Optimal Punishment in the Presence of Victim-offender Overlap: Theory and an Empirical Investigation

This paper studies the victim-offender overlap in the home abuse setting. We introduce a strategic victim, who decides on (1) reporting the case to the police, (2) retaliating, or (3) staying inactive, to the optimal punishment model of Becker (1968). This approach allows us to explain the non-random selection of cases into trial. Then, we bring the model to the Mosgorsud data on domestic violence crimes. First, we estimate the reduced form linear probability regression to extract the important variables that affect the probability of the identity shift. Second, we specify the maximal likelihood estimator and recover key parameters of the model. Our policy experiments, performed with these estimates, show that neglecting the VOO reduces the probability of the identity shift by 20%, leads to stricter sanctions, and decreases the social welfare by 15%.