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

Purchase and effort rates reset (to a lower level) after the first reward is earned and then reaccelerate toward the second reward goal.

“purchase and effort rates reset (to a lower level) after the first reward is earned and then reaccelerate toward the second reward goal.”

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.

“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”

• Also stated in: § The Goal-Gradient Hypothesis Resurrected: Purchase Acceleration, Illusionary Goal Progress, and Customer Retention · p. 2 · plain

  “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.”

Internet users who rate songs in return for reward certificates persist longer in the rating effort as they approach the reward goal.

“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”

Internet users who rate songs in return for reward certificates visit the rating Web site more often as they approach the reward goal.

“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”

The illusion of progress toward the goal induces purchase acceleration.

“the illusion of progress toward the goal induces purchase acceleration”

• Also stated in: § The Goal-Gradient Hypothesis Resurrected: Purchase Acceleration, Illusionary Goal Progress, and Customer Retention · p. 2 · plain

  “The illusion of progress toward the goal induces purchase acceleration.”

Internet users who rate songs in return for reward certificates rate more songs per visit as they approach the reward goal.

“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”

On the subsample of completed transparent cards, there was deceleration (b1 = .15, p < .05; b2 = .05, p > .1).

“Finally, we calibrated the GDM on the subsample of completed transparent cards, and again, we found deceleration ( b 1 = .15, p &lt; .05; b 2 = .05, p &gt; .1).”

The quadratic goal-distance parameter b2 was less than zero (p < .01).

“the negative quadratic parameter b 2 ( p &lt; .01)”

In a statistical test controlling for time-varying covariates and heterogeneity, the first two interpurchase times on the second card were slower than the last two interpurchase times on the first card (p < .01).

“The first two interpurchase times on the second card were slower than the last two interpurchase times on the first card ( p &lt; .01).”

Segments 3 and 4 (7% and 6%, respectively) both had a linear goal-distance parameter near zero.

“Segments 3 and 4 (7% and 6%, respectively) both have a linear goal-distance parameter near zero.”

Segment 2 (29%) had the same linear goal-distance parameter as the largest segment, but the coefficient did not reach statistical significance (p = .13).

“Segment 2 (29%) has the same linear goal-distance parameter as the largest segment, but the coefficient does not reach statistical significance ( p = .13) because of the smaller segment size.”

In the buyback card model, all significant coefficients for control variables had the same sign and interpretation as in the model of redeemed cards.

“Again, all the significant coefficients for the control variables had the same sign and the same interpretation as the model of redeemed cards.”

There was a 20% (.7 day) decrease in average interpurchase times from the first to the last stamp on the card.

“The 20% (.7 day) decrease in average interpurchase times from the first to the last stamp on the card”

Buyback cards were in circulation for a period longer than redeemed cards (X = 65 days versus X = 25 days; t = 7.6, p < .01).

“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 &lt; .01)”

In the process test, respondents in the experimental versus control condition estimated completing the eight required purchases 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]).

“Consistent with H 2 and the results of the field experiment, respondents in the experimental versus control condition estimated completing the eight required purchases in fewer weeks (X ⎯ = 11 versus X ⎯ = 16 weeks; t = 1.6, p &lt; .1; medians = 8 versus 12 weeks; χ 2 = 6.5, p &lt; .05 [nonparametric median test]).”

In the segmentation analysis with unobserved heterogeneity in both hazard rate and goal-distance parameters, Segment 1 (58%) had significant linear and quadratic goal-distance 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.”

In the field experiment, customers in the control condition completed the ten required purchases (for the 10-stamp card) in 15.6 days on average.

“On average, customers in the control condition completed the ten required purchases (for the 10-stamp card) in 15.6 days.”

We found significant unobserved heterogeneity in the hazard rate parameters.

“we found significant unobserved heterogeneity in the hazard rate parameters”

• AssumptionThe authors state this as an assumption: Each day is a potential purchase occasion, except for days on which the café is closed.

A nested likelihood ratio test indicated that the GDM provided an improvement in fit over a 'naive' model in which β1 and β2 were restricted to zero (χ2 = 18.8, d.f. = 2, p < .01).

