Optimal sanctions and endogeneity of differences in detection probabilities

Abstract

Offenders differ with respect to their detection probability in reality. Bebchuk and Kaplow [Bebchuk, L. A., & Kaplow, L. (1993). Optimal sanctions and differences in individuals’ likelihood of avoiding detection. International Review of Law and Economics, 13, 217–224] conclude that optimal sanctions should increase with the ability to avoid detection. We endogenize differences in detection probabilities by letting individuals choose education. The optimal sanction schedule may be reversed if individuals do not account for all benefits of education. This paper thereby demonstrates how incentives for seemingly remote decisions can be manipulated through sanction structures.

Introduction

In reality, the heterogeneity of offenders is common and can have drastic consequences for optimal enforcement policy. For example, Polinsky and Shavell (1991) consider varying wealth levels, finding that the optimal fine equals total wealth for less well off individuals and equals a defined level for those with higher wealth. Bebchuk and Kaplow (1993) introduce differences in detection probabilities. They find that if the enforcement authority can observe the type ex post, it is optimal to let fines increase with the difficulty of apprehension. This feature, namely varying detection probabilities, has not been taken up since, except by Innes (2000), who finds that this realistic feature implies a further rationale for lower self-reporting sanctions.

This paper endogenizes the heterogeneity in detection probabilities. We argue that education makes apprehension probabilities differ and let individuals choose education. In consequence, optimal sanctions in our framework are contingent on the result of an endogenous choice, with the interdependence of the sanction scheme and the choice of education being of central concern. This contrasts to sanctions being dependent on an exogenous characteristic as in Bebchuk and Kaplow (1993).

Differences in individuals’ likelihood of avoiding detection can to a large extent be explained by education and learning.¹ First of all, a well-grounded education contains knowledge somewhat relevant to criminal undertakings and the hiding thereof. For instance, individuals with a high school diploma are presumably more likely to be able to listen to police radio signals or manipulate the circuits of alarm systems. More importantly, previous education enhances the capacity to learn new subject matter. Consequently, more educated individuals have a higher aptitude to diligently prepare new undertakings and learn from previous acts. We assume that education can be acquired by every potential offender, though associated education costs vary across the spectrum of individuals.

Society values education in general. There is a direct benefit to individuals in the form of higher self-valuation and job mobility, for instance. The productivity of educated individuals is also higher, which implies a higher legal income for this group. In addition, there are indirect benefits, examples being synergies in the workplace, the stimulation of technological progress or increased political maturity.² Importantly, an individual’s valuation of education may deviate from that of society due to both indirect benefits and the difference in apprehension probabilities, where the first is a social value not privately recognized, and the latter is only of private value.

We find that sanction schemes may be employed to correct externalities in the realm of education. In consequence, we find that allowing for education can reverse the result by Bebchuk and Kaplow (1993), i.e. that the optimal sanction scheme falls in the ability to avoid detection. The sanction scheme thus functions as a vehicle to internalize the positive externality of education. This is because the respective expected sanctions determine the partition of all individuals into offenders and non-offenders. They also determine the division between those offenders who are more difficult to apprehend due to their education, and those who are more easily apprehended. In this way, the policy maker’s problem can to some extent be interpreted as one of marginal deterrence.³ Marginal deterrence features in our model because undeterred offenders may offend being either educated or uneducated. The policy maker therefore employs sanctions to provide incentives regarding (i) who should undertake the act at all and (ii) who should offend only after they have been educated. As a consequence of our results, policy makers should be very wary when implementing sanction schemes that increase in the ability to avoid detection, for instance, by being more harsh when an act has been superiorly planned and conducted, because of its potential effects on education.

In the literature concerning education and crime, Ehrlich (1975) was the first to empirically test relations between education and crime. More recently, Lochner (2004) finds empirical support for theoretically derived relationships with little bearing on our study. Lochner and Moretti (2004) empirically support the hypothesis that schooling reduces the probability of incarceration and arrest. In the sparse theoretical literature, a choice regarding education is considered in the search-theoretic framework of Huang, Laing and Wang (2004), for example. They allow for legitimate work and criminal activity and find – inter alia – that crime decreases the returns to human capital investments due to the possibility of theft. Usher (1997) assumes that education reduces the utility of any given offense in a general equilibrium model not at all concerned with optimal law enforcement. To our knowledge, our interest, namely that externalities in the education realm may be tackled with sanction schedules, has not been analyzed in the literature.

In Section 2, we set out the model and, in our framework, reiterate the benchmark of Bebchuk and Kaplow (1993) with exogenous differences in detection probabilities. Next, we introduce our generalization and highlight its effect on the optimal sanction scheme. Before we offer concluding remarks and end this study, results are illustrated in a numerical example.