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The Goal-Gradient Hypothesis Resurrected: Purchase Acceleration, Illusionary Goal Progress, and Customer Retention

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The goal-gradient hypothesis denotes the classic finding from behaviorism that animals expend more effort as they approach a reward. Building on this hypothesis, the authors generate new propositions for the human psychology of rewards. They test these propositions using field experiments, secondary customer data, paper-and-pencil problems, and Tobit and logit models. The key findings indicate that (1) participants in a real café reward program purchase coffee more frequently the closer they are to earning a free coffee; (2) Internet users who rate songs in return for reward certificates visit the rating Web site more often, rate more songs per visit, and persist longer in the rating effort as they approach the reward goal; (3) the illusion of progress toward the goal induces purchase acceleration (e.g., customers who receive a 12-stamp coffee card with 2 preexisting "bonus" stamps complete the 10 required purchases faster than customers who receive a "regular" 10-stamp card); and (4) a stronger tendency to accelerate toward the goal predicts greater retention and faster reengagement in the program. The conceptualization and empirical findings are captured by a parsimonious goal-distance model, in which effort investment is a function of the proportion of original distance remaining to the goal. In addition, using statistical and experimental controls, the authors rule out alternative explanations for the observed goal gradients. They discuss the theoretical significance of their findings and the managerial implications for incentive systems, promotions, and customer retention.
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Journal of Marketing Research
Vol. XLIII (February 2006), 39–58
39
©2006, American Marketing Association
ISSN: 0022-2437 (print), 1547-7193 (electronic)
*Ran Kivetz is Sidney Taurel Associate Professor of Business (e-mail:
rk566@columbia.edu), and Oleg Urminsky is a doctoral candidate (e-mail:
opu1@columbia.edu), Graduate School of Business, Columbia University.
Yuhuang Zheng is Assistant Professor of Marketing, Graduate School of
Business Administration, Fordham University (e-mail: ayuzheng@
fordham.edu). The authors are indebted to David Katz, the manager of
Columbia University Café Cappuccino, and to MoodLogic Inc. for their
cooperation. The authors are also grateful for helpful comments and sug-
gestions from Pradeep Chintagunta; Sunil Gupta; Raghu Iyengar; Gita
Johar; Yifat Kivetz; Rajeev Kohli; Donald Lehmann; Oded Netzer; P.B.
Seetharaman; Itamar Simonson; Andrea Vag; participants in seminars at
Columbia University, Stanford University, the University of Florida, the
University of Pennsylvania, and the Society for Judgment and Decision
Making; and the anonymous JMR reviewers. The research reported in this
article was supported by the Lang Faculty Research Fellowship in
Entrepreneurship.
RAN KIVETZ, OLEG URMINSKY, and YUHUANG ZHENG*
The goal-gradient hypothesis denotes the classic finding from behav-
iorism that animals expend more effort as they approach a reward. Build-
ing on this hypothesis, the authors generate new propositions for the
human psychology of rewards. They test these propositions using field
experiments, secondary customer data, paper-and-pencil problems, and
Tobit and logit models. The key findings indicate that (1) participants in a
real café reward program purchase coffee more frequently the closer
they are to earning a free coffee; (2) Internet users who rate songs in
return for reward certificates visit the rating Web site more often, rate
more songs per visit, and persist longer in the rating effort as they
approach the reward goal; (3) the illusion of progress toward the goal
induces purchase acceleration (e.g., customers who receive a 12-stamp
coffee card with 2 preexisting “bonus” stamps complete the 10 required
purchases faster than customers who receive a “regular” 10-stamp card);
and (4) a stronger tendency to accelerate toward the goal predicts
greater retention and faster reengagement in the program. The concep-
tualization and empirical findings are captured by a parsimonious goal-
distance model, in which effort investment is a function of the proportion
of original distance remaining to the goal. In addition, using statistical and
experimental controls, the authors rule out alternative explanations for
the observed goal gradients. They discuss the theoretical significance of
their findings and the managerial implications for incentive systems, pro-
motions, and customer retention.
The Goal-Gradient Hypothesis Resurrected:
Purchase Acceleration, Illusionary Goal
Progress, and Customer Retention
[R]ats in a maze … run faster as they near the food box
than at the beginning of the path.
—Hull (1934)
The goal-gradient hypothesis, originally proposed by the
behaviorist Clark Hull in 1932, states that the tendency to
approach a goal increases with proximity to the goal. In a
classic experiment that tests this hypothesis, Hull (1934)
found that rats in a straight alley ran progressively faster as
they proceeded from the starting box to the food. Although
the goal-gradient hypothesis has been investigated exten-
sively with animals (e.g., Anderson 1933; Brown 1948; for
a review, see Heilizer 1977), its implications for human
behavior and decision making are understudied. Further-
more, this issue has important theoretical and practical
implications for intertemporal consumer behavior in reward
programs (hereinafter RPs) and other types of motivational
systems (e.g., Deighton 2000; Hsee, Yu, and Zhang 2003;
Kivetz 2003; Lal and Bell 2003).
In this article, we build on the behaviorist goal-gradient
hypothesis and generate new propositions in the context of
two real RPs. In the interdisciplinary spirit of bridging the
40 JOURNAL OF MARKETING RESEARCH, FEBRUARY 2006
consumer behavior and marketing science fields (Winer
1999; Wittink 2004), we investigate these propositions
using various methods, data, and modeling approaches
(e.g., field experiments, paper-and-pencil problems, and
secondary customer data; hazard rate, Tobit, and logit mod-
els). Consistent with the goal-gradient hypothesis, its corol-
laries, and their adaptation to the human psychology of
rewards, some key findings indicate the following:
•Members of a café RP (e.g., “buy ten coffees, get one free”)
purchase coffee more frequently the closer they are to earning
a free coffee (on average, interpurchase times decrease by 20%
or .7 days throughout the program).
•The findings generalize beyond coffee purchases to effort
involving repeatedly rating music over the Internet and goal
gradients operationalized by acceleration in intervisit times,
lift in rating quantities, and enhanced persistence closer to the
reward threshold.
•The illusion of progress toward the goal induces purchase
acceleration. For example, customers who receive a 12-stamp
coffee card with two preexisting “bonus” stamps complete the
ten required purchases faster than customers who receive a
“regular” 10-stamp card. Process experiments show that the
illusionary goal progress effect cannot be explained by rival
accounts, such as sunk cost.
•Consistent with the notion that a steeper goal gradient indi-
cates a stronger motivation to earn rewards, people’s tendency
to accelerate toward their first reward predicts a greater proba-
bility of retention and faster reengagement in the program.
•We capture all of the findings with a parsimonious goal-
distance model (GDM), in which effort investment is a func-
tion of the proportion of original distance remaining to the goal
(i.e., psychological distance).
•The observed purchase and effort acceleration cannot be
explained by habituation, expiration concerns, other time-trend
effects, or heterogeneity bias. For example, we observe goal-
motivated acceleration after accounting for weekly sales and
other time-varying covariates, and we find a majority of accel-
erators after accounting for unobserved heterogeneity in both
the hazard rate and the tendency to accelerate. Notably, pur-
chase and effort rates reset (to a lower level) after the first
reward is earned and then reaccelerate toward the second
reward goal.
We organize this article as follows: We begin with a brief
review of the behaviorist goal-gradient hypothesis and con-
sider its relevance for the context of incentive systems.
Then, we propose a theoretical GDM that incorporates the
goal-gradient hypothesis. In subsequent sections, we use
this model to generate and test new propositions that high-
light the intriguing consequences of the goal-gradient
hypothesis for the human psychology of rewards: We dis-
cuss a real café RP and a discrete-time proportional hazard
rate model used to test for purchase acceleration; we report
field and questionnaire experiments that test the effect of
illusionary goal progress; we report data from a second real
incentive system, which generalizes the findings to acceler-
ation and persistence in effort involving repeatedly rating
music; and we explore the implications of the goal gradient
for customer retention. Finally, we discuss the theoretical
and managerial implications of this research.
THE GOAL-GRADIENT HYPOTHESIS IN BEHAVIORISM
Originally formulated by Hull (1932) and refined by
Miller (1944), the goal-gradient hypothesis states that the
tendency to approach a goal increases with proximity to the
goal. The strongest evidence for this hypothesis has been
obtained in the context of animal learning, consistent with
Hull’s (1932, p. 42) prediction “[t]hat animals in traversing
a maze will move at a progressively more rapid pace as the
goal is approached.” Hull (1934) constructed a straight run-
way with electrical contacts placed so that he could pre-
cisely measure the time it took rats to cross each of several
six-foot sections. The key finding, which was replicated in
several variations of the procedures and the apparatus, indi-
cated that the animals ran faster the closer they were to the
food reward. Figure 1 displays a typical set of results from
Hull (1934) that reveals this pattern. In another widely
quoted study, Brown (1948) attached rats to an apparatus
that recorded the force in grams with which the rats pulled
(toward the region of reinforcement) when stopped either
close to or far from the food. Consistent with the goal-
gradient hypothesis, rats that were stopped closer to the
food pulled more strongly than those stopped farther away
(see also Anderson 1933).
A review of the literature (Heilizer 1977) reveals that
most goal gradients were obtained with rats and physical
responses (e.g., speed of locomotion). A considerable por-
tion of goal-gradient studies examined issues that are not
directly related to the current investigation, such as con-
Notes: This is a composite graph from 11 blind rats, showing the length
of time it took to traverse the several sections of a straight runway that
extended from the starting box beginning at Segment 0, continued to the
food, and finished some 21 inches beyond Segment 5. The several points
on the curve represent means from approximately 160 measurements.
Figure 1
TYPICAL FINDINGS FROM HULL’S (1934) EXPERIMENTS WITH
RATS
The Goal-Gradient Hypothesis Resurrected 41
trasting approach versus avoidance gradients (e.g., Förster,
Higgins, and Idson 1998). The limited research conducted
with humans used mostly physiological measurements (e.g.,
galvanic skin response, heart rate, arm pressure) that were
noninstrumental for goal achievement. As Heilizer (1977)
details, it is difficult to interpret noninstrumental behaviors
and physiological measurements as evidence supporting (or
refuting) the goal-gradient hypothesis. To the best of our
knowledge, there is no published study that provides
unequivocal evidence of a systematic, behavioral goal gra-
dient in humans. Thus, a primary goal of this article is to
test for behavioral (approach) goal gradients and their vari-
ous operationalizations (timing, quantity, and persistence of
effort).
In this research, we use real RPs as an empirical context
for an investigation of the goal-gradient hypothesis. Such
programs share a common underlying structure, whereby
people need to invest a stream of efforts to earn future
rewards. This general effort–reward structure applies to
many decision contexts and life domains, including con-
sumer loyalty programs, employee incentive systems, sales
force bonus plans, patient compliance programs, and even
academic tenure tracks. Nevertheless, it is noteworthy that
the empirical impact of RPs on actual customer behavior is
still largely undetermined (cf. Dowling and Uncles 1997;
Lewis 2004; Sharp and Sharp 1997).
THEORY AND MODEL
The notion that progress and distance to the goal affect
consumer motivation is supported by theories of social cog-
nition and human decision making. Dynamic models of
motivation (e.g., Atkinson 1957; Lewin 1951; Miller 1944)
propose that people possess a strong achievement drive,
which is heavily influenced by goals. Carver and Scheier’s
(1990) cybernetic control model suggests that comparisons
of the rate of progress toward the goal with a relevant crite-
rion generate affect; when progress exceeds (falls short of)
the criterion, positive (negative) affect arises (see also Fish-
bach and Dhar 2005; Soman and Shi 2003). Researchers
have also highlighted the impact of people’s psychological
distance from their outcomes and goals on decision making
and behavior (Lewin 1951; Trope and Liberman 2003). In
addition, Heath, Larrick, and Wu (1999) propose that as a
result of the diminishing sensitivity of prospect theory’s
value function, people should exert more effort as they near
their (self-imposed) goals. In summary, prior theorization
about human motivation, affect, and cognition supports the
relevance of the goal-gradient hypothesis for the human
psychology of rewards.
