Anticipation and the Valuation of Delayed Consumption
`Author(s): George Loewenstein
`Source: The Economic Journal, Vol. 97, No. 387 (Sep., 1987), pp. 666-684
`Published by: Blackwell Publishing for the Royal Economic Society
`Stable URL: http://www.jstor.org/stable/2232929
`Accessed: 18/07/2009 10:18
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`The Economic Journal, 97 (September I987), 666-684
`Printed in Great Britain
`
`AND THE VALUATION
`ANTICIPATION
`OF DELAYED CONSUMPTION*
`
`George Loewenstein
`
`'When calculating the rate at whic-h a future benefit is discounted, we must
`be careful to make allowance for the pleasures of expectation.' (Marshall,
`i89i, p. I78)
`Of the various assumptions underlying analyses of intertemporal choice,
`perhaps the assumption of positive discounting is the most widespread and
`noncontroversial. Empirical work which has sought to estimate individual
`discount rates (Hausman, I979; Landsberger, I971) has provided no grounds
`for questioning this assumption. In fact, a recent study which explicitly
`questioned the general applicability of positive discounting concluded that 'the
`case for positive time preference is absolutely compelling' (Olson and Bailey,
`I 98 I).
`Yet it requires little effort to think of examples of behaviour in which negative
`discounting is apparent. The pleasurable deferral of a vacation, the speeding
`up of a dental appointment, the prolonged storage of a bottle of expensive
`champagne are all instances of this phenomenon. Indeed, if R. H. Strotz had
`begun his work thirty years ago with behaviour such as this in mind, he might
`have developed a critique of Discounted Utility theory (DU) equally as
`compelling as his work on myopia but pointing towards research very different
`from what has actually ensued from his work. Instead, in introducing the broad
`concept of 'time inconsistency', Strotz devoted his attention exclusively to a
`subdomain of instances in which the economic actor behaves more myopically
`in the present than he previously had planned. While the focus on impulsivity
`has offered important theoretical insights it may have impeded recognition of
`the existence and interest of other phenomena, such as low or negative
`discounting. A more inclusive theory of intertemporal choice should be able to
`account for both extremes of behaviour - myopic and far-sighted. Such a
`model is proposed here.
`The model modifies DU by introducing an insight once recognised by
`economists: that anticipation of the future has an impact on immediate
`well-being.1 This observation can be traced to Bentham (I789), who included
`among the ingredients of utility, pleasures and pains that derive from antici-
`pation. For Bentham, anticipation, like consumption itself, was an important
`source of pleasure and pain.
`
`* I thank Robert Abelson, Richard Levin, Sidney Winter,John Geanakoplos, Howard Kunreuther, Colin
`Camerer, Mark Machina and Robin Pope for their helpful suggestions. The support of the Institute for
`Advanced Study, in Princeton. is gratefullv acknowledged.
`1 In exploring the relationship between anticipation and time discounting, the current paper is akin to
`the recent work of Pope (1983), who examined the role of anticipation in risk aversion, and Wolf (1970),
`who discussed the implications for intertemporal choice of utility from memory.
`[ 666 ]
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`667
`OF DELAYED
`VALUATION
`CONSUMPTION
`i987]
`[SEPT.
`Jevons who was one of the first to apply the Benthamite concept of utility
`to understanding intertemporal trade-offs, wrote: 'Three distinct ways are
`recognisable in which pleasurable or painful feelings are caused:
`(I) By the memory of past events;
`(2) By the sensation of present events;
`(3) By anticipation of future events.' (I905, p. 3)
`The latter, which Jevons termed 'anticipal pleasure' and 'anticipal pain'
`were, if anything, the most important for understanding economic behaviour:
`'The science of economics is very largely occupied in studying man's efforts to
`obtain anticipal pleasure by the provision of stocks of goods for future use:
`almost all the complicated practices of production and exchange resolve
`themselves ultimately into manifestations of these efforts' (I 905, p. 65) . In what
`follows, the term 'savouring' refers to positive utility derived from anticipation
`of future consumption; 'dread' refers to negative utility resulting from con-
`templation of the future.
