Consumers’ Evaluations of Time-Delayed Purchase Opportunities
MARCUS V. M. DA CUNHA, JR.
CHRIS JANISZEWSKI
ALAN D. J. COOKE*
* Marcus V. M. da Cunha Jr. is doctoral student (marcus.cunha@cba.ufl.edu), Chris Janiszewski
is the Jack Faricy Professor of marketing (chris.janiszewski@cba.ufl.edu), and Alan D. J. Cooke
is assistant professor (alan.cooke@cba.ufl.edu), Warrington College of Business, University of
Florida, P.O. Box 117155, Gainesville, FL 32611-7155. This article is based on the first author’s
doctoral dissertation.
Consumers frequently face situations in which they have to estimate the present value of offers
that will deliver delayed benefits and costs. Existing theories disagree about the effects of time
on the evaluation of these purchase opportunities. We examine whether delay affects (1) the
perceived value of costs and benefits, (2) the weight with which costs and benefits are combined,
or (3) the integrated value of the offer. We find that (1) delay impacts costs and benefits
differentially, with people preferring no delay for small cost-small benefit offers, but preferring a
delay for large cost-large benefit offers, (2) the effects of delay can be attributed to changes in
the weight with which people combine costs and benefits, and (3) the weight of the more
important attribute decreases with a delay.
1
Consumers frequently consider purchase opportunities for which the benefits and costs
are experienced after a delay. A consumer’s willingness to commit to reservation-based
transactions (e.g., health maintenance appointments, airline ticket purchase, vacation property
rental), subscription transactions (e.g., a satellite television contract, a car lease, a time share
condominium), and relationships (e.g., marriage, career, children) depends on his or her
perception of the future benefits and costs associated with the transaction. A consumer must
identify the future benefits and costs accruing from the transaction (henceforth referred to as
“future values”), assess the worth of these future values in the present (henceforth referred to as
“present value”), and then compare this alternative to competing alternatives. To the extent that
the present value of future values is not a monotonic function of time delays, a consumer’s
relative preference for competing alternatives may change as the transaction date approaches
(Akerlof 1991; Rae 1834). In fact, it may be the consumer’s inability to maintain a consistent
preference ordering that leads some sellers to impose severe financial penalties on buyers that
attempt to alter or withdraw from a planned transaction (e.g., airlines charge ticket switching
fees, vacation lodging services charge cancellation fees).
The instability of consumer preferences in time-based decisions has been interpreted as
evidence that consumers discount goods in a non-constant (e.g., hyperbolic) fashion. This
functional form, steeper at shorter delays than at longer delays, implies that individuals may
apply a much higher discount rate to benefits or costs to be experienced in the present than to
those to be experienced in the future (cf. Ainslie 1975; Kirby 1997). For example, people are
known to prefer $100 today over $115 in one week, but prefer $115 in 53 weeks over $100 in 52
weeks. Yet, if people discount hyperbolically, they should also prefer a decreasing sequence of
future benefits to an increasing sequence of future benefits, provided the sums of the future
benefits are constant. Contrary to this prediction, there is overwhelming evidence that people
2
prefer an increasing salary structure to a decreasing salary structure (e.g., Loewenstein and
Sicherman 1991) and, when given tickets to a low quality and a high quality restaurant, prefer to
go to the low quality restaurant first (e.g., Loewenstein and Prelec 1993). These results suggest
that some goods may be discounted negatively, that discounting processes may be highly
sensitive to context, or that a unified theory of how time affects intertemporal decision-making is
not possible.
One strategy for addressing the confusing array of findings on temporal discounting, and
extending these findings to offers consisting of delayed benefits and costs, is to consider the
locus of temporal discounting effects on the valuation process. Time delays may exert their
influence during perception, integration processes, or the response processes. To date, these
points of influence have not been distinguishable due to the nature of the offers studied in
temporal discounting. Many studies have used only single-attribute offers (i.e., assessed the
valuation of different sums of money at different delays) or have used situations that confound
delay with the nature of the different attributes (i.e., assessed the valuation of a good requiring a
single up-front investment in return for future benefits). Neither of these designs allows us to
draw inferences about the locus of intertemporal discounting.
The current research focuses on understanding how people judge the present value of an
offer having a single benefit and a single cost, which we will refer to as a simple mixed offer.
We begin by presenting models that illustrate different loci of temporal discounting effects. We
then review prior research on temporal discounting and integrate this research using a series of
models. We use three studies to determine the locus of temporal discounting. In experiment 1,
we assess whether previous violations of assumptions about temporal discounting generalize to
simple mixed offers. In experiments 2 and 3, we show that that the more important attribute (e.g.,
3
benefit or cost) in the present becomes relatively less important in the future and that this change
in relative importance affects whether a person prefers an immediate or delayed transaction.
TEMPORAL VALUATION
The literature on temporal valuation is complex and disjointed. Temporal valuation
research has produced a large number of interesting phenomena, but few broad theories that can
explain all, or even a sizable number of phenomena. One reason for the disjointed state of the
literature is that researchers often fail to consider the process by which temporal differences
influence consumer evaluations. In what follows, we describe a general framework for the
evaluation of simple mixed offers. The framework represents valuation as a series of component
processes and has been used fruitfully to study phenomena as diverse as social judgment (cf.
Anderson 1981), memory (cf. Anderson 1996), and context effects (cf. Cooke and Mellers 1998;
Lynch, Chakravarti, and Mitra 1991). In this article, we consider how temporal delay might
influence the various stages of this framework.
Figure 1 presents a schematic view of the valuation framework for simple mixed offers.
For example, suppose a consumer is considering vacation cruises that vary in “days at sea” and
“price”. The benefit attribute levels can be designated by Φ Bi , where B refers to the benefit and i
refers to the level of the benefit, and the cost attribute levels can be designated by Φ C j , where C
refers to the cost and j refers to the level of the cost. Perception processes give rise to
psychological scales representing the level of the benefit and cost attributes on a sensory scale
( S Bit , SC jt ). In the integration process, the sensory scale values for each attribute are combined to
form an overall subjective impression of the simple mixed offer, also called an integrated value
( Ψ ijt). In the response process, the integrated value is used to produce an overt response (Rijt)
4
(e.g., rated attractiveness of the cruises, reservation price of the cruises, or choice of a cruise).
