Socially Optimal Crime and Punishment

This paper develops a dynamic life-cycle equilibrium model of crime with hetero-geneous agents and human capital accumulation. Agents decide at each point in time whether to commit crimes by comparing potential gains from crime to the expected cost of punishment (determined from the probability of apprehension, the utility cost of incarceration, and reduced future wages in the legal labor market). Public security policies are defined as pairs of a size of the police force and an average length of sentences. We propose an original micro-founded police production function linking the level of police expenditures to the probability of apprehension. The structural model, estimated using 2000s US data and causal parameters from the empirical literature, allows us to evaluate the global optimality of policies in a way that would not be possible with reduced form estimates or traditional partial equilibrium, static models of crime. Equilibrium effects can be particularly relevant when studying crime, given the interactions across individuals' decisions and policies. We also extend the model to include investments in schooling and explore the potential complementarities across public security and educational policies.