How Much Crime Reduction Does the Marginal Prisoner Buy?
Johnson, Rucker and Steven Raphael (2012) “How Much Crime Reduction Does the Marginal Prisoner Buy?” Journal of Law and Economics, 55(2) 275-310.
We estimate the effect of changes in incarceration rates on changes in crime rates using state-level panel data. We develop an instrument for future changes in incarceration rates based on the theoretically predicted dynamic adjustment path of the aggregate incarceration rate in response to a shock to prison entrance or exit transition probabilities. Given that incarceration rates adjust to permanent changes in behavior with a dynamic lag, one can identify variation in incarceration rates that is not contaminated by contemporary changes in criminal behavior. For the period 1978-2004, we find crime-prison elasticities that are considerably larger than those implied by ordinary least squares estimates. We also present results for two sub-periods: 1978-90 and 1991-2004. Our instrumental variables estimates for the earlier period suggest relatively large crime-prison effects. For the later time period, however, the effects of changes in incarceration rates on crime rates are much smaller.