An Introduction to Behavioral Economics

The most obvious characteristic of Table 7.1 is the very wide disparity between different measures of the discount rate, even within the same study as well as between studies. Thus it is not simply differences in methodology in terms of experimental design that account for these variations. The primary reason for the variability is the existence of confounding factors in the measurement of time preference. This raises the fundamental issue of what constitutes time preference. It is necessary to understand this concept and the factors involved if we are to address and explain the anomalies related to the DUM. We shall see in the second section of the chapter that these anomalies are frequently related to self-control problems. The third, fourth and fifth sections of the chapter then discuss various alternative models to the DUM, while the sixth section examines the relevant empirical evidence from behavioral, evolutionary and neuroeconomic studies. The seventh section concludes with the discussion of various policy implications related to the models and the evidence.

First, we need to examine the various confounding factors involved in the measurement of time preference.

However, there is another effect at work here. People may wish to defer consumption to later periods in order to have a rising consumption over time, but they may lack the self-control to save sufficient income earned now to provide for this future consumption. In such a situation people may welcome some sort of commitment device that allows them to have more money in the future without the opportunity to spend it earlier, in the same sort of way that they may commit to paying into a pension fund. We have already seen something of this effect in the case of the teachers who preferred to be paid 12 times a year rather than 10. In this situation people may prefer to receive the money in the future rather than immediately. This effect exerts a downward bias on discount rates.

This is another phenomenon that has been discussed earlier, in Chapter 3. For example, people may wish to defer consumption of a restaurant dinner, since the anticipation of the future utility may increase total utility. The modeling of this factor is discussed in a later section, but at this stage we can observe that the effect is to exert a downward bias on discount rates and can also cause reverse time-inconsistency of preferences.

Again this factor was discussed in Chapter 3, and is modeled in a later section. The prospect of an immediate reward (the ‘actual presence of the immediate object of desire’ in Rae’s terms) may stimulate visceral factors that temporarily increase the attraction of the reward. However, like uncertainty, it is difficult to unravel these influences from time preference. It is argued by Frederick, Loewenstein and O’Donoghue (2002) that if the visceral factors increase the attractiveness of the immediate reward without affecting its enjoyment (decision utility rather than experienced utility), then ‘they are probably best viewed as a legitimate determinant of time preference’ (footnote 33, p. 383). On the other hand, if visceral factors do affect experienced utility, then ‘they might best be regarded as a confounding factor’.

The original hyperbolic discount function introduced by Chung and Herrnstein (1967) was based on experimental studies with animals, and took the form D(t) = 1/t. Herrnstein (1981) also developed another special case of hyperbolic function, where D(t) = (1 + αt)^–1.

Phelps and Pollak (1968) used a modified version of this function, referred to as a quasi-hyperbolic function. This is described below:

In general β < 1, implying that the discount factor between the current period and the next is lower than the discount factor in later periods. Thus it can be said that measures the degree of present bias. In the limiting case where β = 1 the quasi-hyperbolic function reduces to the exponential function of the DUM. It should also be noted that this model, often referred to as the (β, δ) model, can also accommodate RTI, by allowing β > 1. According to the (β, δ) model, in contrast to the DUM, the utilities in the periods 0, 1, 2,… t are discounted by 1, βδ, βδ²,…βδ^t.

The primary implication of hyperbolic discounting is that time preferences will be inconsistent. We have already seen that there is a large body of empirical evidence that supports the theory of dynamic inconsistency in preferences. It is instructive to illustrate this effect of hyperbolic discounting with a simple example at this stage, and for this purpose we can use the values in the study of Ainslie and Haslam (1992), mentioned earlier. Let us assume that subjects have β = 0.6 and δ = 0.9, and they are faced with the choice between receiving $100 in six years’ time (the SS reward) or $200 in eight years time (the LL reward). We can now write:

Thus at the present time the $200 in eight years is more appealing. However, in six years time the situation has changed so that:

We can also see how the (β, δ) model describes a procrastination situation, by considering the mirror image of the problem above and changing both payoffs into negative ones, so that the first payoff is –$100 in six years and the second one is –$200 in eight years. At the current time the smaller discounted cost of –$31.9 of the SS is preferable to the larger discounted cost of –$51.7 of the LL. However, in six years time, subjects will prefer to switch to LL, with its lower discounted cost of –$97.2 compared with the immediate cost of –$100 of the SS.

The reason for the effectiveness of the (β, δ) model lies in its assumption of a higher discount rate between the current period and the next (for normal time-inconsistency), but a constant discount rate thereafter. The per-period discount rate between now and the next period is (1 – βδ)/βδ, whereas the per-period discount rate between any two future periods is (1 – δ)/δ, a smaller value.

The manner in which such present bias and inconsistency affects behavior depends on the degree of self-awareness of subjects, in terms of how aware they are that their preferences will change over time. There are two extreme situations: people may be completely ‘naïve’, believing that their future preferences will be identical to their current ones. This would imply that people do not learn at all from past experience of changing preferences. It was assumed in the above numerical example that subjects were of this type. Naïve agents think that they will use a constant discount rate in the future, but will actually discount hyperbolically. If we refer to the person’s belief regarding the value of their β as b, then β < b = 1. Thus these consumers believe their preferences in the future are shown in Figure 8.2, seeming that LL will always be preferable to SS, and they will therefore not anticipate any forthcoming conflict.

