Prevalence and Recidivism in Index Arrests: A Feedback Model

Abstract

It is important for both theoretical and policy reasons to partition aggregate crime rates into measures of prevalence (reflecting breadth of participation) and incidence (reflecting intensity of participation by those who do engage in crime). Prevalence is measured by accumulating over age the probability of first arrest as a function of age. Incidence is estimated by the probability of recidivism in a feedback model. The probability of a male in U.S. cities over 250,000 population ever being arrested for an index crime is estimated as 25 percent, and is quite different for black males (51 percent) and white males (14 percent). The probability of re-arrest for an index crime is estimated as 85 to 90 percent for both whites and blacks. These estimates highlight the breadth of involvement in index-crime arrests, and suggest that the large differences in race-specific arrest rates are predominantly attributable to difference in participation, and not to differences in recidivism for those who do get involved.