`
`STUDY
`I. AN ILLUSTRATIVE
`Fig. I summarises results from a survey in which 30 undergraduates were asked
`to specify the 'most you would pay now' to obtain (avoid) each of five outcomes,
`immediately, and following five different time delays. The outcomes were: (i)
`obtain four dollars; (2) avoid losing four dollars; (3) avoid losing one thousand
`
`2 0 -
`
`(D 1*5-
`
`4-
`0
`
`0
`
`0
`v:
`0
`
`1.0
`
`0
`
`0 5
`
`Shock/
`
`~~~~~~~~Lose
`$1000
`
`Lose $4
`
`Gain $4
`
`Immediately 3 hours
`
`3 days
`24 hours
`Time delay
`
`1 year
`
`10 years
`
`Fig. i. Maximum payment to obtain/avoid outcomes at selected times. Proportion of current
`value (N= 30).
`
`dollars; (4) avoid receiving a (non-lethal) one hundred and ten volt shock, and
`(5) obtain a kiss from the movie star of your choice. Time delays were: (i)
`immediately (no delay); (2) in twenty-four hours; (3) in three days; (4) in one
`year; (5) in ten years. Subjects were asked to specify the most they would pay
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`for every combination of outcome and time delay. They were told to assume
`that all outcomes were certain to occur at the designated time. Summary
`statistics for the study are presented in Appeindix i.
`It can be seen that the two non-monetary items, the kiss and the shock, both
`exhibit unusual patterns of devaluation. DU, with positive discounting, predicts
`that people will prefer to consume desired outcomes as soon as possible. This
`prediction is contradicted by the kiss item. Subjects on average were willing
`to pay more to experience a kiss delayed by 3 days than an immediate kiss or
`one delayed by three hours or one day. Data presented later in this paper show
`that the hump-shaped pattern of devaluation evident in Fig. i is common for
`desirable consumption that is fleeting.
`Likewise, DU asserts that people prefer to delay undesirable outcomes
`whenever possible. The shock item contrasts sharply with this prediction.
`Subjects were, on average, willing to pay slightly more to avoid a shock that
`was delayed for 3 hours to 3 days than to avoid an immediate shock. They were
`willing to pay substantially more to avoid a shock delayed by one or ten years.
`In contrast to the patterns of responses for the kiss and shock, the money
`amounts included in the survey appear to be discounted in the normal fashion.
`Why haven't patterns of intertemporal preference such as those exhibited
`towards the kiss and shock appeared in earlier empirical work on intertemporal
`choice? Several answers are possible. In some cases, economists have attempted
`to infer intertemporal preferences from behaviour in which such preferences
`were irrelevant to behaviour. Hausman's attempt to estimate individual
`discount rates from air-conditioner purchases provides an example. Air con-
`ditioners vary in purchase price and energy efficiency, thus creating a choice
`between immediate versus deferred payments. Hausman, by observing the
`price/efficiency rating of a purchased air-conditioner, attempted to impute the
`discount rate of the purchaser. The problem with this approach is that
`individual discount rates should be irrelevant to what model is purchased. If
`consumers are able to save and dissave (or borrow) at established interest rates,
`they should logically purchase the model of air conditioner that minimises at
`the desired level of cooling capacity, the net present value of the time stream
`of payments.2 Similar considerations may have caused subjects in the current
`experiment to discount the money amounts in a conventional manner, in
`contrast to their behaviour towards the kiss and shock.
`In other cases, economists have attempted to estimate discount rate from
`individual saving behaviour, but such attempts are even more problematic since
`individuals have little influence on interest rates. The interest rate at which an
`individual saves or borrows gives no information about his or her own discount
`rate and hence it is necessary to infer discount rates from level or rate of saving,
`a process that is extremely sensitive to the specification of the model used to
`represent the savings decision. Furthermore, savings behaviour depends on so
`many factors other than discount rates (e.g. expected future income streams,
`
`2 His finding of substantial differences in discounting between different income groups suggests either that
`unobserved economic factors such as liquidity constraints were operative, or that consumers were failing to
`behave rationally.
