Agricultural Issues Center
University of California
August 2005
DRAFT
Money-Back Guarantees and the Value of Decision Time:
An Empirical Analysis
Amir Heiman, David R. Just, Bruce McWilliams, and David Zilberman
August 2005 Draft Paper
Amir Heiman is Senior Lecturer of Marketing, Faculty of Agriculture, Food and
Environmental Science, The Hebrew University of Jerusalem, Rehovot 76100, Israel (email: heiman@agri.huji.ac.il). David R. Just is Assistant Professor of Applied
Economics and Management, Cornell University, Ithaca, NY 14853 (e-mail:
drj3@cornell.edu). Bruce McWilliams is Assistant Professor of Marketing, Insitituto
Technologico Autonomo de Mexico (ITAM), Rio Hondo, No. 1, Col. Tizapan San Angel,
Mexico, D.F. 01000 (e-mail: bruce@itam.mx). David Zilberman is Professor of
Agricultural and Resource Economics and Member of the Giannini Foundation of
Agricultural Economics, University of California, Berkeley, CA 94720 (e-mail:
zilber@are.berkeley.edu).
Supported in part by the Agricultural Marketing Resource Center
Draft
Money-Back Guarantees and the Value of Decision Time:
An Empirical Analysis*
Amir Heiman, David R. Just, Bruce McWilliams, and David Zilberman
Amir Heiman is Senior Lecturer of Marketing, Faculty of Agriculture, Food and
Environmental Science, The Hebrew University of Jerusalem, Rehovot 76100, Israel (email: heiman@agri.huji.ac.il). David R. Just is Assistant Professor of Applied
Economics and Management, Cornell University, Ithaca, NY 14853 (e-mail:
drj3@cornell.edu). Bruce McWilliams is Assistant Professor of Marketing, Insitituto
Technologico Autonomo de Mexico (ITAM), Rio Hondo, No. 1, Col. Tizapan San Angel,
Mexico, D.F. 01000 (e-mail: bruce@itam.mx). David Zilberman is Professor of
Agricultural and Resource Economics and Member of the Giannini Foundation of
Agricultural Economics, University of California, Berkeley, CA 94720 (e-mail:
zilber@are.berkeley.edu).
*The authors acknowledge support from AgMRC for their financial support of this
research.
Draft
Money-Back Guarantees and the Value of
Decision Time: An Empirical Analysis
Abstract
This paper uses the disappointment aversion and prospect theory to estimate
consumers’ valuation of basic 30-day money-back guarantees (MBGs). We test how this
valuation changes when the duration of MBGs vary, risk increases (store versus catalog),
and return options change (store credit versus cash back) using data collected in Northern
California. Our results confirm that individuals do not evaluate MBGs using expected
benefit calculations but rather amplify its value similar to disappointment and regret
anticipation effects.
3
Draft
Money-Back Guarantees and the Value of Decision Time: An
Empirical Analysis
Tonning (1956) provides evidence of the earliest known money-back guarantee
(MBG) used in 1777 by a food manufacturer. Research on returns, or MBGs, is much
more recent, covering only the last 30 years. The research on MBGs has been mostly
theoretical and based on the assumption of one type of full return: a 30-day MBG. We
hope to provide empirical answers to two fundamental questions: What is the willingness
to pay (WTP) for an MBG? And what is the incremental WTP for an MBG with extended
duration?
We model MBGs as a put option, where the buyer can return the item and receive
a full refund. Throughout the life of the option, and beyond, the consumer faces risk as to
whether the item will be useful to the consumer or not, which we call fit risk. We develop
a modeling framework to address fit risk incorporating elements of Kahneman and
Tversky’s (K&T 1979) (and Tversky and Kahneman’s 1992) prospect theory model of
loss aversion into our option-value model. Our model assumes that individuals engage in
framing, classifying the return of a product with a refund of money as a loss. In addition
to the cost and hassle of returning a product, consumers experience additional costs of
returning a product due to disappointment or a feeling of loss resulting in an aversion to
returning a product. Finally, individuals weight probabilities of return or fit of a product
in a fashion similar to cumulative prospect theory.
Using data collected in Northern California, we test our model for consistency
with consumer behavior. Consistent with the option theory of MBGs, we find that
consumers’ valuation of MBGs depends heavily on the duration of the MBG agreement.
4
Draft
Consumers value return agreements for store credit significantly less than MBGs.
Further, we find that the data are highly consistent with loss-averse behavior. In fact, the
magnitude of the valuations seems only to be consistent with some cost of
disappointment from discovering a nonfit.
Our analysis suggests that standard 30-day MBGs are evaluated by purchasers to
be worth 25% of the price of a good. This premium appears to be outside of the
reasonable range of valuation if calculations are held assuming that consumers valuate
risky choices using the expected payoff notation. However, the phenomenon known as
loss aversion (or related phenomena), if taken into account, results in a concise and
reasonable explanation for this (over-)valuation of MBGs. The length of an MBG plays a
significant role in the valuation of MBGs. Products sold with store credit guarantees
(SCGs), which are a limited form of MBGs in which the consumer receives a refund of
store credit rather than cash, are valued at nearly 10% less than MBG products.
THE CURRENT LITERATURE ON MBGs
One of the distinctive features of U.S. retailing is its extensive use of postpurchase guarantees, which include extended warranties, price guarantees, and varying
return guarantees. The different post-purchase guarantees reduce the pre-purchase
uncertainty resulting from various sources and differ in many aspects, such as duration,
what events are covered, and how these events are compensated. These post-purchase
guarantees share the same basic goal of reducing uncertainty. There is a natural overlap
between the tools, each having its own distinct features. Warranties provide a guarantee
for durability and performance, but they do not resolve price and fit uncertainty. Price
and fit uncertainty are addressed by MBGs. Warranties and MBGs overlap during the
5
Draft
period of MBG coverage since, with MBGs, the most comprehensive guarantee, the
product can be returned for any reason, including mechanical failure for a limited
duration. While the subject of duration in warranties has been studied (Blair and Innis
1996), little is known about the effect of duration of MBGs on consumer behavior. One
of the goals of this study is to explore consumers’ valuation of the duration of MBGs
using the concept of real-option pricing, which was first applied to MBGs in Heiman,
McWilliams, and Zilberman (2001).
MBGs and other return policies are natural substitutes, where MBGs offer a wider
coverage, thereby increasing the possibility of moral hazard, and possibly imposing
higher costs on retailers than alternative policies. The tradeoff between MBGs and
returns for replacement with an identical item is discussed in Mann and Wissinik (1990),
who focus on moral hazard issues. Another form of return is the store credit guarantee
(SCG,) in which the relationship with MBGs has not been addressed.
MBGs dominate price guarantees that provide only limited protection against the
uncertainty of finding a retailer who sells the product for less. Researchers have proposed
various purposes for offering low price guarantees. Most of the literature explores the
influence of this tool on price strategy and its impact on the market for the purposes of
price collusion and discouraging price competition (see Chatterjee, Heath, and Basuroy
2003; Edlin and Emch 1999; Logan and Lutter 1989) or on the ability to price
discriminate between informed and uninformed buyers (Png and Hirshleifer 1987).