Temporal delay may affect the relationship of separate attributes levels to their sensory scales,
the manner in which different sensory values are weighted and integrated, or the generation of an
overt response, possibilities that are represented by subscripting the relevant values according to
time (t). In the next section, we examine the system of relationships and specify the possible
effects of delay on each of these processes.
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Place Figure 1 about here
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Loci of Temporal Discounting
Perceptual Process. One possibility is that a delay affects the perception of attribute
levels. We assume that attribute levels are valued in a way that exhibits diminishing marginal
sensitivity to changes in attribute level, consistent with a large body of work in both economics
(e.g., Samuelson 1976) and psychophysics (e.g., Stevens 1957). For simplicity, we will represent
this relationship using a logarithmic function.1 We also assume that sensory scales are discounted
hyperbolically (Ainslie 1975; Kirby 1997).2 Collectively, we represent scales as:
S Bit =
ln( Φ Bi )
1+ αB ⋅t
; S C jt =
ln( Φ C j )
1 +αC ⋅ t
(1)
Φ Bi and Φ C j represent level i of the benefit and level j of the cost, both consumed at delay t.
S Bit and SC jt represent the sensory scale values corresponding to the attribute levels. The
1
We could assume any functional form for mapping attribute levels to sensory scale values. The logarithmic
function is a common assumption in information integration models.
2
Loewenstein and Prelec (1992) use a generalized hyperbolic form ( d (t ) = (1 + α t ) − β / α ), α , β > 0 which includes
exponential discounting (when α → 0, d (t ) = e − β t ) and non-discounting (when α = β → 0, d (t ) = 1 ) as special cases.
For simplicity, we chose the more specific hyperbolic representation. This assumption can generally be relaxed with
little impact on our predictions.
5
denominator of each function allows for the possible discounting of these scales values
according to delay. If α B > 0 , subjects discount the benefits according to delay, and if α C > 0 ,
subjects discount the costs according to delay. Two special cases of equation 1 are of particular
interest. When α B = α C = 0 , the individual’s perceptions of attribute levels are insensitive to
delay. When α B = α C > 0 , the individual discounts his or her perceptions of costs and benefits
to the same degree, a condition that is indistinguishable from the post-integration discounting we
discuss later.
Integration Process. A second possibility is that delay influences the weights used to
integrate sensory scale values. We assume that the integrated value of a simple mixed offer can
be represented by a weighted sum of the benefit and cost scales as follows:3
Ψijt = wt ⋅ S Bit + (1 − wt ) ⋅ S C jt
(2)
Delay could conceivably affect the relative weights of the attributes in a variety of ways. For
instance, some theorists have proposed that delay causes people to over-emphasize benefits
relative to costs (Akerlof 1991; Mowen and Mowen 1991). We can represent this hypothesis by
(1 − w ∗ )
wt = 1 −
(1 + β ⋅ t )
(2a)
where wt is the relative weight of the benefit attribute with delay, w* is the relative weight of the
benefit attribute with no delay, and β represents the rate at which weights change with delay.
It is also possible that delay causes people to under-emphasize benefits relative to costs.
In this case, a delay reduces the relative weight (w* ) of the benefit attribute with no delay:
3
The use of an averaging functional form does not imply subadditivity because integrated values feed into a
response function. Thus, a benefit of $10 and a cost of $8, in the present, might be perceived as sensory values of 10
and –8 and an integrated value of 1 (assuming benefit and cost weights of .5 and no discounting), but be expressed
as an overt response of $2 owing to the response function (i.e., Rijt = 2 * Ψ ijt ). Note that the gamma coefficient in the
response function (discussed subsequently) is equivalent to the number of attribute scales being summed.
6
wt =
w∗
(1 + β ⋅ t )
(2b)
A third possibility is that relative integration weights become more moderate (i.e., closer
to equal weighting) with delay:
wt = .5 +
( w ∗ − .5)
(1 + β ⋅ t )
(2c)
Of course, if people integrate benefits and costs in a time-insensitive manner, their behavior can
be represented equally well using any of equations 2a, 2b, or 2c where β = 0. We refer to this
model (2c) as the weight moderation hypothesis.
Response Process. A final possibility is that delay influences the response process.
Although it is common for researchers to make particular assumptions regarding the nature of the
response process (e.g., linearity), we will assume only monotonicity. Simple mixed offers that
have a higher overall subjective value, Ψ γ ijt, will result in a higher overt response, Rijt. We can
represent this relationship by

Rijt = f 
Ψijt
1+ γ


⋅ t 
(3)
where f is the monotonic function relating overall subjective values to responses and γ is a
discount rate applied to the response function. As with the other processes, when γ equals zero,
the response process is deemed insensitive to time.
Ordinal Preference Reversals. The key benefit of this framework is that it allows us to
represent specific hypotheses regarding the loci of temporal discounting as special cases of the
model and to examine the predictions of each hypothesis. If delay influences either the
perception (equation 1) or the integration process (equation 2), there can be time-based ordinal
reversals of preferences for the available alternatives. For example, suppose that delay affects
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only relative weights in the integration process and does so according to equation 2a. In this case,
the relative weight on the benefit attribute increases with delay, implying that benefits have a
greater effect on the valuation of simple mixed offers with longer delay. This predicts ordinal
reversals of a particular sort: people will value a low benefit / low cost offer more than a high
benefit / high cost offer at short delays, but value the high benefit / high cost offer more at long
delays. If the relative weight on the benefit attribute decreases with delay, as in equation 2b,
people should prefer the high benefit / high cost offer at shorter delays, but prefer the low benefit
/ low cost offer at longer delays.
If delay only influences the response process (equation 3), there cannot be time-based
ordinal reversals of preference. This hypothesis, which we refer to as post-integration
discounting, implies that γ > α B = α C = β = 0 . Post-integration discounting predicts that the
value associated with a simple mixed offer will decrease as delay to consumption increases, but
that this discounting will not alter the ordering of the alternatives. In other words, if mixed offer
A is preferred to mixed offer B with no delay (i.e., immediate consumption), mixed offer A will
also be preferred to mixed offer B when the consumption of each is delayed by the same amount
of time. Next, we discuss how particular empirical results in the temporal valuation literature can
be represented in the valuation framework.
