To make the punishment fit the crime: The theory and statistical estimation of a multi-period optimal deterrence model

Abstract

Throughout history, those charged with deterring socially harmful conduct, and punishing it when it occurred, have grappled with problem immortalized by Mikado, devising a punishment to fit cr ime. Since Becker (1968) tackled issue from an economic point of view, it has received considerable attention in literature. Landes and Posner (1975), Polinsky and Shavell (!979), and Keenan and Rubin (1982), for example, have all discussed question of how anti-social conduct can be deterred while avoiding overdeterrence of conduct whose benefits outweigh its costs. However, all writers have approached problem using same one-period model used by Becker. In such a single-period context, penalty should be set equal to value of social injury divided by probability of catching and penalizing violator. In spite of its ubiquity, however, this model has both theoretical and practical shortcomings. The conceptual problem is that a one-period model is unrealistic for many types of infractions that continue over multiple periods until violator is caught. Examples are violations of consumer protection regulations, of health and safety standards of OSHA, of pollution control standards set by EPA, and some crimes. Furthermore, for some of these multi-period infractions, instantaneous probability of detection may change over time. For example, some regulatory violations are detected based on complaints. The likelihood that a firm will be investigated is positively related to cumulative number of complaints in its file, and therefore increases each year violation and complaints continue. A penalty based on dividing injury by the probability of detection makes no