Others examine the possibility of using price guarantees to signal low prices to
consumers (Jain and Srivastava 2000). Alternatively, Inman, Dyer, and Jia (1997) study
price guarantees as a mechanism that decreases the likelihood of regret from having
6
Draft
chosen the wrong store. In this paper, we expand the notion of post-purchase regret to the
context of MBGs.
MBGs have been treated in the literature mainly as a signal of quality. Heal
(1977) modeled MBGs as a signal for product quality, and Moorthy and Srinivasan
(1995) as a signal for retailers’ quality of services. In this paper we adopt the view of
Davis, Gerstner, and Hagerty (1995) that MBGs are mainly tools that enable buyers to
experience the product before a final purchasing decision has been made. We ignore any
aspect of quality signaling, which may play a lesser role after gaining some experience
with brands or stores.
Surprisingly none of the above studies on MBGs supported their arguments with
empirical analysis (such as a consumer survey). Thus, we are still unaware of the basics
of MBGs, e.g., what is the consumer valuation of an MBG, and how is this valuation
affected by the duration of MBGs? This paper will provide an estimation of consumers’
valuation of MBGs in purchases of everyday clothing, and show how this valuation
changes as the duration of the MBG option varies as well as when MBGs are replaced by
SCGs. We also estimate the difference in valuation of MBGs between in-store and
catalog purchases. Several studies have noted significant differences in purchasing
behavior when consumers shop in stores versus through catalogs or the Internet (Bult and
Wansbeek 1995; Jasper and Ouellete 1994; Van den Poel and Leunis 1999; Voss,
Parasuraman, and Dhruv 1998). Here we build on this body of literature focusing on the
context of an MBG contract of fixed duration.
We analyze consumers’ valuation of alternative MBG arrangements within a
modeling framework that builds on K&T’s prospect theory (1979). In particular, we (1)
7
Draft
incorporate the notion of loss aversion (Thaler 1980) and assume that individuals place
extra emphasis on avoiding losses when synthesizing value, and (2) frame the risky
choices within a context, relative to an existing reference point. K&T (1979) and Thaler
(1985) established the concept of loss aversion with results of experimental studies where
individuals were asked to choose among lotteries. Here we assess loss aversion from data
on individuals’ WTP (or accept) for better (or worse) MBG terms. Loss aversion is
interpreted here as the extra cost (above product price) of being disappointed by a product
that does not fit. A longer MBG contract reduces the probability of being stuck with a
product as a result of a bad decision. A related concept is disappointment aversion,
introduced by Bell (1982) and modified by Gul (1991), whereby individuals avoid the
possibility of outcomes that fail to meet their expectations. Within the field of marketing,
anticipation of regret is credited with causing consumers to buy items currently on sale,
rather than wait for other more desirable items, and to buy more well-known brands
(Simonson 1992). In addition to the exaggeration of losses, loss aversion also implies a
systematic misperception of probabilities. It is generally found that individuals
exaggerate small probabilities, and underemphasize near certainties when making
decisions. This is particularly important in the context of returns, which are by nature a
low probability event for most purchases.
We use data collected in the San Francisco Bay area in California to estimate
consumers’ valuation of an MBG and changes in valuation as the duration of the MBG
increases or decreases, the form of compensation (money or store credit), and whether
purchases are ordered through catalogs or bought at stores. In addition to estimating
valuations of various features of MBGs using standard procedures with the data set, we
8
Draft
use the data to assess the consistency of individual choices with our theoretical
predictions.
In the next section we explore the existing literature on MBGs. We then outline a
mathematical model of MBG valuation. In the remainder of the paper, we describe our
survey data and discuss the estimation results.
THE MODEL
Suppose a consumer is considering the purchase of a product, the value of which
is unknown to the buyer. The consumer may be concerned with whether the product will
fit her lifestyle or particular need. For example, a consumer shopping for an item of
clothing may not be certain if it goes well with her other clothes. She may want to receive
some feedback from friends before making a final assessment. The assessment of fit takes
time, and the buyer may want to learn the properties of the new product and how it fits
this idiosyncratic need. When buyers purchase a product without an MBG and find that it
does not fit their needs, they lose money and also suffer from the disappointment of a
failed choice. MBGs provide a return option within a given period of time. Let the price
of the product with an MBG of duration t be denoted by Pt . The MBG allows the
individual to avoid the loss of the price paid for the product and the associated
disappointment. Yet, the buyer must still incur the cost of return, denoted by RC, and gets
back the initial price. For simplicity, we assume that the return costs do not vary with the
MBG duration (the time spent to return the product is the same no matter how long you
have owned the product).1
1
Heiman et al. (2002) develop a model where return costs vary with the MBG duration. Applying their
model here will add much complexity and provides little insight.
9
Draft
We will consider three outcomes resulting from the purchase of a product with an
MBG.
• Fit:
The buyer discovers that the product fits her needs and benefits from it.
• Return: The buyer discovers that the product does not fit her needs during the
guarantee period and returns it.
• Stuck: The buyer discovers that the product does not fit after the MBG expires.2
We assume that the consumer knows the probabilities of these outcomes under
various MBG arrangements. Let the probability of fit be denoted by FP, and let RPt
denote the probability of return (RP) for an MBG contract with a duration of t days. This
is the probability that the consumer discovers that the product does not fit his/her needs
within the MBG coverage period. The probability of being stuck with an unfit product
after the MBG expires is SPt = 1 ! RPt ! FP . We adopt elements of prospect theory and
the disappointment aversion literature to assess two issues that are crucial for our
empirical analysis: (1) The amount that consumers will be willing to pay (or receive) for
extension (reduction) of the length of the MBG return period, and (2) the parameters that
will lead a consumer to buy a product with an MBG of a specific duration. Following
K&T (1979), we will assume that when consumers assess a new prospect with or without
MBGs, they (1) simplify their choices; (2) evaluate new alternatives relative to a
benchmark (reference point) reflecting initial opportunities and treat gains and losses
differently; and (3) evaluate probabilities according to a probability weighting function
" (#):[0,1] $ [0,1] , representing the systematic distortion of probabilities as perceived by
!
10
Draft
the decision maker. While these are not subjective probabilities per se, individuals behave
as if the value of the probability weights were the true probabilities. Hence, for
convenience of discussing the effects of probability weighting, we will refer to " as
perceived probability. According to K&T (1979), the perceived probability increases with
p, small probabilities are overestimated, large probabilities are underestimated, and the
sum of perceived probabilities may be smaller than 1. Thus, "' ( p) > 0 , and that for p
( )
( )
( )
( )
less than some p , ! p > p , ! '' p < 0 , and ! p < p , ! '' p > 0 otherwise. For the
sake of this paper, we will assume that the point p such that " ( p) = p is larger than RP
(according to most estimates this should be true on average; see, for example, Wakker
1994).
To assess the value of change in the MBG duration, let t0 denote the duration of a
baseline MBG arrangement. Heiman et al. (2002) provide evidence that a 30-day MBG
is the most common option in the United States; thus, we set this as our reference point in
the empirical application. The price of the product with this MBG duration is Pt . Let
0
!Pt denote the change in the product price associated with a change in the MBG period
t
0
!
from t0 to t. Let !RPtt denote the change in the RP as the duration of MBG is changed
0
from t0 to t. A longer return period (t > t0 ) is likely to result in a larger return probability
!