What are the implications, then, of the goal-gradient
hypothesis for RPs? As Kivetz (2000) originally proposed,
the notion that achievement motivation increases with
smaller goal distance suggests that customers accelerate and
persist in their efforts as they near the program’s incentive
threshold (i.e., the reward requirement or goal). The opera-
tionalization of “effort acceleration” depends on the
specifics of the particular RP. When the program require-
ments involve discrete purchases or incidents (e.g., “stay
ten nights, and earn a reward”), the acceleration will mani-
fest in more frequent activity (shorter interpurchase or inter-
visit times). When the RP is structured so that more intense
activity (e.g., a larger purchase or more units of effort) in
1Consumers can still be sensitive to absolute magnitude, and the concep-
tualization of psychological goal distance in proportional terms is likely to
apply only within a reasonable empirical range. Note that Hull (1934)
reports that the goal gradient of a 20-foot runway resembles a foreshort-
ened (proportionally contracted) gradient from a 40-foot runway. This
finding can be captured by modeling the rats’ behaviors as a function of
proportional but not absolute goal distance.
any single visit earns more credits toward the reward (e.g.,
“earn one point for each dollar spent”), acceleration may be
detected through both shorter interpurchase times and
increased purchase (or effort) quantities. In the current
research, we investigate both temporal and quantity opera-
tionalizations of goal-motivated acceleration. We also
examine various forms of RP effort, including real pur-
chases (of coffee) and actual work (rating music online).
Finally, we generalize the goal-gradient hypothesis by
examining whether people persist longer in their effort as a
function of smaller goal distance. Next, building on prior
research, we develop a parsimonious GDM that incorpo-
rates the aforementioned and other predictions.
The GDM
A great deal of research in psychophysics and judgment
and decision making has shown that perception and prefer-
ence are sensitive to relative rather than absolute dimen-
sions. For example, Stevens (1957) and his predecessors
demonstrate that sensory experiences reflect ratio (propor-
tionality) judgments rather than absolute magnitude differ-
ences. Preference and choice have also been shown to be
relative rather than absolute, depending on such factors as
the salient reference point (Kahneman and Tversky 1979),
the relative positions of other alternatives in the choice set
(Huber, Payne, and Puto 1982; Simonson and Tversky
1992), the relative accuracy and effort of decision strategies
(Payne, Bettman, and Johnson 1992), the preferences of
other people (Kivetz and Simonson 2003), and the relative
(proportional) value of the choice options (Herrnstein and
Prelec 1991).
The sensitivity to relative and reference values suggests
that consumers spontaneously consider their distance to a
goal, incorporating the total distance as a reference point,
which leads to an evaluation of relative goal distance.
Accordingly, we conceptualize and model the psychological
(or perceived) goal distance as the proportion of the total
(original) distance remaining to the goal. We define this dis-
tance as dt= (r – nt)/r, where r is the perceived total effort
requirement of the reward (i.e., the starting distance to the
goal) and ntis the amount of the requirements already ful-
filled by a person at time t. The observed measure dthas a
possible range from 1 to 0, such that 1 occurs when no
progress toward the goal has yet been made and 0 occurs
when the goal is achieved. The goal-gradient hypothesis
implies that the latent (unobserved) motivation at time t to
achieve the goal (mt*) is a decreasing function of dt; that is,
mt*/dt< 0.1
Because the underlying motivation to achieve the reward
is unobserved, we model the customer’s observed behavior
(or effort investment). Because the observed effort should
increase with stronger goal motivation, we expect there to
be greater effort with smaller proportional goal distance
42 JOURNAL OF MARKETING RESEARCH, FEBRUARY 2006
(dt). We use different operationalizations of the GDM that
capture observed effort behavior as a function of dt. Thus:
H1: Consumers accelerate their efforts to earn a reward as the
psychological distance (dt) to the reward goal decreases.
Next, we test H1using a real café RP. We subsequently
extend the goal-gradient hypothesis to the particularities of
consumer behavior by exploring its implications for cus-
tomer retention and by investigating the effects of illusion-
ary goal progress. The latter allows for a direct test of the
effect of proportional versus absolute goal distance and for
ruling out rational accounts of the goal-gradient effect, such
as time discounting.
THE CAFÉ RP
To facilitate a strong and realistic test of intertemporal
behavior, we conducted a field study in which customers
made real coffee purchases in the context of an actual café
RP. By tracking purchases, we were able to test for pur-
chase acceleration toward the reward goal (i.e., H1). The
study included two control groups: (1) members from
whom we “bought back” incomplete cards and (2) cus-
tomers participating in an experimental control program
that was identical to the actual RP, except that purchasing
coffee did not earn rewards. The inclusion of these control
groups enabled us to compare the intertemporal purchase
behavior of redeemers and nonredeemers (i.e., “loyals” and
“defectors”) and to examine differences between reinforced
and nonreinforced behavior. We also investigate alternative
explanations using various methodologies, including testing
a key corollary termed “postreward resetting,” exploring the
behavior of the two aforementioned control groups, and
incorporating unobserved heterogeneity in the tendency to
accelerate.
Method
The participants in the field study were customers of a
café located within the campus of a large East Coast univer-
sity. At the time of data collection, the café had several on-
campus locations. Customers were offered free enrollment
2Members could also earn a free baked good of equal monetary value
(biscotti, croissant, or muffin). However, the majority (85%) of reward
redemptions were for coffee, and the results did not differ on the basis of
the redeemed reward.
in a café RP, in which they needed to make ten coffee pur-
chases to earn a reward. To enable the tracking of their pur-
chases, members were required to carry a frequent-coffee-
buyer card (see Figure 2, Panel A). They received one stamp
on the card for each coffee purchase they made (only one
stamp per visit was permitted). Stamps were printed with
six-wheel automatic numbering machines that, unbe-
knownst to customers, sequentially numbered each stamp
issued (these numbers did not resemble dates). After mem-
bers accumulated ten stamps from any combination of the
café locations, they were eligible for a free coffee
redeemable on their next visit to one of the café locations.2
Members were asked to indicate their name and e-mail
address on the back of the card, which enabled us to match
cards redeemed by the same member. Overall, we obtained
949 completed (i.e., redeemed) ten-stamp cards, recording
approximately 10,000 coffee purchases.
Buyback of incomplete cards. The design of the café RP
enabled us to collect only those cards that were completed
and redeemed for a reward. Therefore, to sample from the
broader member population (i.e., including the members
that would otherwise fail to complete or redeem their card),
we instituted a card buyback offer. Research assistants pos-
ing as café employees approached individual card-holding
members and offered them the opportunity to return their
cards to the café (regardless of the number of stamps on
them) for a cash award of $4 per card and a 1% chance to
win $100. Members were told that the cards were needed
for the café’s customer research. Overall, we acquired 73
buyback cards.
Recruitment of experimental control group with transpar-
ent cards. We recruited 42 customers for an experimental
control condition in which they carried “transparent cards.
These cards were similar to the regular ten-stamp card but
Figure 2
THE CAFÉ RP CARDS
A: 10-Stamp Card B: 12-Stamp Card with Two “Bonus” Stamps
The Goal-Gradient Hypothesis Resurrected 43
3We excluded from the analysis days on which the café was closed.
were marked on the back so that they could not be
redeemed for a reward. The control customers were ran-
domly sampled from the population of program members.
Research assistants (posing as café employees) intercepted
customers who requested a regular program card and
offered instead to enroll them in a “purchase-habit” study
designed to help the café management better understand its
customers. Participants were asked to carry a “transparent”
card and have it stamped every time they made a qualifying
purchase at the café. They received $5 when they agreed to
participate in the study, and they were told that they would
receive $15 more when they surrendered their cards six
weeks later, regardless of how many coffee purchases they
made during that time. We verified that control participants
did not use the regular RP cards during the study.
Results
A plot of the raw mean interpurchase times, aggregated
across all redeemed cards (excluding transparent and buy-
back cards), demonstrates purchase acceleration as a func-
tion of smaller goal distance (see Figure 3).3Consistent
with H1, as members accumulated more stamps on their
cards, the average length of time before their next coffee
purchase decreased. The mean difference between the first
and the last observed interpurchase times was .7 days (t =
2.6, p< .05), representing an average acceleration of 20%
from the first to the last interpurchase time. As an estimate
of the overall effect of acceleration on the average card, it is
possible to compare the mean observed time to complete a
card, which was 24.6 days, with the number of days it
would have taken to complete a card at the rate of the first
observed interpurchase time, which was 29.4 days. This
yields a difference of nearly 5 days (16%) in card comple-
tion time.
Although the analysis of raw data provides preliminary
support for purchase acceleration (H1), it does not account
for various important factors. Accordingly, we used more
sophisticated data analysis, namely, a discrete-time propor-
tional hazard rate model. This modeling approach incorpo-
rates time-varying covariates and controls (e.g., weekly
number of issued stamps) intended to rule out alternative
explanations, such as time-trend effects. Our modeling
approach also enables us to account for unobserved hetero-
geneity (i.e., individual differences in base purchase rates
and acceleration tendencies).
Hazard rate modeling methodology. In the main data set,
each row represented one day per customer on a card on
which the customer could have made a purchase; we
included the days after the first stamp was received up to
the day of the last stamp. There are variables in the data set
at the customer level, day level, and card level. Overall,
from 949 completed (i.e., redeemed) ten-stamp cards that
captured nearly 10,000 coffee purchases, this data set
yielded 29,076 rows of data.
Hazard rate models (Cox 1972) are an important method
to model interpurchase times. In these models, the instanta-
neous probability of purchase (called the hazard function,
h[t]) is estimated, conditional on the amount of time since
the prior purchase. In the discrete-time model (Gupta 1991;
Helsen and Schmittlein 1993), the hazard model likelihood
is decomposed into probabilities of purchase within given
time intervals.
In a hazard rate model, the baseline continuous survival
function S(t) represents the probability that no purchase
will occur after time t has elapsed since the previous
purchase:
We used a discrete-time proportional hazard model para-
meterized as the discretized survival function. In line with
Seetharaman and Chintagunta’s (2003) derivation, the full
discretized survival function can be expressed as a function
of the baseline hazard function h(t), time-varying covariates
Xt(including the proportional distance to the goal), and
estimated covariate coefficients β(including a constant
term):
In our application, we decompose the survival function
into day-specific components, and our dependent variable is
the probability of purchase on a given day, conditional on
no purchase having yet occurred:
()Pr(, ) (, )
(, ) exp31
11
1
tSt
St
tt
t
X
X
X
==
=
ehudu
St
St
t
u
t
t
u
Xβ()
()
()
l
l
1
eXtβ
.
() (, ) exp ( )2
1
1
St e hwdw
t
u
u
u
t
u
XX
=
=
β
.
() () exp ( ) .1
0
St hudu
t
=
0
.5
1
1.5
2
2.5
3
3.5
12 3456 789
Number of Stamps on Card
Mean Interpurchase Time
dt= .9 .8 .7 .6 .5 .4 .3 .2 .1
Progress toward goal
Figure 3
PURCHASE ACCELERATION AS A FUNCTION OF SMALLER
GOAL DISTANCE
44 JOURNAL OF MARKETING RESEARCH, FEBRUARY 2006
4All the results are replicated when we exclude from the analyses the
subsequent cards of members who redeemed more than one card.