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`669
`i987]
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`OF DELAYED
`VALUATION
`projected needs) that it is exceedingly difficult to isolate the effect of time
`preference on saving.
`In this paper it is argued that patterns of preference such as those exhibited
`towards the kiss and shock, and other DU anomalies discussed below, can be
`explained by incorporating Jevons' anticipal pleasure and pain into an
`otherwise standard model of intertemporal choice. In what follows, such a
`model is developed in the simplest possible terms, and its implications are
`discussed.
`
`II. THE MODEL
`The following model explores the question of how an individual values a single
`future act of consumption under conditions of certainty. The model depicts a
`consumer at time to who anticipates consuming x at time T > to. Consumption
`is assumed to yield a constant stream of utility, U(x), beginning at time T and
`continuing for duration L, after which it drops to zero. Formally:
`for T < t < T+L,
`Utf(X, T, L) = U(x)
`= o otherwise
`where Ut, indicates utility experienced at time t from consumption.
`At any time t between to and T (when consumption begins) the individual
`derives utility from anticipation, UtA. Utility from articipation is assumed to
`be proportional to the integral of utility from consumption discounted at a rate
`of 6. 6 is not the conventional discount rate, but a measure of the degree to
`which the individual derives immediate utility from anticipated consumption.
`Thus savouring or dread at each point t is equal to:
`r T+L
`
`(I)
`
`-
`
`U(x) e-8(T-t)
`
`(I -eaL).
`
`This formulation has four desirable properties discussed by Jevons in his
`enumeration of the laws of anticipal pleasure and pain. Referring to anticipation
`of a planned vacation, Jevons wrote:
`The intensity of the anticipation will be greater the longer the holiday;
`greater also, the more intensely one expects to enjoy it when the time
`comes. In other words the amount of pleasure expected is one factor
`determining the intensity of anticipal pleasure. Again, the nearer the date
`fixed for leaving home approaches, the greater does the intensity of
`anticipal pleasure become: at first when the holiday is still many weeks
`ahead, the intensity increases slowly; then, as the time grows closer, it
`increases faster and faster, until it culminates on the eve of departure
`(I905, p- 64).
`In the current formulation, as Jevons proposed, utility from anticipation,
`UtA, is a positive function of L, the duration of consumption, a positive function
`
`UtA(x, T,L) =
`
`6e-f(T-t) U(x) dT
`e
`
`T
`
`(2)
`
`(3)
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`of U(x), the utility that will be derived from consumption, and a negative
`the time delay prior to consumption. Also, the second
`function of (T-t),
`derivative of UA with respect to ( T- t) is positive, yielding the accelerating path
`of utility from anticipation suggested by Jevons.
`Fig. 2 depicts one possible time path of utility from anticipation and
`consumption.
`
`to
`
`T
`
`T+L
`
`Fig. 2. Utility from anticipation and consumption.
`
`The individual is assumed to evaluate a delayed act of consumption
`according to the integral of discounted utility from anticipation and consump-
`tion that it yields. Thus, the present value Y (measured in dollars) ofa delayed act of
`consumption is defined by:
`
`(i -e-8L)
`
`U(x) e-r(t-to) dt,
`
`(4)
`
`e-r(t-to) dt + J
`
`T+L
`
`CT C
`U( Y) = J X U(x) e-8(T-t)
`utility from
`utility from
`consumption
`anticipation
`where r is the conventional discount rate used to discount future utility from
`all sources and U(Y) is a 'ratio scale' utility function3 with positive first and
`negative second derivative. Throughout the following, r is assumed to be
`positive.
`Setting to = o for simplicity, and integrating:
`
`U(Y) = U(X)[8
`
`(e-rTe-T)
`
`( -e
`
`r e
`
`(i -rL
`
`(5)
`
`& and oc define to the relationship between UA and UC. 6 is a measure of an
`individual's preoccupation with the future. Someone with a low a savours or
`dreads even those outcomes that will occur in the distant future. a is a measure
`of the 'imaginability' or 'vividness' of a particular outcome. Factors that raise
`a or lower a increase utility from savouring or dread. (A later section discusses
`attempts on the part of marketers and policy makers to influence cz.) Since most
`people take account of future outcomes (e.g. save for their retirement) even
`when they do not immediately savour or dread those outcomes, it is assumed
`that & > r.