( !RP
!tt > 0) and likely to lead to a higher price ( !Pt > 0). The higher return probability
t0
0
will reduce the probability that the consumer will be stuck with the unfit product (the
!
2
We assume implicitly that it is worthwhile for the buyer not to return the good at the end of the MBG
period before the extent of fit is resolved. The expected gain from discovery of fit is assumed to dominate
the cost of loss because of unfit.
11
Draft
change in probability is denoted by !SPtt and !SPtt = "!RPtt ). The consumer may lose
0
0
0
RC when discovering that the product is unfit, but she may still feel fortunate not to
suffer the loss of the entire investment and be stuck with the unwanted product, as would
occur once the MBG expires. When the MBG expires and the product does not fit, the
consumer incurs extra costs reflecting loss aversion (K&T 1979) or disappointment
aversion (Gul 1991). Let LC denote this extra cost of loss when the buyer is stuck with
the unfit product. A marginal increase in RP will decrease the value of the purchase
proportional to RC, but, through the associated marginal decline in SP, will also increase
the value proportional to Pt + LC . The overall net effect of a marginal increase of RP is
0
proportional to Pt + LC ! RC .
0
Thus, the overall effect of a change in value accompanying a change of the length
of the MBG duration is denoted by
"NBtt = "# (RP) tt (Pt0 + LC $ RC) $ "Pt # (1 $ RPt0 ) .
0
0
t0
The consumer will prefer the new MBG arrangement if !NBtt " 0. The price
0
change that will make the consumer indifferent to a change in the MBG duration is
(1)
"Pt =
t0
"# ( RP)tt (Pt0 + LC $ RC)
0
.
# (1$ RPt )
0
Equation (1) suggests that the maximal (minimal) amount that consumers will be
willing to pay (receive) for longer (shorter) MBGs is a product of the increase (reduction)
in the RP and the gain from returning an unfit product divided by the reference
probability of either having a fit product or getting stuck with an unfit one.
12
Draft
To illustrate the order of magnitude of the change in price, let us consider the case
where the reference price of the product is $40 and the return period is 30 days. Now
(
)
suppose the perceived RP under the initial arrangement, " RPt 0 , is 10% and assume
that longer return periods (say, 60 days) will increase the perceived RP, "# (RP) tt , by
0
(
)
3%. Suppose for now that the perceived probability of retaining the item, " 1# RPt 0 , is
75% (often it is assumed that " is sub-additive, or " ( p) + " (1# p) < 1 , reflecting a sort
of aversion to uncertainty). If the return cost is $5.00 and the loss aversion cost is $15,
then the extra amount one will be willing to pay is $2.00 (e.g., .03 x 50/.75 = 2.00). The
minimum discount the consumer will demand for eliminating the MBG is $6.67 (e.g., .10
x 50/.75). Alternatively, LC and the weighting function can significantly alter the WTP
for longer MBGs. For example, if LC = $30, then the extra amount the consumer will
pay for the extra MBG is $2.60 (e.g., .03 x 65/.75). One of the main purposes of our
empirical analysis is to estimate the order of magnitude of loss aversion.
From equation (1), we can derive several hypotheses about WTP for MBGs. It is
plausible to assume that the perceived probability of discovery that the product is unfit
and returning the product increases with the duration of the return period, but the
!
marginal effect declines, i.e., "# $ (RP)
t / "t > 0, " 2 #( RP) t / "t 2 < 0. Using these
t0
t0
assumptions and equation (1) suggests:
!
Hypothesis 1 (Positive value of expanded MBG duration). Marginal increase in
the length of the return period increases the price of the product with an MBG.
"#P t / "t > 0.
t0
13
Draft
Hypothesis 2 (Decreasing marginal value of MBG duration). This marginal
increase in price declines for longer return periods. ! 2 "Ptt / ! t 2 < 0 .
0
Since t may be negative, the first hypothesis implies that a shorter MBG duration
will reduce the price the consumer will be willing to pay for a product, and the second
hypothesis suggests that the marginal reduction in the value of the product increases as
the guarantee duration decreases. One of the implications of Hypothesis 2 is that the
WTP for an MBG arrangement that is t days longer than the base arrangement is smaller
than the willingness to accept (WTA) for an MBG that is t days shorter than the base
MBG. This form of WTP < WTA is the result of the declining marginal probability of
discovery and return of a nonfit as duration increases.
MBGs may exist in various forms. Our first two hypotheses apply to cases where
buyers at a brick and mortar store receive money when returning an item. We also
consider other situations. The first is bundling the return with purchases in the same
retailing establishment, i.e., store credit. The second is MBGs for remote purchases (mail
order, catalog, telephone, or online), which are referred to as catalog purchases.
Store credit MBG option. Let PtSC
denote the price consumers will be willing to
0
pay for the purchase of a good with a t 0 return period where the consumers receive store
credit equivalent to the price of the product upon returning the product. The difference
between store credit and cash MBG is that, in the event of return, the buyer gets store
credit instead of cash. Let sc(Pt ) < Pt denote the consumer’s valuation of the store credit
0
0
received for a product with price Pt . A store credit limits the buyer’s choice to shop
0
relative to a more general MBG.
14
Draft
Hypothesis 3(Store credit < cash). Consumers value store credit less than cash, the
difference being given by
"PtSC /C = PtSC # Pt = $ ( RPt )(sc(Pt ) # Pt ) < 0 .
(2)
MBG and catalog purchases. Buying via catalogs reduces search and purchase
costs and increases available choices. However, purchases are riskier as buyers are not
able to inspect and try the products before purchase. We will add ca to the appropriate
variables to denote purchasing from catalogs. Thus, we assume (1) the probability of fit
(and thus perceived probability of fit) for catalog purchases is smaller than for store
purchase, i.e., FPca < FP , (2) the return probability for catalog purchases is higher than
for store purchase, i.e., RPt " RPcat , and (3) the changes in perceived return probabilities
in any time period is likely to be greater for catalog purchases than store purchase, i.e.,
t
t
"# (RP) t2 < " # (PRca)t 2 . It is important to remember that the weighting function is
1
1
concave over this region, and RPt " RPcat . Thus, in order for
t
t
t
"# (RP) t2 < " # (PRca)t 2 to hold, it must be the case that "PRcat 2 is significantly
1
1
1
t
larger than "RPt 2 (enough to overcome the concavity of weighting). Equation (1) is
1
modified to derive the change in price that makes consumers indifferent to a change in
the duration of MBG contract in the case of catalogs to be
(3)
"Pcat =
t0
"# ( RPca)tt (Pcat0 + LCca $ RCca)
0
.
#(1$ RPcat )
0
Since we assume that perceived RP and changes in the perceived RP are larger with
catalog purchases than store purchases, return probability considerations will cause the
price of the products purchased through catalogs to be more responsive to changes in
15
Draft
MBG duration than the price of products purchased in stores. Consider the case where
Pcat0 = Pt0 and assume that LCca ! RCca is approximately equal to LC ! RC .
