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CONSUMER RESPONSE TO UNCERTAIN PROMOTIONS: AN EMPIRICAL ANALYSIS OF CONDITIONAL REBATES

Kusum L. Ailawadi a,*, Karen Gedenk b, Tobias Langer c, Yu Ma d, and Scott A. Neslin e

a Tuck School of Business, Dartmouth College, 100 Tuck Hall, Hanover, NH 03755, U.S., kusum.ailawadi@tuck.dartmouth.edu

b University of Hamburg, Welckerstr. 8, 20354 Hamburg, Germany, karen.gedenk@wiso.uni-hamburg.de

c 1618 N Campbell Ave #3, Chicago, IL 60647, U.S., tobias.langer@wiso.uni-hamburg.de

d University of Alberta, Edmonton, AB, T6G 2R6, Canada, yu.ma@ualberta.ca

e Tuck School of Business, Dartmouth College, 100 Tuck Hall, Hanover, NH 03755, U.S., scott.neslin@tuck.dartmouth.edu

* Corresponding author. Tel.: +1 603 646 2845; fax: +1 603 646 1308.

Note: Authors are listed in alphabetical order to reflect their equal contribution to the paper.

 

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ARTICLE  INFO  

Article  history:  

First received in August 31, 2012 and was under review for 3 ½ months.  

Area  Editor:  Olivier  Toubia  

 

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Acknowledgements:

The authors thank Neeraj Arora of the University of Wisconsin, Imran Currim of the University

of California, Irvine, Rakesh Sarin of UCLA, and session participants at the 2011 Marketing

Science Conference, 2012 ISMS Practice Conference, Universidad Carlos III de Madrid, KU

Leuven, and Tuck School at Dartmouth for helpful comments. They are also grateful to the AE

and reviewers for their valuable suggestions.  

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CONSUMER RESPONSE TO UNCERTAIN PROMOTIONS:

AN EMPIRICAL ANALYSIS OF CONDITIONAL REBATES

Abstract:

We formulate, estimate, and analyze a model of consumer response to promotions where

consumers’ receipt of the promotional reward is uncertain. The model incorporates consumers’

risk aversion and their subjective assessment of the probability that they will get the reward. It is

used to assess the effectiveness of a “conditional rebate”, where the uncertainty arises because

the reward is contingent on an external event, versus a traditional rebate, which is similar in all

respects except that it is certain. We estimate the model using a conjoint choice experiment.

Response to conditional rebates is highly segmented and related to perceived thinking costs and

savings and entertainment benefits of conditional rebates as well as to event involvement and

gambling proneness. In our application, conditional rebates are more cost effective than certain

rebates, mostly because consumers’ subjective probability of the event occurring is higher than

what market wisdom suggests.

Keywords: uncertain rewards, promotions, conditional rebates, consumer utility model, risk

aversion, subjective probability

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1. Introduction

Marketers are always looking for promotions that generate excitement and interest,

stimulate sales, and increase profits. Promotions offer a reward, for example a discount, gift, or

extra product, to the consumer who buys the company’s product. For the majority of

promotions, receipt of the reward is a certainty, but there are also several promotions where it is

not. Uncertainty may be due to (a) the consumer’s own skill, e.g., contests; (b) pure luck, e.g.,

sweepstakes; (c) the marketer’s decision to express the reward level as “tensile”, e.g., “X% to

Y% off this week”; or (d) whether an external event occurs, e.g., “Buy the product now and get

$X off if the Red Sox win the World Series”.

Two issues immediately come into play with uncertain promotions: (1) consumers’ risk

aversion, and (2) consumers’ perceptions of the probability, i.e., their “subjective probability”, of

receiving the reward. Consumers are typically risk averse, which should work against uncertain

promotions. However, consumers may believe the likelihood of receiving a reward is higher

than it really is, due to innate optimism or an upward bias in assessing the probability of positive

events. This should work in favor of uncertain promotions.

Laboratory research provides important insights on how consumers respond to some

types of uncertain promotions (e.g., Dhar, Gonzalez-Vallejo, & Soman, 1995; 1999; Goldsmith

& Amir, 2010; Mazar, Shampanier, & Ariely, 2012). However, these studies simply document

average purchase likelihood or the percentage of consumers who prefer one or the other type of

promotion. To the best of our knowledge no one has developed and estimated a model of

consumer response to uncertain versus certain promotions. The benefit of a model is that, in

addition to the insights one can obtain from lab studies, it provides a decision tool to predict

consumer response to choices not necessarily presented in the measurement.

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We develop such a model in this paper and show how it can be used by marketers to

determine whether, and for whom an uncertain promotion may be more effective than its certain

counterpart. Our model captures risk aversion and the consumer’s subjective probability of

getting a reward, and allows for heterogeneity in these as well as other model parameters. We

apply this model to a class of uncertain promotions that has become increasingly prevalent in

recent years. In these promotions, often termed “conditional rebates”, the consumer makes a

purchase at time t and receives a reward at a subsequent time t+x conditional on an uncertain

external event occurring between t and t+x. For example, many companies offer their customers

money back if their home team wins a sports championship.

Table 1 lists examples of conditional rebates that we have compiled from the internet. As

the table shows, these promotions are used in many countries; they are offered on big-ticket and

relatively high-involvement products; and the external event usually involves sports or the

weather. An entire industry has been built around such promotions, consisting of companies like

Oddsonpromotions.com, Interactive Promotions Group, Sadler Sports and Recreation Insurance,

SCA Promotions, and GrandPrizePromotions.com. These companies help client firms

implement conditional rebates, contests, and sweepstakes and offer insurance indemnification for

these promotions.

< Insert Table 1 about here >  

As noted above, conditional rebates are characterized by uncertainty and delayed

rewards. Figure 1 categorizes different types of promotions in terms of these attributes. Given

our goal of modeling the effectiveness of uncertain versus certain promotions, and our specific

interest in examining conditional rebates, we compare conditional rebates to their closest certain

analog, i.e., traditional rebates (hereafter termed “certain rebates”). As discussed for example by

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Baucells and Heukamp (2012), consumers have both a monetary discount rate (trading off

outcomes they receive immediately versus with a delay) and a probability discount rate (trading

off outcomes they receive with uncertainty versus certainty). Since we are interested in isolating

the impact of uncertainty, it is important to ensure the comparison is between promotions that are

similar in terms of delay. Both conditional rebates and rebates are delayed.

<Insert Figure 1 about here>

To summarize, our objective is to present a model for quantifying consumer response to

conditional rebates, as an example of the broader class of uncertain promotions, compared to

certain rebates. Our substantive contribution lies in (a) assessing the relative attractiveness of a

unique but prevalent type of uncertain promotion that has not been studied previously; (b)

quantifying the market share impact of conditional rebates compared to rebates; and (c)

characterizing segments of consumers who differ in their response to such promotions. Our

methodological contribution lies in developing a consumer utility model that incorporates risk

aversion and subjective probability. We estimate the model using a conjoint experiment,

establish its superior fit and predictive validity over simpler benchmark models, and use the

estimated model to simulate market shares of competing products in different promotion

scenarios. Our model is useful for understanding consumer response to conditional rebates as

well as other types of uncertain promotions, and as a tool that can help managers decide whether

and for whom to utilize these promotions rather than their certain counterparts.

A few of our key empirical findings are as follows. First, we identify three segments that

differ substantially in their response to conditional rebates. Segment membership is driven by

perceived benefits and costs of conditional rebates, gambling proneness, and event involvement.

Second, market share simulations suggest that in our application, a conditional rebate can be

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more cost effective than a certain rebate in that it can recover the share lost to a competitor’s

certain rebate at a lower expected cost and hence greater profit. Third, consumers tend to

overestimate the probability of the event in the conditional promotion, enhancing its cost

effectiveness. Fourth, conditional rebates are more effective for TVs than for washing machines,

perhaps because TVs are hedonic, and washing machines are utilitarian.

The rest of the paper is organized as follows. In section 2 we review prior research,

before we present our modeling framework in section 3. This is followed by a description of our

data in section 4, and our empirical results in section 5. We conclude the paper with a summary

of our key findings and implications for managers and researchers in section 6.