`
`III. IMPLICATIONS OF THE MODEL
`The model, as it stands, suggests the conditions under which people will prefer
`to delay desired consumption or get undesirable consumption over with quickly.
`These two cases are explored in turn.
`invariant with respect to multiplicative transformations.
`
`3I.e.
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`I987]
`
`VALUATION
`
`OF DELAYED
`
`CONSUMPTION
`
`67I
`
`Delaying of Desired Consumption
`Desired consumption will be delayed when (8Y/IT) > o i.e. when the net
`present value of consumption, taking account of both savouring and consump-
`tion itself, increases as a function of time delay. Since U(Y) is monotonically
`increasing, this condition is equivalent to 8U(Y)/8 T> o.
`Differentiating (5) with respect to T:
`
`er(y = U(X [(_)
`
`(4e-11- re-ril) (i -e-1L-1-e-rT (i- e-rL)
`
`(6)
`
`The first term in the brackets is the marginal benefit from savouring,
`that would be gained from delaying. The second term is the marginal cost of
`delay, in terms of increased discounting of consumption.
`Consumption will be deferred when 8U(Y) /D T is positive for T = o. Setting
`T = o:
`
`au(Y)
`= U(x)
`A T T=o0
`A necessary and sufficient condition for delaying desired consumption is,
`therefore,
`t
`
`a
`
`(I-e-L)
`
`- U(x) (I - e-rL).
`
`(7)
`
`(8)
`
`(I-e-L)
`
`>
`
`i-e-rL.
`
`As would be expected, delaying is more likely when a is large and a is small.
`Fig. 3 illustrates the relationship between Y, the net present value of
`consumption and T, the time at which consumption of x begins, for the case
`when (8Y/I T) is initially positive.
`
`co
`
`z
`
`to
`Fig. 3. Value at time to of an outcome to be consumed at time T.
`
`T: time consumption begins
`
`Tm
`
`By reading off the net present value of consumption at any point T on Fig.
`3, and subtracting it from one, it is possible to derive a crude measure of the
`value of consumption of x at time T relative to the value of immediate
`consumption of x. Note that such 'devaluing' (negative or positive) of
`consumption as a function of delay must be distinguished from the individual's
`discounting of future utility, which is based only on r(.). To avoid confusion
`between these concepts a distinction is henceforth drawn between 'discounting',
`which refers to a preference for early over later utility, and 'devaluing', which
`refers to a decrease in the outcome's value at time to as a function of delay.
`'Devaluing' is also synonymous with the rate of time discount which would
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`be estimated by an observer who did not take account of utility from
`anticipation. In Fig. 3, it can be seen, devaluing is initially negative and only
`eventually becomes positive even though time preference is always positive - i.e.
`r > o.
`Point T. in Fig. 3 has special significance. Tm is, for desirable outcomes, the
`individual's most preferred time of consumption. Tm will be greater than to if
`(8 Y/I T) is positive for T= o (condition 8). When condition 8 is met it will
`also be the case that (82Y/I T2) < o, ensuring that the point T. is a maximum
`(see Appendix 2). Under the standard approach (in the absence of planning
`or scarcity effects), T. is always equal to to. T. > to thus constitutes a sharp
`distinction between the predictions of the current model and the standard DU
`approach.
`
`Conditions Conducive to Delaying of Desired Consumption
`By totally differentiating (6) (see Appendix 3), it is possible to derive proposit-
`ions regarding the effect on Tm of changes in the different parameters of the
`model.
`Increasing the duration of consumption, L, raises the marginal cost of
`deferring at Tm more than it increases the marginal benefit of savouring.