In conducting our analysis at the day level, we assume
that each day is a potential purchase occasion, except for
days on which the café is closed. Because we estimate each
day’s probability as the difference in survival probability
from the start of the day to the end of the day, it was neces-
sary to code each day t as a range of continuous times
between the lower bound tland the upper bound tuwhen
applying Equation 3. Purchases made on the same day were
coded as occurring between time tl= 0 and time tu= .5, pur-
chases on the subsequent day were coded as occurring
between tl= .5 and tu= 1.5, and so forth. In the following
likelihood function for an observed purchase, we denote the
observed number of days elapsed at time of purchase by T,
and we code an indicator function δv, which represents
whether a purchase occurred on day v (δv= 1) or did not
occur on day v (δv= 0):
The full likelihood is the product of all the purchase-
specific likelihoods across cards and customers (Seethara-
man and Chintagunta 2003).
We determined the best-fitting base hazard function with
Schwarz’s Bayesian information criterion (BIC) measure.
The BIC measure trades off improvements in the log-
likelihood for increases in the number of parameters. We
used latent classes to account for unobserved heterogeneity
in the hazard rate parameters (Kamakura and Russell 1989),
which is important to rule out heterogeneity bias. Because
the unit of analysis in the latent-class model is the customer,
we took into account the common error variance when mul-
tiple cards belonged to a single individual, and we specifi-
cally accounted for cross-customer unobserved heterogene-
ity.4The latent-class modeling can be considered a
nonparametric multivariate distribution on the hazard rate
parameters across participants; each latent class represents a
support point in the distribution. Although we found signifi-
cant unobserved heterogeneity in the hazard rate parame-
ters, when we ran the models without latent-class segmenta-
tion, all of the results still held. In all models, we used
GAUSS software to implement Newton–Raphson maxi-
mum likelihood estimation, and we determined the number
of latent classes using the BIC criterion.
Analyses of acceleration with common parameters across
consumers. In this subsection, the primary focus of our
modeling is the effect of goal distance on interpurchase
times. Recall that the distance to the reward goal is captured
with the measure dt= (r – nt)/r. In the café RP, ntis the num-
ber of stamps accumulated on the card at time t, and r is the
total number of required stamps. Given that in the main data
set we model probability of purchase when there are
between 1 and 9 stamps accumulated on the card (and r =
10), the measure dtranges between .9 and .1.
To test the goal-gradient hypothesis (H1) in this and the
subsequent empirical applications, we constructed the
GDM, which includes linear and quadratic parameters that
() Pr(, ) [ Pr(, )] .41
1
0
Lv v
vv
v
T
vv
=
=
XX
δδ
5In this and subsequent empirical applications, we examined higher-
order parameters using orthogonal contrast codes (Fisher and Yates 1957),
but we found that these were not significant.
6The control variables also included card type (indicating whether the
member purchased American or Italian coffees) and additional time-
varying covariates, such as midterm break (a code for whether the day was
during the midterm break), day of week (linear trend from Monday
through Thursday), and dummy codes for Friday and Saturday–Sunday.
None of the covariates were allowed to vary across the latent classes.
7All covariates were normalized before model-fitting in this and the sub-
sequent model estimations.
capture the effect of goal distance on observed behavior.5
Here, we added the GDM as a covariate in the proportional
hazard model. We parameterized the model by defining the
probability of purchase for customer i on a given day t as
follows:
where
g = exp[β0+ β1dit + β2(dit – d
i)2+ γXit];
S(t) = the baseline survival function;
dit = the proportion of total distance remaining to
the goal for individual i at time t;
dit – d
i= the mean-centered proportion of total dis-
tance remaining to the goal;
β1and β2= the linear and quadratic goal-distance
parameters, respectively;
Xit = the vector of covariates (i.e., control varia-
bles); and
γ= the corresponding vector of coefficients.
The parameters for estimation in the GDM are the inter-
cept β0, the goal-distance parameters β1and β2, and the
vector of coefficients γ. Consistent with H1, we expect the
parameter β1to be less than zero, capturing the predicted
increase in the probability of purchase (hazard rate) as a
function of smaller goal distance (dit). Note that if β1is
greater than zero, we observe “effort deceleration” (i.e.,
lower probability of purchase as a function of smaller goal
distance). Among the time-varying covariates, we included
both the weekly number of issued stamps and a code for
whether a given day was after the end of the spring classes
to control for alternative explanations based on time trend.6
We accounted for unobserved heterogeneity in the base
hazard rate parameters (but not in the goal-distance or the
covariate parameters) using the methodology we described
previously. Table 1 displays the estimated parameters for
the log-logistic hazard rate function and the GDM in Equa-
tion 5.7The linear goal-distance parameter b1was less than
zero (p< .01). This result supports H1and demonstrates
that members accelerated their coffee purchases as they got
closer to earning a free coffee. Consistent with the goal-
gradient curve in Figure 3, the negative quadratic parameter
b2(p< .01) implies a diminishing rate of acceleration. A
nested likelihood ratio test indicated that the GDM provided
an improvement in fit over a “naive” model in which β1and
β2were restricted to zero (χ2= 18.8, d.f. = 2, p< .01).
() Pr(, ) ()
() ,51
iit u
g
tSt
St
X=
l
The Goal-Gradient Hypothesis Resurrected 45
Tabl e 1
THE GDM WITH UNOBSERVED HETEROGENEITY IN BASE HAZARD RATES (CAFÉ RP)
A: Latent Class-Level Parameters
Class 1 Class 2 Class 3 Class 4 Class 5
Segment size (%) 30 28 7 32 3
γ(hazard rate) .5** .7** 1.5** .06** 1.8***
α(hazard rate) 1.4** 2.3** 3.7** 1.15** 1.9***
β0.4* –.3**–.7** 1.5**0–.02**
B: Parameters Not Varying by Latent Class
Goal-Distance Parameters Estimate
Linear effect of goal distance, b1–.03**
Quadratic effect of goal distance, b2–.04**
Covariate Parameters (i.e., Control Variables)
Weekly number of stamps –.005***
End of semester .04**
Midterm break –.17**
Card type (American versus Italian) –.10**
Day of week (Monday–Thursday) –.02
Friday –.18**
Saturday–Sunday –.39**
*p< .05 (based on Wald test; two-tailed).
**p< .01 (based on Wald test; two-tailed).
Alternative Explanations
Although the observed and estimated purchase accelera-
tion is consistent with H1and the existence of a goal gradi-
ent in RPs, several alternative explanations for this finding
must be examined. One such rival account is that an uniden-
tified time-trend effect led to a decrease in interpurchase
times. For example, members could have developed a card-
usage routine or an addiction to coffee (i.e., habituation).
Relatedly, although café customers had no reason to expect
the RP to expire, such concerns may have motivated mem-
bers to accelerate their purchases.
Postreward resetting. As we previously discussed, we
included in our models two time-varying covariates that are
intended to control statistically for time-trend effects,
namely, the weekly number of issued stamps (essentially a
control for sales trend) and whether the day was after the
end of spring classes (when some students graduate). Nev-
ertheless, to examine the time-trend and habituation
accounts directly, we analyzed the postredemption purchase
behavior of 110 members who completed a first card and
then reengaged in the program to complete a second card.
These members demonstrated strong goal gradients (i.e.,
faster interpurchase times as a function of lower dit) on both
of their cards (b1= –.06 and –.09 for the first and second
card, respectively; both ps < .05).
According to the goal-gradient hypothesis, the motiva-
tion to invest effort increases with progress toward the
reward threshold. Therefore, a corollary of this hypothesis
is that after customers earn their first reward, they should
exhibit a postreward resetting (i.e., a slowdown) in their
purchase rates when they begin working toward their sec-
ond reward, followed by a second pattern of purchase accel-
eration. In contrast, time-trend and habituation accounts
predict monotonic acceleration in coffee purchases across
the two cards, at least until some plateau or ceiling effect is
reached. Therefore, according to these rival accounts, the
interpurchase times on the second card should be a direct
continuation of the trend on the first card.
To contrast the resetting corollary with the time-trend and
habituation accounts, we calibrated a nonparametric model
with individual dummy codes that represented each differ-
ent interpurchase time across the two cards. The advantage
of using this nonparametric model is that we can separately
estimate the 18 interpurchase times for the two sequential
cards, while controlling for the covariates Xit and for the
unobserved heterogeneity in the base hazard rates. Figure 4
reveals a clear overlap between the plots of the interpur-
chase times estimated for the two cards. The figure also
shows that the first two interpurchase times on the second
card (X
= 3.1 and 2.7 days, respectively) are substantially
slower than the last two interpurchase times on the first card
(X
= 2.2 and 2.1 days, respectively) and are similar to the
first two interpurchase times on the first card (X
s = 3.2 and
2.8 days, respectively).
To test for postreward resetting statistically while con-
trolling for time-varying covariates and heterogeneity in the
base hazard rates, we modeled only the last two interpur-
chase times on the first card and the first two interpurchase
times on the second card. Instead of linear and quadratic
goal-distance parameters, we included a contrast code for
first versus second card. The first two interpurchase times
on the second card were slower than the last two interpur-
chase times on the first card (p< .01). The test was in the
same direction and significant when we compared only the
first interpurchase time on the second card with the last
interpurchase time on the first card (p< .05).
In summary, consistent with the goal-gradient hypothe-
sis, purchase rates revealed a clear postreward resetting.
Members accelerated their coffee purchases toward their
first reward (a free coffee) and then slowed down when they
46 JOURNAL OF MARKETING RESEARCH, FEBRUARY 2006
began working toward a second similar reward; the same
members subsequently reaccelerated their purchases as they
approached the second reward. These findings rule out the
habituation account and other forms of time trend (e.g.,
graduation or expiration concerns). Next, we examine the
purchase behavior of two control groups, which enables us
to compare reinforced and nonreinforced behavior and fur-
ther rule out alternative explanations.
Analysis of nonreinforced behavior (transparent cards).
According to the goal-gradient hypothesis (H1), card-
holding customers accelerate their purchases because they
experience enhanced motivation as they get closer to the
goal (i.e., the reward threshold). A corollary of this hypoth-
esis is that customers will fail to exhibit acceleration when
carrying a transparent card (similar to the regular ten-stamp
card but unredeemable for a reward), that is, when their pur-
chase behavior is not reinforced with any purchase-
contingent reward. In contrast, if purchase acceleration
reflects other factors, such as a time trend in sales, we
would expect to observe similar acceleration among cus-
tomers enrolled in the transparent card control group. The
intertemporal purchase behavior of customers carrying
transparent cards can serve as a benchmark or control for
the assessment of the acceleration we detected in the main
data set.
Unlike the main data set, which included only complete
(redeemed) ten-stamp cards, some of the transparent cards
were incomplete. Therefore, we first analyzed all transpar-
ent cards that included at least three stamps. We estimated
the GDM (shown in Equation 5) using the same log-logistic
hazard function, accounting for unobserved heterogeneity
in the base hazard rates. All the significant coefficients for
the control variables have the same sign and the same inter-
pretation as in the model of redeemed cards. However, to
account for observed differences in base hazard rates
between cards collected with fewer or more stamps, we
added a coefficient that captures the effect of the final num-
ber of stamps on the card.
In the GDM for transparent cards, we found deceleration
(b1= .3, p< .01) and no curvature (b2= .006, p> .1). The
interpurchase times on the transparent cards steadily
increased as customers neared the nonreinforced (unre-
warded) completion of the card. Note that this model was fit
with data (i.e., days) only up to the last purchase on the
transparent card. We found an even stronger deceleration
effect (b1= .4, p< .01; b2= –.1, p> .1) when we included
all observed days up to the collection of the transparent card
(i.e., including days after the last purchase on incomplete
transparent cards). Finally, we calibrated the GDM on the
subsample of completed transparent cards, and again, we
found deceleration (b1= .15, p< .05; b2= .05, p> .1).
