Deterrence and the Optimal Use of Prison, Parole, and Probation

In this article we derive the mix of criminal sanctions--choosing among prison, parole, and probation--that achieves any target level of deterrence at lowest cost. We assume that prison has higher disutility and higher cost per unit of time than parole and probation and that potential offenders discount the future disutility of sanctions at a higher rate than the state discounts the future costs of sanctions. Our primary insight is that there is a front-loading advantage of imprisonment due to these differential discount rates. This advantage implies that whenever a sentence includes both a prison term and a parole term, the prison term should be imposed first, and that it may be optimal to employ a prison term even if prison has a higher cost per unit of disutility than parole and probation and even if prison is not needed to achieve the target level of deterrence.