A good illustration of the differences between the behavior of exponential discounters, naïve and sophisticated hyperbolic discounters, which incorporates commitment, is given by Ho, Lim and Camerer (2006). They give a hypothetical numerical example relating to the situation of buying and consuming potato chips. They use a three-period model as follows:

1 Purchase decision: this involves a choice between a small (one serving) bag or a large (two servings) bag which involves a quantity discount.

2 Consumption decision: this involves a choice between consuming one serving or two, and an instantaneous utility related to consumption. If the smaller bag is purchased in the first period, only one serving can be consumed, but purchase of the larger bag offers the choice between consuming a single serving and leaving the other to a later period, or consuming both servings in the same period. Thus buying a smaller bag acts as a commitment in this case, as far as eating less and improving health is concerned.

3 Health outcome: this is adverse because chips are bad for you, but is much worse if two servings are consumed rather than one.

Under these conditions, and using reasonable parameters for discounting and outcomes, the authors conclude that each group of discounters may behave differently:

1 Exponential discounters: these may buy a large bag to benefit from the quantity discount, but only consume a single serving in the second period to avoid the worst health outcome.

2 Naïve hyperbolic discounters: these may buy a large bag, believing that they will behave like the exponential discounters and only consume one serving in the next period. However, in the second period they discount hyperbolically, applying a high discount factor to the adverse health effects in the third period, and they end up consuming both servings.

3 Sophisticated hyperbolic discounters: these may choose the small bag as a self-control or commitment device, knowing that in the next period they would be unable to resist the temptation of consuming both servings if they bought the large bag.

A numerical example will illustrate this situation. We assume for simplicity that δ = 1 (so that exponential discounters do not discount future outcomes at all) and that β = 0.5. Let c = number of servings consumed in any time period, and p = the price per serving. We assume p = 1.5 for a small bag, and p = 1 for a large bag, to reflect the bulk discount. We model the utility flows as follows:

1 At the purchase decision (t₀) there is negative utility given by U₀ = –cp, which is the cost of purchasing the chips.

2 At consumption decision (t₁) there is instantaneous utility given by U₁ = 1 +5c

3 Health outcome occurs with a one-period lag after consumption and is negative, given by U₂ = 3 – 6c

1 S refers to purchasing a small bag, limiting consumption to one serving in the following time period.

2 L(1) refers to the purchase decision to buy a large bag and then consume a single serving in the next time period. It is assumed that the remaining serving is consumed in time period 2, so in this time period there is a health outcome of –3 related to consumption in the previous period and a positive consumption utility of 6, yielding a net utility of 3. In time period 3 there is the negative health outcome of –3 related to consumption in period 2.

3 L(2) refers to the decision to buy a large bag, and then consume both servings in the next time period.

It can be seen from Table 8.1 that the rational consumer who discounts exponentially will maximize PV₀ at the purchase decision by choosing L(1), buying a large bag and planning to consume one serving in the next period, with the remaining serving being consumed in t₂. When t₁ is reached, the consumer will still maximize utility by sticking to his plan and consuming a single serving in each of the next two time periods.

Let us now consider the situation for naïve consumers. This is shown in Table 8.2.

The model fits empirical findings well, mimicking the qualitative property of the hyperbolic discount function. This can be seen in Figure 8.1 where hyperbolic, quasi-hyperbolic and exponential functions are compared. DellaVigna (2009) summarizes several studies that support the (β, δ) model, explaining anomalies in the DUM. These studies relate to: excessive preference for membership contracts in health clubs (DellaVigna and Malmendier, 2006); positive effects of deadlines on homework grades and preference for deadlines (Ariely and Wertenbroch, 2002); preference for pre-teaser rather than post-teaser interest rates in credit-card take-up (Ausubel, 1999); liquid credit card debt combined with simultaneous illiquid wealth accumulation (Laibson, Repetto and Tobacman, 2009); demand for illiquid savings as commitment devices (Ashraf, Karlan and Yin, 2006); demand and default for payday loans (Skiba and Tobacman, 2008); and default settings in retirement savings plans (Madrian and Shea, 2001; Cronqvist and Thaler, 2004). The findings of these studies are discussed in more detail in the section related to empirical evidence.

It is fair to say that hyperbolic discounting has entered into the mainstream of behavioral economics, largely due to its well-documented empirical superiority over the exponential model and its analytical convenience. However, it has not been without its critics. It should be noted that these critics are largely not defenders of the traditional DUM, but are proponents of newer and more radical models.

Let us examine criticisms from defenders of the DUM first. These fall mainly into three categories, all of which have been mentioned earlier:

1 Failure to use front-end delay. This results in a confound with transactions costs explained in the last chapter.

2 Use of hypothetical rewards. This may lead to unreliable results due to a lack of incentives compared with the use of monetary rewards.

3 Failure to provide information relating to the annual interest rates implied in the different options. Most studies simply give the options in terms of choice or matching tasks without such information. Coller and Williams (1999) found that discount rates were significantly lower when annual interest rate information is provided.

