Identity errors and the standard of proof

The paper inquires into the impact of mistakes of identity (ID errors) on the optimal standard of proof. A wrongful conviction due to a mistake of identity happens when an individual is punished for someone else's crime; while the criminal escapes the sanction (at least for this crime). Therefore, the decision to engage in a criminal activity generates a negative externality, as the expected number of ID errors increases. Our objective is to understand how public law enforcement can deal with this type of error by means of the standard of proof. Our main results are twofold. First, we show that too many crimes are committed at equilibrium. Moreover, when the probability of an ID error for each false negative increases, the discrepancy between the socially optimal deterrence threshold and the equilibrium deterrence threshold is exacerbated. Second, we find that the optimal standard of proof is higher in the presence of ID errors when the net effect on punishment costs is negative, i.e. when the savings induced by the lower probability of a conviction for each crime exceed the costs induced by less deterrence.