Key Findings in Temporal Valuation
Discounted Utility. The oldest formal account of temporal valuation is given by
Samuelson (1937). Samuelson claimed “that all of the disparate motives underlying
intertemporal choice could be condensed into a single parameter, the discount rate” (Frederick et
al. 2002, p. 355). Samuelson’s (1937) Discounted Utility (DU) model was the first to formalize
the discounting assumption, although Samuelson himself argued the discounting model was
8
neither descriptive nor normative (cf. Frederick et al. 2002). Samuelson proposed that the current
value of a good consumed later could be represented by the full utility of the good, multiplied by
an exponential discount factor. The exponential function was chosen for its similarity to the
compound interest formula and the ease with which it could be derived from axioms (Koopmans
1960), and was soon adopted as a normative standard for temporal valuation.
Although Samuelson (1937) did not specify the process that was affected by a temporal
delay, the fact that he applied the discount factor to aggregate goods suggests a post-integration
formulation (i.e., discounting occurs in the response function). In other words, DU could be
represented within our framework if γ > α B = α C = β = 0 and if the form of the discounting
function was exponential rather than hyperbolic. A critical prediction of this post-integration
formulation is that there will be no systematic changes in preference orders among alternative
offers with delay. Regardless of the form of temporal discounting, post-integration theories
predict that if mixed offer A is preferred to mixed offer B with no delay, it will also be preferred
at all delays.
Violations of Dynamic Consistency. Dynamic consistency represents a more restricted
form of the post-integration theory prediction about preference orders: if single attribute offer A
is preferred to single attribute offer B with no delay, it will also be preferred at all delays. Strotz
(1956) provided one of the first challenges to the prediction of dynamic consistency. Strotz
showed that people were willing to give up large amounts of value to speed consumption in the
near future (e.g., prefer $100 today over $115 in one week), but small amounts of value to speed
consumption in the distant future (e.g., prefer $115 in 53 weeks over $100 in 52 weeks). This
preference reversal with single attribute offers is informative because it fixes the locus of the
discounting in perception or the response process, as it is assumed that there are no integration
9
weights. Violations of dynamic consistency have been used as evidence of a non-constant
discount function having a steeper slope for short time periods and a flatter slope for long time
periods; a discount function that has been described as hyperbolic (Ainslie 1975; Kirby 1997). In
effect, hyperbolic discounting can be viewed as a response function account of dynamic
inconsistency.
Rate-Period Equivalence. Although a hyperbolic discounting can be used to explain
many violations of dynamic consistency, it does make one prediction that is often violated.
Hyperbolic discounting implies rate-period equivalence, the property that a specific time delay
will result in a common discount rate for two different single attribute offers, provided these
offers are judged in the same context. Contrary to this prediction, people discount gains (e.g.,
require an additional $3 to delay a $5 gain by a week) more than losses (e.g., forego an
additional $1 to delay a $5 loss by a week), will pay less to speed the receipt of a gain (e.g., pay
$54 to speed the delivery of a VCR by a year) than they require to delay the receipt of a gain
(e.g., require $126 to compensate for a delay in the delivery of a VCR by a year), and overweight
concrete attributes (i.e., attributes used to assess feasibility) and underweight more abstract
attributes (i.e., attributes used to assess desirability) in the present relative to the future
(Liberman and Trope 1998; Loewenstein 1988; Thaler 1981). Moreover, the discrepancy in these
discount rates increases, rather than decreases, in within-subject experimental designs (cf.
Frederick et al. 2002).
Violations of rate-period equivalence can be interpreted in two ways. First, they may
imply that delay affects the perception of different attributes differently (i.e., α B ≠ α C > 0 ). For
example, a cost may be discounted at a higher (or lower) rate than a benefit. Second, they may
imply that attribute integration weights are adjusted at different rates (see equation 2). For
10
example, Akerlof (1991) hypothesized that people procrastinate because the relative importance
of a cost becomes smaller in the future (i.e., people assume it will cost less to perform the task
tomorrow than today). Similarly, Mowen and Mowen (1991) propose that people overweight
losses (costs) and underweight gains (benefits) in the present, but that the loss dimension
becomes significantly less important than the gain dimension in the future. The observations of
Akerlof (1991) and Mowen and Mowen (1991) are consistent with integration weight
adjustment, as exemplified in equation 2a.
EXPERIMENT 1
Our initial investigation focused on the valuation of a set of simple mixed offers and the
possibility that discounting occurs in the response function. Subjects were asked to consider sets
of nine offers that (1) consisted of a positive and a negative attribute, (2) could be grouped into
three net positive, three net neutral, and three net negative valuations in the present, and (3)
varied the magnitude of the offers in a given group. For each offer, we asked the respondent to
indicate whether she/he preferred to purchase the offer in the present or the future.
If respondents engage only in post-integration discounting of mixed offers, they should
exhibit rate/period equivalence (i.e., γ > α B = α C = β = 0 ) and exhibit three patterns of
response. First, respondents should show an increasing preference to transact for a positive netcurrent-value offer in the present as the magnitude of the value becomes more positive. This
preference can be attributed to higher magnitude positive integrated values being discounted
more with a delay. Second, respondents should show a decreasing preference to transact for a
negative net-current-value offer in the present as the magnitude of the value becomes more
negative. Again, delays should have more impact on higher magnitude negative integrated
11
values. Third, respondents should be indifferent between consuming a neutral net-current-value
offer in the present or future. If the integrated value is neutral, then post-integration discounting
cannot change the value.
Method
Design. The experiment used a benefit (low, medium, high) by cost (low, medium, high)
within-subject design with six replicates (Caribbean cruise, professional cleaning, paid
experiment, movie discount card, part-time job, clothing store sale). For each of the nine offers
in each of the six replicates, respondents were asked to indicate whether they preferred to
purchase each product/service in the present or after a delay.