The first two criticisms have largely been countered over the last decade by numerous field studies involving hyperbolic discounting, many of which were summarized earlier in the section. These studies have often involved situations with delayed SS rewards or costs and these rewards and costs have been real rather than hypothetical.

As far as the third criticism is concerned, it has been sometimes suggested that there are legal requirements in many countries that require the provision of such information, and that this makes the provision of interest rate information a realistic condition. This may be true in different types of lending/borrowing situations, but the majority of intertemporal choice decisions are not of this type. When we are debating whether to eat a dessert, or join a health club, or tidy the garage, these are not situations where interest rate information is realistically going to enter the decision process.

However, the main criticism that has been aimed at hyperbolic discounting, which applies also to subadditive discounting, is that it lacks a psychological foundation. It is basically a descriptive theory rather than an explanatory one. Although one can say that the (β, δ) model describes ‘temptation’ and procrastination self-control problems, this begs the question why people should use such a discounting method, particularly since it does not appear to result in optimizing welfare, and therefore is maladaptive in evolutionary terms. For example, a study of procrastination by students has shown that those with time-inconsistent preferences performed worse than those with consistent preferences, and this was true even with sophisticated students who had full awareness of their time inconsistency (Wong, 2008).

Even though the phenomenon has been widely observed among animals as well as humans, and has been studied by researchers in many disciplines, its strongest proponents have failed until recently to provide a good psychological foundation for it. Most researchers have entirely ignored this aspect, and of course this is quite legitimate from the standpoint of standard economic theory, which is only concerned with behavior, not psychological processes. However, given that there are alternative theories to explain the same behavior, which have different implications, it is worthwhile to examine psychological foundations. In the last decade some researchers have been conscious of this failure. For example, Ainslie (2001), a psychiatrist, has considered the possible evolutionary origins of such a psychological mechanism, in terms of how it might have increased inclusive fitness compared with the more intuitively appealing exponential discounting approach. Ultimately he admits that he has no idea how a hyperbolic discounting mechanism could have evolved. However, more recently there have been attempts to explain this (Robson, 2002; Robson and Samuelson, 2007, 2009). These explanations are discussed in the section on empirical evidence, in terms of evolutionary biology.

In the last chapter we described various anomalies observed in the DUM, and in the first section of this chapter many of these are viewed as confounds as far as measuring time preference and discount rates are concerned. It can be argued that it is more appropriate to treat these confounding factors as additional aspects of the instantaneous utility function. Models that attempt to achieve this are now discussed.

As mentioned above, shifting reference points have important implications for habit formation. Another important factor related to habit formation is diminishing marginal sensitivity. Since both of these factors are elements of prospect theory, a more complete discussion of habit formation necessitates an examination of prospect theory models. We will also see in a later section that there are some important policy implications related to habit formation, especially as far as food intake and diet are concerned.

Perhaps the single most salient characteristic of prospect theory is its use of reference points, as explained in Chapter 5. When a person’s reference point for current consumption is past consumption, a reference-point model is identical with a habit-formation model. However, this is only a special case of the more general reference-point model. Reference points can also be dependent on expectations of the future, or on social comparisons, as we have seen. The importance of social comparisons is considered in Case 8.3, in connection with the preference for rising consumption profiles.

The nature of visceral influences has been discussed earlier, both in this chapter and in Chapter 3. In particular, we have seen that the temporal proximity of an outcome may increase its desirability. This may cause a higher rate of discount to be computed for near-future outcomes when factors like anger, hunger, lust and sleeplessness are involved, thus seeming to support the hyperbolic discounting approach. However, it may be more appropriate to modify the instantaneous utility function to allow for a momentary increase in utility in certain circumstances (Loewenstein, 1996; 2000). It should be noted that temporal proximity of the outcome is only one of these circumstances. Other cues may also be important, for example spatial proximity, or the presence of associated sights, sounds or smells.

The influence of visceral factors is more complicated than just the effect on the instantaneous utility function. It has been found, for example, that when people are under their influence they tend to overestimate how long their effect will last, while when people are not under their influence they tend to underestimate the magnitude of their effect in the future. People also tend to perceive immediate emotions as being more intense than previous emotions, a phenomenon referred to as ‘immediacy bias’ (Van Boven, White and Huber, 2009). This bias may be caused by salience or by greater availability of information regarding the present emotion. When people are reminded that information about emotions naturally decays from memory, this tends to reduce immediacy bias.

In Chapter 5 we saw that it was possible to distinguish between conventional modifications to expected utility theory and non-conventional alternatives. However, even these non-conventional alternatives, like prospect theory, are really best viewed as extensions of the standard model rather than outright rejections of it. Similar considerations apply to the DUM, but it is more difficult here to draw the line between the conventional and the non-conventional. So far the alternative models to the DUM that we have examined have involved modifying either the discount function or the instantaneous utility function. Even here, though, some of the modifications involve non-conventional factors related to prospect theory. The models examined in this section involve more radical differences from the DUM, although in some cases they are still often considered conventional models, like the dual-self model of Fudenberg and Levine (2006). The reason for this lack of clarity, or blurring of distinctions, is that intertemporal models are more complex than static models of preference, consisting of more components. This has led to a hybridization of models, in that some components of a model may be ‘conventional’ while other components may be ‘non-conventional’. This issue is best explained in more detail as we examine the individual models.