2. Prior Research

2.1 Consumer Response to Uncertainty

Prior research on consumer response to uncertainty suggests a tension with respect to

which will be more effective – a certain rebate or an uncertain conditional rebate. On one hand,

consumers may prefer a certain promotion because of risk aversion. Consumers have been found

to be risk-averse, even extremely so, in a variety of situations (Iyengar , Jedidi, & Kohli, 2008;

Narayanan & Manchanda, 2009; Roberts & Urban, 1988; Gneezy, List, & Wu, 2006).

On the other hand, a conditional rebate may be more effective because consumers

overestimate the probability that the event will occur. They may believe they are luckier than

others (Wagenaar & Keren, 1988) or have innate optimism (Alloy & Abramson, 1988;

Goldsmith & Amir, 2010). There is a strong “affinity” aspect to these rebates when they are

linked to sporting events, e.g., the Boston Red Sox winning the World Series or the German team

winning the European Soccer Championship, and people overestimate the probabilities of vivid

(Johnson et al., 1993; Lichtenstein et al., 1978; Weber & Hilton, 1990), desirable (Babad, 1987;

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Fischer & Budescu, 1995) and salient events (Bar-Hillel, Budescu, & Amar, 2008). They may

therefore think the likelihood of receiving a reward is higher than it really is. This tension

underscores the need to empirically assess the effectiveness of conditional rebates versus rebates

and to incorporate both risk aversion and subjective probability in modeling consumer response.

2.2 Effectiveness of Uncertain Promotions

Laboratory experiments have found positive consumer response to uncertain promotions

in some situations. Mobley, Bearden, and Teel (1988) and Dhar, Gonzalez-Vallejo, and Soman

(1995; 1999) show that consumers prefer tensile claims, where the size of the discount is

uncertain, over certain discounts when the probability of getting a discount is low. Goldsmith

and Amir (2010) show that in a low-stakes situation that does not demand much thinking (e.g.,

choices involving candy as a reward) consumers prefer uncertain rewards almost as much as the

more preferred outcome, and suggest that this is driven by innate optimism. Mazar, Shampanier,

and Ariely (2012) show that given a choice between a certain promotion (e.g., 1/3 off the price of

a candy bar) versus an uncertain promotion of equal expected value (e.g., 1/3 chance of getting

the candy bar free) consumers are generally more likely to choose the latter because they want to

avoid the “pain of paying”.

However, conditional rebates differ from the types of uncertain promotions studied

previously in important ways that leave open the question of their effectiveness. First, they

require the consumer to make a purchase decision with the possibility of getting a reward later if

the event occurs. Thus, they do not alleviate the “pain of paying”. Second, conditional rebates

are usually offered on big-ticket products, as are rebates. Thoughtful consideration, which

Goldsmith and Amir (2010) find inhibit the attractiveness of uncertain promotions, is much more

likely in such contexts. Third, the uncertainty in conditional rebates depends not on stated odds

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as in the studies discussed above, but on the consumer’s subjective probability that the external

event will occur. This needs to be modeled given evidence from prior research that there are

biases in probability assessment, especially for vivid and desirable events.

Finally, previous studies only report average purchase likelihood or percentage of

consumers who prefer one or the other type of promotion. Without an underlying model of

consumer utility, one cannot simulate choices and market shares under different scenarios to

assess the effectiveness of different types of promotions from the firm’s perspective.

2.3 Heterogeneity in Response to Uncertain Rewards

To the best of our knowledge, there is little research on heterogeneity in response to

uncertain promotions. However, the literature suggests promotions provide not only economic

benefits like savings, but also hedonic benefits like entertainment (Chandon, Wansink, &

Laurent, 2000; Raghubir, Inman, & Grande, 2004), and consumers may differ in how they

perceive these benefits. Gambling has entertainment value and shares some elements with

uncertain promotions, so gambling proneness may be associated with response to conditional

rebates. Excitement and sensation-seeking are important motivations for gambling (Coventry

&Brown, 1993; Pantalon et al., 2008). Presumably, consumers who are more involved with the

external event will get more excitement from participating in a conditional rebate. Conditional

rebates may require more thinking, a cost which some consumers can handle better than others.

Finally, demographic variables may contribute to heterogeneity since they are associated with

gambling and promotional games (Chalmers & Willoughby, 2006; Fang & Mowen, 2009; Mok

& Hraba, 1991).

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In summary, response to conditional rebates may be associated with consumer

characteristics such as the perception of savings and entertainment benefits, thinking costs,

gambling proneness, and involvement with the event, as well as demographics variables.

3. Modeling Framework

3.1 Overall Approach

We formulate a utility model that incorporates the consumer’s risk aversion and

subjective probability of the event occurring, while allowing for heterogeneity in these as well as

the other elements of the model. We first use a simulated data test to ensure we can identify the

model. We then estimate the model using choice data from a conjoint experiment. Respondents

choose between two products offered in a series of choice sets. A product may be offered

without a promotion, with a certain rebate, or with a conditional rebate, and the promotions have

different discount levels. Finally, we use our parameter estimates to simulate choices under

different scenarios and compare the effectiveness of conditional rebates to that of rebates.

3.2 Consumer Utility Model

We assume the consumer makes choices to maximize expected utility, which depends on

(1) the consumer’s preference for the brand associated with the product, (2) the quality of the

product, (3) the discount offered with a conditional rebate or a certain rebate, (4) the consumer’s

subjective probability that the event will occur in the case of a conditional rebate, and (5) other

factors not observed by the researcher. We employ a quadratic utility function (e.g., Iyengar,

Jedidi, & Kohli, 2008; Narayanan, Manchanda, & Chintagunta, 2005), which can capture both

risk averse and risk prone behavior.

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A disadvantage of the quadratic utility function is that it is potentially non-monotonic in

the amount of the discount. However, within the range of discounts investigated in our study,

this occurred in only one out of twelve cases (two types of promotion × three segments × two

categories). We also tested a piece-wise linear model, exponential and logarithmic functions.

None of these alternatives dominated the quadratic function in hold-out fit and prediction. The

hold-out log-likelihood with the exponential function was slightly better in one product category

but clearly worse in the other, and the exponential model estimates were highly sensitive to

starting values. Therefore, we use the quadratic function in all our analyses.

Expected utility is given by:

(1)  

 ,  

where:

E(Uijc) = Consumer c’s expected utility for product i in choice set j.

Qualijc = Quality of product i in choice set j of consumer c.

Discijc = Discount offered for product i in choice set j of consumer c.

Rebijc = 1 if certain rebate offered for product i in choice set j of consumer c, 0 otherwise.

CRijc = 1 if conditional rebate offered for product i in choice set j of consumer c, 0

otherwise. pc = Consumer c’s subjective probability that the condition specified in the

conditional rebate will occur. βic0 is consumer c’s baseline preference for the brand associated with product i (there are

two brands in the study); and εijc reflects factors influencing customer c’s expected utility for

product i in choice set j, not observed by the researcher. If a certain rebate is offered, the

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expected contribution to utility from the discount is , whereas if a

conditional rebate is offered, the expected contribution is .

Note that we allow different discount parameters for the certain rebate versus the

conditional rebate (βc2 and βc3 vs. βc4 and βc5). This is important given the distinction made in

decision science research between strength of preference, i.e., the marginal value of additional

outcomes, and intrinsic risk attitude (e.g., Dyer & Sarin, 1982; Smidts, 1997). For both certain

rebates and conditional rebates, we compute the traditional Arrow-Pratt index of relative risk

aversion, Rc (Pratt, 1964) which equals the negative of the elasticity of marginal utility:1

(2)  , and

(3)  .  

For the certain rebates, Rc captures strength of preference, i.e., a positive RcREB would

simply mean that marginal utility becomes smaller with increasing discounts. Because

conditional rebates contain uncertainty, RcCR captures the consumer’s inherent risk attitude in

addition to strength of preference.

As we discussed previously, consumers typically have biases in their subjective

probability assessment. This makes it important to use their self-assessed probabilities of the

event even if a more objective measure (e.g., based on the wisdom of the market) is available.