Stimuli. We developed and pre-tested six scenarios with positively and negatively valued
attributes (see appendix). Each benefit and cost was operationalized at three different levels. For
example, a scenario involving a Caribbean cruise varied the number of nights at sea (four, six, or
eight) and the price level ($899, $1,099, or $1,299). The nine combinations of benefits and costs
for the cruise replicate are shown in table 1 along with an illustration of the hypothesized sensory
scale values for a given level of an attribute. Options above the diagonal (f, b, and c) were
expected to have positive current values (Rij0 > 0 for all i > j), options on the diagonal (a, e, and i)
were expected to have neutral current values (Rij0 = 0 for all i = j), and options below the
diagonal (h, d, and g) were expected to have negative current values (Rij0 < 0 for all i < j). Note
that the current values in table 1 are meant to illustrate the intended relationship between the
values of the offers, an assumption that will be verified with a manipulation check.
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Place Table 1 about here
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Procedure. The entire experiment was conducted using a computer program. At the
beginning of the experiment, respondents made choices for a practice scenario in order to
familiarize themselves with the task. After the practice task, a scenario was randomly selected
and the respondent was given an introduction to the scenario followed by a description of the
levels of the benefit and cost attributes. This description included a presentation of the worst and
the best offers available in order to create judgment anchors and decrease noise in the data. Then,
the nine choices for a replicate were randomized per respondent and presented one at a time on
the computer screen. On each trial, respondents chose between purchasing the offer immediately
(or after or negligible delay) or after a considerable delay. The side of the screen on which the
immediate and delayed offers were presented was randomized per choice. After choosing
whether they preferred an offer in the present or after a delay, respondents rated the
attractiveness of the offer in the present using a scale ranging from -100 to +100. This measure
was used as a manipulation check to confirm the pattern of values shown in table 1. After
making choices and providing attractiveness ratings for the nine offers in the first replicate, a
respondent followed the same procedure for the remaining five replicates.
Eighteen respondents participated in the experiment in exchange for extra credit in an
introductory marketing or statistics course. The experiment was conducted in a web-based
behavioral lab using a program designed to work remotely so respondents could participate from
home. Each respondent made 54 choices for a total of 972 choices.
Analysis and Results
The nine offers were classified into three types of current value (henceforth called the
current value factor); positive (offers f, b, and c), neutral (offers a, e, and i), and negative (offers
h, d, and g). The nine offers were also classified into three magnitude levels (henceforth called
13
the magnitude factor) of the current value (f, b, and c are the low, moderate, and high magnitude
levels in the positive net current value condition).
Manipulation Check. The manipulation check showed that respondents perceived the
current values of the offers in a pattern similar to that represented in table 1 (see figure 2). The
interaction of the current value and magnitude factors was significant for the attractiveness
ratings (F(4, 68) = 31.98, p < .05). A simple effect test showed that the attractiveness ratings
increased as the magnitude increased in the positive current value condition (Mf = 27.9, Mb =
38.6, Mc = 69.2; F(2, 16) = 76.01, p < .05). Likewise, the attractiveness ratings decreased as the
magnitude increased in the negative current value condition (Mh = -17.1, Md = -17.5, Mg = -56.5;
F(2, 16) = 25.49, p < .05). The attractiveness means did not vary significantly for the neutral
current value offers (Ma = 8.3, Me = 1.0, Mi = -0.9; F(2, 16) = 0.96, p > .10). The replicate factor
did significantly interact with the current value factor (F(10, 170) = 1.98, p < .05), but did not
significantly interact with the magnitude factor (F(2, 170) = 1.10, p > .10). The higher order
interaction was significant (F(20, 340) = 2.12, p < .05), but an examination of the pattern of the
univariate means indicated that these interactions were due to the degree of variation of the
slopes in the positive and negative current value conditions and not to changes in the sign of
these slopes.
An independent manipulation check employing a choice task provided additional
evidence that people perceived the net neutral alternatives as equally valued alternatives.
Twenty-six respondents were asked to choose between non-dominated. The choice proportions
of [e] over [a] ( πˆ = .485; z = -0.37, p > .10), [i] over [e] ( πˆ = .451; z = -1.23, p > .10) and [i]
over [a] ( πˆ = .482; z = -0.45, p > .10) were not significantly different from the 50% indifference
point.
14
Choice Data Analysis. Next, we conducted a repeated measures analysis of the choice
proportions (see figure 2). The interaction of the current value and magnitude factors was
significant (F(4, 68) = 12.90, p < .05). Follow-up tests showed preference for transacting in the
present increased as the magnitude increased in the positive current value condition ( πˆ f = .66,
πˆ b = .80, πˆ c = .88; F(2, 16) = 8.32, p < .05). Second, preference for transacting in the present
decreased as the magnitude increased in the negative current value condition ( πˆ h = .19, πˆ d = .18,
πˆ g = .07; F(2, 16) = 5.26, p < .05). Third, the preference for transacting in the present varied
with the magnitude of the neutral current value offers ( πˆ a = .60, πˆ e = .43, πˆ i = .28; F(2, 16) =
12.24, p < .05). Although the positive and negative current value results are consistent with postintegration discounting, the neutral current value results are not.
Additional analyses showed that the replicate factor did not significantly interact with the
current value (F(10, 170) = 0.82, p > .10) or the magnitude (F(2, 34) = .50, p > .10) factors. The
higher order interaction was significant (F(20, 340) = 1.83, p < .05), but again this interaction
was due to differences in the degree of the slopes for different replicates.
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Place Figure 2 about here
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Discussion
Experiment 1 was designed to assess whether people engaged in post-integration
discounting when valuing delayed simple mixed offers. Post-integration discounting implies that
a preference to contract for a neutral mixed offer in the present or the future will not depend on
the magnitude of the benefits and costs that are combined to create the mixed offer. Contrary to
this prediction, respondents preferred to contract for a low benefit / low cost mixed offer in the
present, but for a high benefit / high cost mixed offer in the future, even though these two mixed
15
offers were judged as equivalent in the present. The implication is that the effects of delay on the
valuation of simple mixed offers cannot be explained solely by changes in the response process.
Delay must also affect perception and/or the integration process.
Perception and the integration process allow considerable flexibility when describing the
nature of temporal discounting. Perception allows for the discount rate to be higher for the
benefit than the cost ( α B > α C ) or lower for the benefit than the cost ( α B < α C ) (see equation 1).
