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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 dt→0), 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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