`Therefore, increasing L discourages delaying behaviour (8 Tm/IL < o). Con-
`versely, delaying is more likely when consumption is fleeting. Intuitively this seems
`plausible. Those forms of consumption that are commonly delayed typically
`provide brief but intense pleasure. In such cases anticipation (and sometimes
`memory) serves to extend the otherwise fleeting benefit provided by
`consumption.
`Raising a, as would be expected, also encourages delaying behaviour. a, for
`desirable outcomes, can be viewed as a measure of the 'savourability' of
`consumption. Outcomes that can be readily imagined and that are pleasurable
`to contemplate are therefore more likely to be delayed. The effect of changes in
`a on Tm is ambiguous.
`The 'kiss from the movie star of your choice' in the study was chosen for its
`fleeting quality and high degree of 'savourability', characteristics which are
`predicted to promote delay. It was also chosen to rule out, as much as possible,
`alternative explanations for delaying behaviour. Two such explanations are
`worthy of note. The first, the 'planning effect', provides an incentive for delay
`when, by delaying a desired outcome, preparations can be made that will
`enhance utility from consumption. This is certainly true of food consumption,
`in which case fasting (within limits) enhances pleasure from subsequent eating.
`In the case of the kiss it also seems reasonable to assume that some preparations
`(such as gargling, or moving to a dimly lit room) could intensify the experience.
`But it is difficult to see how a delay of three days, which was generally preferred
`to a single-day delay, could add much to such preparations.
`The second alternative explanation for delaying is the 'scarcity effect'. The
`basis of this argument is that some items are scarcer in the future (e.g.
`raspberries in winter) than they are in the present and thus should be more
`highly valued. The kiss from a movie star of your choice, which is a scarce item
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`673
`I987]
`CONSUMPTION
`OF DELAYED
`VALUATION
`at any time and certainly as scarce in three days as at the present moment, was
`chosen to avoid this alternative explanation.
`Accelerating Undesirable Consumption
`The shape of Uto( T) for an undesirable outcome, which is a negative reflection
`of its shape for desirable outcomes, is shown in Fig. 4. In the case of undesirable
`outcomes a different point, Ti, has behavioural significance. Ti is the point at
`which an individual is indifferent between immediate and deferred consump-
`tion. If allowed to defer a negative outcome beyond Ti, the individual will do
`so. If constrained to consume x prior to 7i, however, his preferences will be
`reversed, and he will prefer to get x over with immediately. A common example
`of such behaviour is associated with medical or dental treatment. One puts off
`visiting the doctor or dentist as long as possible, but once a maximum delay
`is imposed - e.g., when one receives a card in the mail urging a visit - typically
`one asks for the first available appointment. Under the standard approach Ti
`always equals t0.
`
`T: time consumption begins
`
`to
`
`0
`
`;O.
`
`E 1-
`0.
`
`z
`
`T,
`I
`
`? --1___
`
`Fig. 4. Value at time to of consumption at time T.
`
`Equation (g) defines Ti.
`
`(
`
`- (erL)
`
`- U(X)
`
`) (e-rT
`
`(I-e-L)
`
`+ U(x)- erTi
`
`-e-rL)
`
`(9)
`
`The left-hand side of (g) represents the (negative) utility that would be
`experienced if x were consumed beginning immediately. The right-hand side
`expresses discounted utility (from dread and consumption) when consumption
`is delayed until T7 > to. When these expressions are equal, the individual at to
`is indifferent between consuming immediately or at Ti. If constrained to
`consume at any point prior to 7i, he would prefer to consume immediately.
`Again we are interested in the specific conditions that encourage individuals
`to get unpleasant outcomes over with quickly - i.e. make T > to. These
`conditions turn out to be analogous to those for Tm (see Appendix 4). The more
`fleeting an undesirable outcome - i.e. the shorter L - the greater is the tendency
`to get consumption over with quickly. People should therefore be especially
`likely to get fleeting outcomes over with quickly and defer those for which
`consumption is prolonged. This has the sensible implication that people will
`always defer outcomes whose effects are prolonged or permanent, e.g. loss of
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`JOURNAL
`[SEPTEMBER
`a leg. It is also the case that 8 7i/8a > o; people are likely to get those outcomes
`over with quickly that can be vividly imagined beforehand.