Hypothesis 4 (MBG catalog >MBG store). Consumer valuations change more in
response to changes in the duration of the MBG of products purchased through catalogs
than those in stores. Namely, !Pcatt > !Ptt for!t > t 0 :!!Pcatt < !Ptt for!t < t 0 .
0
0
0
0
Our data contain information on consumers’ WTP for extending the MBG
duration and their WTA for reducing the MBG duration of a product. We will use these
data to assess the consistency of individual choices with Hypotheses 1-4. Our data also
contain respondents’ recall of their historical RP. We will investigate whether differences
in the average RP among individuals will affect their valuation of changes in MBGs.
First, we derive hypotheses regarding the behavior of d!Pt / d RP under various
t0
durations and conditions of the MBG arrangements, using equation (1) and assumptions
about the relationships between the variables we observe, the stated average RP, which
we denote RP , and variables that affect !Pt .
t0
We assume that shoppers vary according to their shopping imprecision (denoted by
SI) and their loss aversion (LC). 3 Among individuals with the same LC, less precise
shoppers (with higher SI) have a: (1) higher average RP, ! RP/ !SI > 0 , (2) higher RP for
any MBG duration, and in particular for the baseline duration, !RPt / ! SI > 0 , and (3)
0
are more responsive to changes in the duration of the MBG, " #RPt0 / "SI > 0 where
is
absolute value. These assumptions suggest that under plausible conditions, shoppers with
16
Draft
higher average RP are likely to have higher RP with the base MBG duration,
!RPt / ! RP > 0 , and larger changes in RP in response to changes in the MBG duration (a
0
larger increase in their perceived RP if the MBG duration is increasing and a larger
decline if the MBG duration gets shorter), so that
"#$ ( RP)tt / "RP < (> )0 for t > (< )0 .
(4)
0
Our second assumption is that shoppers face products with varying fit risk and
will not buy a product if the expected benefits of the purchase are not positive. If all
consumers have the same perception function, shoppers with lower loss aversion (smaller
LC) will buy more risky products (higher probability of a nonfit, and thus a higher RP),
as the positive benefit constraint is relaxed. The effect of changes in loss aversion on the
positive benefit constraint is especially strong for high levels of loss aversion. Thus, we
expect to find an inverse and concave relationship between the average RP, RP , and loss
aversion, LC. Thus, we suppose (see Heiman et al. 2005 for a more detailed treatment):
(5)
0!
"LC
"RP
; 0!
" 2 LC
"RP 2
.
To assess the impact of changes in average RP on the value of changes in MBG duration,
we differentiate (1) to obtain
!"Pt
(6)
t0
!RP
! % "# RP
'
= &
t
/ # (1 $ RP) (
*)
(Pt + LC $ RC) + "# RP
0
!RP
( )t
t
( )t
0
0
!LC
!RP
.
The assumptions represented by (4) suggest that the first element in the left-hand
side of (6) is positive, representing the shopper’s “imprecision” effect. Namely, the
3
Differences in return costs are assumed to be relatively less important than loss costs.
17
Draft
higher average RP reflects higher imprecision which induces increased (reduced) RP
when the MBG duration is increased (decreased) which, in turn, contributes to increased
WTP for longer MBG duration (and reduced WTA compensation for shorter MBG
duration). The second element of the right-hand side of (6) represents the loss aversion
effect of an increase in the average RP. The nonpositive relationship between average
RP and loss aversion, represented in (6), suggests that the impact of disappointment is
likely to become increasingly negative as the average RP increases. Since the shopper’s
imprecision effect is positive (for increases in the MBG duration) for all levels of RP and
due to the negative effect of the loss aversion actually growing for larger levels of RP,
!Pt is likely to be a nonlinear function of the average RP, which we approximate using
t0
a quadratic function.
Hypothesis 5: The WTP for longer duration MBGs, "Pt if t > t0 is
t0
approximately an increasing concave function of the average RP. The WTA for a
reduction in the MBG duration, "#P t if t < t0 , is approximately an increasing convex
t0
function of the average RP, i.e.,
(7)
!Pt
ah + bh RP "ch RP 2 if t > t0 and
!Pt
al " bl RP +cl RP 2 if t > t0 ,
t0
t0
where ah " 0,bh " 0,c h " 0,and al # 0,bl " 0,c l " 0 .
DATA AND ESTIMATION
In order to test the five hypotheses presented in the previous section, we used a
survey that was conducted between November and December, 2000. Respondents were
18
Draft
randomly chosen at various shopping malls in Northern California and were instructed to
assess their personal value of an item purchased with varying MBGs. On average, the
survey took about 10 minutes to complete. Of the 220 consumers interviewed, 48% were
male and 52% were female. The average age of respondents was 27, with 16 of them
below the age of 18. The oldest respondent was 76 years old.
The baseline MBG option was a 30-day MBG on a $40 item of clothing (shirt).
We asked for the discount required for no MBGs and for a 7-day MBG on the same
article of clothing, and the amount of money compensation they require to switch from a
30-day MBG to a 30-day SCG. We also asked for the individual’s WTP for a 60-day and
infinite-length MBG. These same questions were repeated for a $40 item of clothing
(shirt) ordered from a catalog. Individuals were asked to estimate the percentage of
clothing purchases they return (in store and through catalogs) during the last year.
Respondents on average demand a $10.43 discount to buy the $40 shirt that would
otherwise be offered with a 30-day guarantee, without any guarantee. At 25% of the
original product price, this assessment seems high. However, there is anecdotal evidence
leading us to believe that individuals are willing to pay high prices for guarantees.
Table 1 contains several examples of price differences in similar products that may be
due to differences in MBGs. In all cases we find large price differences for very similar
(if not identical products). In each case the MBG terms are very different and may
provide an explanation for at least part of the price difference. Although we have
attempted to use examples of stores with similar reputation and target customers, there
are always other explanations for these price differences. Other evidence can be found
during sales promotion. When items go on sale, they are typically discounted between
19
Draft
25% and 50%, and the MBG is eliminated. In this natural setting, consumers are used to
being compensated at least 25% for eliminating the MBG. In support of our survey
results, consumers are willing to pay very different amounts for nearly identical items
differing only in the MBG agreement.
The percentage of clothing items returned in stores (10.13% on average) and
through catalogs (18.63% on average) is similar to that reported in the professional
literature. We find that 16% of respondents report never having returned an item. The
literature reports the average percent of catalog purchases that are returned is 5%, but
there is a large variance between differences in product categories and customers. Most
of the customers (67%) return less than 5% (Del Franco 2000a), but the return rate for
first-time online shoppers can reach 35% (Del Franco 2000b). The categories of goods
with the lowest return rates include CDs and books at 2%-5%. Shoes have return rates of
10%-25%, clothing 10%-20%, and tailored apparel an astounding 30% (Catalog Age
2002; Del Franco 2000a). In the latter category (apparel), returns of fitted (high fashion,
designer dresses) is more than double that for casual apparel and can reach 40% for some
items. A higher price is probably an additional motivation for making returns in apparel.
The most common reasons for return are wrong size and color (Catalog Age 2002).
