Self-control models

Our goal in this chapter has been to outline some simple models of the relationship between self-control problems and addictive behavior. Researchers who use mathematical models to study human choice— mostly economists—traditionally approach intertemporal choice problems by assuming time consistency. By focusing on self-control problems, therefore, we depart from this traditional approach. We conclude by discussing some of the advantages of our self-control model of addiction relative to rational choice models of addiction. 

Throughout, we have not addressed the issue of whether self-control problems can lead to behaviors that cannot be explained with time-consistent preferences. In fact, such smoking guns—qualitatiw predictions that are inconsistent with rational choice theory—are difficult to come by in our highly stylized and simplified models. In these models, only a few types of behavior can arise, and most of these behaviors could arise from time-consistent preferences.27 One might ask, then, why it is worthwhile to study a self-control model of addiction. We feel there are a number of reasons. 

It is also the case that rational choice models of addiction tend not to make qualitative predictions that are inconsistent with self-control models of addiction. Essentially all qualitative implications emphasized in rational choice models of addiction are also consistent with our self-control model of addiction. For instance, extensions of our model (and all other reasonable models we can imagine) would be consistent with the prediction that demand for addictive products decreases with the price of those products—... 

MANY OBSERVERS suspect that self-control problems and related time inconsistencies play an important role in the consumption of addictive, products, leading people to develop and maintain addictions against their long-run interests. People often consume addictive products despite an expressed desire to quit. For many people, it would appear that the long-run harm caused by an addiction outweighs its short-run benefits. In extreme cases, people destroy their lives with harmful addictions. Our goal in this chapter is to carefully explore the role that self-control problems—and people s awareness of those problems— play in harmful addictions. To do so, we develop a formal model of the decision to consume addictive products that explicitly incorporates a time-inconsistent taste for immediate gratification. 

Economists have proposed rational choice models of addictive behavior (Becker and Murphy 1988 Becker, Grossman and Murphy 1991,1994). These models characterize how consuming harmful addictive products can decrease future well-being while at the same time increasing the desire for those products in the future. Because these models consider only time-consistent agents, however, they a priori rule out the possibility of self-control problems. 

Like the rational choice models of addiction, our model assumes that the choice to consume an addictive product is volitional, in the sense that people balance their current desire for the addictive product against their perceptions of the future consequences of current consumption. Our model is quite different, and less extreme, than rational choice models, however, because it assumes that people may be overattentive to their immediate gratification (that is, they may have self-control problems) and... 

We begin with a stationary model of addiction, in which the temptation to hit can depend on the addiction level but otherwise remains constant over time, which allows us to identify some basic insights. We first ask what is the direct implication of self-control problems by comparing TCs and naifs. In the stationary model, naifs are always more likely to hit than TCs. Since naifs are unaware of future self-control problems, they perceive that they will behave exactly like TCs in the future and... 

The standard economics model, in contrast, assumes that intertemporal preferences are time consistent People s relative preference for well-being at an earlier date over a later date is the same no matter when they are asked. In the example above, such time consistency would require that, irrespective of the specific choice, people make the same choice on February 1 and April 1. The standard economics model therefore, a priori, rules out self-control problems. 

A small set of economists and psychologists has over the years proposed formal models of time-inconsistent preferences and self-control problems.8 Edmund S- Phelps and Robert A. Poliak (1968) put forward an elegant model of intertemporal preferences in the context of inter-generational altruism, which David Laibson (1994a) later used to capture self-control problems within individuals.9 If ut is the instantaneous utility people get in period x, then their intertemporal preferences at time f, U, can be represented by the following utility function ... 

The assumptions of naivete and sophistication are essentially the same in this environment as in the basic model. In any given period, naifs believe that they will behave like TCs in the future. Sophisticates, on the other hand, are completely aware of their self-control problems, including the effects of consumption-induced myopia, and they therefore correctly predict future behavior.21... 

Related to the issue of realism, we predict that models incorporating self-control problems (especially, we conjecture, models that include an element of naivete) will be better calibrated than rational choice models and hence make sounder quantitathv predictions. We do not have empirical evidence for this conjecture, but to illustrate our reasoning we present a simple calibration exercise within our framework We demonstrate how very patient people with very small self-control problems can get addicted in situations in which time-consistent people would get addicted only if they were to discount the future at an implausibly heavy rate. 

The crucial intuition driving these calibration results is the incremental nature of most addictive behavior. At each point in time, people choose whether to indulge now, and the cumulative effect of these decisions determines whether people get and remain addicted. With self-control problems, a sequence of incremental decisions can lead to behavior very different from how people would behave if committing up front to a lifetime path of behavior. In a rational choice model, in contrast, the incremental nature of addiction is irrelevant. If people know exactly what the future holds, and have no self-control problems, then people become addicted only if that is the optimal lifetime path of behavior. 

Conspicuously absent from our model is the ability to use external commitment devices. Alcoholics sophisticated about their self-control problems may, for instance, choose to check themselves into the Betty Ford Clinic. Note that naifs would not use external commitment devices since they always believe they will behave themselves in the future. 

Navarick, S. and Fantino, E. (1976) Self-control and general models of choice , Journal of Experimental Psychology Animal Behavior Processes 2, 75-87. 

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