This is an example of a phenomenon that was discussed earlier. People’s tastes change over time, and there is a general tendency to underestimate the magnitude of these changes (Kahneman and Snell, 1992). The presence of visceral influences, discussed above, is only one of the factors that can cause this; habit formation and the shifting of reference points are two other important factors that can cause the same phenomenon. This bias is contrary to the assumption of rational expectations in the standard model, which implies that people can forecast changes in their tastes accurately. It has been modelled by Loewenstein, O’Donoghue and Rabin (2003), who review extensive evidence for the phenomenon. In the case of habit-formation the utility function in (8.2) may be appropriate as the instantaneous utility function at time t: U_t = f(C_t, Z_t). This can be expressed more simply as U_t(C_t, Z_t), where Z_t again represents a composite variable reflecting past consumption. At time t +1 an individual’s true instantaneous utility function may be U_t+₁(C_t+₁, Z_t+₁), and their expectation of this function at time t may be Ũ_t+₁(Ĉ_t+₁, Z_t+₁ | Z_t). This represents expected utility in time t +1 of expected consumption in time t +1 and past consumption up to that period, given the current level of past consumption at time t. According to the projection bias model:

U_t(C_t, Z_t) < Ũ_t+₁(Ĉ_t+₁, Z_t+₁ | Z_t) < U_t+₁(C_t+₁, Z_t+₁)

This can be modeled more precisely using a weighted function to indicate how accurately people forecast future utilities:

The higher the value of α, the greater the degree of projection bias, meaning that there is a greater tendency to underestimate future utilities.

One of the main implications of lack of budget fungibility is that different discount rates are applied to different goods. We have seen that small purchases may be classified as ‘petty cash’, with the result that people may be more inclined to spend on these, using a higher discount rate. Goods involving a larger expenditure, such as durables, may be evaluated more carefully, using a lower discount rate.

There are also a number of implications of choice bracketing which contradict the predictions of the DUM. We have seen that people often prefer to prepay for various expenses to avoid the ‘pain of paying’ later for something they have already consumed (Prelec and Loewenstein, 1998), whereas the DUM predicts a preference for paying later. Furthermore, they may prefer to receive payment for work after rather than before performing it, again in contradiction to the DUM. We have also discussed the preference for payment decoupling, which may lead to fixed-fee pricing with zero marginal costs, as for example with many health club membership schemes. This is another contradiction of the DUM, which predicts a dislike for up-front fees. This situation is examined in more detail in Case 8.1.

Another anomaly of the DUM observed earlier, that relates to choice bracketing, is the preference for spread of consumption. Loewenstein and Prelec (1993) found that people tend to prefer to spread the ‘treats’ of dining at a fancy French restaurant, although in this case there was also a preference for an improving sequence of outcomes, as predicted by prospect theory. The preference for spread is a separate phenomenon, and appears to be related to anticipatory utility.

Fudenberg and Levine emphasize the advantages of their model over hyperbolic discounting, in that it produces a single equilibrium for behavior, rather than the multiple equilibria that are associated with hyperbolic discounting and the multiple-self model. While being analytically simpler and making more precise predictions, they claim that it can explain empirical facts just as well.

There are a number of predictions or implications of this model. For example, the authors find that self-control costs lead to longer delays. They also develop a banking-savings model where it is predicted that people will use self-control in limiting the amount of pocket cash that they have available to spend later in a nightclub scenario. It is notable that this aspect of the model incorporates mental accounting concepts, in that bank cash is regarded differently from pocket cash in terms of the marginal propensity to consume. The concept of a reference point is also used, in that the amount of pocket cash is used as the reference point for spending, not one’s total wealth. It is important that the constraint on spending here is not liquidity, since in principle one could write a check or use a credit card in the night club. However, these are ‘nonanonymous’ accounts, meaning that spending from them will result in an identifiable transaction later, which may cause self-recrimination – or recrimination from one’s partner. Cash, on the other hand, is an anonymous account, as we discussed in the chapter on mental accounting. Fudenberg and Levine also explain Rabin’s ‘risk paradox’ (2000) in a similar way: people are averse to taking small risks which involve pocket cash, but do not have similar risk-aversion for large gambles that involve bank cash.

Dual-self models have also been proposed by psychologists and neuroscientists, and there is an element of consilience here, in that findings in different disciplines using different approaches have tended to come to similar conclusions. Brocas and Carrillo (2008b) approach the subject from the neurological basis of brain modularity, where there is ample evidence (examined in the next section) that the brain not only consists of different systems, but also that these systems are in conflict in various ways. They propose three main sources of conflict: asymmetric information, temporal horizon, and incentive salience. So far we have concentrated mainly on the second of these sources, although the first is relevant in the ‘planner-doer’ model. Brocas and Carrillo propose that decreasing impatience and hyperbolic discounting emerge as a result of these two conflicts. However, there is another ‘dual-self’ aspect related to incentive salience that has been referred to in Chapter 3 related to wanting and liking. Robinson and Berridge (2003) and Berridge (2001) show that there is one system that mediates the feeling of pleasure and pain (the ‘liking’ system) and a different system that mediates the motivation or incentive to seek pleasure and avoid pain (the ‘wanting’ system). The evidence relating to this is discussed later in relation to neurological studies.