These figures are very close to online returns as reported by Quick (2000), who indicated
a 30% return rate in apparel, 20% in shoes, and 15% in jewelry.
Figure 1 displays the great heterogeneity of behavior within our sample with
respect to average RP. While the largest group returns fewer than 5% of their clothing
purchases, there are still a significant number that return more than 20% of their clothing
purchases. Similarly, we find significant heterogeneity in the discount required when no
20
Draft
MBG is offered. While 6% of shoppers value the MBG at less than $5.00, more than 50%
demanded a discount that was above $10. Such diversity underlines the notion that
individuals may have very different abilities to predict fit, and adjust purchasing behavior
when MBGs are altered.
The discounts demanded by respondents for eliminating the MBG entirely were
quite heterogeneous. The average consumer demanded $14.96 off a $40 item if there
were to be no MBG, with a standard deviation of $13.56 (with 220 responses). The modal
response was $0, with 47 observations, the next most frequent response demanded a $10
discount with 40 observations. Responses were highly variable with nearly every whole
number between 0 and 15 represented. The maximum response was $40, suggesting that
individuals would not be willing to pay anything for the shirt if the MBG were not
offered.
Testing for Behavioral Consistency
There is a large literature documenting the failure of expected utility models, and
other models of rational behavior (see Camerer 1995 for a review). For this reason, it is
necessary to test our data for all available signs of consistency with our model’s
predictions. If the data suggest that individuals are not behaving according to our model,
it may be that individuals largely use MBGs as a simple signal and pay little attention to
details such as length or conditions under which the MBG is offered. Because
Hypotheses 1 through 4 are not conditional on the parameters of the model, it is possible
to test these hypotheses without estimating (1). While we appeal to the specific model to
justify our hypotheses, our hypotheses are stated in terms of comparing valuation to time.
21
Draft
Hence, the general nature of our hypotheses allows us to investigate their truth without
the use of data more specific to our model.
For each individual, we have recorded changes in WTP !MBG300 , !MBG307 ,
log
, for both in-store and catalog purchases, where the
!MBG3060 , !MBG30" , !MBGtt ,cata
,store
comparison group is the 30-day MBG (and, hence, !P3030 = 0 ). This information allows us
to construct data on the slope of each segment. We can then check directly for violations
of the four hypotheses, and use classical hypothesis testing to check for significant
violations. Let Si j = !MBGi j . Then the hypotheses discussed earlier imply the following:
t
Hypothesis 1 (Positive Value of Time): !Pt j for all j > i.
i
( ) < 0.
t
Hypothesis 2 (Decreasing Marginal Value of Time):
! "Pt j
i
!t
t ,SC
Hypothesis 3 (Store Credit Discount): "Pt,cash # 0 .
t ,cata log
Hypothesis 4 (Store versus Catalog): "Pt,store
>0.
K&T (1979) (among others) have noted that individuals tend to depress WTP and inflate
WTA when answering survey questions. This may cause Hypothesis 2 to appear to be
true, even if it is not, if we compare only line segments left of 30 days to those right of 30
days. The test we construct here overcomes this problem by also comparing different line
segments on the same side of the 30-day MBG (from 0 to 7, 7 to 30, 30 to 60, and 60 to
infinity). For the case of the infinite-length MBG, it is impossible to construct a slope.
However, if the segment between 30 days and 60 days has positive slope, then a finite
value for the infinite length MBG implies concavity. In the spirit of Camerer’s (1989)
tests of models of risk and uncertainty, we examine the primary testable hypotheses of
22
Draft
our model using individual data. Table 2 displays the number of violations and number of
possible violations for each hypothesis. While the table shows that a significant number
of individuals (37%) violate the hypotheses at least once, the violations occur less than
8% of the time. It would be hard to reject the notion that these violations were occurring
due to idiosyncratic errors.
By regressing the slope parameters on a constant, it is possible to test these
hypotheses using traditional hypothesis testing. We employ a regression structure rather
than direct means tests to take advantage of the correlated error structure from survey
data. Hence, we employ Zellner’s Seemingly Unrelated Regression (SUR) technique in
estimating the means. Results of this estimation appear in Table 3.
We can test Hypotheses 1 through 4 by jointly testing all restrictions included in
each individual hypothesis for rejection. However, this test holds little power and, indeed,
cannot be rejected for any of our hypotheses. A more powerful method is to test
independently for each possible failure, maintaining failure as the null hypothesis.
Hypothesis 1 (Positive value of MBG duration)
To test Hypothesis 1, we need only independently test the hypotheses that the
marginal value of MBG duration is declining between each individual duration (both instore and using a catalog). From the results in Table 3, it is obvious that we can reject a
negative slope for each possible line segment at any reasonable level of confidence (tvalues of 10.08, 10.33, 4.28, 7.72, 10.33, 12.69, 4.79, and 6.79).
Hypothesis 2 (Decreasing marginal value of MBG duration)
To test Hypothesis 2, we construct the Wald statistic for each of the consecutive
segments, with null hypothesis Si j < S kl for j < k (implying an increasing slope). A test
23
Draft
that the value of the infinite length MBG is not of infinite value is not interesting. This
test produces the test statistics F(1, 1630): 32.93, 65.24, 23.69, 109.02. All of these reject
at any reasonable level of significance.
Hypothesis 3 (Store credit < cash)
This hypothesis may be tested by using a null hypothesis that the value of the
SCG is greater than the 30-day MBG. From Table 3, it can be seen that these tests are
easily rejected for both in-store and catalog purchases at any level of significance (tvalues of 8.871, 11.256).
Hypothesis 4 (MBG catalog > MBG store)
Hypotheses 4 and 4A may be tested again using the Wald statistic to see if the
null hypothesis of Si j > C Si j for all j > i can be rejected. This test produces F(1,1630)
statistics of 1.02, 19.33, 1.54, and .50 in order of line segments. These produce p-values
of 0.16, 0.00, 0.10, and 0.24, respectively. Hence, while there is some support for this
claim, it is not as well supported by the data as are the other three hypotheses. In
particular, this may not hold for very short or very long MBGs.
HETEROGENEITY AND THE EFFECT OF DISAPPOINTMENT
To test Hypothesis 5 requires estimation of the relationship between RP and the
WTP/WTA for various length MBGs. Estimation in the previous section determines the
average value of a day over different lengths of MBGs ($0.67 per day for the first seven
days, $0.25 for the next 23, and $.07 for the next 30 days). In this section we wish to
outline how heterogeneous buyers can have differing valuations. We approximate the
relationship in equations (6) and (7) using the following form
24
Draft
(8)
!P30t =
&
t $0,7,60,%
(" + "
t
RPt
2
)
2
RP # t + " SCG# SCG + " + RP # t >30 + " ' RP # t (30 ,
where ! t is a dummy variable taking on the value 1 if the MBG duration is equal to t ,
and ! SCG is a dummy representing a 30-day SCG. The coefficients ! + , ! " represent the
quadratic effects of RP for longer and shorter MBGs, respectively. Table 4 reports the
results of the regression. Due to the nature of heterogeneity in the sample, we report
standard errors using White’s (1980) consistent correction.
