Socially optimal crime and punishment

Soares, Rodrigo Reis
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The first essay of this thesis, co-authored by Rodrigo Soares, develops a dynamic life-cycle equilibrium model of crime with heterogeneous agents and human capital accumulation. 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 public security technology linking the level of police expenditures to the probability of arrest. This essay also contributes to the literature by proposing a dynamic equilibrium framework to evaluate public security policies. Equilibrium effects can be potentially relevant because of dynamic interactions between the classical incapacitation and deterrence effects. The model allows us to explore the optimality of policies in a way that would not be possible with reduced form empirical estimates or with the traditional, partial equilibrium, static, theoretical models of crime. We conduct an exploratory quantitative exercise calibrating the model to US property crime data from the 2000s. The calibrated model points to overspending in police protection and over incarceration in that period, when compared to the optimal public security policy. The second essay of this thesis develops a dynamic equilibrium model of crime with heterogeneous agents and several types of wrongs---actions that generate inefficiencies. Criminal codes define which wrongs are punishable by the state and penal codes define the length of the sentence if an agent is apprehended by the police committing a crime. %Agents decide at each point in time whether to commit crimes by comparing potential gains from crime to the expected loss due to the probability of apprehension and the associated cost (freedom deprivation). Criminal justice systems are defined as triplets of a criminal code, a penal code and a size of the police force. The dynamic framework with a multi-crime/multi-punishment setting, allows exploring substitution across different types of crime and might generate counter-intuitive results, mostly unexplored in the literature. The model developed in this essay also allows the endogenous definition of the set of actions that constitute crimes, as part of the welfare maximizing design of the criminal justice system. The third essay, co-authored by Braz Camardo, develops a 3-period model in which agents have time-inconsistent preferences and have access to an illiquid financial asset. The model developed in this essay studies the relationship between risk aversion and the demand for a commitment device, as represented by the illiquid asset. The main result is that, in an environment with uncertainty, a higher risk aversion implies a higher demand for the illiquid asset, due to a commitment motive. This counter-intuitive theoretical result is able to reconcile seemingly contradictory evidence found in the recent empirical literature.

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