The integration process allows a delay to increase the relative importance of benefits (equation
2a), decrease the relative importance of benefits (equation 2b), or moderate the relative
importance of both attributes (equation 2c). Interestingly, the data from experiment 1 are
inconsistent with three of these five explanations. First, if the discount rate is higher for the
benefit than the cost ( α B > α C ), then high benefit / high cost mixed offers should be more
preferred in the present because delays discount benefits at a quicker rate. This prediction is
inconsistent with the choice share of high magnitude, neutral mixed offer (stimulus i) in
experiment 1 (see figure 2).4 Second, if a delay increases the relative importance of benefits
(equation 2a), then any mixed offer should be preferred with delay. This prediction is
inconsistent with the finding that the choice shares of the positive current value mixed offers
(stimuli f, b, and c), offered in the present, are above 50% ( πˆ = .77; z = 5.87, p < .05; see figure
2). Third, if a delay decreases the relative importance of benefits (equation 2b), then any mixed
offer should be preferred in the present. This prediction is inconsistent with the finding that the
choice shares of the negative current value mixed offers (stimuli h, d, and g), offered in the
present, are below 50% ( πˆ = .15; z = 9.57, p < .05; see figure 2).
4
The choice shares of the negative current value simple mixed offers are not diagnostic because differences in the
level of the benefit and cost are confounded with differences in the discount rates for benefits and costs.
16
The data from experiment do not differentiate between the two remaining accounts of
discounting. First, the discount rate may be lower for the benefits than for the costs ( α B < α C )
during perception, an explanation that is consistent with the choice share of stimulus (i), and the
pattern of choice shares for the neutral stimuli, in experiment 1. Second, integration weights may
become more moderate with delay (i.e., equation 2c). For example, if the cost attribute weight is
relatively larger in the present, and becomes more moderate in the future, then the preference for
consuming the neutral current value offer in the future should increase as the magnitude of the
current value increases. This is what we found in experiment 1. We address these two
explanations in experiment 2.
EXPERIMENT 2
The two remaining explanations of the observed temporal discounting are (1) a lower
discount rate for benefit scale values during perception and (2) a weight moderation hypothesis.
These explanations are not mutually exclusive because both perception and integration are
required to form an overall impression of an offer. This implies that it is possible to provide
evidence that (1) scale values are being differentially discounted with delay or (2) scale values
are being differentially discounted and integration weights are becoming more moderate with
delay. It is not possible to show that scale values are unaffected by delay, but that integration
weights become more moderate with delay (cf. Anderson 1981; Mellers and Cooke 1994). Thus,
the goal of experiment 2 was to assess whether integration weights are influenced by temporal
delay in a systematic fashion.
Our strategy was to observe how the ranges of the benefit and cost attribute ratings vary
over time and use it as evidence about delay-based changes in integration weights. If delays in a
17
transaction encourage only the discounting of the scale values (i.e., α B , α C > 0 ), then the range
of attractiveness ratings from the low level to the high level of both attributes should shrink as
the transaction becomes more delayed (see figure 3a). The range of attractiveness ratings should
shrink because transaction delays should result in a discounting of the value of all offers and a
reduction in the perceived difference between those values. However, if delaying a transaction
makes the more important attribute relatively less important and the less important attribute
relatively more important, then the range of attractiveness ratings for the more important
attribute should decline and the range of attractiveness ratings for the less important attribute
should increase (see figure 3b). Of course, this pattern of results can only be observed if the
impact of a change in the relative integration weights is greater than the impact of scale
discounting.
******************************
Place Figure 3 about here
******************************
Method
Design. The experiment was a delay (immediate/future purchase) by salience (benefit
weight larger/cost weight larger) by replicate set (replicates 1-3/replicates 4-6) by benefit level
(low/moderate/high) by cost level (low/moderate/high) design with three replicates. The weight
and replicate set factors were manipulated between-subjects while all of the remaining factors
were manipulated within-subjects.
Stimuli and Procedure. The stimuli were the same as in experiment 1. The key
experimental manipulation consisted of a salience manipulation to influence the importance
respondents assigned to the benefit and cost in the present. Prior to each set of nine ratings, we
presented a scenario that encouraged respondents to believe one attribute was more important in
18
the present. For example, in the cruise scenario respondents were asked to imagine that they
thought, based on their preferences and constraints, the number of nights was extremely
important (somewhat important) and that the price was somewhat important (extremely
important). After the salience manipulation, we provided respondents all levels of benefit and
cost along with the worst and the best offers. Then respondents were asked to rate the
attractiveness of each of nine combinations of attributes in the present, using a –100 (very
unattractive) to +100 (very attractive) scale, followed by ratings of the same nine combinations
of attributes in the future. After a practice replicate, respondents rated the present and future
combinations of three experimental replicates (replicates one through three or replicates four
through six). Thus, subjects made 54 judgments about experimental stimuli.
The order of presentation of each set of nine mixed offers was randomized per
respondent. One hundred and sixteen respondents received extra credit in an introductory
marketing or statistics class to participate in the experiment.
Analysis and Results
The critical analysis was performed on attribute ranges. For each respondent, ranges were
computed as the difference between the marginal means of the highest and the lowest level for a
given attribute. For instance, in the cruise scenario, the ranges of the benefit attribute were
computed by taking the difference of the marginal mean of the ratings of a four-night trip and an
eight-night trip. For the cost attribute, the ranges were computed by taking the difference of the
marginal mean of the ratings of $899 and $1,299.
Manipulation Check. A repeated-measures analysis confirmed the salience manipulation
interacted with the attribute factor for ratings in the present (F(1, 112) = 40.97, p < .05). When
the salience of the benefit attribute was manipulated to be larger than the salience of the cost
attribute, the range of ratings for the benefit attribute was larger (Mbenefit = 64.72) than the range
19
of the ratings for the cost attribute (Mcost = 39.60; F(1, 112) = 19.77, p < .05). When the salience
of the cost attribute was manipulated to be larger than the salience of the benefit attribute, the
range of ratings for the cost attribute was larger (Mcost = 72.91) than the range of ratings for the
benefit attribute (Mbenefit = 46.46; F(1, 112) = 21.21, p < .05).