`Thus we should expect that the tendency to get unpleasant outcomes over
`with quickly will be greatest for outcomes that are fleeting and vivid. The shock
`item in the study was chosen to have these characteristics. Lest the survey results,
`which involve hypothetical responses, be questioned, it should be noted that
`several other studies involving real shocks produced similar results (Carlsmith,
`In fact even rats, in one experiment, when
`I962; Barnes and Barnes, I964).
`faced with a choice between an immediate or moderately delayed shock, tended
`to choose the immediate shock (Knapp et al. I 959). Furthermore, when rats are
`exposed to delayed shocks they typically exhibit physiological signs of fear such
`as elevated heartbeat and blood pressure while they wait, suggesting that fear
`may be a motivating factor in the choice of the immediate shock.
`A problem with the use of the shock item is that it is difficult to generalise
`the findings to economic behaviour in naturalistic settings. This particular
`problem is avoided in subsequent research in which subjects were asked among
`other questions: 'What is the least amount of money you would accept for
`cleaning i OO hamster cages at the Psychology Department's animal laboratory.
`You will be paid the money immediately. You should be willing to do the job
`for the amount you specify but not if you were offered only one dollar less. The
`job is unpleasant but takes only 3 hours. How much would you need to be paid
`to clean the cages: (i) once during the next 7 days; (2) once during the week
`beginning two months from today; (3) once during the week beginning one year
`from now?'
`The mean reservation wage for cage cleaning in the following week was $30
`(standard error 3 i). For cleaning the cage in a year respondents required an
`average of $37 in immediate payment (standard error 3-8). In fact, of 37
`respondents only 2 gave a smaller response to question (3) than to question (i)!
`
`Positive Devaluation
`When condition (8) is not met - i.e. for consumption that is lasting, or if a is
`small - we should not expect to observe negative devaluing. Nevertheless, utility
`from anticipation will still affect the devaluation of consumption. Fig. 5
`illustrates the effect of variations in L on devaluation of future consumption.
`Decreasing L will attenuate devaluing, flatten the slope 8U, /8 T and thus
`(see Appendix 5, which demonstrates that 82Y/ITOL < o). As L
`8Y/IT
`increases, therefore, Y(T) will lose its hump and will begin to take on the
`
`> 1- G
`a)
`
`X~~~Fleeting
`c~~~~~onsumption
`
`e)
`
`Prolonged
`consumption
`
`T: time of consumption
`
`Fig. 5.
`
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`675
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`OF DELAYED
`CONSUMPTION
`VALUATION
`reversed 'S' shape depicted in Fig. 5. Savouring, even when it does not cause
`devaluing to be negative, attenuates devaluing for small delays, bridging the
`gap between sporadic or short-lived consumption and pleasure of ownership.
`
`IMPLICATIONS
`
`IV. ECONOMIC
`Attempts to Manipulate a,
`The concept of 'vividness' or imaginability embodied in the a term played a
`central role in historical formulations of intertemporal choice. For example,
`Bohm-Bawerk cited 'the fragmentary nature of the imaginary picture that we
`construct of the future state of our works' (I889, p. 269) first in his list of causes
`for the systematic tendency to undervalue future wants. Marshall noted that
`a person's willingness ... to wait depends on his habit of vividly realising the
`future' (I89I, p. 293). Although modern accounts of intertemporal choice have
`not included discussions of vividness, perhaps because vividness is not directly
`observable, its meaning is nevertheless intuitively comprehensible, and there
`are numerous examples of attempts to manipulate it.
`Drivers' education films depict the gruesome consequences of car accidents
`in an effort to make those consequences more vivid to young (and presumably
`myopic) drivers. But facts and statistics and even photographs of accidents have
`only a limited impact. Faced with continuing high accident rates among young
`drivers, several school districts have taken more drastic measures. A device
`intended to demonstrate the violence of even a low-speed collision has been
`put into use in several school districts. Students are accelerated down a
`ramp on a wheeled chair which, after gaining a speed of 5 miles per hour, is
`abruptly halted. It is difficult to understand this device in purely informational
`terms. Rather, the intention is to give immediate emotional significance to an
`otherwise abstract outcome. An analogous attempt to counter youthful myopia
`through manipulation of vividness is depicted in the documentary movie
`'Scared Straight', in which high-school students thought to be at risk of future
`delinquency toured a maximum security prison, were harassed by inmates, and
`were given as vivid an image of prison life as is possible without actually being
`locked up.
