Crime, punishment, and background risks

We show that if the punishment for a property crime effectively eliminates an individual’s initial wealth, as with a very long prison sentence, then such criminal activities become less desirable for a risk-averse and prudent individual if his initial wealth distribution undergoes a second-order stochastic dominant improvement. Similar results obtain under additional restrictions if the punishment reduces an individual’s initial wealth by some factor less than 1. In a general-equilibrium model where the endogenous victimization risk is part of individuals’ background risks, we also show that the availability of insurance for the victimization risk lowers economy-wide crime rates.