In the discussion of hyperbolic discounting it was noted that its most important failing was the lack of a psychological foundation. Rubinstein (2003) both disputes the empirical evidence for hyperbolic discounting, and provides an alternative framework for decision-making which he claims does have a legitimate psychological foundation. Like various other models we have seen, Rubinstein’s approach is based on a heuristic process. This proposes that the decision-maker uses a procedure that applies similarity relations, involving a money dimension and a time dimension, in a series of three steps.

The objects of choice in intertemporal situations can be described as being in the form (x, t), where $x is received with a delay of t units of time. Thus a decision-maker may have to compare two choices: A = (x, t) and B = (y, s). According to Rubinstein (2003) many decision-makers go through the following three steps:

If x > y and t < s then A dominates B, since it is preferable in both dimensions (a larger reward is received sooner).

If the decision-maker finds similarity in one dimension only, he determines his preference using the other dimension only. For example, if x is similar to y, but t > s, then B is preferred to A, since the rewards seem similar, but B involves less delay.

More recent studies by psychologists have generally supported the theory of increasing costs of self-control, for example Gailliot et al. (2007), Vohs et al. (2008), Burger, Charness and Lynham (2011), Fedorikhin and Patrick (2010), Usta and Häubl (2010) and Bucciol, Houser and Piovesan (2011). Bucciol, Houser and Piovesan (2011) find that exposure to temptation reduces the productivity of young children, aged 6 to 13, but not older children. This is in keeping with the findings of the Mischel studies described earlier.

However, the empirical evidence regarding the costs of self-control and its effects is sometimes surprising. Burger, Charness and Lynham (2011) study procrastination by students, and report two main findings. First, unlike previous studies, they find that the imposition of interim deadlines for a fairly long-term project (five weeks) does not improve performance in terms of completing a given task. Second, they find that in the short term over a two-day period, exposure to temptation reduces productivity in the first day, but actually increases the probability of completing a task over the whole two-day period. The authors suggest that this may be due either to the self-signaling effect of exerting willpower, or to the suffering on the first day creating a commitment to persevere and ‘see things through’ on the second day.

Fedorikhin and Patrick (2010) find that although positive mood generally facilitates resistance to temptation as far as healthy food choices are concerned, any emotional arousal accompanying this mood can reduce this resistance by increasing the cognitive load. For example, the study indicates that watching an exciting video clip while in a positive mood is more likely to be associated with choosing M&Ms as an unhealthy snack rather than grapes as a more healthy option. Thus it is not just the kind of mood, but also the intensity of feeling, that affects choice.

Failure to optimize behavior also arises in situations where people tend to underestimate usage. Miravete (2003) examined people’s choice of telephone calling plan when South Central Bell changed their tariff structure. The new structure involved either paying a flat monthly rate, or paying a fixed rate plus call charges. Again the study finds that many people chose the wrong option, but in this case people tended to be quicker to learn from their mistakes. Whereas 40% of people initially chose the wrong option, paying too much, two months later this proportion was reduced to 33%. Not all studies of situations where naïve consumers underestimate usage present such an optimistic picture. Heidhues and Köszegi (2010) find that naïve consumers overborrow on both credit cards and subprime mortgages, where the baseline repayment terms are cheap. However, there are large penalties for delaying repayment, and the study finds that these consumers end up paying the penalties, thus suffering large welfare losses.

It is important to realize that the issues above related to present bias and optimization do not arise with the constant exponential discounting of the DUM. With the constant discounting model, as stated earlier, there is no conflict between short term and long term: one path of action will at all times seem preferable. In the example where one yields to the temptation of having the dessert one had previously not intended to have, according to the DUM one will at all times either want the dessert or not want it; there is no scope for the exertion of willpower. If the discounted benefits of eating the dessert exceed the discounted costs one will indulge, and if they do not then one will not indulge. The important implication here, discussed extensively by Ainslie (2001) in his book Breakdown of Will, is that in the DUM the concepts of temptation and willpower are redundant. Of course, present bias is not the only factor related to non-optimization in some cases; overconfidence and self-serving bias are also relevant.

The role of self-awareness is always important in good decision-making, and it is particularly important in the context of self-control situations. Psychological conflict arises because the subject will normally remember that their preference in the past was different, and, if the subject is sufficiently self-aware, they will also realize that in the future they will come to regret their action if they indulge, because from that future standpoint, discounted costs exceeded discounted benefits.

However, there is a final twist to this situation that we have also touched on earlier, and this relates to self-signaling. When the self-control problem is repeated, as is often the case, a yielding to temptation (or ‘defection’) in the first round can lead to a loss of self-confidence, thus making defection more likely in the next round and so on. Thus a far-seeing self may envisage the likely succession of failures if too harsh a rule is made initially, and decide instead to adopt a less strict policy as far as commitment is concerned.

It is therefore difficult to draw definite conclusions regarding how individuals should make commitments in self-control situations. The main general conclusion is that those agents who know themselves, and can predict their future selves, best are also best able to maximize their own welfare in terms of experienced utility.