`While the accident simulator and the visit to the prison were aimed at youth,
`such efforts are not limited to teenagers. For example, a recent television
`advertisement for a supplementary retirement plan showed a young couple in
`the first frame opting not to participate in the plan, and then showed them
`physically ageing against a backdrop of increasing poverty. Each of these efforts
`at persuasion can be viewed as attempts to decrease ac so as to raise dread and
`enhance evaluation of the future consequences of current actions.
`
`Estimation of Discount Rates
`The sensitivity of intertemporal choice behaviour to savouring and dread
`suggests that the standard model may be mis-specified, leading to systematic
`bias in the estimation of discount rates. Since DU does not ordinarily
`incorporate savouring or dread, and since both of these factors attenuate
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`devaluation, conventional estimates of discount rates should be biased down-
`ward, especially in situations where savouring or dread significantly affect
`devaluation. As demonstrated, these include situations in which future out-
`comes are fleeting or can be vividly imagined. Also, savouring and dread exert
`their greatest impact at short and moderate time delays, so discount rates
`estimated from short-term trade-offs will tend to be more biased than rates
`estimated from long-term trade-offs.
`The bias in estimation of discount rates will be especially serious if savouring
`and dread are different for different categories of consumption. If this were the
`case, then the general assumption that 'the discount rate is independent of the
`category of consumption goods for which it is calculated' (Landsberger, I97I,
`p. I35I) would be invalid. Thus, for example, Hausman, in his I979 study,
`implicitly assumed that discount rates imputed from air-conditioner purchases
`would also apply to other intertemporal trade-offs. What he failed to consider
`was the possibility that air conditioners or other energy-using appliances have
`special characteristics that promote steep discounting. Monthly payments for
`electricity are spread over time and made less salient by being combined with
`pre-existing electrical charges, leading to the prediction of high devaluing even
`when time discounting is low. In contrast, purchase cost is immediate and
`lump-sum. This myopia-inducing quality of fuel- or electricity-consuming
`durables seems to have been recognised by various agencies of government that
`require efficiency ratings for appliances, and estimates of fuel consumption and
`yearly operating costs, to be affixed to new cars.
`
`Savings Behaviour
`The concepts of savouring and dread may help to explain the anomalous
`observation that - rather than dissaving following retirement (as is predicted
`by the permanent income and life-cycle theories of saving) - individuals
`typically increase their rate of saving following retirement and continue to
`amass increasing amounts of wealth until they die. A number of explanations
`have been offered for this phenomenon, including uncertain life expectancy
`is that
`and bequest motives.4 Another explanation offered by Moore (1978)
`individuals derive utility from wealth itself. The current model bolsters Moore's
`account by providing a reason why wealth may be a source of utility.
`Accumulations of wealth can constitute, in effect, a 'licence to savour' - i.e. to
`imagine and thus derive immediate pleasure from the consumption which the
`wealth could finance.
`But the theory also provides a second, perhaps even more plausible,
`explanation for the observed failure to dissave following retirement. Retirement
`for the young is a non-vivid event - perhaps partly because thinking about
`old age is aversive and tends to be avoided (resulting in a small a). Young
`middle-aged couples and individuals, possibly for this reason, often 'live like
`there's no tomorrow'. As retirement approaches, however, the prospect of
`having inadequate funds for retirement becomes increasingly vivid and causes
`
`4 For a recent summary of this debate see Modigliani (I986).
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`VALUATION
`anxiety, anxiety that can be allayed in part by stepping up savings. The onset
`of retirement itself, and the sudden loss of wage income, of course, greatly
`increases this anxiety for the future. This an