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In modern times, social researchers continue to explain these Odysseus-like situations involving, most notoriously, cigarettes, alcohol, drugs, gambling, food, and
procrastination. While these are all different scenarios, they still overlap to various degrees, under the general theme of addiction and self-control.
There is an extensive, multi-disciplinary body of literature explaining these themes under the framework of biology, psychology, and economics. The earliest theories of addiction were pioneered by psychologists and are often used as the causal underpinnings behind the tractable economic theories. Recently, neurobiological explanations are gaining traction as technology allows researchers to visually map the brain.
The following literature review was constructed using the VOSviewer network analysis tool [9] for mapping citation impact for various keywords related to addiction, self-control, and self-awareness.
The literature review goals are two-fold, then: firstly, to provide a brief explanation of the relevant theories, terms, and models so to develop a foundation that, secondly, allows even an unfamiliar reader to understand the rational for the research questions this paper aims to address.
2.1 Discounted Utility
Intertemporal choices, tradeoffs between costs and benefits that occur in a sequence of time periods, were neatly mathematically modeled by Paul Samuelson in 1937 [10] when he published the Discounted Utility (DU) model, with functional form:
Where,
And Ut = total period utility
U(Ct+k)= per period (period t+k) utility D(k)= (1/1+p)k = the discounting component
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Note that consumption preferences are independent across periods – one period’s consumption does not affect the marginal rate of substitution for different periods.
Secondly, per period utility is independent – knowledge about future periods wouldn’t influence present period utility. Samuelson himself disavowed the models realism [10].
Becker and Murphy’s rational addiction model modifies the assumption of consumption independence throughout periods [11]. Formally:
Where u(t) = the utility at any moment as a function of goods y and c, and S is the stock of “consumption capital” of previous c, which removes the consumption independence in the Samuelson DU model.
Then, the investment function is expressed by:
Where Ṡ(t) is the rate of change over time in S, c is learning by doing, ẟ is the depreciation of consumption capital, and D(t) are the endogenous expenses on appreciation or depreciation.
Finally, lifetime utility, with a lifetime of T, and constant discount rate of α is given by:
Where utility over time is not separable in y and c alone. This captures the changing inter-period marginal rate of substitution between goods.
Finally, Consumers are aware that consumption in addictive goods may have detrimental effects in the future and even account for it in their utility maximizations. Consumption decisions are based on a lifetime cost-benefit maximization, and “…present and future consumption of addictive goods are complements, and a person becomes more addicted at present when he expects events to raise his future consumption. That is, in our model, both present and future behavior are part of a consistent maximizing plan. [11]”
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The exponential discounting form, then, is time-consistent: lifetime utility would be indifferent between a two week delay in utility a week from present, or a year. A person who plans to quit smoking next week would do it absolutely. People wouldn’t
procrastinate if they previously planned not to. Yet, while these examples are
unexplained under the above models, they are a common occurrence in the real world.
Lifetime utility maximization, then, depends on intertemporal choices. Utility
maximization in the present will also plan future optimal consumption decisions. The problem, then, is that each time period presents a new consumption choice, and therefore a chance to re-evaluate the previously established consumption plans. In this sense, plans in the present need to consider whether the future plans will be carried out obediently. In a sense, the present self needs to consider whether the future self will be obedient or disobedient. Strotz [12] has considered this problem of self-control, coined
“intertemporal tussle,” which occurs when future utility is not discounted time consistently or when preferences change.
Secondly, he specifies whether people are even aware of self-control problems. If people are aware of their self-control problems, they are sophisticates while those unaware of their self-control problems are coined naïfs. He further explains some options the
sophisticates have for making sure the future plans are carried out obediently. One option is pre-commitment: taking away or changing the terms, by increasing costs of undesired consumptions choices, of the future decision to ensure they agree with the previously laid out consumption path. The second, and less desirable, plan is carefully choosing future consumption decisions to ensure obedience.
Animal behaviorists also noticed that time-consistent behavior poorly described experimental results. A more useful model for the real world, then, was hyperbolic discounting [13]. True hyperbolic discounting takes a form similar to:
Where the discount rate is relativistic with time from present (𝜏), then f(𝜏)=1/1+kτ
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However, most economic models actually use a slightly different form, commonly called quasi-hyperbolic preferences.