Range of Ratings. The perceptual discounting hypothesis predicted a main effect of delay
on the attribute ranges. A test for the main effect of delay was not significant (F(1, 112) = 0.63, p
> .10) nor was the delay by attribute interaction (F(1, 112) = 0.47, p > .10).5 The weight
moderation hypothesis predicted a three-way interaction. Consistent with this prediction, the
salience by delay by attribute interaction was significant (F(1, 112) = 25.57, p < .05) (see figure
4). When benefits were salient, the average range of the attractiveness ratings of the benefit
attribute decreased from 64.7 in the present to 59.7 in the future (F(1, 112) = 4.56, p < .05) and
the average range of the attractiveness ratings of the cost attribute increased from 39.6 in the
present to 49.1 in the future (F(1, 112) = 7.49, p < .05). When costs were salient, the average
range of the attractiveness ratings of the benefit attribute increased from 46.5 in the present to
55.8 in the future (F(1, 112) = 15.45, p < .05) and the average range of the attractiveness ratings
of the cost attribute decreased from 72.9 in the present to 63.2 in the future (F(1, 112) = 7.57, p <
.05). This pattern of data is consistent with a process that depends on the delay-based moderation
of integration weights (equation 2c).
******************************
Place Figure 4 about here
******************************
5
We examined this interaction because the main effect of time could have been offset if one of the attributes was
discounted at a very small α.
20
Additional analyses for the influence of replicates showed that the salience by attribute
by replicate set (F(1, 112) = 4.08, p < .05), the salience by replicate set by replicate (F(2, 224) =
6.15, p < .05), and the salience by attribute by replicate set by replicate (F(2, 224) = 5.04, p <
.05) interactions were significant. An inspection of these interactions revealed that none of the
replicate means exhibited a pattern diverging from the one predicted by the weight moderation
hypothesis. More importantly, the delay factor did not interact with any of the remaining factors
(beside the predicted three-way interaction). None of the remaining two-way or higher-order
interactions were significant.
EXPERIMENT 3
In experiment 1, we found evidence that as the magnitude of a neutral benefit option
increased, people became less likely to prefer the option in the present than in the future. We
explained this result by assuming that the costs received larger weights than benefits in the
present and that these larger weights were moderated as the transaction was delayed. In
experiment 2, we showed that when costs (benefits) were more salient in the present, delaying
consumption made the range of ratings associated with the cost (benefit) attribute decrease and
the benefit (cost) attribute increase, a pattern of results that can only occur if time is influencing
integration weights. However, the changes in the range of attractiveness documented in
experiment 2 may not directly affect a consumer’s choice of when to consume a product.
Experiment 3 was designed to show that making cost (benefits) more salient in the present would
also influence preference for consuming a mixed offer in the present or in the future. In the
salient cost condition, we expected to replicate the results of experiment 1. In the salient benefit
condition, we expected that as the magnitude of a neutral benefit option increased, people would
21
be more likely to prefer the option in the present than in the future, reversing the results of
experiment 1.
Method
Design. The experiment was a salience in the present (benefit more important / cost more
important) by benefit (low / medium / high) by cost (low / medium / high) design with six
replicates. The salience manipulation was a between-subjects factor and all of the remaining
factors were within-subjects factors.
Stimuli and Procedure. The stimuli were the same as in the previous two experiments and
the procedure was a blend of experiments 1 and 2. For each combination of benefit and cost
attributes, respondents indicated whether they preferred to purchase a given offer in the present
or the future. As in experiment 2, the key experimental manipulation consisted of a salience
manipulation. After the salience manipulation, we provided respondents all levels of benefit and
cost along with the worst and the best offers. Then respondents chose between purchasing an
alternative in the present or the future. Twenty-three respondents participated in the experiment
in exchange for extra credit in an introductory marketing or statistics course.
Results
As in experiment 1, we classified the nine offers into three levels of current value and
three magnitude levels. We conducted a repeated measures analysis employing the choice
proportions as the dependent measures. The interaction of the salience, current value, and
magnitude factors was significant (F(4, 84) = 9.32, p < .05). An examination of the means
revealed that this interaction was due to the changes in the pattern of choices at different levels
of the salience factor. Since the net neutral level of the current value factor is the most diagnostic
22
to our predictions6, we focused our analysis on testing the effects of the salience manipulation
and the magnitude factor at the neutral level of the current value factor (see figure 5).
******************************
Place Figure 5 about here
******************************
A repeated-measures analysis of the choice proportions of the neutral current value
alternatives revealed a significant interaction between the attribute weight manipulation and the
magnitude factor (F(2, 42) = 9.13, p < .05). A simple effect test showed that when the cost
attribute was emphasized in the present, preference for the neutral current value offers in the
present decreased as the magnitude of the offers increased ( πˆ a = .58, πˆ e = .44, πˆ i = .31; F(2, 20)
= 4.36, p < .05). When the importance of the benefit attribute was emphasized in the present,
preference for the neutral current value offers in the present increased as the magnitude of the
offers increased ( πˆ a = .39, πˆ e = .61, πˆ i = .69; F(2, 20) = 4.36, p < .05). The replicate factor did
not interact with the magnitude factor (F(10, 210) = 1.74, p >.05) and these two factors did not
interact with the weight manipulation (F(10, 210) = 0.52, p > .05).
Discussion
Experiment 3 provides evidence that the relative importance of the benefit and cost
attributes in the present determines the direction of the delay-based adjustments to integration
weights. More specifically, it demonstrates that the more important attribute in the present
became relatively less important in the future and the less important attribute in the present
became relatively more important in the future. The changes in integration weights influenced
6
Results for alternatives with positive or negative current values are sensitive to the ratio of the benefit and cost
scale values, thus are not diagnostic. However, these alternatives were included in the stimulus set because they
created a context for the neutral current value stimuli.
23
whether people were willing to purchase in the present or the future. These results are consistent
with the hypothesis that a time delay moderates integration weights (equation 2c).
GENERAL DISCUSSION
Three experiments tested assumptions about the temporal valuation of simple mixed
offers. Unlike previous research, we investigated a multi-attribute context encompassing small
benefits / small costs, small benefits / large costs, large benefits / small costs, and large benefits /
large costs. Our results show that time-based discounting of integrated values is insufficient to
account for the temporal valuation of simple mixed offers. Likewise, our results are inconsistent
with the hypothesis that consumers simply discount product attributes using different discount
rates. Instead, we provide evidence that people (1) adjust the weights used to integrate attribute
values when offers are delayed, (2) decrease (increase) the integration weight of the more (less)
important attributes when offers are delayed, and (3) adjust the integration weights of the
attributes to a larger degree than they discount scale values.