However, cumulative prospect theory suggests that using consumers’ stated probabilities as is

may not be wise, because when making decisions under uncertainty consumers overweight small

probabilities and underweight moderate and high probabilities (Tversky & Kahneman, 1992).

                                                                                                                           

1 A negative Arrow-Pratt index implies risk proneness and a positive value implies risk averseness.

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We therefore use each consumer’s self reported probability of the event (sp) but apply the

probability weighting function proposed by Prelec (1998):2

(4) ,

where 0 < α < 1. As α approaches 1, there is no weighting, i.e., pc equals the stated probability.

As α approaches 0, pc is constant at 0.37, and for α values in between, small stated probabilities

are over-weighted, while large probabilities are under-weighted.

One could also estimate pc from consumers’ choices. However, this would require

constraining the discount parameters to be the same for certain rebates and conditional rebates

(βc2=βc4 and βc3=βc5) in order to identify the model. Conceptually, we believe it is better to use

the information contained in self-reported probabilities and retain the important property of

different discount parameters for rebates vs. conditional rebates. Still we did test a model with

estimated pc and found that it did not improve fit and prediction compared to our proposed model

described in Equations 1 and 4.3

We can write Equation 1 as:

(5)

,

where Vijc is consumer c’s deterministic utility for product i in choice set j. Assuming the

unobserved factors εijc are independently distributed extreme value Type 1 (Gumbel), and the

consumer is choosing between two products i and k, we have a binomial logit model:

(6) ,

                                                                                                                           

2 We thank the review team for suggesting this weighting function. We tried a more flexible two-parameter weighting function also proposed by Prelec (1998), but it was not identified.

3 Details are available from the authors upon request.

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where Probijc is the probability that consumer c chooses product i rather than k in choice set j.

3.3 Heterogeneity

We model heterogeneity using a latent class model with concomitant variables

(Kamakura, Wedel, & Agrawal, 1994; Wedel & Kamakura, 2000). This model is very flexible

in that we do not need to make assumptions about the distribution of parameters, and it allows us

to derive meaningful interpretations for managers who are used to thinking about segments of

consumers with different preferences. Our model thus becomes:

(7) ,

(8) ,

(9)

where: Probijcs = Probability that consumer c chooses brand i in choice set j, conditional on

belonging to segment s. Vijcs = Deterministic utility of consumer c for product i in choice set j, conditional

on belonging to segment s. L = Likelihood function. ηcs = A priori probability that consumer c belongs to segment s. Yjc = 1 if consumer c chooses brand i in choice j; 0 if consumer c chooses brand k.

We ensure that the a priori probabilities of segment membership ηcs lie between 0 and 1

and sum up to 1 across segments for each consumer through the following formulation:

(10) .

The probabilities of segment membership are in turn a function of concomitant variables.

Based on the literature reviewed previously, we include perceptions of savings and entertainment

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benefits, thinking costs, gambling proneness, and involvement with the event as concomitant

variables:

(11) mcs = γs0 + γs1Savec + γs2Entc + γs3Thinkc + γs4Invevc + γs5Gambc ,

where:

Savec = Savings benefit of conditional rebates perceived by consumer c. Entc = Entertainment benefit of conditional rebates perceived by consumer c. Thinkc = Thinking costs of conditional rebates perceived by consumer c. Invevc = Involvement of consumer c with the event in the conditional rebate. Gambc = Gambling proneness of consumer c.

We initially also included gender, education, income, and age, but their effects were not

statistically significant and likelihood ratio tests showed that, jointly, they did not improve fit.

Therefore, we have dropped these demographic variables from subsequent analyses. We obtain

maximum likelihood estimates of all the model parameters jointly.4

3.4 Model Identification

The procedure we use to check model identification is as follows. We create simulated

data sets for 200 consumers based on our conjoint design with known values for the parameters

and three segments. We then see whether our estimation can recover those parameters. We do

not include concomitant variables because our interest here is simply in ensuring identification of

our core utility model. In the Appendix, we present results for two sets of true parameter values

– one very similar to our results in the washing machine category, the other arbitrary. The

                                                                                                                           

4 We test various sets of starting values for the model parameters. We also rescale the Discount variable to avoid very small discount parameters and facilitate estimation. We thank Kenneth Train for suggesting this rescaling.

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parameter estimates are not sensitive to starting values and none is significantly different from its

true value. Thus, we are confident that our model is identified.

4. Data

We utilize data from a choice-based conjoint experiment. Compared to methods for

measuring utility functions common in decision analysis, where respondents have to indicate a

certainty or probability equivalent (Smith & von Winterfeldt, 2004; Wakker & Deneffe, 1996),

making choices between pairs of products is easier and more realistic (see Iyengar, Jedidi, &

Kohli, 2008 for another example of using conjoint analysis to estimate utility functions). While

we would have liked to make our conjoint analysis incentive-compatible (Ding, Grewal, &

Liechty, 2005; Dong, Ding, & Huber, 2010), this is not feasible for the high-ticket products that

rebates are typically used with – we could not make consumers pay that much and live with their

decisions. Note however, that any bias due to the lack of incentive-compatibility applies to both

certain and conditional rebates and should not affect the comparison between them.

We investigate two product categories, TV sets and washing machines. Both are high-

ticket durables but TVs are more hedonic and washing machines are more utilitarian. We

conducted the study with German consumers solicited from an online panel provider in the

summer of 2011. The external event for conditional rebates is often a major sports event (see

Table 1). We therefore chose the 2012 European Football Championship as our event, and the

condition for getting the conditional rebate was that the German team wins the championship.

The questionnaire consisted of three sections. The first screened respondents to select

those who either owned a washing machine/TV or were planning to buy one in the next two

years, and who are involved in the purchase decision. The second section was the choice-based

conjoint task. The third section obtained additional information from respondents including

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perceived benefits and costs of conditional rebates, involvement with the event, and gambling

proneness. Demographic information was available from the panel provider.

4.1 Design of Conjoint Experiment

For each product category, we designed a full-profile choice-based conjoint study. The

washing machines were specified to be front-loading and offered at a regular price of 600 €. The

TV sets were 32” flat screen HDTVs, also offered at a regular price of 600 €. The stimuli

differed in brand, quality, and promotion (Table 2). In each category, we chose two well-known

national brands that sell at similar prices. We used quality ratings by Stiftung Warentest, a

consumer product rating agency (similar to Consumer Reports in the U.S.), that is well-known

and highly respected in Germany. The ratings are on the same scale as German school grades

(from 1 for “excellent” to 5 for “not sufficient”) and therefore very familiar to consumers. We

used two levels, 2.3 representing “good” and 2.7 representing “satisfactory”.

< Insert Table 2 about here >

A brand may be offered without a promotion, with a certain rebate, or with a conditional

rebate. We chose three discount levels for the certain rebate – 30, 60, and 90 €, which

correspond to price reductions of 5, 10, and 15% respectively. Both the absolute amount and

percentage discount are realistic given values observed in practice (Silk, 2004; Spencer, 2002).

At the time of our survey, a well-known betting website (www.bwin.com) offered odds that

translated to a 20% probability of the Germans winning the 2012 tournament. This “market

wisdom”, based on the assessment of the betting market, is a reasonable proxy for the objective

probability of the event a company might use in its planning. Accordingly, we used a 20%

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probability to compute conditional rebate discounts that are actuarially equivalent to the certain

rebate discount levels. These conditional rebate discount levels are 150, 300, and 450 €.5

In the survey, respondents first saw a scenario description. For TV, it read (for washing

machines, only the category name and product details were replaced):

“Imagine that today is two weeks before the beginning of the 2012 European Football Championship (UEFA EURO 2012), which will take place from June 8 to July 1, 2012 in Poland and Ukraine. Assume that Germany has qualified as section winner and will play Croatia, Sweden, and France in the first round. Beside the hosts – Poland and Ukraine – Spain, the Netherlands, Italy, Portugal, England, Russia, Czech Republic, Slovakia, Denmark, and Slovenia have qualified for the tournament.

Imagine you have decided to buy a new TV. You have already gathered information about current TV models and decided that you will buy a 32‘‘ flat screen HDTV from an electronics retailer close to your home.