Overall, the analysis of the transparent cards supports the
notion that the purchase acceleration we found in the main
data set was driven by goal motivation rather than by time-
trend effects or habituation. Although participants in the
transparent card program were sampled from the population
of RP members, because their reward ($20) was not contin-
gent on their purchase behavior, tendency to accelerate
toward the ten-stamp threshold was reversed.
Analysis of incomplete (buyback)cards. We believe that
the sample of buyback cards differs from the sample of
redeemed cards (used in the main analyses) in that members
from whom we bought back cards exhibited a lack of goal
motivation. Buyback cards were in circulation for a period
of time that was longer than that of redeemed cards (X
= 65
days versus X
= 25 days; t = 7.6, p< .01), which suggests
that without our intervention, such buyback cards would
have resulted in “breakage” (i.e., nonredeemed stamps or
cards). This allows for a comparison of the intertemporal
purchase behavior of nonredeemers (defectors) and
redeemers (loyals).
We calibrated the GDM on the sample of buyback cards
using the log-logistic hazard function, accounting for unob-
served heterogeneity in the base hazard rates. We included
buyback cards with at least three stamps and added the final
number of stamps on the card as a covariate to account for
observed differences in the base hazard rates of cards with
fewer or more stamps. Again, all the significant coefficients
for the control variables had the same sign and the same
interpretation as the model of redeemed cards.
In the GDM for incomplete buyback cards, we found no
linear effect of goal distance (b1= .02, p> .1), but there was
a quadratic effect (b2= –.1, p< .05). This pattern suggests
that, unlike redeemers, buyback customers do not accelerate
their purchases as a function of progress toward the reward.
Moreover, when we modeled all observed days up to the
buyback of the incomplete card (i.e., including days after
the last purchase on the card), we found an increasing
deceleration effect (b1= .3 and b2= –.1, respectively; ps <
.01). Overall, customers from whom we bought back
incomplete cards (defectors) differed from redeemers (loy-
als) in that the former did not accelerate and even deceler-
ated their purchases as a function of accumulated stamps.
Analysis of unobserved heterogeneity in goal-motivated
acceleration. A final alternative explanation that we must
Card 1
Card 2
Number of Stamps on Card
dt =
0
0.5
1
1.5
2
2.5
3
3.5
4
1
.9
2
.8
3
.7
4
.6
5
.5
6
.4
7
.3
8
.3
9
.1
Mean Estimated
Interpurchase Time
Figure 4
AVERAGE INTERPURCHASE TIMES ON FIRST AND SECOND
CARDS
The Goal-Gradient Hypothesis Resurrected 47
Tabl e 2
PARAMETER ESTIMATES WITH UNOBSERVED HETEROGENEITY IN GOAL-DISTANCE AND HAZARD RATE PARAMETERS (CAFÉ RP)
Latent Class-Level Parameters Class 1 Class 2 Class 3 Class 4
Segment size (%) 58 29 7 6
γ(hazard rate) 0.6***00.07***01.5***00 0.900***
α(hazard rate) 1.7***01.2***00 3.5***00 1.3***00
β00.09*** 1.4***00 –.7***00 0.5***00
Goal-Distance Parameters
Linear effect of goal distance, b1–.04***–.04***0 –.003*** 0.007***
Quadratic effect of goal distance, b2–.06*** 0.005*** –.10***0 –.009***
*p< .1 (based on Wald test; two-tailed).
**p< .05 (based on Wald test; two-tailed).
***p< .01 (based on Wald test; two-tailed).
Notes: The model includes the same control variables as those we report in Table 1. The covariate estimates were nearly identical, and we do not report
them here.
8The first interpurchase time was 3.3 days, whereas the total card time
yielded an average rate of 2.7 days per purchase. This is equivalent to 9
purchases per month based on the first interpurchase time, compared with
11 purchases per month based on the observed rate that includes purchase
acceleration.
consider is heterogeneity bias. Specifically, although we
accounted for unobserved heterogeneity in the base hazard
rates, it is possible that the estimation of homogeneous
goal-distance parameters gave rise to an apparent goal gra-
dient that did not exist among a majority of individual
members. Therefore, we calibrated the GDM on the main
data set by simultaneously (i.e., jointly) estimating unob-
served heterogeneity in both the hazard rate and the goal-
distance parameters. Table 2 displays the estimated segment
(class) sizes and segment-level parameters. Segment 1, the
largest segment (58%), has significant linear and quadratic
goal-distance parameters; this pattern of acceleration is
similar to that which we obtained previously with the
homogeneous goal-distance parameters. Segment 2 (29%)
has the same linear goal-distance parameter as the largest
segment, but the coefficient does not reach statistical sig-
nificance (p= .13) because of the smaller segment size.
Segments 3 and 4 (7% and 6%, respectively) both have a
linear goal-distance parameter near zero. Overall, the seg-
mentation analysis is inconsistent with the heterogeneity
bias rival account; we found a majority of significant accel-
erators after accounting for unobserved heterogeneity in the
tendency to accelerate.
Evidence for the Goal-Gradient Hypothesis in the Café
RP: Discussion
Consistent with the goal-gradient hypothesis (H1), the
findings from the café RP indicate that customers acceler-
ated their purchases as a function of smaller goal distance.
We observed the decrease in interpurchase times in the raw
data and estimated it using a discrete-time proportional haz-
ard rate model. The 20% (.7 day) decrease in average inter-
purchase times from the first to the last stamp on the card
implies that in a typical month, on average, members pur-
chased two more coffees than they would have without an
RP in order to earn one free coffee.8
We ruled out several alternative explanations for the
observed purchase acceleration using an experimental con-
trol (i.e., the transparent cards) and statistical controls. We
also found that members exhibited a markedly similar
acceleration pattern on two sequential cards; that is, we
observed a slowdown in purchase rates after participants
earned the first reward and began to work toward the sec-
ond. Such postreward resetting is inconsistent with the rival
accounts based on time trend or habituation, whereas it is
consistent with the notion that the motivation to expend
effort depends on goal distance.
The analysis of the incomplete (buyback) cards revealed
that defectors were less likely to exhibit a goal gradient
than were members who redeemed at least one card. This
finding suggests that insufficient motivation to earn
rewards underlies both defection (churn) and deceleration
in purchase rates. In a subsequent section, we use
individual-level acceleration estimates to examine more
systematically the relationship between goal motivation
and customer retention. Next, we extend the goal-gradient
hypothesis to the particularities of the human psychology
of rewards by exploring the effect of illusionary progress
toward the goal.
THE ILLUSION OF PROGRESS TOWARD THE GOAL
Building on the behaviorist goal-gradient hypothesis, we
predicted and found that customers accelerate their pur-
chases as they get closer to the reward threshold. Although
this result is consistent with our conceptualization that goal
proximity increases motivation, it could also be explained
on rational, cost–benefit grounds. In particular, as the dis-
tance to the reward diminishes, any additional unit of effort
reduces a greater percentage of the remaining discrepancy
to reward attainment. In addition, time-discounting theories
imply that (temporal) proximity enhances the value of
rewards. Thus, the perceived benefit from an incremental
unit of effort may increase closer to the reward threshold.
The rational explanations for purchase acceleration rely
on the absolute distance to the reward. In contrast, our con-
ceptualization suggests that the key determinant of goal
motivation is the proportion of original distance remaining
to the goal. The GDM captures this psychological quantity
through the measure dt, which is influenced not only by the
absolute distance remaining to the reward, r – nt, but also by
the perception of the original goal distance, r (i.e., the total
a priori effort requirement for the reward). Thus, we posit
that, all else being equal, goal motivation is influenced by
the perceived rather than by the real progress toward the
48 JOURNAL OF MARKETING RESEARCH, FEBRUARY 2006
9This is easy to verify algebraically by investigating the change in the
function dt= (r – nt)/r after an addition of to both r and nt. Specifically,
dt+= ([r + ] – [nt + ])/(r + ) = (r – nt)/(r + ) < (r – nt)/r = dt. That is,
unlike absolute goal distances, proportional distances are affected by a
common addition, such that dt+< dt.
goal. Perceived and real progress are distinct when the per-
ception of the original goal distance can be systematically
manipulated without affecting the real, absolute distance
remaining to the goal.
Marketers (or researchers) can create “illusionary goal
progress” by increasing the total original distance to the
reward (i.e., increasing r), while increasing the perception
of the distance (requirements) already completed (i.e.,
increasing ntby the same quantity). Such a manipulation
reduces the psychological (or proportional) distance to the
reward, dt, while holding constant the real, absolute remain-
ing distance (i.e., the actual remaining requirements, r –
nt).9Accordingly, in the subsequent tests, we create illu-
sionary progress by increasing the total requirements of a
baseline RP, while awarding consumers with an equivalent,
yet bogus, “head start” (i.e., bonus credit or points in the
amount of the incremental requirements).
A manipulation of illusionary progress distinguishes
between our goal-gradient conceptualization and the
rational accounts of purchase acceleration. If the psycho-
logical distance to the reward influences motivation, as
defined by the proportion of original distance remaining to
the goal (dt), illusionary progress should enhance goal moti-
vation and consequently lead to increased efforts to earn the
reward. In contrast, because illusionary goal progress does
not affect the absolute (real) distance to the reward, cost–
benefit calculations and time discounting cannot account
for the predicted effort acceleration. Thus:
H2: Illusionary progress toward the reward goal motivates con-
sumers to accelerate their efforts to earn the reward.
In H2, we predict that illusionary goal progress leads to
faster completion of the reward requirements. We begin
with a strong and realistic (field) test of H2, in which we
examine actual purchase behavior. We then report the
results of process tests that are intended to rule out alterna-
tive explanations based on the idiosyncratic fit heuristic
(Kivetz and Simonson 2003) and sunk cost (Thaler 1980).
A Field Experiment of Illusionary Goal Progress
Method. The participants were 108 customers of the café
we described previously. They were randomly assigned to
either a control condition or an experimental (illusionary
goal progress) condition. Specifically, research assistants
posing as café employees randomly offered customers
either a 10-stamp or a 12-stamp coffee card (see Figure 2,
Panel A and Panel B, respectively). The 10-stamp and the
12-stamp cards indicated that members were required to
accumulate 10 and 12 coffee purchases, respectively, to
earn one free coffee. However, customers assigned to the
12-stamp experimental condition received two preexisting
bonus stamps, described as an offer to anyone who opted to
join the program. Thus, although the two groups faced iden-
tical effort requirements when joining the program (i.e., r –
nt= accumulating 10 coffee purchases), the experimental
group started with a lower proportion of original distance
remaining to the goal than did the control group (i.e., dt+2 =
.83 and dt= 1.0, respectively). All other aspects of the pro-
gram were held constant across the two conditions and were
identical to those we described previously for the café RP.
Results. Consistent with H2, the results indicate that illu-
sionary goal progress led to faster completion of the reward
requirement. On average, customers in the control condition
completed the ten required purchases (for the 10-stamp
card) in 15.6 days. In contrast, customers in the experi-
mental (illusionary goal progress) condition completed the
ten required purchases (for the corresponding 12-stamp
card) in only 12.7 days, nearly three days or 20% faster (t =
2.0, p< .05; medians = 15 versus 10 days; Z = 2.1, p< .05
[Mann–Whitney U test]).
Process Tests of Illusionary Goal Progress
In these questionnaire-based experiments, we tested H2
and the alternative explanations using travelers who were
waiting for trains at sitting areas in a major train station. We
randomly assigned 65 travelers to either a control or an
experimental condition of a hypothetical frequent-diner
program offered by their favorite pizza chain. In the control
condition, respondents were told that they would need to
carry an eight-stamp card (shown in a picture), on which
they would receive one stamp for each pizza meal they
bought at the chain. After they accumulated eight stamps,
they would earn a free medium-sized pizza of their choice.