Our results show that there are at least two drivers of purchase timing; the net current
value of the offer and attribute weights. First, people prefer to purchase attractive offers in the
present and delay the purchase of unattractive offers. While this finding is not surprising, it is
inconsistent with simplistic explanations about time discounting like the hypothesis that costs
(benefits) are discounted at a higher rate than benefits (costs). Second, people moderate their
integration weights as transactions are delayed. If benefits are more important for immediate
purchases, they will be weighted less with delay. This may explain why many people are
uninterested in receiving rain checks for out-of-stock items or fail to execute their plans to return
to make a purchase. If cost are more important for immediate purchases, they will also be
24
weighted less with delay. This may be one reason for the popularity of delayed payment
purchases.
The results provide insight into purchase timing decisions. Experiment 3 shows that
people are predisposed to purchase low cost / low benefit products in the near future when they
are overly concerned about costs but prefer to delay these purchases when they are not concerned
about costs. In contrast, contrary to much work on purchase deferral, people are predisposed to
purchase high cost / high benefit products in the near future when they are not concerned about
cost but prefer to delay these purchases when they are concerned about costs. Thus, our findings
suggest it may not be the case that people defer all purchasing in bad economic times and
accelerate all purchasing in good economic times. Instead, people may be selective in the types
of purchases they defer / accelerate. Especially interesting is the counter-intuitive prediction that
people may increase their propensity to purchase small ticket items in tough economic times,
independent of a substitution effect.
The results provide insight into some common findings about the influence of time on
valuation. First, consider the finding that people prefer $100 today over $115 in one week, but
prefer $115 in 53 weeks over $100 in 52 weeks. Suppose the one year delay is similar to the
delay in our studies and the one week delay in payment is perceived as a cost. If costs are more
important in the present, then the cost of an one week delay will have much less importance in
the future than in the present and people should shift their preference to the higher benefit option.
Similarly, consider the finding that people prefer an increasing salary structure. It could be
argued that salary is used to pay for living expenses, that living expenses are a cost, and that
costs are more important in the present. If weights moderate with time, the benefit (salary) will
become relatively more important in the future and people will prefer to have a higher salary in
the future.
25
A third implication derived from the proposed model is related to the idea of advanced
selling (Xie and Shugan 2001). Companies that have products exhibiting a superior value on an
underweighted attribute should benefit from advance selling their products. For instance, if a
company offers a better price but an inferior set of features in comparison to a competitor, and
price is an underweighted factor for a segment, our results suggest that this company would
benefit from offering its product in the future (i.e., advance sell).
Limitations. One limitation of our research is its focus on mundane, common products. In
other words, our benefit attributes do not lead to extreme pleasure and our cost attributes do not
lead to permanent damage. Thus, this research cannot comment on combinations of extreme
benefits and costs such as addiction (see Rachlin 1997 for a comprehensive review of models on
addiction). However, as Akerlof (1991) claims, the additive nature of the temporal decision
making biases may imply large, long-term consequences. For example, postponing a trip to the
dentist or doctor will lead to larger costs in the future. Likewise, many small biases in purchase
decisions may constrain one’s future access to options. For example, buying too many small
goods for immediate consumption (e.g., junk food) will limit one’s ability to purchase more
globally attractive alternatives (e.g., a car). Unfortunately, these simple maintenance activities
may be sensitive to contextual factors that alter the perceived importance of benefits and costs in
the present. However, the many types of costs (e.g., money, time, effort) and benefits (e.g.,
utilitarian or hedonic) applied in our studies cover a large range of time-related decisions.
A second limitation is that we focus on the issue of time as an exogenous variable. In
other words, people are not assessing trade-offs between time and different amounts of reward.
Although our approach allows for an unconfounded test of time-based trade-offs, it cannot
account for situations where time is an endogenous factor as discount function theories assume.
26
Future Research. We believe that future research should focus on the underlying
psychological mechanisms that lead people to adjust the weights of the attributes over time.
Future research should address issues such as attention, cognitive resources, context effects, and
motivational frameworks as mechanisms driving the time-based weight adjustments. For
example, when choosing in the present, people can be susceptible to contextual factors that make
an attribute more important and make choices sub-optimal. However, when making future
evaluations, it could be the case that contextual factors do not play a major role and people can
be less biased in their choices.
Another testable implication of the moderation hypothesis illustrated by equation 2c is
that the same pattern of results should be observed whether there is trade-off between a benefit
and cost or a trade-off between two benefits or two costs. In other words, the same pattern of
results should emerge if time delayed evaluations are made using attributes of the same valence.
For instance, we should expect the same sort of effects for alternatives that have two (or more)
positive (desirable) attributes or two (or more) negative (feasible) attributes, assuming people are
integrating sensory scale values.
27
APPENDIX
Caribbean cruise: # of nights = 4 nights, 6 nights, 8 nights; price = $899, $1,099, $1,299.
Professional cleaning: # of rooms cleaned = 1 room (bedroom), 2 rooms (bedroom + bathroom),
3 rooms (bedroom + bathroom + kitchen); price charged = $30, $60, $90.
Paid experiment: amounts = $3.00, $5.00, $7.00; duration = 45 minutes, 60 minutes, 75
minutes.
Movie discount card: amount of discount = 10% discount, 20% discount, 30% discount; # of
companies that will receive your personal data = 25 companies, 125 companies, 225 companies.
Part-time job: salary = $7/hour, $8/hour, $9/hour; # of weekends you have to work = 2
weekends/month, 3 weekends/month, 4 weekends/month.
Clothing store sale: amount of discount = 10%, 15%, 20%; # of people in line ahead of you = 5
people, 12 people, 19 people.
28
REFERENCES
Ainslie, George (1975), “Specious Reward: A Behavioral Theory of Impulsiveness and Impulse
Control,” Psychological Bulletin, 82 (July), 463-496.
Akerlof, George A. (1991), “Procrastination and Obedience,” American Economic Review, 81
(May), 1-19.
