4.1 Self-control devices models and Test 1
In psychology, self-control is typically seen as part of self-regulatory control processes (e.g., Carver and Scheier
1982) or as response inhibition in the context of modern neuropsychological models of behavior (Diamond
2013). Within BE, self-control models encapsulate the basic game-theoretical intuition that fewer options can be good by working as a commitment device. Because of the natural way in which this research stems from this intuition from economics rather than psychology, the case for satisfying Test 1 is reasonably straightforward, and specific policy predictions follow from these models in health contexts to support this. Self-control devices can work as commitment devices to promote positive health outcomes (Bryan et al.
2010).
Three modeling approaches to self-control problems are choice-set utility (Gul and Pesendorfer
2001), intertemporal choice (Bernheim and Rangel
2004) and multiple selves (Gruber and Köszegi
2001). While these models embody a similar intuition, they sometimes draw different policy implications. For example, on the one hand studies employing a hyperbolic discounting function generally suggest the use of fiscal interventions such as tax to manipulate the price of tempting goods (Gruber and Köszegi
2001). On the other hand, Bernheim and Rangel (
2004) predict that a price increase may not discourage consumption of tempting goods when self-control is restricted in the hot state of mind. They suggest that avoiding environmental stimuli that drive individuals to impulsive behavior may be a potential solution to address self-control problem. While the specificity of these predictions ensures that Test 1 is passed, they create potential problems of identification of the kind we discussed in the context of social interactions.
4.2 An illustrative model and Test 2
This section presents a simple model of self-control problems based on quasi-hyperbolic discounting (Phelps and Pollak
1968). For illustrative purpose, we consider a smoking decision. Similarly to O’Donoghue and Rabin (
2006), we assume that smoking gives positive immediate utility and affects health next period. Let
S denote smoking, which takes 1 if the person smokes and 0 otherwise. The immediate utility of smoking is represented by
\(v\left( S \right) \), and the health damage is represented by
\(-h\left( S \right) \), where we assume
\(v\left( 0 \right) =h\left( 0 \right) =0\). The cost of smoking is
p. The rest of the person’s instantaneous budget
M is spent on the composite good (which gives linear positive utility) and the price is normalized to 1. Finally, we assume that the intertemporal utility is given by the following standard quasi-hyperbolic discounting formulation:
$$\begin{aligned} u_0 +\beta \sum \limits _{k=1}^T \delta ^{k}u_k , \end{aligned}$$
where
\(\beta \),
\(\delta \le \)1. The parameter
\(\beta \) is often interpreted as the degree of self-control problem. If
\(\beta =1\), the function is the usual exponential discounting function.
For simplicity, we consider three periods (t=0, 1 and 2). In period 0, the person plans whether or not to smoke in period 1; then, in period 1, the utility from smoking materializes; and finally, the health damage of smoking is incurred in period 2. In period 0 the person just plans (i.e.,
planner), and the actual behavior is taken in period 1 (i.e.,
doer). From the planner’s perspective in period 0, the utility in period 1 is given by
\(\beta \delta \left[ {v\left( 1 \right) +M-p} \right] \) if she smokes, and
\(\beta \delta M\) if she does not smoke. Also, the utility in period 2 is given by
\(\beta \delta ^{2}\left[ {-h\left( 1 \right) } \right] \) if he or she smokes in period 1 and 0 otherwise. The planner decides to smoke in period 1 if the net utility of smoking exceeds the net utility of non-smoking:
\(\beta \delta \left[ {v\left( 1 \right) +M-p} \right] +\beta \delta ^{2}\left[ {-h\left( 1 \right) } \right] \ge \beta \delta M\). Hence, the person plans to smoke if:
$$\begin{aligned} p\le v\left( 1 \right) -\delta h\left( 1 \right) . \end{aligned}$$
For the planner, the reservation price of a cigarette is given by
\(p^{*}=v\left( 1 \right) -\delta h\left( 1 \right) \). In period 0, the person plans to smoke in period 1 if the cost of smoking is lower than the immediate utility of smoking minus the discounted future health damage.
We turn to consider the
doer’s problem in period 1. The immediate utility of smoking is given by
\(v\left( 1 \right) -M-p\) if she smokes, and
M if she does not. The utility in the next period is given by
\(\beta \delta \left[ {-h\left( 1 \right) } \right] \) if she smokes, and 0 if she does not. The individual smokes in period 1 if
\(v\left( 1 \right) -M-p+\beta \delta \left[ {-h\left( 1 \right) } \right] \ge M\). The doer smokes if:
$$\begin{aligned} p\le v\left( 1 \right) -\beta \delta h\left( 1 \right) . \end{aligned}$$
The doer’s reservation price is given by
\(p^{**}=v\left( 1 \right) -\beta \delta h\left( 1 \right) \). Compared to the previous condition to smoke for the planner, the doer discounts the future health damage more heavily by
\(\beta \delta \) (where
\(\beta \),
\(\delta \le \)1). This means that the doer accepts a higher cigarette price than the planner. More specifically, if the actual cigarette price is between
\(p^{*}\) and
\(p^{**}\):
\(v\left( 1 \right) -\delta h\left( 1 \right)<p<v\left( 1 \right) -\beta \delta h\left( 1 \right) \), the doer smokes in period 1 even though he or she planned not to smoke, a
preference reversal.
