اثرات تشویقی و بازداشت در مدل تعادل عمومی جرم و جنایت

An intertemporal general equilibrium model of criminal behavior is used to analyze the effect on crime of changing policy parameters, specifically the length of the prison term, the severity of punishment, and the amount of police resources. The number of crimes in society can be decomposed into an incentive part, an incarceration part, and a crime competition part.

In the literature on crime and punishment, it is common to distinguish between the incentive and the incarceration effect of prison sentence.1 This is intuitively natural; a longer prison term is likely both to discourage (the incentive effect) and to disable (the incarceration effect) people from engaging in criminal activities. One reason why these two components of crime are so often discussed is probably that knowledge of their respective magnitudes is important for the evaluation of crime policy. An emerging standard in the literature is to discuss crime and punishment in a general equilibrium framework; this will be done in the present paper, too. Also, a meaningful treatment of prison sentences requires an intertemporal model.2 In the present paper, we will provide an analysis of incentive and incarceration effects within the framework of an intertemporal general equilibrium model based on individual preferences. In virtually all papers on the economics of crime following Becker (1968), people are assumed to differ with respect to their productivity in honest work. Low-productivity individuals will thus choose to become criminals. An interesting feature of the intertemporal approach is that it allows for other assumptions as to what determines people's choice of whether to engage in criminal activities. We have thus assumed that everybody has the same productivity in honest work, but that people differ in terms of time preference. This is technically a minor issue; the model could be solved using the standard assumption (i.e., different productivity and identical rates of time preference) as well, but since the assumption of different time preferences has not been made before, we choose it for the sake of novelty. Some writers have observed that in reality, criminals seem to have a very strong preference for immediate gains as compared to future costs (see, for instance, DiIulio, 1996). This has sometimes been interpreted as a contradiction to Becker's approach to crime, indicating that criminals are simply irrational. However, a high propensity to commit crimes can equally well be interpreted as a high rate of time preference that is perfectly compatible with rational behavior. In our model, we abstract from human capital accumulation. In a more complicated model, where such accumulation is taken into account, one might obtain an interesting correspondence between differences in wages and differences in time preference. One would expect that a consequence of being patient is the acquisition of more human capital, resulting in differences in wages across individuals even if all individuals have the same intrinsic productivity. It would then be difficult to tell empirically whether a high propensity to commit crimes is the result of a low wage or of a high rate of time preference. To evaluate social policy, empirical knowledge is needed with respect to the relative impact of the severity of punishment and the length of the prison term. These relative impacts could differ depending on the set-up of the underlying theoretical model. It is therefore important to work out different model formulations. For instance, if people differ with respect to time preference instead of wages, a longer prison term will have smaller and smaller effects on incentives, and in the limit only the incarceration effect remains.3 It therefore seems like an important avenue for future research to work out the predictions of the two approaches in order to assess their relative degree of realism against empirical data. The paper deals basically with positive issues, in the sense of using a general equilibrium model to derive empirically tractable expressions for some magnitudes often discussed in the literature. It is organized as follows. In Section 2, the basic model is presented. Section 3 contains a general characterization of the model by means of numerical simulations. In Section 4, we make numerical simulations of the effects of policy changes, and Section 5 concludes the paper.

In the classical articles on the economics of crime, beginning with Becker, punishment has no time dimension but can be interpreted as the payment of a fine. This means that the essential aspects of crime and punishment can be captured within the framework of an atemporal model. The advantage of this is analytical simplicity; the drawback is that punishments that are intrinsically intertemporal cannot be analyzed in a satisfactory way. For instance, capital punishment and imprisonment, while having well-known incentive effects, also have the effects of keeping criminals off the streets. In the present analysis, we take two dimensions of punishment into account: the severity of punishment (f) and the length of the prison term (n). Fines, being atemporal in nature since they are in principle paid immediately, could be regarded either as the present value of (the monetary equivalent of) our f variable or as a third dimension of punishment (since no f is executed if n = 0). Including fines in the policy spectrum could thus make a more efficient punishment structure possible. This could be especially relevant if agents differ, not with respect to productivity (as in the standard models) but with respect to time preference. If criminals have a particularly high rate of time preference (a low value of δ), a higher n or f may not affect incentives much, while an exorbitant fine might do the job. On the other hand, fines require that the criminals can pay them, which does rarely seem to be the case in the real world. Introducing more dimensions of punishment into the analysis thus seems like an interesting avenue for future research. This would, however, require a model quite different from ours. Within the framework of our model, some of these aspects could perhaps be captured by allowing for a varying time profile of f. In fact, a high initial f, falling over time, is more like a fine, and is also quite common in practice. One particular aspect of crime and punishment calling for a more sophisticated policy spectrum is the occurrence of errors of both Types I and II (i.e., a guilty criminal can be acquitted, and an innocent bystander can be punished). Traditionally, the economics literature has dealt with Type I errors only. It may be the case that different types of punishment differ with respect to their ability to cope with Types I and II error. For instance, capital punishment is irreversible, while a fine could be paid back if the person found guilty later turns out to be innocent. There are many other examples where the time element is important for the analysis of crime. Most of these seem to involve the development of human capital for those outside as well as those inside prison. Also, productivity changes could refer to productivity in ordinary work as well as in criminal activities. In particular for internees, learning a profession while in jail increases productivity in legal activities. On the other hand, internees are often educated in crime techniques by other inmates, increasing their productivity in criminal activities. A further development of general equilibrium models along these lines seems to be high on the research agenda today.