In the experimental condition, we asked respondents to
evaluate a similar frequent-diner program, except that they
needed to carry a ten-stamp card (i.e., the program suppos-
edly required purchasing ten pizza meals). In this condition,
respondents were exposed to an illusionary goal progress.
In particular, they were told that as a special offer for join-
ing the program, they would receive two free bonus stamps
(they were shown a ten-stamp card with the first two stamp
slots already checked). Thus, whereas the control and the
experimental groups faced identical effort requirements
(i.e., r – nt= eight pizza meals), the proportion of original
distance remaining to the goal was lower for the experi-
mental group than for the control group (i.e., dt+2 = .8 and
dt= 1.0, respectively).
We first asked respondents in both conditions to rate the
likelihood that they would join the program on an 11-point
scale, ranging from 0 (“definitely would not join”) to 10
(“definitely would join”). Then, we told respondents to
assume that they actually joined, and we asked them to esti-
mate how many weeks it would take them to complete the
program. Consistent with H2and the results of the field
experiment, respondents in the experimental versus control
condition estimated completing the eight required pur-
chases in fewer weeks (X
= 11 versus X
= 16 weeks; t =
1.6, p< .1; medians = 8 versus 12 weeks; χ2= 6.5, p< .05
[nonparametric median test]).
We elicited respondents’ likelihood of joining to rule out
an alternative explanation (based on the idiosyncratic fit
heuristic; Kivetz and Simonson 2003) for the predicted illu-
sionary goal progress effect. In particular, according to the
idiosyncratic fit heuristic, consumers decide whether to join
RPs and other promotional programs on the basis of their
individual fit (relative to typical other consumers) with the
program. Therefore, in both the aforementioned field
experiment and in the current test, we deliberately used a
The Goal-Gradient Hypothesis Resurrected 49
manipulation of illusionary goal progress that we did not
expect to affect respondents’ idiosyncratic fit with the RP.
Specifically, we described the two free bonus stamps in the
experimental conditions as an offer to anyone who opted to
join the program. Indeed, consistent with the notion that
idiosyncratic fit was not affected by the manipulation of
illusionary goal progress, we found no effect on the likeli-
hood of joining the frequent-diner program (X
= 5.9 and
X
= 5.8 in the experimental and control condition, respec-
tively; t = .1, not significant [n.s.]).
An alternative explanation for the observed illusionary
goal progress effect is that the two bonus stamps were con-
sidered a (virtual) sunk cost (e.g., Thaler 1980). Relatedly,
the bonus stamps may have enhanced the perceived value of
the card, thus leading to estimations of faster completion
time. To examine this rival account, we randomly assigned
118 new respondents (sampled from the same population of
travelers) to one of three conditions: (1) the previous
illusionary goal progress experimental condition (i.e., a ten-
stamp card with two preexisting bonus stamps), (2) the pre-
vious control condition (i.e., an eight-stamp card with no
stamps yet), and (3) a sunk-cost condition. The experi-
mental and control conditions were identical to the corre-
sponding conditions we described previously, except that
we asked respondents to imagine that they had recently
joined the program. In the sunk-cost condition, we asked
respondents to imagine that they had recently joined a ten-
stamp frequent-diner program, had made two pizza meal
purchases, and therefore had two stamps on their card.
Thus, the sunk-cost condition was identical in all aspects to
the experimental condition (including the picture of a ten-
stamp card with two stamps already on it), except that the
two stamps were due to the respondent’s own purchase
effort. Note that all three conditions entailed the same
absolute remaining distance to the reward goal (eight addi-
tional pizza purchases).
In all three conditions, we asked respondents to imagine
that they lost their current frequent-diner card. We then
asked them to rate on four scales how sad, mad at them-
selves, upset, and disappointed they would feel as a result of
the loss of the card. Participants rated these items on four
seven-point scales, ranging from 1 (e.g., “not at all sad”) to
7 (e.g., “very sad”). We averaged the scales into a single
measure of feeling valence (α= .88).
Respondents’ ratings indicated that they felt worse about
losing their card in the sunk-cost condition (X
= 2.1) than in
either the experimental (illusionary goal progress) condition
(X
= 1.7; t = 1.9, p< .05) or the control condition (X
= 1.7;
t = 1.9, p< .05). Importantly, there was no difference in
feeling valence between experimental and control respon-
dents (t = .2, n.s.). These results are inconsistent with the
sunk-cost alternative explanation. In particular, if illusion-
ary goal progress gives rise to a faster purchase rate because
bonus credits are construed as sunk cost, we would expect
respondents to feel a greater sense of loss after losing the
experimental rather than the control card. Because the sunk-
cost respondents felt worse about losing their card, we can
rule out the possibility that a measurement problem gave
rise to the similarity in (good) feelings between the experi-
mental and the control respondents.
The Illusion of Progress Toward the Goal: Discussion
The effect of illusionary goal progress provides direct
support for our proposition that psychological goal distance
(dt) is a key determinant of achievement motivation and
willingness to invest effort. Whereas this effect is consistent
with the GDM and the conceptualization of proportional
goal distance, it is inconsistent with the rational accounts of
purchase acceleration. That is, illusionary goal progress
does not reduce the absolute distance to or the delay of the
reward and therefore should have no effect according to the
cost–benefit and time-discounting explanations.
THE JABOOM MUSIC-RATING INCENTIVE PROGRAM
Thus far, we have operationalized our test of the goal gra-
dient (H1) using acceleration in interpurchase times. In this
section, we generalize the findings to effort involved in
repeatedly rating music and to goal gradients operational-
ized through acceleration in both intervisit times and rating
quantities and through increased persistence closer to the
goal. We analyze secondary data we obtained from a real
incentive system, in which participants earned rewards for
rating songs over the Internet. Next, we describe the music-
rating program in detail.
The Methodology of the Music-Rating Incentive Program
The music-rating program was launched by MoodLogic
Inc., a technology company that develops and sells music
organization software. The company initiated the program
to build a database of music perceptions and tastes (required
for its music organizers and preference engines). The pro-
gram, labeled “Jaboom,” was operated on a dedicated Web
site (members were addressed on the site as “Jaboomers”).
Internet users, recruited through an e-mail marketing cam-
paign, were offered free enrollment in the RP, in which they
needed to rate 51 songs on the Jaboom Web site to earn a
$25 Amazon.com certificate. The RP, which was presented
to participants as an ongoing program, continued for a
period of 24 months after our observation period. Thus,
expiration concerns should not have affected the behavior
of program members.
On joining, members were asked to provide a valid e-
mail address and select a unique login name and password.
This information was used to determine the dates of each
member’s site visits and the number of songs the individual
member rated on each visit. There were no constraints on
the number of songs that could be rated in a single visit or
on the number of certificates that could be earned by a
single member.
Members could rate songs from one of six genres of their
choice (e.g., rock, country, jazz) and could skip a given
song or terminate their rating session at any point. Each
song was rated on approximately 50 scales, while the mem-
ber repeatedly heard the same 30-second song snippet. The
scales elicited subjective perceptions and tastes (e.g., mood
and likeability of the song) and more objective judgments
(e.g., predominating instruments). On average, it took about
four minutes to rate a typical song. A screen shot of the
Jaboom music-rating interface appears in Figure 5.
Results
The data set includes the rating behavior of 148 mem-
bers, who rated a total of 14,866 songs in 472 separate Web
50 JOURNAL OF MARKETING RESEARCH, FEBRUARY 2006
Figure 5
THE JABOOM MUSIC-RATING WEB INTERFACE
10In this section and in the subsequent subsections, we obtained similar
results when we excluded from the analyses the data from subsequent cer-
tificates of members who earned more than one certificate.
site visits. Given that during most (i.e., 96%) of the Web
site visits members rated multiple songs, we examined both
the quantity of ratings in each visit and the intervisit times.
We modeled intervisit times using the discrete-time propor-
tional hazard rate model we described previously. The find-
ings were similar to those of the café RP. We briefly
describe them here and then report the analyses and results
of the quantity and persistence operationalizations of the
goal-gradient hypothesis.
Tests of the Goal-Gradient Hypothesis with Intervisit Times
In our data set, there were 371 attempted reward certifi-
cates (i.e., with at least 1 song rated toward the certificate)
and 262 earned certificates (i.e., with 51 songs rated). Of
the 262 earned certificates, 114 were completed in a single
visit. Although such single-visit certificates arguably sig-
nify strong goal motivation, they must be excluded from the
analyses of intervisit times because they do not permit test-
ing for acceleration (or deceleration). Therefore, we cali-
brated the hazard rate version of the GDM on the data from
the remaining 148 certificates, which were earned in two or
more visits. The data set was constructed such that each row
represented a unique day on which a particular member
could have visited the Jaboom Web site; we included the
days after the first visit had occurred up to the day of the
last visit.10
We parameterized the survival function with the GDM
shown in Equation 5 and used the likelihood function
shown in Equation 4. Recall that the variable capturing the
hypothesized acceleration is dt= (r – nt)/r, that is, the pro-
portion of total distance remaining before the goal. In this
empirical application, r is equal to 51 songs (i.e., the origi-
nal total distance to the goal), and ntis the number of song
ratings accumulated at time t toward earning the reward cer-
tificate. Given that we modeled the probability of visiting
when there were between 0 and 50 song ratings accumu-
lated, the measure dtranges between 1 (when no goal
progress has yet been made) and .02 (when the goal is
almost achieved), respectively.
Table 3 displays the parameters for the GDM that we
estimated with Weibull hazard parameterization. The linear
goal-distance parameter was less than zero (p< .01). This
result supports H1and demonstrates that members visited
the Jaboom Web site more frequently as they got closer to
earning the reward (i.e., intervisit times decreased as a func-
tion of goal proximity). Consistent with Hull’s (1934) find-
ings with rats and our results of the café RP, the rate of
acceleration diminished, as indicated by the negative quad-
ratic goal-distance parameter (p< .01). Note that the model
includes two variables as controls: (1) the total number of
visits to the Jaboom Web site at the day level, which was
intended to control for time-trend effects, and (2) the num-
ber of visits it took to complete each certificate, which was
intended to rule out aggregation bias. We obtained similar
results when we excluded either or both of these controls
from the model. In addition, the linear and quadratic goal-
distance parameters remained significant and did not vary
The Goal-Gradient Hypothesis Resurrected 51
Tabl e 3
THE HAZARD RATE GDM OF INTERVISIT TIMES (MUSIC-
RATING PROGRAM)
A: Latent Class-Level Parameters
Class 1 Class 2
Segment size (%) 71 29
α(hazard rate) 0.5** 2.1**
β01.4**–.9**
B: Parameters Not Varying by Latent Class
Acceleration Parameters Estimate
Linear effect of goal distance, b1–.25**
Quadratic effect of goal distance, b2–.22**
Covariate Parameters (i.e., Control Variables)
Daily number of visits 0.10**
Total visits to earn certificate –.01**
Saturday–Sunday 0.03**
*p< .05 (based on Wald test; two-tailed).
**p< .01 (based on Wald test; two-tailed).
0
5
10
15
20
25
30
35
012345
Visit Number
Songs Rated
2-visit certificates
3-visit certificates
4-visit certificates
Figure 6
NUMBER OF SONGS RATED AS A FUNCTION OF GOAL
PROGRESS
in magnitude across models with different numbers of latent
classes in the base hazard rate.
We also calibrated the GDM by simultaneously estimat-
ing unobserved heterogeneity in the acceleration and hazard
rate parameters. Although the BIC favors a one-class solu-
tion, we report the two-class solution to rule out hetero-
geneity bias. In the larger class (65%), we found linear
acceleration (b1= –.6, p< .1; b2= –.1, p> .1), and in the
smaller class (35%), we found nonsignificant linear
acceleration (b1= –.1, p> .1; b2= –.3, p< .1). The finding
that both segments demonstrate acceleration is inconsistent
with the heterogeneity bias rival account.