The results in the table largely confirm Hypothesis 5. First, we find that the higher
RP increases the WTP for longer MBGs (positive signs for RP, t = 60, ∞), and decreases
WTA for shorter MBGs (negative signs for RP, t = 0, 7) and for SCGs. Further, we find
that the relationship is significantly nonlinear, with WTP concave in RP for longer
MBGs, and convex for shorter MBGs. This relationship is consistent with the prospect
theory and notion of disappointment we have proposed earlier. Similar results hold for
catalog purchases, with some important differences. First, in accordance with hypothesis
4, RP has a stronger interaction effect with duration on WTP for catalog purchases than
with in-store purchases. However, this result only holds for shorter duration MBGs. On
!
the contrary, the value of longer MBGs has less to do with RP for catalogs than in store.
In fact, it appears the value of the MBG for a catalog purchase is lower for durations
longer than 30 days. In other words, it appears the first few days of inspection are
extremely important and valuable. The nature of risk with catalog purchases behaves
somewhat differently however, resolving itself more quickly. This in itself seems a little
strange and may reflect a different set of expectations from catalog purchases, thus
altering the level of disappointment from a nonfit. The results from Table 4 can be can
25
Draft
be combined with average reported RP (10.13% in store and 18.63% through catalog) to
obtain the predicted value of various length MBGs. For example, the predicted WTA for
no MBG is $10.90. Alternatively, an individual with RP of 5% would have a WTA of
$10.30. Remarkably, it appears that the RP has little (yet still a significant) effect on the
valuation of the MBG. This again highlights the poor ability of individuals to deal with
probabilistic events, as they appear to only vaguely take account of the differences in
likelihood that they will need to use the MBG. The effect of RP is somewhat larger for
catalog purchases (here $12.11 vs. $12.98) but still reflects a very small impact. In
calibrating the probability weighting function, K&T (1979) note that probabilities smaller
than .3 tend to be overstated, in a way that would reduce the decline in perceived
probability as true probability tends towards zero. Thus, this result is very similar to the
prediction made by prospect theory. Table 5 contains predicted WTA and WTP amounts
for the average return percentage.
From the model, we can calculate both the implied
loss cost for a given WTP/WTA and stated RP, as well as the change in RP over time.
Equation (6) can be rearranged to find
(9)
LC " RC =
#P t $ (1" RPt0 )
t0
# $ ( RP) tt
" Pt0 .
0
If we let t = 0 , we know that " ( RP) t = #" ( RP) tt , and the stated RP. However, we
0
0
have not calibrated the probability weighting function. Other than the probability weight,
all variables in the right-hand side of (9) are known. If we consider return cost to be
!
negligible, and if we knew the probability weighting function, the calculation in (1)
yields a reasonable gauge of the cost of disappointment aversion. Further, given our
26
Draft
estimate of LC - RC , we can manipulate (6) to obtain an estimate of the change in RP
over time.
% # (1$ RPt )
(
0
"RPtt = # $1'
"P t + # RPt 0 * $ RPt 0 .
0
& (Pt0 + LC $ RC) t0
)
(
)
Table 6 contains estimates of both the loss cost and the RP over time predicted from our
estimates for various RPs. Tables 6A and 6B show that loss cost can be substantial for the
range of return probabilities found in our data. The results in the tables suggest that
probability weighting must accompany loss aversion in any reasonable explanation of the
( )
survey responses. Table 6A assumes that no weighting takes place (i.e., ! p = p ), and
Table 6B assumes the probability weighting function estimated in Tversky and
Kahneman (1992), namely,
&
p#
(
1 if "Loss"
( #
# #
( p + (1$ p)
" + ( p,x ) = '
p%
(
(
1 if "Gain"
%
( p% + (1$ p) %
)
(
)
(
)
where they estimate g = 0.61 and d = 0.69. In our case, a return is considered a loss,
while a fit is considered a gain. For the average range of RP from the survey (about
10%), the predicted loss costs are much more reasonable employing the weighting
function, $5.30 instead of $58. The multiplicative nature of probability in the value of the
option means that misperception in probability can greatly increase the option value of
the MBG, while not substantially increasing the true RP. This makes MBGs an especially
valuable tool to increase profits.
27
Draft
CONCLUSION
The importance of the MBG as a marketing tool is confirmed by their prevalence
in American retailing. In this paper we attempt to outline factors affecting the value of
MBGs and the size of these effects. These factors include the length of MBG, the ability
to examine a product prior to purchase, conditions placed on the recovered purchase
price, and the prior-return behavior. As well, we propose that many noted behavioral
anomalies may have a potentially large impact on the perceived value of an MBG. We
verify that the (1) length of an MBG, (2) aversion to loss, and (3) probability distortion
all play a significant role in the valuation of MBGs.
The results of our analysis display significant deviation from rational valuation.
Our statistical analysis suggests that a MBG may be worth 25% of the value of a product
on average. Because ex ante purchase values are systematically lower than ex post
purchase values (due to loss aversion), it may be possible for store owners to extract this
high value from the customer for purchase insurance. Table 6B suggests that for this
sample, loss aversion may dominate other purchase risk considerations, inflating a
modest cost of a nonfit. Individuals were asked to assess the value of an MBG for an
article of clothing. Clothing seldom comes with a performance warranty like those
offered with electronic equipment. One would expect an MBG to have a lower value if
other marketing mechanisms were used to insure against product failure.
Because the value of an MBG is increasing but concave in length, it stands to
reason that there must be an optimal length MBG for a particular marketer. Various
factors may affect this optimal length. We have found that higher income individuals are
willing to pay more for longer MBGs. This may explain why some high-end stores (for
example, Nordstrom’s) offer lifetime MBGs on their clothing. If such differences in value
28
Draft
are prevalent, MBGs might be used as a tool for price discrimination. In general, loss
aversion should lead marketers to provide extended-length MBG agreements, as
consumers overvalue the option to return relative to the marketers’ cost of a returned
item.
SCGs are less valuable than MBGs, particularly among the higher income groups.
Our estimates suggest the difference in value is nearly 10% of the price of the item. This
would suggest that stores should only use SCGs when more than 10% of their items are
returned without the customer purchasing another item. SCGs may increase the loss
aversion of the buyer as the purchases with the returned money are done for unplanned
and not budgeted items (Novemsky, and Kahneman 2005). This might be the case at
specialty stores or gift stores with a narrow selection. MBGs appear to have increased
value in shorter durations for catalog purchasing, where initial experience with the item is
delayed until after purchase.
Several areas of research are suggested by this study. Of prime importance is to
understand the heterogeneity in individuals’ evaluations of MBGs. A more thorough
analysis of socioeconomic factors affecting this valuation may allow marketers greater
ability to design optimal marketing tools. The analysis of other marketing strategies, for
instance, using MBGs together with performance warranties and in-store demonstrations,
may yield a more accurate picture of how individuals deal with purchasing risk. Larger
samples and data involving actual (rather than hypothetical) products would help
eliminate some of the biases inherent in this study. Beyond this, future research should
seek to quantify important variables such as return costs, and the factors affecting the
ability of individuals to return an item. Such an exploration may provide better insight
into the motivations of the higher income individuals we have noted here.
