied Elasticity

78 to 84 85 to 91 92 to 98

-0.06 0.04

-0.03

-1.14 0.31

-0.14

-0.10 0.03

-0.02

-0.74 0.36

-0.14

-0.04 0.07

-0.01

-0.18 0.24

-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 (1.296)

-36.117 (10.330)

-2.418 (1.151)

-30.182 (9.778)

-0.705 (0.744)

-11.706 (5.341)

85 to 91 -1.559 (0.778)

-8.351 (3.146)

-0.697 (0.740)

-7.525 (3.215)

-0.802 (0.745)

-5.763 (3.019)

92 to 98 -1.205 (0.321)

-2.798 (0.814)

-0.989 (0.317)

-2.871 (0.923)

-0.964 (0.325)

-3.967 (0.954)

Implied Elasticity

78 to 84 85 to 91 92 to 98

-0.05 -0.07 -0.09

-1.07 -0.40 -0.22

-0.07 -0.03 -0.08

-0.89 -0.36 -0.22

-0.02 -0.04 -0.07

-0.35 -0.27 -0.31

Control Variables

No No Yes Yes Yes Yes

Year Effects

No No No No Yes Yes

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

-0.001 (0.005)

-0.085 (0.030)

-0.003 (0.005)

-0.056 (0.028)

0.003 (0.004)

-0.006 (0.025)

85 to 91 0.009 (0.004) 0.040 (0.015) 0.007 (0.004) 0.044 (0.016) 0.011 (0.004) 0.032 (0.014) 92 to 98 -0.003 (0.002) -0.008 (0.004) -0.004 (0.002) -0.010 (0.004) -0.005 (0.002) -0.010 (0.004) Rape 78 to 84

-0.031 (0.013)

-0.279 (0.085)

-0.028 (0.012)

-0.125 (0.068)

-0.017 (0.012)

0.032 (0.067)

85 to 91 -0.035 (0.010) -0.012 (0.037) -0.039 (0.010) -0.031 (0.039) -0.029 (0.009) -0.049 (0.037) 92 to 98 -0.009 (0.005) -0.035 (0.012) -0.007 (0.005) -0.030 (0.014) -0.005 (0.005) -0.020 (0.013) Robbery 78 to 84

-0.031 (0.129)

-2.863 (0.918)

-0.146 (0.126)

-2.512 (0.929)

-0.117 (0.111)

-1.313 (0.719)

85 to 91 -0.053 (0.076) -0.127 (0.281) -0.051 (0.074) -0.016 (0.288) -0.059 (0.069) -0.364 (0.271) 92 to 98 -0.032 (0.032) -0.075 (0.078) -0.033 (0.032) -0.073 (0.088) -0.031 (0.033) -0.060 (0.086) Assault 78 to 84

-0.182 (0.085)

-1.106 (0.456)

-0.193 (0.082)

-0.119 (0.426)

-0.034 (0.076)

0.601 (0.467)

85 to 91 0.180 (0.108) 0.961 (0.426) 0.168 (0.110) 1.014 (0.464) 0.285 (0.100) 1.047 (0.413) 92 to 98 -0.013 (0.044) -0.143 (0.110) -0.003 (0.045) -0.156 (0.128) 0.015 (0.045) -0.126 (0.119) Burglary 78 to 84

-0.250 (0.564)

-17.39 (4.95)

-0.604 (0.505)

-14.87 (4.77)

-0.409 (0.337)

-5.832 (2.506)

85 to 91 -1.064 (0.305) -4.228 (1.279) -0.529 (0.279) -3.531 (1.256) -0.624 (0.286) -3.159 (1.209) 92 to 98 -0.275 (0.087) -1.083 (0.239) -0.232 (0.088) -1.152 (0.281) -0.229 (0.090) -1.201 (0.274) Larceny 78 to 84

-1.363 (0.736)

-15.24 (4.81)

-1.695 (0.668)

-13.23 (4.73)

-0.512 (0.469)

-4.779 (2.930)

85 to 91 -1.072 (0.471) -3.925 (1.816) -0.653 (0.452) -3.429 (1.853) -0.565 (0.459) -2.203 (1.781) 92 to 98 -0.730 (0.207) -1.128 (0.512) -0.575 (0.204) -1.063 (0.569) -0.545 (0.204) -1.994 (0.574) Motor Vehicle Theft 78 to 84

-0.233 (0.164)

-3.478 (1.102)

-0.119 (0.161)

-2.075 (1.000)

0.216 (0.143)

-1.095 (0.894) 85 to 91 0.576 (0.164) -0.196 (0.619) 0.484 (0.161) -0.565 (0.664) 0.386 (0.157) -0.401 (0.621) 92 to 98 -0.200 (0.080) -0.592 (0.204) -0.183 (0.078) -0.656 (0.229) -0.189 (0.082) -0.771 (0.231) Control Variables

No No Yes Yes Yes Yes

Year Effects No No No No Yes Yes

Estimating the Monetary Value of an Additional Prisoner Using Period-Specific Point Estimates

Point Estimates 1978 to 1984 Adjusted for under-reporting Money Damages per Crime Quality of Life Costs Total SavingsMurder -0.006 -0.006 17,000 2,700,000 $16,302Rape -0.032 -0.055 9,800 40,800 $2,768Robbery -1.313 -2.626 2,900 14,900 $46,743Assault 0.000 0.000 1,800 10,200 $0Burglary -5.832 -11.664 1,200 400 $18,662Larceny -4.779 -16.910 200 0 $3,382Motor Vehicle theft -1.905 -2.667 4,000 0 $10,668

Total -13.867 -33.928 $98,526

Point Estimates 1992 to 1998 Adjusted for under-reporting Money Damages per Crime Quality of Life Costs Total SavingsMurder -0.010 -0.010 17,000 2,700,000 $27,170Rape -0.020 -0.034 9,800 40,800 $1,730Robbery -0.060 -0.120 2,900 14,900 $2,136Assault -0.126 -0.275 1,800 10,200 $3,299Burglary -1.201 -2.402 1,200 400 $3,843Larceny -1.994 -7.056 200 0 $1,411Motor Vehicle theft -0.771 -1.079 4,000 0 $4,318

Total -4.182 -10.976 $43,907