In the following we will show you several pairs of TVs. The TVs differ in brand name, picture quality, and the type of promotion offered if any. Assume that the regular price of both TVs is 600 € and they are also identical in all other respects.”

This was followed by a description of the brand, quality, and promotion attributes, in which the

promotions were described as follows:

“Rebate promotion: Buy this flat screen HDTV before the beginning of the UEFA EURO 2012. Just mail in your receipt and the company will refund X € to you within six weeks of receiving your receipt.

Conditional promotion: Buy this flat screen HDTV before the beginning of the UEFA EURO 2012. Just mail in your receipt and if Germany wins the Championship, the company will refund X € to you within six weeks of receiving your receipt.”

Thus, the description of the promotions is identical except for the condition in the latter.

Next, respondents faced several choice tasks in each of which they chose one product out

of two.6 Figure 2 shows a sample choice task. We created stimuli and conjoint choice sets using                                                                                                                            

5 Our design may inflate the importance of promotions because the number of levels for this attribute is higher than for the others (Wittink, Krishnamurthi, & Reibstein, 1990), and because our design uses only three attributes. However, if such a bias exists, it applies to certain rebates and conditional rebates to a similar degree, and we are more interested in their relative than absolute impacts. We therefore did not increase the number of levels for other attributes, which would have increased respondent burden.

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the “complete enumeration” procedure in Sawtooth. This produces a randomized conjoint

design wherein each consumer receives different stimuli and this design accounts for the

principles of (1) minimal overlap, i.e., each attribute level is shown as few times as possible

within a single choice task; (2) level balance, i.e., the levels of an attribute occur with equal

frequency; and (3) orthogonality, i.e., all attribute levels are chosen independently of other

attribute levels (Hennig-Thurau et al., 2007; Huber & Zwerina, 1996). Each respondent

completed twelve choice tasks that were used for model estimation. We randomized the order of

brand presentation to avoid order effects, but always presented product attributes in the same

order to avoid respondent confusion.

< Insert Figure 2 about here >

4.2 Consumer Characteristics

Respondents indicated their subjective probability of the event occurring by answering

the following question: “What do you think is the percentage chance that Germany will win the

2012 European Football Championship? (Please write in a number between 0 and 100)”.

Respondents also indicated whether they had bought something with a certain or conditional

rebate during the last three years. Finally, we measured perceptions of the benefits and costs of

conditional rebates as well as the other consumer characteristics that serve as concomitant

variables in our model. Most items were taken from previously validated scales, as indicated in

                                                                                                                                                                                                                                                                                                                                                                                                         

6 We did not include a no-choice option to discourage respondents from choosing the “easy way out”. Our choice tasks are complex, and previous research has shown that task complexity increases the likelihood of choosing the no-choice option (Dhar, 1997; Tversky & Shafir, 1992). Not having a no-choice option does not pose a problem for our analysis since we predict market shares not absolute sales levels. Also, choice sets with pairs are less efficient and realistic than choice sets with more alternatives (Sándor & Wedel, 2002) but they are easier for respondents to process. This increases internal validity (Louviere et al., 2008) and allows us to use more choice sets (Zeithammer & Lenk, 2009).

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Table 3. Participants were asked to indicate their agreement with these statements on a scale

from 1 (strongly disagree) to 5 (strongly agree).

< Insert Table 3 about here >

4.3 Data Collection

The data were collected through an online survey in June 2011. Both certain and

conditional rebates are rather new to the German market, so we do not expect a bias from

respondents being more familiar with one type of promotion than the other. One year before the

event used in our conditional rebate is an appropriate time for data collection. The event was

sufficiently salient, since the national teams were in the process of qualifying for the tournament,

and ticket sales had started. Also, the odds of the German team winning were stable and not

affected by short-term news, e.g., about players’ injuries.

We specified to the panel provider a sampling frame of adults between the ages of 18 and

79 with at least a secondary school degree (“Realschule” or higher) in order to assure response

quality, and asked that our sample reflect the gender and age distribution of the German

population. This sampling frame accounts for 92% of the online provider’s panel and about 60%

of the German adult population over 20 years of age (www.destatis.de). Respondents were

randomly assigned to the washing machine or the TV category.

The samples contained 376 respondents for washing machines and 375 for TVs.

Respondents who took less than 4 minutes, more than 24 hours, or gave straight line responses to

all the choices were deleted as part of survey quality control. The eliminated respondents were

not significantly different from those retained except for a slightly lower education level in the

washing machine sample. Our final sample size is 293 for washing machines and 271 for TV.

4.4 Descriptive Statistics

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We summarize key characteristics of the two samples in Table 4. The data confirm that

German consumers have low experience with both certain and conditional rebates. Interestingly,

their self-reported probability is highly optimistic. The average (58% / 57%) is much higher than

what is suggested by market wisdom (20%). This is consistent with prior research showing

consumers’ propensity to overestimate the probability of desirable and salient events or engage

in wishful thinking. Such overestimation may be surprising given that we ran our study one year

before the event actually took place and construal-level theory suggests that temporal distance

activates abstract construal which in turn leads to under-estimation of probability (Trope &

Liberman, 2003; Wakslak & Trope, 2009). However, psychological distance is just as important

as temporal distance and the event’s salience is likely to reduce its psychological distance.

< Insert Table 4 about here >

5. Results

We first determine the number of segments for our model using the Bayesian Information

Criterion (Schwarz, 1978). We find that the BIC is best for the three-segment solution in both

categories, so we use three segments for all further analyses. In the following, we compare our

model with simpler benchmark models. We then discuss our parameter estimates and conduct

market share simulations.

5.1 Comparison with Benchmark Models

We compare our proposed model to three benchmark models nested within it. Since the

key characteristics of the utility function for conditional rebates are subjective probability and

risk aversion, we choose benchmark models with simpler treatments of pc and of the discount

parameters. We start with a model without promotions, i.e., with only brand and quality as

independent variables (model B1). We then add promotion effects in their simplest form, i.e., we

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use respondents’ stated subjective probabilities directly and constrain the discount parameters to

be equal for certain and conditional rebates (model B2). Next we relax the equality constraint on

the discount parameters (model B3). Finally, we bring in the probability weighting, which leads

to our proposed model.

We estimate all models using 200 randomly selected respondents leaving the rest (93 for

washing machines and 71 for TVs) for hold-out analysis. Table 5 presents in-sample fit and

hold-out performance for all the models. We obtained hit rates as follows. For each hold-out

respondent, we first computed choice probabilities and consequent hit rates in each of the three

segments. Next, we computed the overall hit rate for the respondent as the weighted mean across

segments, using the a posteriori probabilities of segment membership as weights. Finally, we

aggregated this hit rate across all the hold-out respondents.

< Insert Table 5 about here >

Our benchmark comparisons confirm that promotions are important – in-sample and

hold-out log-likelihoods improve significantly when we add promotion to the model (B2 vs. B1).

The improvement in hit rates is not large – brand and quality are relatively important for

respondents and already explain a large portion of consumers’ behavior, yielding hold-out hit

rates of 72.8% (washing machines) and 78.6% (TV). This could be due to the choice tasks being

hypothetical and not incentive-compatible – in practice promotion effects may be larger because

consumers spend and save real money. While this means we may be underestimating the

absolute effectiveness of promotions, it should not influence the comparison between certain and

conditional rebates, which is of key interest.

Next, we make the discount parameters promotion-specific. This significantly improves

in-sample fit (B3 vs. B2). Also hold-out performance becomes better, and the extent of that

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improvement is meaningful, given that hit rates are already high in a model with no promotion

effects (B1). Finally, we move to our proposed model by adding the weighting of stated

probabilities as specified in Equation 4. Hold-out performance stays rather similar with a slight

improvement for TV, but not for washing machines (PM vs. B3). However, in-sample fit

improves in both categories, so we report results based on our proposed model.

5.2 Model Estimates

Table 6 provides estimates for the washing machines sample. We find one large segment

with 58% of respondents, and two smaller segments with 18% and 24%. The estimates of β0

reflect brand preferences, which vary across the three segments. The estimates of β1 are

plausible: utility increases with higher quality (β1 > 0), and there is substantial heterogeneity

across segments. Quality sensitivity is rather high in the largest segment. This is consistent with

our earlier finding of high hold-out hit rates even without promotion in the model.