29
Draft
Table 1
Price Differences and Length of MBGa
Item
description
Women’s jeans,
MBG
Store 1
Walmart.com
MBG
Store 2
length
Price
length
Price
Price
No. of days
dollars
90
16.92
Kmart.com
30
10.19
51.11
19.99 -
Sears.com
90
10.80
59.69 -
No. of days dollars
difference
percent
regular fit
White dress
JCPenney.com
No limit
shirt (plain)
25.99
Men’s short-
Abercrombie
sleeve cotton
and Fitch
pique polo
online
No limit
39.50
a. All prices as of March 2, 2005.
30
82.58
Gap.com
14
19.99
65.59
Draft
Table 2
Violations of Hypotheses
Possible
Individuals
Hypothesis
Violations
violations
violating
Hypothesis 1
7
1776
5
Hypothesis 2
98
1332
64
Hypothesis 3
0
444
0
Hypothesis 4
66
888
42
All hypotheses
171
4440
82
The results are based on a total of 220 respondents.
31
Draft
Table 3
Estimated Values of Changes in MBG Duration and Conditions
Variable
Mean
Standard error
dollars
dollars
0.25
0.02
0.07
0.02
"
!P60,store
*
2.62
0.34
30,SC
!P30,cash
-6.78
0.76
7
!P0,cat
/ 7 MBG/day 1-7 cat
0.73
0.07
30
!P7,cat
/ 23 MBG/day 23-30 cat
0.35
0.03
60
!P30,cat
MBG/day 30-60 cat
0.08
0.02
"
!P60,cat
*
2.76
0.41
30,CSC
!MBG30,cash
"0
-8.95
0.79
30
!P7,store
/ 23 MBG/day 7-30
60
!P30,store
/ 30
*
MBG/day 30-60
Because a slope cannot be calculated, we estimate the average rise of
!MBG60" .
32
Draft
Table 4
Estimation Results for Willingness to Pay
Coefficient
Constant (t = 0)
30-day SCG
7-day MBG
60-day MBG
Infinity MBG
RP (t = 0)
RP (t = 7)
RP, SCG (t = 30)
RP (t = 60)
RP (t = ∞)
RP2 t < 30
RP2 t > 30
In-store estimate
-9.570***
(0.904)
5.460***
(1.034)
4.705***
(1.091)
10.813***
(0.989)
13.486***
(1.105)
-0.162**
(0.076)
-0.192***
(0.058)
-0.249***
(0.070)
0.121**
(0.055)
0.127**
(0.062)
0.003***
(0.001)
-0.002**
(0.001)
Catalogue estimate
dollars
-11.054***
(1.040)
5.674***
(1.266)
3.835***
(1.289)
12.393***
(1.141)
14.938***
(1.276)
-0.233***
(0.090)
-0.355***
(0.083)
-0.261***
(0.089)
0.102**
(0.057)
0.102
(0.067)
0.004***
(0.001)
-0.001*
(0.001)
33
Draft
Table 5
Predicted WTA and WTP for Average Probability of Return
Coefficient
In stores
With catalogs
dollars
WTA, no MBG
10.90
14.00
WTA with a 7-day MBG
6.50
10.95
WTP with a 60-day MBG
1.24
1.32
WTP with an infinite MBG
3.90
4.10
WTA with a 30-day store
credit
4.11
15.69
34
Draft
Table 6A
Calibrated Loss Cost and Change in Probability of Return over Time for Various RP
Assuming No Probability Weighting
In-store products
RP
WTA for no MBG
Loss cost
7-day MBG
60-day MBG
Infinity length MBG
5.000
10.305
155.795
10.000
10.890
58.010
15.000
11.325
24.175
-0.020
0.006
0.019
-0.038
0.011
0.036
-0.054
0.016
0.052
35
Catalogue products
dollars
20.000
5.000 10.000 15.000
11.610
12.169 13.184 14.099
6.440 191.211 78.656 39.894
Change in RP
-0.071
-0.030 -0.055 -0.077
0.021
0.006
0.010
0.014
0.067
0.016
0.029
0.041
20.000
14.914
19.656
-0.097
0.018
0.052
Draft
Table 6B
Calibrated Loss Cost and Change in Probability of Return over Time for Various RP
using Probability Weighting
In-Store Products
Catalogue Products
dollars
WTA for no MBG
Loss cost
5.000
10.305
26.537
10.000
10.890
5.2957
15.000
11.325
-4.199
7-day MBG
60-day MBG
Infinity length MBG
-0.039
0.019
0.053
-0.083
0.047
0.118
-0.128
0.080
0.181
36
20.000
5.000
11.610 12.169
-10.216 38.573
Change in RP
-0.175 -0.045
0.113
0.016
0.235
0.042
10.000
13.184
14.837
15.000
14.099
4.570
20.000
14.914
-1.740
-0.094
0.038
0.090
-0.144
0.064
0.135
-0.195
0.090
0.175
Draft
Figure 1
Distribution of Average Probability of Return
37
Draft
REFERENCES
Bell, D. (1982), “Regret in Decision Making Under Uncertainty,” Operations Research,
30, 961-81.
Blair, M. E. and D. E. Innis (1996), “The Effects of Product Knowledge on the
Evaluation of Warranteed Brands,” Psychology and Marketing, 13, 445-56.
Bult, Jan R. and Tom Wansbeek (1995), “Optimal Selection for Direct Mail,” Marketing
Science, 14(4), 378-94.
Camerer, Colin (1989), “An Experimental Test of Several Generalized Utility Theories,”
Journal of Risk and Uncertainty 2, 61-104.
---- (1995), “Individual Decision Making,” in The Handbook of Experimental
Economics, J. Kagel and A. Roth, eds. Princeton, NJ: Princeton University Press.
Catalog Age (2002), “Holiday Returns Rates Hold Steady For Most Mailers,” 19(3), 1.
Chatterjee, Subimal, Timothy B. Heath, and Suman Basuroy (2003), “Failing to
Suspect Collusion in Price-Matching Guarantees: Consumer Limitations
in Game-Theoretic Reasoning,” Journal of Consumer Psychology, 13,
255-267.
Davis, Scott, Eitan Gerstner, and Michael Hagerty (1995), “Money-Back
Guarantees in Retailing: Matching Products to Consumer Tastes,” Journal
of Retailing, 71(1), 7-22.
Del Franco, Mark (2000a), “Good News about Returns,” Catalog Age, 17(4) (March),
41-42.
---- (2000b), “Reducing Web Returns,” Catalog Age, 17(10) (September), 47.
38
Draft
Edlin, A. and E. Emch (1999), “The Welfare Losses From Price Matching Policies,”
Journal of Industrial Economics, 47, 145-68.
Gul, Faruk (1991), “A Theory of Disappointment Aversion,” Econometrica, 59, 667-86.
Heal, Geoffrey M. (1977), “Guarantees and Risk Sharing,” Review of Economic
Studies, 44 (October), 549-560.
Heiman, Amir, Bruce McWilliams, and David Zilberman (2001),
“Demonstrations and Money-Back Guarantees: Market Mechanisms to
Reduce Uncertainty,” Journal of Business Research, 54(1), 71-84.