One other aspect of self-control problems that has important policy implications concerns the effects of diminishing marginal sensitivity and shifting reference points. For controlling food intake there are a number of relevant factors in particular:

1 There is a multi-sensory system in operation, involving visual, olfactory and gustatory senses. The interdependence of seeing, smelling and tasting foods is not well-known at present, but it may be possible that if just one of these senses suffers from diminishing sensitivity in eating a meal, this may override the other senses. On the other hand diminishing sensitivity may only occur when all three senses are affected.

2 The phenomenon of diminishing marginal sensitivity is highly specific to different foods (Epstein et al., 2009). People who eat meals with more varied foods, or whose intake in general is more varied, tend to eat more in total. This is especially true of sugary and fatty foods, where a large number of convenient snacks are available. When we eat a monotonous diet we eat less as diminishing sensitivity sets in much earlier.

Historically US laws have been very strict regarding sales of such drugs, imposing severe penalties, but not so strict regarding possession. This policy may have a perverse effect on behavior, as noted by Fudenberg and Levine (2006). Severe penalties have the effect of increasing the fixed cost of making a transaction, causing consumers to buy larger quantities in each transaction. Such stockpiling is likely to lead to greater consumption, as we saw in the hypothetical example involving potato chips. Fudenberg and Levine, along with other economists, have therefore recommended legalization of such ‘temptation’ goods, combined with a high excise tax, similar to the policies used in many countries in relation to cigarettes. Such a policy provides a greater incentive to reduce consumption of harmful products.

A recent approach to government policy in general has been outlined by Thaler and Sunstein (2008), in the term ‘nudge’, which is the title of their book. This was briefly discussed in Chapter 6, but the implications are particularly important for intertemporal decisions. The authors describe their approach as libertarian paternalism, where people are not forced into making decisions of a certain type, but are ‘nudged’ by the framing of the decision situation into making decisions that later, in retrospect, they believe were in their best interests. They suggest that this is especially important in the areas of health care and saving for retirement. In particular they are critical of recent legislative changes in US health care on a number of grounds, such as the randomization of default settings for choices and the offering of too many choices, which they suggest is confusing to many people. Furthermore, the authors suggest that the ‘nudge’ approach can be applied to a wide variety of social policies, such as environmental policy, involving fuel economy and electricity usage, smoking, littering, teenage pregnancy and filing tax returns. However, not all behavioral economists are convinced by the ‘nudge’ approach. Some are of the opinion that people should be free to make their own mistakes. This is essentially a normative issue.

Case 8.1 Price plans for gym memberships

We have already mentioned various policy implications following from studies by DellaVigna and Malmendier (2004, 2006). One particular situation these authors examined was the optimal pricing structure for firms facing consumers with hyperbolic preferences for gym memberships. They developed a three-stage model as follows:

Period 1

The firm offers the consumer a membership plan with a membership fee F and a per-use fee p. The consumer either accepts or rejects the contract.

Period 2

If the consumer accepts the contract, he or she pays F and then makes the decision whether to exercise (E) or not (N). If the consumer chooses E, he or she incurs a cost c which relates to the personal effort of exercising, and also pays the firm the usage fee p. If the consumer chooses N, then there is no cost c or usage fee p.

Period 3

If the consumer chooses E then there is the delayed health benefit b; this is obviously not received if the consumer chooses N.

The firm incurs a setup cost of K whenever a consumer accepts the contract, and a unit cost a if the consumer chooses E. The consumer is also assumed to be a hyperbolic discounter with parameters β, b and δ, as explained in the section on hyperbolic discounting. For simplicity, the firm is assumed to be time consistent with a discount factor δ.

For the naïve hyperbolic discounter choosing to exercise, the decision process can be described as follows:

Period 1

The utility from choosing E is βδ (βb − p − c), and the payoff from N is 0. Therefore the consumer chooses E if c ≤ δb − p.

Period 2

Choosing E only gives a utility of βδb − p − c, so the consumer actually chooses E only if c ≤ δb − p, a smaller amount than in period 1.

Thus we can see that the naïve hyperbolic discounter, by misinterpreting his or her own future discounting process, overestimates the net utility of E when buying the membership. Such consumers choose to exercise less often than they planned to when buying the membership.

The sophisticated consumers, on the other hand, are under no illusions regarding their propensity to exercise and correctly predict their choice of E.

Assuming profit maximization, DellaVigna and Malmendier predict that, for time-consistent consumers (with β = 1), the firm simply sets p* (the optimal per-use fee) equal to the marginal cost a. However, for hyperbolic discounters with β < 1, the optimal pricing contract involves setting the per-use fee below marginal cost (p* < a), and the membership fee F* above the optimal level for time-consistent consumers. There are two reasons for this result:

1 Sophisticated consumers like the lower per-use fee because it serves as a commitment device for increasing the probability of exercising. They know that they will be tempted to skip going to the gym unless the per-use fee is low.

2 The higher membership fee allows the firm to exploit the overconfidence of naïve consumers. They will be willing to pay the higher membership fee because they overestimate their frequency of usage and the resulting benefits.

DellaVigna and Malmendier also present empirical evidence in support of their model. They showed that firms in the health club industry typically charged high membership fees and low, often zero, per-use fees. More specifically, they found that the average membership fee was about $300 per year. Most gyms also have the option of paying no membership fee but paying a higher per-use fee (about $15 per visit) instead. The study found that the average gym member goes to the gym so rarely that their actual per-use cost works out at about $19 per visit. These consumers would be better off not buying the membership and just paying on a per-use basis. Therefore this forecasting mistake allows us to conclude that many gym members behave like they are naïve hyperbolic discounters.