< Insert Table 6 about here >

For each segment, Table 6 also lists the mean subjective probabilities stated by

respondents (sp) as well as the transformed p’s based on the probability weighting coefficient α.

In all three segments the transformed p’s are smaller than the probabilities stated by respondents

(.49, .47, and .37 vs. .56, .65, and .57). Thus, the transformed p’s are more realistic than the

stated probabilities, but still substantially larger than the .20 suggested by market wisdom. This

is in line with previous research showing that consumers tend to overestimate probabilities of

favorable and salient events, and bodes well for the effectiveness of conditional rebates. In

segment three, the estimated weighting parameter α approaches zero, making the transformed

probability .37, and this segment is not sensitive to the conditional rebate discount. We note that

α would not be identified if the discount parameters were zero. Here, the parameters are non-

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zero, albeit statistically insignificant, and we did not find any indication of a problem either in

model convergence or in robustness to starting values.

Table 6 also shows the segment-level Arrow-Pratt indices for certain and conditional

rebates, computed by substituting the estimated discount parameters and medium discount levels

(60 € for rebates and 300 € for conditional rebates) into equations (2) and (3) respectively. We

find that respondents are mostly risk averse (R > 0). In segments 1 and 2 the index is similar for

certain and conditional rebates. In contrast, segment 3 is very risk averse for certain rebates, but

not for conditional rebates. Recall, though, that the conditional rebate discount parameters are

insignificant for this segment, implying that consumers do not respond to them.

Table 7 contains parameter estimates for the TV sample. As for washing machines, we

find one large segment and two smaller ones of about equal size. Again, brand preference and

quality sensitivity are heterogeneous across segments, with quality sensitivity being high in the

largest segment (segment 1). Segment 1 is also not sensitive to either the certain or the

conditional rebate discount levels. In contrast, segment 2 is sensitive only to conditional rebate

discounts and segment 3 is sensitive only to certain rebate discounts. Although the discount

parameters are often insignificant, we still compute the Arrow-Pratt index which indicates that

consumers are mostly risk averse.

< Insert Table 7 about here >

Segment 3’s stated probabilities do not need to be weighted (α approaches 1). In the

other two segments, as for washing machines, transformed p’s are smaller than stated p’s.

Again, the overall picture is that subjective probabilities (.42, .36, and .48) are smaller than

stated but larger than the .20 suggested by market wisdom. Whether consumers respond better to

certain or conditional rebates is determined by the interplay of subjective probability and risk

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aversion. Next, we analyze how these effects balance out in the different segments and the

overall market based on market share simulations.

5.3 Market Share Simulations

To gain further insights into the relative effectiveness of certain vs. conditional rebates

and the segment structure, and to demonstrate the value of our model as a managerial tool, we

conduct market share simulations. We take the perspective of a brand manager working on a

promotion program with a specific retailer, having to choose between offering a certain or

conditional rebate. We assume the manager knows that a competitor will be offering a certain

rebate. Brand A is the focal brand and brand B has instituted a certain rebate at a specified

discount level. If unanswered, this would switch many consumers to brand B. Brand A can

recoup its baseline share by offering the same rebate discount or a conditional rebate. We ask:

What discount level for a conditional rebate would brand A have to implement in order to win

back its baseline share? We call this the “CR equivalent”. Assume the manager believes the

market-based assessment of the probability of the event (.20 in our case). Let Discr = the certain

rebate discount. If .20 × CR equivalent < Discr, the expected value of the conditional rebate

discount that brand A would have to pay is lower than the certain rebate discount necessary to

recoup market share, indicating that conditional rebates are more effective than certain rebates.

We first simulate a base case in which consumers choose between brands A and B when

they are of equal high quality and neither is on promotion. We use individual parameters to

compute choice probabilities for each respondent and aggregate to obtain baseline market shares.

Next we repeat the simulation assuming brand B offers a certain rebate of a given discount level,

and re-compute market shares. We also confirm that brand A can recoup its baseline share by

offering the same certain rebate. Finally, we determine the conditional rebate discount that brand

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A would have to offer in order to recoup its baseline market share. We repeat these simulations

for different levels of the certain rebate discount for brand B and for both categories.7

Figure 3 summarizes the results at the segment level. For washing machines, Bosch

served as brand B, which uses a certain rebate, and AEG served as brand A, which uses a

conditional rebate. For televisions, brand B was Sony; brand A Philips. Figure 3 shows the CR

equivalents for different rebate values. For example, in the washing machine category, if brand

B (Bosch) offers a 30 € certain rebate, brand A (AEG) would have to offer a conditional rebate

of 117 € to recoup its baseline share with consumers in segment 1.

< Insert Figure 3 about here >

The pattern of consumer response is similar in the two product categories. In both

categories, Figure 3 shows that conditional rebates are most effective in segment 2 – CR

equivalents are lowest here, i.e., the smallest discounts are needed for brand A to recoup its

market share. The large segment 1, which comprises over half the sample in both categories,

responds less strongly to conditional rebates, but even for this segment, conditional rebates are

more cost effective than certain rebates. For example, in the washing machine category, the CR

equivalent of brand A (AEG) for a certain rebate of 90 € by brand B (Bosch) is 295 €. If the

manager of AEG assumes the probability of the German team winning the championship is .20

(the wisdom of the market value), then AEG is better off offering a conditional rebate because

the expected discount to be paid out, 59 € = .20 × 295 €, is much less than the 90 € certain rebate

brand A would need to recoup its share. The same pattern holds at other discount levels.

                                                                                                                           

7 Results are substantively similar in simulations where brand B begins by instituting a conditional rebate instead of a rebate.

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For consumers in segment 3, however, it is not profitable (or even not possible) for brand

A to recover market share with a conditional rebate. The relative values of the discount

parameters are such that for washing machines, the CR equivalents are too high (more than the

regular price of 600 € to offset a certain rebate of 60 or 90 €). For TV we cannot even compute

CR equivalents because a conditional rebate discount of up to 1,200 € is not sufficient to recoup

market share and beyond that point, utility starts to decrease with discount.

For managers it is important to study CR equivalents at the level of the total market.

Figure 4 shows these simulations, and reveals that conditional rebates are more cost effective

than certain rebates at all discount levels. For example, in the washing machine category, the CR

equivalent of brand A (AEG) for a rebate of 90 € by brand B (Bosch) is 342 €. Thus, the

expected discount to be paid out for a conditional rebate, 68.40 € = .20 × 342 €, is lower than the

90 € certain rebate brand A would need to recoup its share. Note that a conditional rebate of 450

€ has an actuarial equivalent of .20 × 450 € = 90 €. So brand A can offer a conditional rebate

anywhere between 342 € and 450 € and be better off than if it offered a 90 € certain rebate. It

can recoup its share with a conditional rebate of 342 € or use a conditional rebate between 342 €

and 450 € and achieve a higher share at the same expected expense as a certain rebate of 90 €.

< Insert Figure 4 about here >

Lower CR equivalents for TVs show that conditional rebates are more cost effective in

this category than for washing machines. This lends support to the benefit congruency

hypothesis proposed by Chandon, Wansink, and Laurent (2000), that hedonic promotions are

more effective in hedonic than in utilitarian categories. An alternative explanation could be the

higher usage complementarity for TVs than for washing machines – consumers watch soccer on

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their new TV. This type of fit has been shown to increase the effectiveness of other promotions

like premiums (e.g., Harlam et al., 1995).

Overall, we find that conditional rebates are more cost effective than certain rebates: they

can recoup baseline market share at lower expected cost. Further, they are more effective for

TVs than for washing machines. Note that our calculations do not account for possible

differences in slippage rates (Gilpatric, 2009; Gourville & Soman, 2011) and insurance or other

costs for certain versus conditional rebates. However, our analysis allows firms to assess how

large these differences can be for one or the other type of promotion to be more profitable.