Heiman, Amir, Bruce, McWilliams, Jinhua Zhao, and David Zilberman (2002),
“Consumer’s Valuation of Money Back Guarantee Option,” Journal of
Retailing, 78(23), 193-205.
Heiman, Amir, and David Zilberman (2005), “Incorporating MBGs with Prospect
Theory,” Working paper, Department of Agricultural and Resource
Economics, University of California, Berkeley.
Inman, J. Jeffrey, James S. Dyer, and Jianmin Jia (1997), “A Generalized Utility
Model of Disappointment and Regret Effects on Post-Choice Valuation,”
Marketing Science, 16, 97-111.
Jain, Sanjay and Joydeep Srivastava (2000), “An Experimental and Theoretical
Analysis of Price-Matching Refund Policies,” Journal of Marketing
Research, 37(3), 351-62.
Jasper, C. R. and S. J. Ouellete (1994), “Consumers’ Perception of Risk and the Purchase
of Apparel from Catalogs,” Journal of Direct Marketing, 8 (Spring), 23-36.
39
Draft
Kahneman, Daniel, Jack L. Knetsch, and Richard H. Thaler (1990), “Experimental Tests
of Endowment Effect and the Coase Theorem,” Journal of Political Economy, 98,
1325-49.
Kahneman, D. and A. Tversky (1979), “Prospect Theory: An Analysis of Decision under
Risk,” Econometrica, 47, 263-92.
Logan, J. and R. Lutter (1989), “Guaranteed Lowest Prices: Do They Facilitate
Collusion,” Economics Letters, 31, 189-92.
Mann, Duncan P. and Jennifer P. Wissinik (1990), “Money-Back Warranties vs.
Replacement Warranties: A Simple Comparison,” American Economic
Review, 80(2), 432-36.
Moorthy, Sridhar and Kannan Srinivasan (1995), “Signaling Quality with a
Money-Back Guarantee: The Role of Transaction Costs,” Marketing
Science, 14(4), 442-66.
Novemsky, Nathan and Daniel Kahneman (2005), “The Boundaries of Loss
Aversion,” Journal of Marketing Research, 42(2), 119-128.
Png, I. P. L. and D. Hirshleifer (1987), “Price Discrimination Through Offers to
Match Prices,” Journal of Business, 60, 365-83.
Prelec, D. (1998), “The Probability Weighting Function,” Econometrica, 60, 497-528.
Quick, Rebecca (2002), “E-commerce (A Special Report): The View from Above—
Return to Sender: Having a Physical Store Is a Big Advantage When It Comes to
Dealing with Dissatisfied Customers,” Wall Street Journal, New York (July 17).
40
Draft
Simonson, Itamar (1992), “The Influence of Anticipating Regret and Responsibility of
Purchasing Decisions,” Journal of Consumer Research, 19(1), 105-118.
Thaler, Richard (1985), “Mental Accounting and Consumer Choice,” Marketing Science,
4, 199-214.
---- (1980), “Toward a Positive Theory Consumer Choice,” Journal of Economic
Behavior and Organization 1(1), 39-60.
Tversky, A. and D. Kahneman (1992), “Advances in Prospect Theory: Cumulative
Representation of Uncertainty,” Journal of Risk and Uncertainty, 5, 297-323.
Van den Poel, Dirk and Joseph Leunis (1999), “Consumer Acceptance of the
Internet as a Channel of Distribution,” Journal of Business Research,
45(3), 249-56.
Voss, Glenn B., A. Parasuraman, and Dhruv Grewal (1998), “The Roles of Price,
Performance, and Expectations in Determining Satisfaction in Service
Exchanges,” Journal of Marketing, 62(4), 46-61.
Wakker, Peter P. (1994), “Separating Marginal Utility and Probabilistic Risk
Aversion,” Theory and Decision, 36, 1-44.
White, H. (1980), “A Heteroscedasticity Consistent Covariance Matrix Estimator and a
Direct Test for Heteroscedasticity,”Econometrica, 48, 817-38.
41
Draft
APPENDIX: LOSS COST AND THE PROBABILITY OF RETURN
Assume consumers vary in their loss cost (LC) and shopping imprecision (SI).
They face a product that costs Pt and provides value that is equivalent to X dollars when it
0
fits. The probability of discovering that a product is unfit when before or at t = t1 ,
conditional on an unfit product, is given by Ft (t = t1 ) , where Ft ( ) is a cumulative density
function. Let Z denote the probability of an unfit product purchased by a shopper, where Z
ranges in value from 0 to Z . When the product is purchased with t0 days of MBG, the RP
will be Ft (t0 )Z and the probability of being stuck with an unfit product is (1" Ft (t0 ))Z .
A product with MBG of t0 will be purchased if the expected benefit is greater than
0. Namely, if
(A.1)
! (1 " Z )(X " Pt0 ) " ! ( Ft (t 0 )Z )
RC " ! [ (1 " Ft (t 0 ))Z ]
(Pt0 + LC) > 0.
For every individual, there must exist a critical Z = ZC (LC) , representing the upper
bound of the probability of purchasing an unfit product. The net benefit of purchase at the
critical Z is zero. This critical Z is declining with LC. Differentiation of A.1 yields
(A.2)
" [(1# Ft (t0 ))Zc ]
dZc
=
<0
dLC #"' (1# Zc )(X # Pt ) # " ' (Ft (t 0 )Zc ) Ft (t0 )RC # " ' [(1# Ft (t0 ))Zc ](1# Ft (t 0 ))(Pt + LC)
0
0
[
]
The value of Z will vary for each item an individual will purchase. Let the distribution of
Z be given by g( Z | SI ) where SI is the shopping imprecision. The average RP for a
consumer with a particular SI is
Z C (LC)
(A.3)
!
suggesting that
RP = Ft (t0 )
"
0
42
Zg(Z | SI)dZ ,
Draft
(A.4)
Z C (LC)
#
&
dRP = % Ft (t0 ) " ZgSI (Z | SI)dZ ( dSI
%
(
0
$
'
Ft (t0 )ZC2 g(ZC | SI)* [(1) Ft (t0 ))Zc ]
)
dLC
* '(1) Zc )(X ) Pt0 ) + *' ( Ft (t0 )Zc ) Ft (t0 )RC + * ' [(1) Ft (t0 ))Zc ](1) Ft (t0 ))(Pt 0 + LC)
[
]
Thus,
Z C (LC)
&
dRP #%
= Ft (t0 ) " ZgSI (Z | SI)dZ ( > 0 ,
dSI %
(
0
$
'
or, increasing SI will increase the RP for a given length MBG.
We can also derive
Ft (t 0 )ZC2 g(ZC | SI)# [(1" Ft (t 0 ))Zc ]
dRP
="
< 0.
dLC
# '(1" Zc )(X " Pt 0 ) + # ' ( Ft (t0 )Zc )Ft (t0 )RC + # ' [(1" Ft (t 0 ))Zc ](1" Ft (t0 ))(Pt 0 + LC)
[
The relationships
]
dRP
< 0 and the concavity of RP over time results in Hypothesis 5.
dLC
43