The quasi-hyperbolic model was first developed by Phelps and Pollack [14] to explain intergenerational time preferences for savings. Later, Laibson, applied this model to individuals to explain under-saving for retirement [15].
Formally, the model follows this form:
Where,
Ut= lifetime utility
Et= expected instantaneous utility u(ct)=utility at period t
B= present bias
Sτ=discount rate at time in relativistic years from present(τ) u(ct+τ) = utility at period t+τ
By adding a B that takes the value 0>B>1, it’s clear from the model that inconsistent time preferences arise. B=1 implies time consistent preferences.
This model is often called the Beta-Delta model as it can be modelled accordingly:
Again, where 0>B>1. Notice that from relativistic time=0 to time=1, the change in discount rate is sharply B*S, while after that, the change in S is decreasing as a function of relativistic time from t=0.
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Graphically, we can see the differences in the functional forms. Exponential model with S=.99, and quasi-hyperbolic with B=.6 and S=.97
[15]
Lastly, from Laibson [15], hyperbolic discounters are willing to give up income to create
incentives to fight against present bias. Under quasi-hyperbolic discounting conditions, a desired behavior can be perpetually procrastinated.
The possibility of perpetual procrastination, then, explains why a sophisticated, present-biased, quasi-hyperbolic discounter would need costly commitment devices to force obedience upon the future decision maker in order to maximize lifetime utility.
The idea is empirically explored as it relates to cigarette smoking. Kan 2006, offers evidence against the Becker rational addiction model. Specifically, by developing an empirical model and showing that smokers with an intention to quit have a demand for pre-commitment devices: cigarette taxes and smoking bans. These pre-pre-commitment devices increase the cost of future period smoking, enough to stop current period smoking.
Because rational addicts with time consistent preferences shouldn’t do anything to
minimize their utility, this casts doubt upon the time consistent preferences in the rational addiction model [16].
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The hyperbolic discount model used in the Kan paper follows the hyperbolic discounting form, developed by Phelps and Pollack [14]:
Where, Ut=is lifetime utility at time, t Sand B are discount factors ct = consumption at time t u(ct) = utility at time t
Then, per period options are Q for quit smoking, S for continue smoking, and N, for non-smoking. Ordinal per-period utilities are Q<S<N
Precisely, the individual will be a perpetual procrastinator if the following conditions holds:
[16]
So, in order to quit smoking, the smoker may choose to impose a cost, C, upon themselves in future periods to swing the lifetime utility of smoking in their favor. C must be large enough for the following inequality to hold:
[16]
Finally, empirical support indicated that a desire to quit increased the demand for controls – a demand for C. Under the Becker Rational Addiction model, this shouldn’t happen because time consistent smokers wouldn’t give up utility.
However, Gruber and Köszegi [17] empirically test the assumptions of the BRM and find support for the forward thinking utility maximizers. However, in line with psychological research, they modify the model to allow time inconsistent preferences. Importantly, they specify different types of cessation support that those who plan to stop smoking may
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employ: (1) costly commitment (self-control) devices, like the Kan paper provides support for, or (2) quitting aids, for example counseling or nicotine replacement therapy.
This has important implications: the commitment devices decrease utility from smoking while the quitting aids decrease disutility associated with cessation. Then, time consistent decision makers could use a quitting aid, but would never opt for a costly commitment device. Also, time-inconsistent decision makers would only use commitment devices if they are sophisticated.
Rabin and O’Donoghue further specify present biased decisions by differentiating between immediate costs couples with delayed rewards and immediate rewards coupled with delayed costs, highlighting the different game theoretic outcomes under
sophistication or naivety. Present biased, sophisticated agents fare better than naïfs when facing immediate cost situations because naïfs can fall into the perpetual procrastination loop. Given immediate rewards, however, the sophisticated agent is worse off because they fall into a sort of repeated prisoner’s dilemma: they simply consume now the immediate cost now, knowing they lack self-control in the future. [18]