Finally, we recalibrated the same GDM on the data
obtained from “incomplete” certificates (i.e., those with less
than 51 songs rated toward the unattained certificate). There
were 36 incomplete certificates with at least two Web site
visits (i.e., at least one intervisit time that could be modeled
as a function of goal distance). Consistent with the analysis
of the incomplete cards in the café RP, we found decelera-
tion (b1= .7, p< .1; b2= .01, p> .9). Furthermore, we cal-
ibrated the GDM on a data set that combined both complete
and incomplete certificates, and we added an interaction
term, βINT, between completion (yes versus no) and linear
acceleration. We found significantly stronger linear acceler-
ation for complete than for incomplete certificates (bINT =
–.5; Wald χ2= 16.2, p< .01). That is, whereas acceleration
is related to retention and goal attainment, deceleration is
associated with program defection and goal abandonment.
Tests of the Goal-Gradient Hypothesis with Rating
Quantity
Thus far, we have examined how goal distance influences
interpurchase and intervisit times. In many cases, however,
customers can accelerate their efforts by increasing the
quantity of credits earned in a given interaction with the RP.
Accordingly, in this subsection, we test the goal-gradient
hypothesis by examining whether the quantity of songs
rated per visit increases with goal proximity. We report sep-
arate tests of pooled and segment-level quantity accelera-
tion, behavior on incomplete certificates, and postreward
resetting.
Figure 6 presents the raw data obtained from the 148
complete certificates (with at least two visits) that we
observed. Consistent with the goal-gradient hypothesis, as
members approached the 51-song goal, they rated more
songs in later visits.
To model the quantity of songs rated in a visit, we used a
Type I Tobit model (Tobin 1958). This approach enables us
to capture the underlying motivation to rate songs, while
taking into account the constraint of 51 songs per certifi-
cate. Specifically, in the final visit of each certificate, the
number of song ratings is censored at 51 – nt, where ntis
the number of song ratings accumulated toward the certifi-
cate at the start of visit t. By definition, any additional songs
rated in visit t beyond the 51 – ntlimit would be credited
toward the next certificate rather than the goal of earning
the present 51-song certificate. Relatedly, as 51 – nt
approaches zero, the inherent motivation to rate songs may
increase (because dt0), but the 51-song constraint (i.e.,
the reward threshold) would suppress such an effect.
For uncensored data, the Tobit model is equivalent to
maximum likelihood regression. However, because apply-
ing a regression to censored data leads to biased parameter
estimates (Breen 1996), the Tobit models the censored data
as the probability of rating 51 – ntor more songs. Thus, we
model the quantity Qit rated in each visit t by participant i,
incorporating the GDM into a Type I Tobit model:
() (, )651
51 51
Qt gifgn
nifg n
iit
it
it it
X=
<
>
,
52 JOURNAL OF MARKETING RESEARCH, FEBRUARY 2006
where g = β0+ β1dit + β2(dit – d
i)2+ γXit + ε, ε~ N(0, σ2).
Here, g can be considered a latent variable that represents
the tendency to rate songs, which can be directly observed
in the data Qit only when sufficient songs remain on the cer-
tificate (i.e., when g < 51 – nit). This model generalizes the
GDM to the domain of effort quantity and uses the opera-
tionalization of goal distance (dit) we used previously to test
for temporal goal gradients. We expect the parameter β1to
be negative, indicating that a smaller goal distance leads to
a greater quantity of song ratings. We also included a visit-
level control, which captures daily variations in the total
number of songs rated on the Jaboom Web site, and a varia-
ble that represents certificates already earned in the visit by
the participant.
Following Breen’s (1996) exposition, we define the like-
lihood function as follows:
Here, the first sum Σ1is the likelihood function for the
linear regression summed over all the noncensored cases
(i.e., visits in which the certificate is not completed). The
second sum Σ0is the probability of observing at least the
censored amount 51 – nit, defined by the standard normal
cumulative distribution function Φand summed over the
visits in which a certificate was completed (i.e., the cen-
sored cases). Note that in this model, the error variance σ2
is a separate parameter to be estimated.
We calibrated this model on the data from the 148 certifi-
cates that were earned in two or more visits. Consistent with
the goal-gradient hypothesis, we found a negative linear
goal-distance parameter (p< .01; see Table 4) that indicated
that members rated more songs per visit when they were
closer to the goal. There was also a quadratic effect (p<
.01) that indicated a diminishing rate of acceleration. In
addition, we found a negative effect of the number of cer-
tificates already earned during the same visit (p< .01), con-
sistent with satiation or fatigue. We obtained similar results
when we forced the constant and error variance to vary
across latent classes.
We also estimated the GDM using data from the 36
incomplete certificates (certificates with fewer than 51 song
()
()exp ()
.
7
225
1
01 2
L
Qddd
i
it it it i
=
−− −
πσ ββ β 22
2
01 2 2
2
1
+++ +
γγ
γγ
X
X
it
it it
ddd
i
σ
ββ β
Φ()
iit it
n−−
()
.
51
0σ
ratings but at least two visits). We found a weaker (though
significant) effect of goal distance (dit) in these data (b1=
–2.5, p< .01; b1= 2.9, p< .01). Furthermore, we calibrated
the GDM on a data set that combined both complete and
incomplete certificates, and we added an interaction term,
βINT, between completion (yes versus no) and linear accel-
eration. Consistent with the findings from the analyses of
intervisit times, we found that completed certificates exhib-
ited a significantly stronger quantity goal gradient than did
incomplete certificates (bINT = –8.5, p< .01).
Postreward resetting. An alternative explanation for the
observed quantity acceleration is learning (or habituation).
For example, it is possible that with repeated visits to the
Jaboom Web site, members learned to rate songs faster, thus
rating more songs in later visits. To examine the learning
alternative explanation, we tested whether the 34 Jaboomers
who earned two multivisit certificates exhibited postreward
resetting. The resetting corollary predicts that members
should rate more songs on the last visit of their first certifi-
cate (when dit < 1) than on the first visit of their second cer-
tificate (when dit = 1). These members demonstrated strong
goal gradients (i.e., greater rating quantities as a function of
lower dt) on both of their earned certificates (b1= –11.6 and
–9.0 for the first and second certificate, respectively; ps <
.01). Moreover, consistent with postreward resetting and
inconsistent with the learning explanation, these members
rated an average of 24 songs on the last visit of their first
certificate compared with 16 songs on the first visit of their
second certificate (pairwise t = 2.3, p< .05).
Unobserved heterogeneity in goal-motivated accelera-
tion. To rule out heterogeneity bias as an explanation for the
quantity goal gradient, we calibrated the GDM on the data
from completed certificates by simultaneously estimating
unobserved heterogeneity in the goal-distance parameters,
the constant, and the error variance. Although the BIC
favored a one-class solution, we report the two-class solu-
tion. The size of the larger class was 97% (b1= –12.4, p<
.01; b2= –7.4, p< .01), and the size of the smaller class was
3% (b1= –13.6, p< .01; b2= 1.5, p> .7). Thus, inconsistent
with heterogeneity bias, both segments demonstrate accel-
eration in rating quantities as a function of goal proximity.
Tests of the Goal-Gradient Hypothesis with Persistence in
Effort
In this subsection, we generalize the goal-gradient
hypothesis to the domain of effort persistence. On the basis
of the notion that the motivation to achieve a goal increases
with its proximity, we predict that consumers will be more
likely to persist in their effort when the reward is proximal,
and equivalently, they will be more likely to cease their
efforts when the reward is distal. In the context of the
music-rating program, this prediction implies that the more
songs the member has accumulated toward the 51-song goal
(i.e., the smaller is dt), the less likely the member will be to
end an active song-rating visit.
To test the persistence version of the goal-gradient
hypothesis, we model the probability of terminating a visit
at any point in the song-rating process as a function of the
distance to the goal, dt, and other covariates. We use a logit
model that accounts for unobserved heterogeneity in the
baseline probability of ending a visit. The probability of
Tabl e 4
THE TOBIT GDM OF QUANTITY
Model Parameters Estimate
Intercept 29.9*
Variance (σ2) 253.4*
Linear effect of goal distance, b1–13.0*
Quadratic effect of goal distance, b2–7.5*
Daily number of songs .8
Total visits to earn certificate –10.9*
Saturday–Sunday –.2
Number of certificates already earned during the visit –4.0*
*p< .01 (based on Wald test; two-tailed).
The Goal-Gradient Hypothesis Resurrected 53
0
10
20
30
40
50
60
70
80
90
Visit Terminations
1 .9 .8 .7 .6 .5 .4 .3 .2 .1 0
dt =
Figure 7
NUMBER OF VISIT TERMINATIONS AS A FUNCTION OF GOAL
DISTANCE
participant i terminating the visit t after rating q songs in
that visit is given by
where g = β0+ β1ditq + β2(ditq – d
i)2+ β3Citq + γXitq.
In Equation 8, we generalize the GDM to the domain of
effort persistence and use the definition of proportional goal
distance we used previously. In particular, ditq = (r – nitq)/r,
where r = 51 song ratings and nitq is the number of songs
accumulated by individual i toward earning the reward after
rating q songs in visit t (ditq [.02, 1.0]). The parameter β1
captures the effect of goal distance on the probability of ter-
minating a visit. We expect β1to be positive, indicating that
a greater goal distance (ditq) leads to a greater likelihood of
defection (and, equivalently, a smaller ditq leads to
enhanced effort persistence). We used a dummy variable,
Citq, that we coded as 1 if the previous rating in the visit
earned a certificate (i.e., if ditq = 1) and 0 if otherwise. The
goal-gradient hypothesis predicts an increased likelihood of
visit termination (or RP defection) when ditq reverts to 1.0,
and therefore we expected β3to be positive. We estimated
the effect of ditq = 1.0 separately to guarantee that the
hypothesized goal-gradient effect (captured by β1) could
not be explained solely on the basis of an increased likeli-
hood of defection at ditq = 1.0, that is, just after reward
attainment. We also included a day-level control that cap-
tures daily variations in the total number of songs rated on
the Jaboom Web site.
We calibrated the GDM on the entire data set, including
ratings (and participants) that did not eventually earn a
reward certificate. Thus, we jointly modeled visit termina-
tion and overall program defection. Table 5 displays the
model estimates. Consistent with the goal-gradient hypothe-
sis, the linear goal-distance parameter b1was positive (p<
.01), indicating that members were more likely to defect
when they were farther away from the reward goal (or,
equivalently, they were more likely to persist when they
(8) Pr ( , ) exp( )
[exp( )],
iitq
tg
g
X=
+1
were closer to the goal). Furthermore, as we predicted, b3
was positive (p< .05), indicating that the highest probabil-
ity of terminating a visit occurred just after goal achieve-
ment, that is, when members were the farthest away from
the (new) goal (at ditq = 1.0). Figure 7 illustrates these
results and shows that a majority (17% or 80/473) of all
visit terminations occurred at ditq = 1.0. The figure also
shows that the percentage of visit terminations continued to
decrease as a function of smaller distance to the goal. For
example, among the 473 terminations we observed, 8.7%
(41/473) occurred when only one song was accumulated
toward the next reward (i.e., when ditq = .98), whereas only
.2% of visit terminations (1/473) occurred when as many as
50 songs were accumulated (i.e., when ditq = .02).