5.4 Observed Heterogeneity

The five consumer characteristics – perceived savings benefits, entertainment benefits,

thinking costs, gambling proneness, and involvement with the event – help explain heterogeneity

across segments. The bottom halves Tables 6-7 show the impact of these variables on the

likelihood of being in a particular segment, with segment 3 as the base case.8 To interpret these

effects, it is useful to recall that for both categories, segment 2 is the most responsive to

conditional rebates, followed by segment 1, and segment 3 is the least responsive.

In the washing machine category, we find that higher thinking costs make respondents

less likely to be in the conditional rebate prone segments 1 and 2; hence more likely to be in

segment 3, which does not like conditional rebates. Higher involvement with the event and

higher entertainment value makes respondents less likely to be in the large segment 1, and more

                                                                                                                           

8 We use principal component scores for the consumer characteristics to alleviate multicollinearity. Details of the principal component analysis are available from the authors upon request.

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likely to either love (segment 2) or hate (segment 3) promotions around the event. In the TV

category, higher thinking costs make respondents less likely to be in segment 1. Higher

perceived savings and entertainment benefits, along with higher gambling proneness, place

respondents in segment 2, the most conditional rebate-prone segment.

Overall, we find that consumer response to conditional rebates is driven by perceived

thinking costs, but also by perceived savings and entertainment benefits as well as event

involvement and gambling proneness. The hedonic aspect of conditional rebates is at least as

important as the utilitarian aspect: In the washing machine category, respondents who have high

event involvement and associate conditional rebates with high entertainment benefits either love

or hate these promotions, whereas in the TV category, conditional rebate proneness is associated

with high entertainment benefits and gambling proneness.

6. Discussion and Implications

We have developed and estimated a model for assessing the effectiveness of uncertain

promotions, focusing on a specific type – conditional rebates. The key features of our model are

the incorporation of risk aversion and the subjective probability that consumers use in evaluating

such promotions. We have used the model to generate insights on how conditional rebates work.

We have compared the effectiveness of a conditional rebate linked to a popular sports event

versus a traditional certain rebate which is the closest analog amongst traditional promotions

without uncertainty. We have done this in the context of choices made by German consumers in

two product categories and have generated several interesting results:

First, our model successfully recovers the choices consumers make when they trade off a

conditional rebate versus a rebate. This is evidenced by hit rates of about 80%, plausible

coefficients, and superiority over several benchmark models. We find evidence that risk

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aversion is different for conditional vs. certain rebates and that subjective probabilities are

smaller than stated, but much larger than the probabilities suggested by market wisdom.

Second, we find evidence of substantial heterogeneity with respect to response to

conditional rebates. Using a latent class approach, we find similar three-segment solutions for

both televisions and washing machines. There are high, medium, and low segments with respect

to their responsiveness to conditional rebates. We identify consumer characteristics that

distinguish between the segments and hence drive the effectiveness of conditional rebates:

perceived savings and entertainment benefits, perceived thinking costs, gambling proneness, and

event involvement. These results are plausible, and reinforce the segmented response to

conditional rebates.

Third, conditional rebates are more cost effective than certain rebates in that the expected

cost of the discount required to off-set a competitor’s rebate is lower than the cost of that rebate.

Finally, while the general pattern of results is similar for TVs and washing machines, conditional

rebates are more effective for TVs, the more hedonic product. This is consistent with benefit

congruency (Chandon, Wansink, & Laurent, 2000), but it could also be due to other reasons such

as higher usage complementarity between TVs and sporting events.

Our results have important implications for researchers. First, we have developed a

consumer utility model that can be used to evaluate consumer response to uncertain promotions

and shown that the key phenomena to include are the subjective probability of getting the reward

and risk aversion. Second, we add substantively to the literature on uncertain promotions. Some

recent research has argued that positive response to uncertain promotions occurs only in low

stakes situations with relatively small-ticket items, when consumers do not deliberate (Goldsmith

& Amir, 2010) or because consumers want to avoid the pain of paying (Mazar, Shampanier, &

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Ariely, 2012). None of these situations holds for conditional rebates, which are almost always

offered on big-ticket items and the reward is delayed so the consumer does not avoid the pain of

paying. Yet we find that conditional rebates can work better than certain rebates. This result is

mainly driven by the fact that subjective probabilities are larger than “objective” probabilities

based on market wisdom.

Third, we add to the literature on deal proneness, which suggests that response to

promotion is highly segmented and segmentation varies by type of promotion (e.g., Schneider &

Currim, 1991). Indeed, we find that almost a quarter of the consumers in our sample are not at

all receptive to conditional rebates, about 50-60% are quite receptive, and the remainder are

highly receptive. Fourth, we contribute to the literature on benefits and costs of promotions. We

show that hedonic benefits can be as important as utilitarian benefits for explaining consumer

response to promotions and the cost of thinking is very relevant, supporting Chandon, Wansink,

& Laurent’s (2000) call for more work on these costs.

For managers, our key messages are as follows. First, conditional rebates have a role to

play in the brand’s promotion mix. We find them to be more cost effective than certain rebates

in recovering market share when a competing brand uses a certain rebate. Second, promotions

are a targeting device (e.g., Nies & Natter, 2010), and conditional rebates are no exception. The

segment most attracted by conditional rebates is one that finds promotions less taxing on the

brain. Perceived entertainment benefits, gambling proneness, and event involvement can also

play a role, but this may differ across product categories. Third, in their communication of

conditional rebates, managers should not only emphasize the potential savings, but also how

much fun it is to participate. Fourth, models can be used to show how the market for conditional

rebates is segmented and to simulate alternative promotion scenarios. The analysis here is not

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overly complex – it requires a conjoint-type survey followed by a model that can be estimated

using maximum likelihood. Our procedure may be especially useful for managers who have

never used conditional rebates before and are seeking guidance before a full roll-out.

Our work has limitations that suggest avenues for future research. First, the conditional

rebates we studied involved a positive event, i.e., a soccer team winning a tournament. In recent

years, companies are also offering conditional rebates as “insurance” against negative events.

For example, a German manufacturer of solar heating systems offered a discount if the number

of hours of sunshine falls below a certain level. And Pirelli promised a refund of up to 50% on

the purchase of winter tires, if there are not enough cold days in the next winter. During the

recent financial crisis, some car manufacturers in the U.S. offered to cover monthly payments for

a while if the customer lost his/her job. It would be interesting to see the impact of a negative

external event on the effectiveness of such promotions.

Second, the event in our analysis was a low but not very low-probability event. It would

be interesting to study the response to much lower probability scenarios. There are at least two

reasons why those may be even more effective. One is that consumers overweight very low

probabilities and exhibit risk proneness when it comes to longshots, i.e., very small chances of

large pay-offs, as evidenced by the popularity of state lotteries, especially jackpots (Chew &

Tan, 2005). Another is that very low-probability scenarios are often associated with free

products (e.g., Jordan’s Furniture Monster Hit promotion) and there is evidence that consumers

have much higher affect for free offers than for other price offers (Shampanier, Mazar, & Ariely,

2007). In addition, it may be interesting to study medium probabilities, which may be more

attractive for consumers because chances of winning are higher.

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Third, it would be interesting to compare response to conditional rebates across cultures.

In Germany, neither certain nor conditional rebates are widely used. This was good for the

purposes of our study, since it equalized baseline responsiveness. However, in the U.S., certain

rebates are very common, although widely criticized, so it would be interesting to see whether

conditional rebates would suffer from the negative halo from traditional rebates, or benefit as a

more entertaining form of rebate.

Fourth, while we employed realistic scenarios with a real event – the European Football

Championship – the purchase situation was hypothetical. As explained above, because our

measurement approach is not incentive-compatible, it may underestimate the absolute

effectiveness of both types of promotions studied. In addition, we may underestimate the

effectiveness of conditional rebates relative to certain rebates because we do not capture effects

of the advertising that often accompanies conditional rebates. We also ran our study one year

before the actual event, so response in our study is probably less emotional than in practice.

Thus, our findings on the effectiveness of conditional rebates may be conservative, and it would

be worthwhile to validate them with field data.

Fifth, we rely on the information in self-stated probabilities and use a probability

weighting function to transform them into subjective probabilities. Future researchers could

design a study and gather data that permit the direct estimation of consumers’ subjective

probabilities.

