1. 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

2. Basic Identification Strategy Shocks to underlying criminal behavior have immediate as well as lagged effects on annual incarceration rates. Shocks to underlying criminal behavior have immediate as well as lagged effects on annual incarceration rates. Changes in crime in a period when there is a shock to criminal behavior will be driven by the change in behavior as well as any changes in incarceration. Changes in crime in a period when there is a shock to criminal behavior will be driven by the change in behavior as well as any changes in incarceration. Change in crime along the dynamic adjustment path between equilibrium crime rates will be driven by changes in incarceration alone. Change in crime along the dynamic adjustment path between equilibrium crime rates will be driven by changes in incarceration alone.

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

6. Characterizing the dynamic adjustment paths of incarceration and crime to a permanent shock to criminality

7. We can derive a similar equilibrium adjustment path for crime 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.

8. t=0 t=1 S*, t=0 S*, t>0 Incarceration rate Time since shock

9. t=0 t=1 S*, t=0 S*, t>0 Incarceration rate Time since shock Crime rate C*, t=0 C*, t>0

10. Deriving explicit expressions for the periodic changes in incarceration and crime for t=0 and t=1 where ΔS t =S t+1 -S t Changes in the incarceration rate

11. Implementing the identification strategy using a state-level panel data set Estimating cp and θ by state and year Estimating cp and θ by state and year Identifying permanent shocks and adopting the identification strategy to the reality of serial shocks to the underlying transition probabilities rather than single shocks. Identifying permanent shocks and adopting the identification strategy to the reality of serial shocks to the underlying transition probabilities rather than single shocks.

12. Constructing the instrument

15. Remaining data issues Data covers the periods from 1978 to 2004. We present estimates for the entire period and separately for two sub-periods. Data covers the periods from 1978 to 2004. We present estimates for the entire period and separately for two sub-periods. Data on crime (7 part 1 felony offenses) from the Uniform Crime Reports Data on crime (7 part 1 felony offenses) from the Uniform Crime Reports Population totals come from the Census bureau as do a number of state-level demographic measures. 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. Regional economic indicators come from either the Bureau of Labor Statistics or the Bureau of Economic Analysis.

16. Table 4 OLS and IV Estimates of the Effect of Changes in Incarceration Rates on Changes in Overall Violent and Property Crime Rates Using the Entire State-Level Panel Dependent Variable=ΔViolent Crime RateDependent Variable=ΔProperty Crime Rate Specification (1)Specification (2)Specification (1)Specification (2) OLSIVOLSIVOLSIVOLSIV ΔIncarceration rate 0.048 (0.044) -0.116 (0.118) 0.038 (0.045) -0.230 (0.136) -0.994 (0.233) -2.315 (0.625) -1.109 (0.237) -3.272 (0.721) Year EffectsYes State EffectsNo Yes No Yes R2R2 0.4710.4680.4870.4810.5030.4960.5320.516 N1,321 Implied elasticity at the mean 0.023-0.0570.019-0.113-0.064-0.151-0.072-0.213

17. Table 5 OLS and IV Estimates of the Effect of Changes in Incarceration Rates on Changes on Individual Crimes Using the Entire State-Level Panel Specification (1)Specification (2) Dependent Variable OLSIVOLSIV ΔMurder-0.002 (0.001) -0.005 (0.003) -0.001 (0.001) -0.005 (0.004) ΔRape-0.005 (0.003) -0.029 (0.009) -0.005 (0.004) -0.033 (0.011) ΔRobbery-0.025 (0.025) -0.165 (0.066) -0.028 (0.025) -0.227 (0.077) ΔAssault0.079 (0.030) 0.082 (0.080) 0.072 (0.031) 0.035 (0.092) ΔBurlgary-0.398 (0.080) -0.857 (0.216) -0.414 (0.082) -1.064 (0.248) ΔLarceny-0.498 (0.146) -1.182 (0.392) -0.573 (0.149) -1.720 (0.449) ΔMotor Vehicle Theft -0.097 (0.055) -0.275 (0.146) -0.122 (0.056) -0.487 (0.167) Year EffectsYes State EffectsNoYesNoYes

18. Comparison of these results to those from previous research Our violent crime-prison elasticity estimates range from -0.06 to -0.113 and property crime estimates range from -0.15 to -0.21. Our violent crime-prison elasticity estimates range from -0.06 to -0.113 and property crime estimates range from -0.15 to -0.21. Levitt (1996) estimates range from -0.38 to -0.42 for violent crime and - 0.26 to -0.32 for property crime. Levitt (1996) estimates range from -0.38 to -0.42 for violent crime and - 0.26 to -0.32 for property crime.