The Music-Rating Program: Discussion
The Jaboom music-rating program enabled us to test the
goal-gradient hypothesis in an empirical context that was
different from the café RP, using an incentive system that is
akin to a freelance employment contract. With this empiri-
cal application, we were able not only to replicate the find-
ing of goal-motivated acceleration in visit rates (in the con-
text of Web site rather than café visits) but also to extend
the goal-gradient effect to the domain of quantity decisions
and effort persistence. The various operationalizations of
the goal-gradient hypothesis were examined with several
generalizations of the GDM, which all relied on a common
measure of goal distance, namely dt. These varieties of the
GDM included a hazard rate model of the timing of visiting
the Jaboom Web site, a Tobit model of the quantity of rat-
ings per visit, and a logit model of the probability of effort
termination and program defection.
We found significant goal gradients even after we
accounted for unobserved heterogeneity and statistically
controlled for time trends in visit and song-rating frequen-
cies. Moreover, we observed the phenomenon of postreward
resetting, whereby members accelerated toward each of two
subsequent rewards but exhibited a drop in their rating
quantities after earning the first reward and starting to work
toward the second (i.e., when dtreverts to 1.0). The finding
Tabl e 5
THE LOGIT GDM OF EFFORT PERSISTENCE AND DEFECTION
Latent Class-Level Parameters
Class 1 Class 2
Segment size (%) 94 6
Constant –3.5** –4.5**
Par ameters Not Varying by Latent Class
Acceleration Parameters Estimate
Linear effect of goal distance, b1.49**
Quadratic effect of goal distance, b2.12*
Effect of certificate completed (dtq = 1), b3.27**
Covariate Parameters (i.e., Control Variables)
Daily number of songs –.05
Total visits to earn certificate .40**
Saturday–Sunday .05
Number of certificates already earned during the visit .17*
*p< .05 (based on Wald test; two-tailed).
**p< .01 (based on Wald test; two-tailed).
54 JOURNAL OF MARKETING RESEARCH, FEBRUARY 2006
of postreward resetting is a key corollary of the goal-
gradient hypothesis; it demonstrates that effort expenditure
is a function of goal distance and rules out learning and
other time-trend effects as well as a self-selection (or sur-
vivor) rival account. Self-selection is also inconsistent with
the analysis of participants’ entire sequence of ratings
(including ratings that did not eventually lead to reward),
which revealed significant goal gradients.11 Next, we use
individual differences to explore the relationship between
the goal gradient and customer retention.
IMPLICATIONS OF THE GOAL GRADIENT FOR
CUSTOMER RETENTION
Prior research with animals has shown that a steeper goal
gradient was generated by an increased drive (e.g., hunger)
to attain the reward (Hull 1934). This finding suggests that
RP members who exhibit enhanced acceleration possess a
stronger motivation to earn free rewards (e.g., due to a
higher achievement motivation). If, indeed, the motivation
to earn free rewards is related to the steepness of the goal
gradient, individual differences in the tendency to acceler-
ate (when we hold constant the overall program effort)
should predict customer retention after attainment of the
first reward. Specifically, we expect members who acceler-
ate more strongly toward their first reward to be more likely
to reengage in the program and earn a second reward. Relat-
edly, we expect stronger acceleration to lead to faster
reengagement in the RP.
To examine these predictions, we recalibrated the GDM
with unobserved heterogeneity in both the hazard rate and
the goal-distance parameters, using a subsample of the café
RP data that excluded subsequent cards. We used this model
to obtain individual-level linear acceleration estimates
based on the member’s first coffee card. We calculated these
estimates by multiplying the latent class parameters of goal
distance (i.e., acceleration) by the individual-level probabil-
ities of class membership. We then used the individual-level
acceleration estimates as independent variables in predict-
ing member reengagement in the café RP. Importantly, the
tests we report subsequently included covariates that statis-
tically controlled for the length of time it took participants
to complete the first card (i.e., the participant’s overall pro-
gram effort and product liking) and the date of completion
of the card. That is, we investigated the effect of individual
differences in the slope of the goal gradient (the linear goal-
distance parameter), holding constant the base hazard rate
(i.e., the average interpurchase time) and possible seasonal-
ity (or right-censoring) effects.
Retention Probability
We used a logistic regression to test the prediction that
members who accelerate more strongly toward their first
reward will be more likely to earn a second reward. The
(dummy) dependent variable received a value of 1 if the
member earned a second reward and 0 if otherwise. The
effect of the first-card individual-level acceleration estimate
for the member was in the hypothesized direction (b= –.5,
Wald χ2= 5.3; p< .05). In particular, members who accel-
erated more strongly toward their first reward were more
likely to earn a second reward. To demonstrate this effect
visually, we also split the sample on the basis of first-card
estimated linear acceleration into three equally sized
groups: decelerators (mean b= .1), accelerators (mean b=
–.05), and strong accelerators (mean b= –.1). Figure 8 (left
panel) depicts the probability of completing a second card
(based on the raw data) for each of these three groups.
0%
5%
10%
15%
20%
25%
30%
35%
40%
Probability of Earning Second Reward
Decelerator Accelerator Strong
Accelerator
Decelerator Accelerator Strong
Accelerator
0
1
2
3
4
5
6
7
8
Average Reengagement Time (Days)
Figure 8
EFFECT OF FIRST-CARD ACCELERATION ON REENGAGEMENT PROBABILITY AND TIMING
11Detailed analyses that rule out the self-selection (survivor) account are
available on request.
The Goal-Gradient Hypothesis Resurrected 55
12Detailed results are available on request.
Reengagement Time
To test the hypothesis that steeper acceleration predicts
faster reengagement, we analyzed the subsample of 110
members who completed both a first and a second card. We
computed reengagement time as the period between the last
purchase on the first card and the first purchase on the sec-
ond card. We fit a new (Weibull) hazard rate model that pre-
dicted the reengagement times using the individual-level
estimates of first-card acceleration as an independent varia-
ble. We also included the covariates we used previously in
the hazard rate model of interpurchase times and controlled
for the duration and completion date of the first card. The
effect of acceleration toward the first reward on the time to
reengage in the program was in the hypothesized direction
(b= –2.6, Wald χ2= 13.8; p< .01). That is, members who
accelerated more strongly toward their first reward were
faster to begin working toward their second reward (when
we hold constant the base hazard rate, or the average inter-
purchase time, on the first card). Figure 8 (right panel) illus-
trates this result using the aforementioned tertiary split.
Implications for Customer Retention: Discussion
We posited that individual differences in the goal gradi-
ent capture variations in the motivation to earn free
rewards. Consistent with this argument, we found that cus-
tomers who accelerated more strongly toward their first
reward subsequently exhibited greater retention and faster
reengagement in the café RP. We replicated these effects in
the context of the Jaboom music-rating program.12 Given
the previously reported findings of postreward resetting,
our results cannot be explained as a simple continuation of
the increased purchase rates of accelerators. Overall, the
findings underscore the importance of incorporating the
goal-gradient construct in the modeling and analysis of
RPs.
GENERAL DISCUSSION
The goal gradient is one of the classic phenomena dis-
covered in the animal-learning and behaviorism literature
of the early twentieth century. It has important implications
for achievement motivation and goal pursuit but, neverthe-
less, has been understudied in humans. This is particularly
surprising, given that the goal-gradient hypothesis provides
considerable insights into the psychology of rewards and
the optimal design of customer, employee, and sales force
incentive systems. In this research, we extended the goal-
gradient hypothesis to the domain of consumer behavior
and investigated its consequences for illusionary goal
progress and customer retention.
The current research can be viewed as part of the ongo-
ing (fruitful) attempt to bridge the consumer behavior and
marketing science disciplines (e.g., Bell and Lattin 2000;
Hardie, Johnson, and Fader 1993; Kivetz, Netzer, and Srini-
vasan 2004; Simonson and Winer 1992; Wertenbroch 1998;
Winer 1986; for related discussion, see Wittink 2004). Such
intradisciplinary endeavors often test behavioral theories
with econometric modeling, secondary data, and/or field
studies. In the current research, we built on prior analyses in
behaviorism, social cognition, and behavioral decision 13Given the exclusivity of the café on campus, the observed purchase
acceleration is likely a consequence of increased consumption rather than
brand switching. Brand switching was not a possibility in the case of the
music-rating program.
research, and we used various modeling frameworks and
empirical tests in the context of two real incentive systems.
We primarily relied on field experiments and econometric
analyses of actual multiperiod customer behavior. Such
methodologies are crucial for the study of dynamic goal
pursuit and intertemporal responses to RPs and other pro-
motions (see, e.g., Gupta 1988; Simonson 1990; Van
Heerde, Leeflang, and Wittink 2000). The alternative
approach, whereby respondents are asked to assume a
hypothetical state (e.g., “imagine that you have accumu-
lated x points”) provides an adequate test of lay theories
and self-perception but not of the actual evolution of goal
motivation and behavior.
Key Findings and Their Implications
We found that members of a café RP accelerated their
coffee purchases as they progressed toward earning a free
coffee. The goal-gradient effect also generalized to a very
different incentive system, in which shorter goal distance
led members to visit a song-rating Web site more fre-
quently, rate more songs during each visit, and persist
longer in the rating effort. Importantly, in both incentive
systems, we observed the phenomenon of postreward reset-
ting, whereby customers who accelerated toward their first
reward exhibited a slowdown in their efforts when they
began work (and subsequently accelerated) toward their
second reward. To the best of our knowledge, this article is
the first to demonstrate unequivocal, systematic behavioral
goal gradients in the context of the human psychology of
rewards.
For marketers, the goal gradient may provide profitable
opportunities. In addition to facilitating segmentation, tar-
geting, and promotions (we discuss this subsequently), the
goal gradient may lead to a sales lift that exceeds the cost of
the reward. For example, the results of the café RP imply
that to earn one free coffee, customers bought two more
coffees than they would have otherwise.13 At the same time,
consumers may derive pleasure from working toward future
goals. This idea is consistent with the findings of an obser-
vational study, in which research assistants unobtrusively
recorded the behavior and affect of the café customers. The
results indicate that customers who participated in the RP
(as opposed to customers who did not) were more likely to
smile when buying coffee (3.8 versus 3.4 on a five-point
scale; p< .05), chat for a few minutes with café employees
(26% versus 7%; p< .05), say “thank you” (95% versus
87%; n.s.), and leave a tip (21% versus 3%; p< .01).
Although these results should be interpreted with caution
because customers self-select into the RP, they suggest that
goal striving is intrinsically motivating beyond extrinsic
rewards.
We posited that people are influenced by the proportional
(or psychological) distance to the goal (i.e., dt= [r – nt]/r).
Accordingly, we proposed that the illusion of progress
toward the goal would enhance achievement motivation by
reducing the perceived proportion of distance remaining to
the goal. One test of this hypothesis involved a field experi-
ment, in which customers who received a 12-stamp card
56 JOURNAL OF MARKETING RESEARCH, FEBRUARY 2006
with two preexisting bonus stamps completed the ten
required coffee purchases faster than customers who
received a regular 10-stamp card. It is noteworthy that the
goal-gradient and illusionary goal progress effects can be
captured by a mathematically equivalent GDM, in which
effort depends on the proportion of original goal distance
already accomplished (i.e., dt= nt/r). Further research could
explore the impact of framing goal progress in terms of
completed versus remaining effort.
The illusion of goal progress and its boundary conditions
merit further research. Beyond its theoretical importance,
this phenomenon has substantial managerial implications
for the design of RPs and other incentive systems. Cur-
rently, many RPs award bonus points to new members (e.g.,
American Express Membership Rewards Program, Hyatt
Gold Passport). Given the rich, complex structure of such
programs, it is easy for managers to increase the point
requirements of rewards by an amount equivalent to the
bonus, effectively creating illusionary goal progress.