When this preference reversal is likely to happen, there are ways for the planner to restrict the doer’s behavior. The planner should make the doer’s reservation price of cigarette (\(p^{**})\) closer to the planner’s original reservation price \(p^{*}\). Stronger restriction will be needed depending on the degree of the self-control problem: a smaller \(\beta \) (i.e., larger discount) implies the need for stronger restrictions.
Commitment helps restrict the doer’s behavior. For instance, the planner can commit to pay a higher price for a cigarette in period 1, so that the doer faces the higher price. Similarly, he or she can commit to paying some amount of money in case she smokes. Both commitments directly decrease the reservation price of cigarette for the doer \(p^{***}=v\left( 1 \right) -\beta \delta h\left( 1 \right) -C\), where C is either the increased price or the punishment. Incurring additional cost to smoke in this way brings the doer’s reservation price closer to \(p^{*}\).
Test 2 is met, in the sense that specific predictions for public health contexts follow from these models. Some interventions can be regarded as self-control devices of a similar kind. For example, fiscal interventions, such as tax or income transfer, can alter the reservation price for the doer in the same way as the self-commitment. As in O’Donoghue and Rabin (
2006) and elsewhere, exercising a higher tax on cigarettes may prevent self-control lapses. Rewarding individuals for not smoking by lump-sum transfer will work in the same direction as the price intervention. Immediate rewards may be more effective, if the individual discounts the future rewards heavily (Loewenstein et al.
2007).
Sometimes commitments may be considered as not involving (only) pecuniary incentives but, for example, may include social image costs. In the above example, the (shadow) price of cigarette
p may include social image costs (e.g., of smoking being seen as ‘uncool’), and people may use this to correct their future behavior. As another example, Babcock and Hartman (
2011) conduct a field experiment to examine the impact of financial incentives on attending sports gym. They find that participants whose peers are also treated are more likely to attend the gym. The potential problem here is that, unless we add some psychological or BE story of why these should matter in the given setting,
3 this prediction does not in itself follow from the self-control models, therefore failing Test 2.
4.3 Test 3: Empirical evidence
Table A2 in the Online Appendix summarizes a significant body of research on the potential usefulness of self-control devices in health settings.
Voluntary use of self-control devices. People may deliberately seek contracts that could be construed as implying a desire to constrain their choice set as predicted by self-control models (Halpern et al.
2012). For example, in a field experiment, Gine et al. (
2010) investigated the effect of a voluntary commitment device on smoking cessation, i.e., Committed Action to Reduce and End Smoking (CARES). Smokers were offered a saving account in which after six months they are refunded subject to passing a nicotine test. Some smokers took up the scheme, with social pressure possibly having played a role. The smoking cessation rate was higher for the participants than for the control group, and the effects persisted in surprise tests one year later. However, given the well-documented frequent failure of consumers’ best intentions in health (e.g., London
2013), there is again a question of whether something else, such as social pressure, may have also been at work. Using US sports gyms data, DellaVigna and Malmendier (
2006) find that consumers tend to enter fixed-term contracts and end up paying more per visit than they would have paid in fees for single visits. They interpret this as a form of overconfidence about either future self-control or future efficiency of gym visits.
It is not clear from existing evidence how much commitment one should make and it is also not clear how predictions from the self-control models would be verified, either in terms of learning (Ali
2011) or in terms of trade-off between flexibility and commitment (Amador et al.
2006). Moreover, if long run tastes change (Loewenstein et al.
2003), predicting the optimal commitment from the self-control model may not be appropriate.
Policy interventions. Non-voluntary commitment devices include governmental interventions, and there is a long strand of related literature (see Table A2 in the Online Appendix for a summary). For example, Charness and Gneezy (
2009) conducted a field experiment with university students to evaluate the impact of financial incentives on attendance to a sports gym. Participants received money if they attended the gym as they were assigned. Charness and Gneezy found that this incentive scheme increased gym attendance even after the experimental intervention period, at least in the short term.
A problem in interpreting findings on the effect of price changes (or equivalent) on healthy behavior is that a more straightforward interpretation would be in terms of law of demand from basic microeconomics: as the price goes up, demand goes down. This would not explain an effect beyond the intervention period, and other theories would be needed for that, such as reinforcement theories from traditional behavioral psychology (e.g., Fantino and Logan
1979; Rachlin
1989), modern psychological habit system theories (e.g., Daw et al.
2011) or economic theories of rational addiction or habit formation (Becker and Murphy
1988; Rabin
2011). Self-control models however
also do not explain effects beyond the intervention period, unless they are combined with other theories.
This brings us to the more general problem: these studies are all generally about the link between policy recommendations and empirical evidence (the link 6 of Fig.
1), but the empirical evidence is largely consistent with self-control models
as well as a number of other models, and therefore is not the specific support of self-control models that we would like in terms of Test 3.
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