Complement or Substitute? Punishment and Self-Interested Enforcement

Abstract This study examines the problems that law enforcement agencies face with self-interested agents who (1) prefer to punish wrongdoers and reduce crime rates and (2) would suffer a loss of reputation resulting from law enforcement investigations that do not lead to convictions. Next, we examine how agents’ enforcement responses change with sanction size. This is fundamental to how higher-ranking authorities (e.g., the judiciary) can implement sanction policies to mitigate law enforcement agency problems. Our analysis shows that enforcement and sanctions can function as either complements or substitutes. When agents have strong preferences for reducing crime, stricter sanctions complement enforcement and increase deterrence. Conversely, when concerns about reputation loss dominate, stricter sanctions substitute for enforcement and may decrease deterrence. Consequently, a non-maximal sanction may be optimal when sanctions substitute for enforcement. This yields a novel justification for imposing non-maximal sanctions based on the behavior of the enforcer.