Questions

1 Compare and contrast the purchasing decision in the health club situation with the purchasing situation modeled earlier in the chapter relating to buying potato chips.

2 If naïve consumers learn to become more sophisticated, how is this likely to affect their buying behavior and firms’ strategy in the health club industry?

3 Explain the implications if a health club were to abandon a fixed fee structure and just charge a relatively low per-use fee of $10.

Case 8.2 The savings problem

Over the last 20 years household savings rates in many of the rich OECD countries have fallen sharply. The so-called Anglo-Saxon countries – US, Canada, UK, Australia and New Zealand – have the lowest rates of household saving. Americans save on average less than 1% of their after-tax income today compared with 7% at the beginning of the 1990s. In Australia and New Zealand personal saving rates are negative, as people borrow in order to consume more than they earn. The general pattern can be seen in Figure 8.4.

Figure 8.4 Trend in household savings rates

Source: OECD *Estimate

Other countries with rapidly ageing populations, especially Japan and Italy, have also seen their personal saving rates plummet, though from a higher level. The Japanese today save 5% of their household income, compared with 15% in the early 1990s. Only a few of the rich countries, notably France and Germany, have avoided this pattern of reduced saving. Germans saved around 11% of their after-tax income in 2004, up slightly from the mid-1980s.

In the US the overall trend in saving masks sub-trends in the components of saving. Evidence suggests that while saving of high-income earners has proved stable, middle income saving has collapsed, and low-income earners are increasingly dissaving (Bunting, 2009).

This general trend in the rich countries raises a number of issues:

1 What is the appropriate way to measure a country’s savings?

2 Are rich countries saving enough?

3 What kinds of government policy are effective in encouraging saving?

All of these issues involve certain aspects of behavioral economics, although some of the aspects are not directly related to intertemporal choice. We will focus on those aspects that are related to intertermporal choice, observing differences between the standard model and its behavioral alternatives.

The appropriate way to measure savings

The most fundamental point here is that, as far as countries are concerned, it is the total amount of savings by households, firms and governments that is important. Thus saving by firms in the form of retained profit, and budget surpluses by governments can in principle make up for any deficit by households. However, there appears to be at least some interrelationship between these different categories. A theory called ‘Ricardian equivalence’ holds that increases in public saving are cancelled out by falls in private saving as individuals anticipate future tax cuts. An OECD study (Pelgrin and de Serres, 2003) of 16 rich countries between 1970 and 2002 has found that, on average, about half of any improvement in public finances is offset by lower private saving in the short term, and about two-thirds in the long term. However, in the US, one of the most extreme cases of low national saving, the offset was smallest. This raises policy issues discussed later.

As far as the household saving rate is concerned, this is calculated by subtracting consumption spending from after-tax income. One measurement problem is that the definitions of both income and spending that statisticians use in the national accounts often bear little resemblance to what people think of as saving and spending. Realized capital gains, for instance, are not included in income, even though the taxes paid on capital gains are deducted from income. There is an aspect of mental accounting that is relevant here. As seen in Chapter 6, people tend to classify income and wealth into different accounts and their marginal propensities to spend and save from these different accounts are also very different. For example, people tend to have a high MPC with current income, but a much lower one for various categories of wealth, like capital gains. We shall see that this lack of fungibility has important implications for government policy.

Adequacy of saving

There are both macro and microeconomic aspects of this issue, and both have become the subject of highly controversial debate amongst economists and policy-makers in recent years. The macroeconomic aspects relate to the function of saving in the economy as a whole, and in particular its role in funding investment and stimulating growth. We are not so much concerned with this issue here, although many economists would say that, with a current net national savings rate of only 2%, the US economy would definitely benefit from a boost in saving as far as economic growth is concerned. As a result of fiscal stimulus and multiple bailouts, the budget deficit for 2010 is estimated at 9% of GDP, a historical high. Investment tends to be low, and the sustainability of overseas borrowing is questionable.

The main issue from a behavioral point of view concerns the microeconomic aspects of saving: are individuals saving enough? In the last decade at least four studies have suggested that people in the US are not saving enough, while at least another four studies have suggested that they are saving enough. The reason for the disagreement is that different studies are based on different assumptions regarding expected earnings, attitudes to saving, retirement age, desirable levels of consumption during retirement, government policy and other crucial factors that affect savings adequacy.

In order to address the issue of savings adequacy we must consider the three main motives for individual saving:

1 Precautionary – people want to insure against a sudden drop in income.

2 Consumption smoothing – people often wish to consume more than their income when they are both young and old, and therefore save most in their middle age.

3 Bequest motive – people want to leave assets to their children.

Therefore, the issue whether people are setting aside enough from their current income depends on assumptions regarding what those people will want to consume or bequeath in future, what wealth they have already accumulated, and what returns on those assets will be.

In the 1990s many economists argued that in the US individual saving was insufficient, notably Bernheim (1993). However, more recent studies have argued the opposite case, for example Engen, Gale and Uccello (1999) and Scholz, Seshadri and Khitatrakun (2003). The last of these studies concluded that 80% of US households had accumulated adequate saving.