Anderson, Norman H. (1981), Foundations of Information Integration Theory, New York:
Academic Press.
Anderson, Norman H. (1996), A Functional Theory of Cognition, Mahwah, NJ: Erlbaum.
Cooke, Alan D. J. and Barbara A. Mellers (1998), “Multiattribute Judgment: Attribute Spacing
Influences Single Attributes,” Journal of Experimental Psychology: Human Perception &
Performance, 24 (April), 496-504.
Frederick, Shane, George Loewenstein, and Ted O'Donoghue (2002), “Time Discounting and
Time Preference: A Critical Review,” Journal of Economic Literature, 40 (June), 351-401.
Kirby, Kris N. (1997), “Bidding on the Future: Evidence Against Normative Discounting of
Delayed Rewards,” Journal of Experimental Psychology: General, 126 (March), 54-70.
Koopmans, Tjalling C. (1960), “Stationary Ordinal Utility and Impatience,” Econometrica, 28,
287-309.
Liberman, Nira and Yaacov Trope (1998), “The Role of Feasibility and Desirability
Considerations in Near and Distant Future Decisions: A Test of Temporal Construal
Theory,” Journal of Personality & Social Psychology, 75 (July), 5-18.
Loewenstein, George (1988), “Frames of Mind in Intertemporal Choice,” Management Science,
34 (February), 200-215.
Loewenstein, George and Drazen Prelec (1992), “Anomalies in Intertemporal Choice: Evidence
and an Interpretation,” Quarterly Journal of Economics, 107 (May), 573-597.
29
Loewenstein, George and Drazen Prelec (1993), “Preferences for Sequences of Offers,”
Psychological Review, 100 (January), 91-108.
Loewenstein, George and Nachum Sicherman (1991), “Do Workers Prefer Increasing Wage
Profiles?” Journal of Labor Economics, 9 (January), 67-84.
Lynch, John G., Dipankar Chakravarti, and Anusree Mitra (1991), “Contrast Effects in
Consumer Judgments: Changes in Mental Representations or in the Anchoring of Rating
Scales?” Journal of Consumer Research, 18 (December), 284-297.
Mellers, Barbara A. and Alan D. J. Cooke (1994), “Trade-offs Depend on Attribute Range,”
Journal of Experimental Psychology: Human Perception & Performance, 20 (October),
1055-1067.
Mowen, John and Maryanne Mowen (1991), “Time and Offer Valuations: Implications for
Marketing Decision Making,” Journal of Marketing, 55 (October), 54-62.
Rachlin, Howard (1997), “Four Teleological Theories of Addiction,” Psychonomic Bulletin &
Review, 4 (December), 462-473.
Rae, John (1834), The Sociological Theory of Capital, London: Macmillan.
Samuelson, Paul (1937), “A Note on Measurement of Utility,” Review of Economic Studies, 2
(February), 155-161.
Stevens, S. Smith (1967), “On the Psychophysical Law,” Psychological Review, 64, 153-181.
Strotz, Robert H. (1956), “Myopia and Inconsistency in Dynamic Utility Maximization,” Review
of Economic Studies, 23, 165-180.
Thaler, Richard (1981), “Some Empirical Evidence on Dynamic Inconsistency,” Economic
Letters, 8, 201-207.
Xie, Jinhong and Steven Shugan (2001), “Electronic Tickets, Smart Cards, and Online
Prepayments: When and How to Advance Sell,” Marketing Science, 20 (Summer), 219-243.
30
TABLE 1
SAMPLE STIMULI FROM EXPERIMENT 1
Cost
Hypothesized
Scale Value
SB[4 night]
+1
Benefit
SB[6 night]
+3
SB[8 night]
+4
(0)a
[b]
(+2)
[c]
(+3)
-3
[a]
[d]
(-2)
[e]
(0)
[f]
(+1)
-4
[g]
(-3)
[h]
(-1)
[I]
(0)
SC[ $899]
SC[$1099]
-1
SC[$1299]
a -- The values between parentheses indicate the offers’ integrated value.
31
FIGURE 1
VALUATION FRAMEWORK FOR
DELAYED SIMPLE MIXED OFFERS
Perception:
Φ Bi
Response:
Integration:
S Bit
Ψijt
ΦC j
R ijt
S C jt
NOTE. -- Φ are attribute levels, S are sensory scale values, Ψ are integrated values, and R are overt responses.
32
FIGURE 2
EXPERIMENT 1 RESULTS
Preference for Alternative in Present
100%
c = 69.2
b = 38.6
50
f = 27.9
0
a = 8.3
e = 1.0
i = -0.9
h = -17.1
d = -17.5
-50
g =-56.5
-100
Choice Proportions
Attractiveness Ratings
Current Values
100
c=88.0%
b=79.6%
75%
f=65.7%
50%
a=60.2%
e=42.6%
i=27.8%
25%
h=19.4%
g=7.4%
d=18.5%
0%
Low
Net Negative
Moderate
High
Stimulus Magnitude
Net Neutral
Net Positive
Low
Net Negative
Moderate
High
Stimulus Magnitude
Net Neutral
Net Positive
33
FIGURE 3
EXPERIMENT 2 PREDICTIONS
3b. Moderation of Integration Weights
Attribute Ranges
Attribute Ranges
3a. Perceptual Discounting
Present
Future
Attribute 1
Attribute 2
Present
Important Attribute
Future
Unimportant Attribute
34
FIGURE 4
EXPERIMENT 2 RESULTS
4a. Benefits Emphasized
4b. Costs Emphasized
80
80
70
64.7
60
49.1
50
40
59.7
39.6
30
Attribute Ranges
Attribute Ranges
72.9
70
63.2
60
50
55.8
46.5
40
30
Present
Benefit Attribute
Future
Cost Attribute
Present
Benefit Attribute
Future
Cost Attribute
35
FIGURE 5
EXPERIMENT 3 RESULTS
Preference for Alternative in Present
Choice Proportions
100%
75%
58.3%
68.5%
61.1%
50%
25%
38.9%
44.0%
31.0%
0%
Low-Low
Moderate-Moderate
High-High
Benefit-Cost Magnitude
Benefits Emphasized
Costs Emphasized