Consistent with the notion that a steeper goal gradient
implies a greater drive to achieve the reward, we found that
stronger accelerators reengaged in the program faster and
were more likely to earn a second reward. Relatedly, failure
to persist in the effort stream and fulfill the requirements
was associated with weaker acceleration and even decelera-
tion. The relationship between the goal gradient and reten-
tion was also evident in the finding that just after reward
attainment (when goal distance regressed to 100%), cus-
tomers exhibited a drop in activity (postreward resetting)
and were also most likely to defect. These findings have
important implications for customer segmentation and the
design of marketing interventions aimed at reducing churn.
For example, it is particularly important to communicate
with and motivate customers immediately after they earn a
reward.
Extending the GDM. Using a common measure of goal
distance (dt) and logit, hazard rate, and Tobit frameworks,
the GDM captured three forms of goal gradients: increased
persistence, rate, and quantity of effort closer to the reward
threshold. These three goal gradients predict increases in
the recency of the last transaction, the average frequency of
all transactions, and the average monetary value of these
transactions; thus, the goal-gradient and its modeling have
important implications for the widely used RFM approach.
Given the robustness and generality of the GDM, we
believe that it can be applied to a broad range of goal-based
motivational systems, including more complex incentive
systems. Further research can employ the GDM to account
for consumer and employee behavior in sophisticated
incentive systems, such as those that airlines, retailers, and
sales organizations use; in such programs, r and ntare often
expressed in terms of miles, points, and dollars or units
sold. Such incentive systems often use rich, complex struc-
tures that offer a multitude of different rewards at various
requirement levels. Customers can exhibit goal gradients in
various ways, including purchase timing and quantity accel-
eration and increased retention and lock-in. However, the
goal-gradient effect may be more difficult to detect in such
complex incentive systems for the following reasons: First,
a priori, the researcher cannot identify (or observe) the con-
sumer’s goal. Second, the observed ex post goal (based on
the actual reward redeemed) is self-selected by the con-
sumer, and thus it is difficult to draw causal inferences
about differences in the behavior of consumers who redeem
different rewards. Third, in the presence of multiple effort–
reward combinations, the consumer’s chosen goal may
change during the program, thus complicating the investiga-
tion of the goal-gradient hypothesis. Finally, the issue of
right censoring in observed behavior (compared with under-
lying motivation) that arises in the test of the music-rating
quantity acceleration applies to complex RPs as well. This
last problem can be solved with the Tobit version of the
GDM. Despite the various challenges, we believe that cap-
turing the goal gradient in more complex situations is a
worthy endeavor, and the GDM can facilitate it.
The implications of the goal gradient for promotion, pric-
ing, and competition. The goal-gradient effect has important
implications, which merit further research, for key market-
ing variables. The findings suggest that goal proximity
increases customers’ responsiveness to credit-earning pro-
motions and offers. For example, frequent flyers’ willing-
ness to purchase miles may increase closer to program
goals. This hypothesis is consistent with the results of an
unpublished study, in which we asked 329 respondents to
imagine that they participated in a frequent-flyer program
that offered a free domestic round-trip ticket for accumulat-
ing 25,000 miles. We told respondents that they had already
accumulated either 13,000 or 23,000 miles (distant versus
near goal, respectively; manipulated between subjects); we
asked them to indicate whether they would agree to receive
weekly marketing e-mails in return for 1000 bonus
frequent-flyer miles. As we predicted, respondents in the
near-reward condition were more likely than those in the
distant-reward condition to accept the promotional offer
(56% versus 38%, χ2= 10.7; p< .001). Note that an
increase in promotion sensitivity due to goal proximity
could be attenuated when (1) the promotional effort is iden-
tical to the main program effort (e.g., “fly next week and
earn triple miles”) and (2) effort acceleration is subject to
behavioral ceiling effects (e.g., frequent flyers cannot accel-
erate their flights beyond a certain point).
The goal-gradient effect has important implications for
price sensitivity and competition. It suggests that the own-
and cross-price elasticities of the RP sponsor are lower for
members who are closer to the program’s goals. Compared
with nonmembers of the RP, members may be willing to
pay a price premium or forgo convenience (e.g., purchase
more expensive and/or layover flights), particularly when
they near a program goal. In addition, the increased motiva-
tion to achieve RP goals may reduce competition and price
wars by escalating customer lock-in and switching costs
and enhancing consumption rates (i.e., expanding the
category).
Conclusion
Building on the behaviorist goal-gradient hypothesis, we
proposed that people working toward future rewards would
accelerate their effort as they near the reward goal. Based
on a wide range of empirical and modeling approaches, the
findings we report in this article provide converging evi-
dence for the impact and importance of goal gradients in the
human psychology of rewards. Not only do customers
accelerate toward rewards (in terms of timing, quantity, and
persistence of effort), but their acceleration also predicts
The Goal-Gradient Hypothesis Resurrected 57
loyalty and future engagement with similar goals. The
GDM unifies these results and predicts the effect of illu-
sionary goal progress. On the basis of this research, we pro-
pose that the goal gradient and its modeling have important
theoretical and practical implications for achievement moti-
vation and goal behavior and for incentive systems and mar-
keting promotions.
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58 JOURNAL OF MARKETING RESEARCH, FEBRUARY 2006
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... Instead, the inflation factor may play a critical role in motivating the developer because she will be guaranteed a relatively high chance of approval if the inflation factor is sufficiently high. This is also consistent with the concept of the goal gradient hypothesis (Kivetz et al. 2006). ...
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Marketing scholars commonly characterize market structure by studying the patterns of substitution implied by brand switching. Though the approach is useful, it typically ignores the destabilizing role of marketing variables (e.g., price) in switching behavior. The authors propose a flexible choice model that partitions the market into consumer segments differing in both brand preference and price sensitivity. The result is a unified description of market structure that links the pattern of brand switching to the magnitudes of own- and cross-price elasticities. The approach is applied in a study of competition between national brands and private labels in one product category.
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Consumer choice is often influenced by the context, defined by the set of alternatives under consideration. Two hypotheses about the effect of context on choice are proposed. The first hypothesis, tradeoff contrast, states that the tendency to prefer an alternative is enhanced or hindered depending on whether the tradeoffs within the set under consideration are favorable or unfavorable to that option. The second hypothesis, extremeness aversion, states that the attractiveness of an option is enhanced if it is an intermediate option in the choice set and is diminished if it is an extreme option. These hypotheses can explain previous findings (e.g., attraction and compromise effects) and predict some new effects, demonstrated in a series of studies with consumer products as choice alternatives. Theoretical and practical implications of the findings are discussed.
Article
Consumers’ purchase time decisions are important elements of their buying decision process. Stochastic models of interpurchase time, which have been used extensively in the marketing literature, are parsimonious, easy to estimate, and usually fit and predict the data well. However, there has been a striking omission of marketing variables in these models. Because empirical evidence suggests that marketing variables, such as promotions, can affect consumers’ purchase time decisions, the author presents a methodology for including such variables in these stochastic models. Four commonly used models are discussed: exponential, Erlang-2 (no heterogeneity), and these two models with gamma heterogeneity. Thus one can include duration dependence, heterogeneity, and nonstationarity in the model, and also account for right-censored data. Special care is shown to be needed when covariates, such as marketing variables, vary over time. The models are analytically tractable, which makes their estimation and validation simple and fast. An illustration of the methodology is provided with scanner panel data for coffee. Inclusion of duration dependence, heterogeneity, and marketing variables is shown to improve the model's diagnostics, fit, and predictions.
Article
The effectiveness of a sales promotion can be examined by decomposing the sales “bump” during the promotion period into sales increase due to brand switching, purchase time acceleration, and stockpiling. The author proposes a method for such a decomposition whereby brand sales are considered the result of consumer decisions about when, what, and how much to buy. The impact of marketing variables on these three consumer decisions is captured by an Erlang-2 interpurchase time model, a multinomial logit model of brand choice, and a cumulative logit model of purchase quantity. The models are estimated with IRI scanner panel data for regular ground coffee. The results indicate that more than 84% of the sales increase due to promotion comes from brand switching (a very small part of which may be switching between different sizes of the same brand). Purchase acceleration in time accounts for less than 14% of the sales increase, whereas stockpiling due to promotion is a negligible phenomenon accounting for less than 2% of the sales increase.
Article
Two consumer strategies for the purchase of multiple items from a product class are contrasted. In one strategy (simultaneous choices/sequential consumption), the consumer buys several items on one shopping trip and consumes the items over several consumption occasions. In the other strategy (sequential choices/sequential consumption), the consumer buys one item at a time, just before each consumption occasion. The first strategy is posited to yield more variety seeking than the second. The greater variety seeking is attributed to forces operating in the simultaneous choices/sequential consumption strategy, including uncertainty about future preferences and a desire to simplify the decision. Evidence from three studies, two involving real products and choices, is consistent with these conjectures. The implications and limitations of the results are discussed.
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What techniques can social scientists use when an outcome variable for a sample is not representative of the population for whom they would like to generalize the results? This book provides an introduction to regression models for such data including censored, sample-selected and truncated data.
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The compromise effect denotes the finding that brands gain share when they become the intermediate rather than extreme option in a choice set. Despite the robustness and importance of this phenomenon, choice modelers have neglected to incorporate the compromise effect in formal choice models and to test whether such models outperform the standard value maximization model. In this article, the authors suggest four context-dependent choice models that can conceptually capture the compromise effect. Although the models are motivated by theory from economics and behavioral decision research, they differ with respect to the particular mechanism that underlies the compromise effect (e.g., contextual concavity versus loss aversion). Using two empirical applications, the authors (1) contrast the alternative models and show that incorporating the compromise effect by modeling the local choice context leads to superior predictions and fit compared with the traditional value maximization model and a stronger (naive) model that adjusts for possible biases in utility measurement, (2) generalize the compromise effect by demonstrating that it systematically affects choice in larger sets of products and attributes than has been previously shown, (3) show the theoretical and empirical equivalence of loss aversion and local (contextual) concavity, and (4) demonstrate the superiority of models that use a single reference point over "tournament models" in which each option serves as a reference point. They discuss the theoretical and practical implications of this research as well as the ability of the proposed models to predict other behavioral context effects.
Article
The effectiveness of a sales promotion can be examined by decomposing the sales "bump" during the promotion period into sales increase due to brand switching, purchase time acceleration, and stockpiling. The author proposes a method for such a decomposition whereby brand sales are considered the result of consumer decisions about when, what, and how much to buy. The impact of marketing variables on these three consumer decisions is captured by an Erlang-2 interpurchase time model, a multinomial logit model of brand choice, and a cumulative logit model of purchase quantity. The models are estimated with IRI scanner panel data for regular ground coffee. The results indicate that more than 84% of the sales increase due to promotion comes from brand switching (a very small part of which may be switching between different sizes of the same brand). Purchase acceleration in time accounts for less than 14% of the sales increase, whereas stockpiling due to promotion is a negligible phenomenon accounting for less than 2% of the sales increase.
Article
Consumers' purchase time decisions are important elements of their buying decision process. Stochastic models of interpurchase time, which have been used extensively in the marketing literature, are parsimonious, easy to estimate, and usually fit and predict the data well. However, there has been a striking omission of marketing variables in these models. Because empirical evidence suggests that marketing variables, such as promotions, can affect consumers' purchase time decisions, the author presents a methodology for including such variables in these stochastic models. Four commonly used models are discussed: exponential, Erlang-2 (no heterogeneity), and these two models with gamma heterogeneity. Thus one can include duration dependence, heterogeneity, and nonstationarity in the model, and also account for right-censored data. Special care is shown to be needed when covariates, such as marketing variables, vary over time. The models are analytically tractable, which makes their estimation and validation simple and fast. An illustration of the methodology is provided with scanner panel data for coffee. Inclusion of duration dependence, heterogeneity, and marketing variables is shown to improve the model's diagnostics, fit, and predictions.