However, the main weakness of these more optimistic studies lies in the assumptions made. First, they include individuals’ equity in their house as part of their financial assets. Again the fungibility issue is relevant here. While there is some evidence in both the US and the UK that increases in property values have fuelled increased consumption, people still do not treat such wealth in the same way as other forms of wealth. Not only are such unrealized paper gains subject to reversal, but there is also an endowment effect here; many old people are reluctant to sell their house to finance their retirement consumption. If only half an individual’s house equity is included, the most optimistic study suggests that just under 60% of US households have adequate savings.

A second important assumption in the studies mentioned is that future state pension benefits will be paid as promised. Given the budgetary pressures posed by the baby-boomers in many countries, a reduction in benefits is quite probable, particularly in the US. For poorer Americans, any cut in promised pension benefits would significantly reduce the adequacy of their current saving. Projected payments from social security exceed the value of all other financial assets for the bottom one-third of the income distribution.

In the UK, where the government’s level of pension provision is set to replace a much smaller proportion of earnings than in the US, the situation is similar. A recent report by Britain’s Pension Commission argued that, given downward trends in the occupational pensions provided by employers and the erosion of state pensions, 60% of workers over 35 are not saving enough.

A third assumption concerns the rate of return on savings. In recent years, the biggest difference between high-saving and low-saving OECD countries has been the return on assets. A recent report from the McKinsey Global Institute (Farrell, Ghai and Shavers, 2005) observes that between 1975 and 2003 asset appreciation was responsible for almost 30% of the increase in the value of household financial assets in the US, whereas in Japan high saving rates made up for negative returns on assets. Based on current rates of return and saving patterns in big industrial economies, the McKinsey study is not optimistic regarding the adequacy of global wealth accumulation. There is currently much uncertainty regarding future rates of asset appreciation.

Implications for government policy

How can governments increase the amount households save? Tighter monetary policies would certainly help. In the US in particular policy has been loose by most standards for many years, encouraging borrowing at the expense of saving. Most governments also use tax-incentives to some extent. The simplest incentive would be to switch from an income-tax structure, where tax is deducted twice (once from company profit and again when people receive investment income), to a consumption-based structure. However, governments tend to limit such a switch because it is regressive in nature, shifting the tax burden from rich to poor.

Some government policies have the effect of reducing saving rather than encouraging it. For example, in the US eligibility for welfare assistance such as food stamps is phased out if a couple has assets over $3000. In the UK, the means-tested pension credit, designed to help pensioners, has the perverse result of making saving for workers on low incomes an unattractive proposition: for every pound of savings income they can incur marginal tax rates of at least 40%. However, the new pension system which came into operation in 2011 should address some issues, by incorporating a default of participation in the scheme, with a 4% level of income contribution (Independent Public Service Pension Commission, 2011).

One major alternative tax incentive has been to shelter retirement accounts, in effect subsidizing them. In the US the subsidy on retirement-saving accounts is 27% of the value, amounting to 1% of GDP in terms of foregone tax revenue. There is a debate regarding the effectiveness of this policy, with some economists arguing that it merely displaces saving from one form to another, without increasing overall saving. However, a study by Venti and Wise (1987) concluded that ‘the vast majority of IRA (Individual Retirement Account) saving represents new saving, not accompanied by a reduction in other saving’ (p. 38). These results were confirmed using a different methodology by Feenberg and Skinner (1989).

In summary, there are three main aspects of behavioral economics that have important policy implications in terms of the adequacy of saving:

1 Fungibility

Different forms of saving and wealth are not treated as being fungible or substitutable. This is demonstrated by the evidence from the Venti and Wise study and the Feenberg and Skinner study. Governments can make use of this lack of fungibility to encourage more saving.

2 Self-control and commitment

IRAs, like other retirement accounts, are illiquid, since they involve a 10% tax surcharge if money is withdrawn before the investor reaches 59½ years old. Venti and Wise (1987) commented: ‘Some persons of course may consider the illiquidity of IRAs an advantage: it many help to insure behavior that would not otherwise be followed. It may be a means of self-control’. As stated earlier, the general trend in global financial markets towards greater liquidity may have discouraged saving by removing such commitment devices. Therefore governments can encourage more saving by creating additional commitment devices in the form of illiquid savings accounts with tax incentives, such as Individual Savings Accounts (ISAs) in the UK.

3 Framing

The desire to save, particularly for retirement, can be much influenced by the way in which the options in retirement plans are framed, as noted in Chapter 5. Poorer people, for example, are more likely to be enrolled in private retirement plans if that is the employer’s default option than if workers have to elect to enrol. A study by Madrian and Shea (2001) indicated that shifting to automatic enrollment raised participation among poorer workers from just over 10% to 80%. UK pension policy has now moved in this direction. This kind of ‘nudge’ policy is very much endorsed by Thaler and Sunstein (2008).

Questions

1 Why have different studies come to different conclusions regarding the adequacy of saving?

2 Explain why the putting of money in a retirement account might not reduce other forms of saving.

3 Explain why fungibility is an issue as far as increasing saving is concerned.

4 In what circumstances is illiquidity of assets a desirable characteristic?