How much crime reduction does the marginal prisoner buy? / created by Rucker Johnson and Steven Raphael

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 subperiods: 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