Overall, our findings are that conditional rebates can be modeled at the level of the

consumer utility function, response to them is highly heterogeneous, and they provide a viable

alternative to traditional rebates. We urge further research on uncertain promotions in general,

and on conditional rebates in particular as a promising form of promotion.

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Table 1

EXAMPLES OF CONDITIONAL REBATES

Name of Company Year Country Product

Category Nature of External Event

PanelCraft Inc. 1998 U.S. Sun rooms, spas, and gazebos

Sports: Minnesota Vikings win last five games of year by 7 points or more (football)

BrandsMart 1999 U.S. Electronics Sports: Kansas City Chiefs beat San Diego Chargers on Halloween (football)

Epson 2003 Multiple Printer Sports: Home nation wins rugby World Cup Canandaigua Wine Company

2003 U.S. Champagne Weather: ≥ 4 inches of snow on New Year’s Day  

Media Markt 2004 Germany TV Sports: Germany wins soccer EURO Hipercor 2004 Spain Electronics Sports: Spain wins soccer EURO Bayerische Hypo- und Vereinsbank AG

2006 (yearly)

Germany Savings account Sports: FC Bayern Munich scores/becomes German soccer champion

Media Markt 2006 Germany TV Sports: Germany scores in soccer World Cup Media Markt 2006 Italy TV Sports: Italy wins soccer World Cup Ashley Furniture HomeStore

2007 U.S. Furniture Sports: Memphis Tigers win NCCA championship (basketball)

Furniture & Appliance Mart

2007 U.S. Furniture, appliances  

Sports: Green Bay Packers win Super Bowl (football)

Jordans’ Furniture

2007 U.S. Furniture Sports: Boston Red Sox win World Series (baseball)

Springers Jewelers

2007 U.S. Jewelry Weather: ≥ 6 inches of snow on Christmas

World Furniture Mall

2007 U.S. Furniture Sports: Chicago Bears shut-out Green Bay Packers (football)

Media Markt 2008 Germany Electronics Sports: Germany scores in soccer EURO final Panasonic 2008 Germany TV Sports: Germany wins Olympics gold PAYBACK Rabattverein

2008 Germany Purchases in partner stores

Sports: Germany wins Olympics gold

Powerade 2008 U.K. Sports drink Sports: Great Britain wins medal in randomly assigned Olympics event

Jordans’ Furniture

2008 U.S. Furniture Sports: Boston Red Sox sweep World Series (baseball)

Stacy Furniture 2008 U.S. Furniture Sports: Dallas Mavericks win NBA Finals (basketball)

Paradise 2009 Canada Spas, hot tubs Sports: Saskatchewan Roughriders win Grey

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Leisurescapes Cup (football) Golfsmith 2009 U.S. Golf driver Sports: Phil Mickelson or Rocco Mediate

wins U.S. Open (golf) Jordans' Furniture

2009 U.S. Furniture Sports: Boston Red Sox sweep World Series (baseball)

Simpson Furniture

2009 U.S. Furniture Weather: ≥ 2 inches of snow on January 14, 2010

TomTom 2010 Multiple   GPS Sports: Home nation wins soccer World Cup Currys 2010 England TV Sports: England scores in soccer World Cup Nationwide 2010 England Bond Sports: England wins soccer World Cup Trafalgar Wharf 2010 England Boat storage Sports: Andy Murray wins Wimbledon

(tennis) Toshiba 2010 Multiple   Laptop, TV Sports: Home nation wins soccer World Cup Carrefour 2010 France TV Sports: France advances at least to semi-final

in soccer World Cup  Saturn 2010 France TV Sports: France wins soccer World Cup Media Markt 2010 Germany TV Sports: Germany advances at least to round of

last 16 in soccer World Cup  Banesto 2010 Spain Deposit account Sports: Spain wins soccer World Cup

Media Markt 2010 Spain TV, projector or TFT monitor

Sports: Spain wins soccer World Cup without losing

Pc City 2010 Spain TV Sports: Spain scores in soccer World Cup Slovenian tourist board

2010 U.K. Trip to Slovenia Sports: Slovenia advances at least to quarterfinal in soccer World Cup  

Golfsmith 2010 U.S. Golf driver Sports: Phil Mickelson wins Masters (golf) Perry’s Emporium

2010 U.S. Jewelry Weather: ≥ 3 inches of snow on Christmas

Tom Kadlec Honda

2010 U.S. Cars Weather: ≥ 5 inches of snow on Christmas  

Trafalgar Wharf 2011 England Boat storage Sports: England wins rugby World Cup

Trafalgar Wharf 2011 England Boat storage Weather: ≥ 1 inch of snow on Christmas

Victor Chandler 2011 U.K. Sports bets Sports: Andy Murray wins Wimbledon (tennis)

Jordans’ Furniture

2011 U.S. Furniture Sports: Boston Red Sox player hits homerun on Jordans' sign (baseball)  

Mysportworld 2012 Germany Sports goods Sports: Germany wins soccer EURO  PAYBACK Rabattverein

2012 Germany Purchases in partner stores

Sports: Germany wins Olympics gold

Cadbury 2012 U.K. Chocolate bars Sports: Randomly assigned British athlete wins Olympics medal

Santander 2012 U.K. Bank account Sports: Rory McIllroy wins a “Major” (golf)  

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Table 2

ATTRIBUTES IN THE CONJOINT TASK

Washing Machines   TV  

Brand - Bosch - AEG

- Sony - Philips

Quality

Rating of washing performance by Stiftung Warentest: - Good (2.3) - Satisfactory (2.7)

Rating of picture quality by Stiftung Warentest: - Good (2.3) - Satisfactory (2.7)

Promotion - None - Rebate 30 € - Rebate 60 € - Rebate 90 € - Conditional rebate 150 € - Conditional rebate 300 € - Conditional rebate 450 €

- None - Rebate 30 € - Rebate 60 € - Rebate 90 € - Conditional rebate 150 € - Conditional rebate 300 € - Conditional rebate 450 €

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Table 3

MEASUREMENT SCALES FOR CONCOMITANT VARIABLES

Items Reference Alpha

Savings benefit Conditional promotions let me save money. … allow me to spend less.

Chandon, Wansink, and Laurent (2000)

.73

Entertainment benefit … are fun. … are entertaining.

Chandon, Wansink, and Laurent (2000)

.86

Thinking costs ... are hard to figure out. … require a lot of thinking.

.68

Involvement with event The performance of the German team in the European Football Championship 2012 is very important to me. I am very interested in how well the German team does in the European Football Championship 2012.

Steenkamp, van Heerde, and Geyskens (2010)

.91

Gambling proneness I like to gamble. I like to take risks.

Burton et al. (1998) .91

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Table 4

DESCRIPTIVE STATISTICS

Washing Machines (n = 293)  

TV (n = 271)  

Respondents with rebate experiencea 12.6% 15.9%  

Respondents with conditional rebate experiencea

6.5% 6.3%  

Mean stated probability of event 58% (26)   57% (25)  

Mean savings perception 2.9 (1.1)   2.9 (1.1)  

Mean entertainment perception 2.8 (1.2)   2.7 (1.2)  

Mean thinking perception 2.5 (1.1)   2.5 (1.1)  

Mean involvement with event 3.2 (1.4)   3.1 (1.4)  

Mean gambling proneness 2.4 (1.1)   2.4 (1.1)  

Males 48.5%   50.7%  

Mean age 45.2 (14.8)   47.7 (15.6)  

Mean household income (€/month) 2,495 (1,261)   2,640 (1,334)  

Employed full time 52.7%   43.7%  

Employed part time 14.1%   16.7%  

Unemployed 33.2%   39.6%  

College degree 34.1%   37.0%  

High school degree (Abitur) 24.6%   21.1%  

Secondary degree 41.3%   41.9%  

Standard deviations are in parentheses where necessary. a % of respondents who have bought something that had a rebate (conditional rebate) offer in

the last 3 years.

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Table 5

HOLD-OUT COMPARISON WITH BENCHMARK MODELS

Model # Param.

In-Sample LL

χ2 a Hold-Out LL

Hold-Out Hit Rate

Washing Machines

B1: No promotion (β2, β3, β4, β5 = 0)

18 -1,062.00     -522.29 .728

B2: Common discount parameters (β2 = β4, β3 = β5, pc = stated prob.)

24 -968.56   168.88*** (vs. B1)  

-482.55 .775

B3: No probability weighting (pc = stated prob.)

30 -923.02   91.08*** (vs. B2)  

-460.04 .793

PM: Proposed model 33 -918.03   9.98** (vs. B3)  

-468.16 .790

TV

B1: No promotion (β2, β3, β4, β5 = 0)

18 -1,053.27     -344.11 .786

B2: Common discount parameters (β2 = β4, β3 = β5, pc = stated prob.)

24 -968.03   170.48*** (vs. B1)  

-327.99 .811

B3: No probability weighting (pc = stated prob.)

30 -950.13   35.80*** (vs. B2)  

-302.38 .827

PM: Proposed model 33 -941.68   16.90*** (vs. B3)  

-301.17 .830

Estimation on 200 respondents for each category Hold-out analysis on 93 respondents for washing machines and 71 for TVs. a Likelihood ratio improvement of in-sample LL (nested models); ** p < .05. *** p < .01.

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Table 6

MODEL PARAMETERS FOR WASHING MACHINES

Segment 1 Segment 2 Segment 3 Estimate

(SE) Estimate

(SE) Estimate

(SE) β0 Brand preference for Bosch -.09

(.14)

-.83

(.24) ***

.80

(.15) ***

β1 Quality valuation 3.47 (.24)

***

.46

(.23) **

.26

(.11) **

β2 Certain rebate discount parameter

4.07 (1.34)

***

3.22

(1.43) **

4.96 (.89)

***

β3 Certain rebate discount2 parameter -1.99 (1.41)

-1.37 (1.36)

-3.21 (.96)

***

β4 Conditional rebate discount parameter

2.10 (.54)

***

2.92 (.96)

***

-.06 (.39)

β5 Conditional rebate discount2 parameter

-.22 (.11)

**

-.30 (.18)

.14 (.09)

α Weighting parameter for stated probability of event

.48 (.18)

***

.30

(.16) *

.00

(.54)

sp Mean stated probability .56 .65 .57 p Mean transformed probability .49 .47 .37 RREB(60) Arrow-Pratt index for rebate of

60€ 1.42

1.04

3.48

RCR(300) Arrow-Pratt index for conditional. rebate of 300€

1.69

1.61

-1.08

η Segment size .58 .18 .24 γ0 Constant 1.00

(.22) ***

-.29

(.43)

⎯

γ1 Impact of savings benefit -.04 (.19)

.02 (.26)

⎯

γ2 Impact of entertainment benefit -.39 (.20)

*

-.16 (.27)

⎯

γ3 Impact of thinking costs -.46 (.20)

**

-.78

(.31) **

⎯

γ4 Impact of involvement with event -.40 (.21)

*

-.15

(.34)

⎯

γ5 Impact of gambling proneness .12 (.20)

.35 (.30)

⎯

* p < .10 ** p < .05 *** p < .01 p and η computed based on parameter estimates for α and γ0-γ5 respectively. Discount divided by 100 to facilitate the estimation.

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Table 7

MODEL PARAMETERS FOR TV

Segment 1 Segment 2 Segment 3 Estimate

(SE) Estimate

(SE) Estimate

(SE) β0 Brand preference for Sony .15

(.22)

-.82

(.12) ***

1.05 (.14)

***

β1 Quality valuation 3.44 (.28)

***

.48

(.12) ***

.60

(.16) ***

β2 Certain rebate discount parameter

1.69 (1.68)

1.40 (.87)

4.60

(1.05) ***

β3 Certain rebate discount2 parameter -.96 (1.79)

.16

(.93)

-2.27

(1.12) **

β4 Conditional rebate discount parameter

.95 (.83)

2.82 (.55)

***

.60

(.40)

β5 Conditional rebate discount2 parameter

-.07 (.17)

-.30 (.12)

**

-.05 (.08)

α Weighting parameter for stated probability of event

.24 (.38)

.00 (.09)

1.00 (.89)

sp Mean stated probability .56 .62 .48 p Mean transformed probability .42 .37   .48 RREB(60) Arrow-Pratt index for rebate of

60€ 2.14

-.12

1.45

RCR(300) Arrow-Pratt index for conditional rebate of 300 €

.79

1.76

1.00

η Segment size .51 .26 .23 γ0 Constant .90

(.25) ***

.13

(.28)

⎯

γ1 Impact of savings benefit .18 (.21)

.46 (.24)

*

⎯

γ2 Impact of entertainment benefit .30 (.21)

.42

(.24) *

⎯

γ3 Impact of thinking costs -.41 (.20)

**

-.25

(.24)

⎯

γ4 Impact of involvement with event .10 (.21)

.40 (.25)

⎯

γ5 Impact of gambling proneness .00 (.21)

.38 (.23)

*

⎯

* p < .10 ** p < .05 *** p < .01 p and η computed based on parameter estimates for α and γ0-γ5 respectively. Discount divided by 100 to facilitate the estimation.

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Figure 1

TYPES OF PROMOTIONS

Temporary price reductions

Multi-item promotions

Coupons

Free gifts/samples

Traditional mail-in rebates

Instant win sweepstakes

Tensile promotions (X% - Y% off)

Contests

Sweepstakes

Conditional rebates (Buy now, get Y% off if Z happens)

ate Reward Delayed Reward

Certain Reward

Uncertain Reward

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Figure 2 EXAMPLE OF A CHOICE TASK

Which HDTV would you rather buy?

 

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Figure 3 MARKET SHARE SIMULATIONS: SEGMENT LEVEL

Note: TV Segment 3 is not shown because its discount parameters are such that even very high CR discounts cannot recoup base market share.

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Figure 4 MARKET SHARE SIMULATIONS: OVERALL SAMPLE

Note: All segments are included in these simulations.

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Appendix

MODEL IDENTIFICATION SIMULATIONS

Simulation 1

Segment 1 Segment 2 Segment 3

TV SV Est. TV SV Est. TV SV Est.

β0 -.08 -1.19 -.04 √ -.78 -.24 -.62 √ .88 1.17 .97 √

β1 3.41 4.18 3.63 √ .36 -.22 .27 √ .24 .26 .40 √

β2 3.88 6.61 4.14 √ 3.65 5.36 3.73 √ 4.98 6.84 4.61 √

β3 -1.82 -1.22 -1.82 √ -1.77 -3.07 -1.84 √ -3.23 -2.06 -3.25 √

β4 2.09 2.16 2.58 2.55 4.00 2.37 √ -.07 -.56 -.72 √

β5 -.22 -.44 -.42 -.22 .29 -.42 √ .13 .45 .00 √

α .20 1.40 .13 √ .33 -.78 .22 √ .00 -1.43 .00 √

γ0 .96 .26 1.07 √ -.19 -.94 .09 √ ⎯ ⎯ ⎯

Simulation 2

Segment 1 Segment 2 Segment 3

TV SV Est. TV SV Est. TV SV Est.

β0 .00 1.23 .03 √ 2.00 3.51 1.96 √ -2.00 -2.38 -2.15 √

β1 .00 .92 .00 √ -2.00 -3.80 -2.00 √ 2.00 2.30 1.93 √

β2 2.00 1.99 2.01 √ 3.00 2.89 3.17 √ .00 -1.41 .06 √

β3 -1.00 .16 -.97 √ -2.00 -1.02 -1.96 √ .00 -.51 .06 √

β4 2.00 1.11 1.91 √ -3.00 -2.88 -3.66 √ 2.00 1.42 2.21 √

β5 -1.00 -2.07 -1.00 √ .00 1.20 .44 -1.00 -2.05 -.76

α .50 1.00 .55 √ .10 -.40 .23 √ .01 -.03 .00 √

γ0 .80 .87 .78 √ -.80 -2.14 -.84 √ ⎯ ⎯ ⎯

TV = true value; SV = starting value; Est. = estimate; √ = estimate within 1 std. error of the true value.

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