“A nested likelihood ratio test indicated that the GDM provided an improvement in fit over a 'naive' model in which β 1 and β 2 were restricted to zero ( χ 2 = 18.8, d.f. = 2, p &lt; .01).”

In the transparent card model, all significant coefficients for control variables had the same sign and interpretation as in the model of redeemed cards.

“All the significant coefficients for the control variables have the same sign and the same interpretation as in the model of redeemed cards.”

When including all observed days up to the collection of the transparent card, there was an even stronger deceleration effect (b1 = .4, p < .01; b2 = -.1, p > .1).

“We found an even stronger deceleration effect ( b 1 = .4, p &lt; .01; b 2 = -.1, p &gt; .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).”

In the café RP main data set, the linear goal-distance parameter b1 was less than zero (p < .01).

“The linear goal-distance parameter b 1 was less than zero ( p &lt; .01).”

When modeling all observed days up to the buyback of the incomplete card, there was an increasing deceleration effect (b1 = .3 and b2 = -.1, respectively; ps < .01).

“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 ( b 1 = .3 and b 2 = -.1, respectively; p s &lt; .01).”

The goal-gradient effect extends to the domain of effort persistence.

“With this empirical application, we were able not only to replicate the finding of goal-motivated acceleration in visit rates (in the context of Web site rather than café visits) but also to extend the goal-gradient effect to the domain of quantity decisions and effort persistence.”

In both incentive systems, postreward resetting was observed: customers who accelerated toward their first reward exhibited a slowdown in efforts when they began work toward their second reward.

“Importantly, in both incentive systems, we observed the phenomenon of postreward resetting, 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.”

Completed certificates exhibited a significantly stronger quantity goal gradient than did incomplete certificates (b_INT = -8.5, p < .01).

“we found that completed certificates exhibited a significantly stronger quantity goal gradient than did incomplete certificates ( b INT = -8.5, p &lt; .01).”

Members who accelerated more strongly toward their first reward were more likely to earn a second reward.

“In particular, members who accelerated more strongly toward their first reward were more likely to earn a second reward.”

There was no effect of the illusionary goal progress manipulation on the likelihood of joining the frequent-diner program (experimental mean = 5.9, control mean = 5.8; t = .1, n.s.).

“we found no effect on the likelihood of joining the frequent-diner program (X ⎯ = 5.9 and X ⎯ = 5.8 in the experimental and control condition, respectively; t = .1, not significant [n.s.]).”

The 34 Jaboomers who earned two multivisit certificates demonstrated strong goal gradients on both of their earned certificates (b1 = -11.6 and -9.0 for the first and second certificate, respectively; ps < .01).

“These members demonstrated strong goal gradients (i.e., greater rating quantities as a function of lower d t ) on both of their earned certificates ( b 1 = -11.6 and -9.0 for the first and second certificate, respectively; p s &lt; .01).”

Shorter goal distance led members to persist longer in the rating effort.

“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 frequently, rate more songs during each visit, and persist longer in the rating effort.”

In an observational study, customers who participated in the RP (vs. nonparticipants) were more likely to chat for a few minutes with café employees (26% vs. 7%; p < .05).

“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 &lt; .05), chat for a few minutes with café employees (26% versus 7%; p &lt; .05), say 'thank you' (95% versus 87%; n.s.), and leave a tip (21% versus 3%; p &lt; .01).”

The effect of acceleration toward the first reward on time to reengage was in the hypothesized direction (b = -2.6, Wald χ2 = 13.8; p < .01).

“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 χ 2 = 13.8; p &lt; .01).”

Completed certificates exhibited significantly stronger linear acceleration than incomplete certificates (b_INT = -.5; Wald χ2 = 16.2, p < .01).

“We found significantly stronger linear acceleration for complete than for incomplete certificates ( b INT = -.5; Wald χ 2 = 16.2, p &lt; .01).”

In an observational study, customers who participated in the RP (vs. nonparticipants) were more likely to smile when buying coffee (3.8 vs. 3.4 on a five-point scale; p < .05).

“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 &lt; .05), chat for a few minutes with café employees (26% versus 7%; p &lt; .05), say 'thank you' (95% versus 87%; n.s.), and leave a tip (21% versus 3%; p &lt; .01).”

Members who accelerated more strongly toward their first reward were faster to begin working toward their second reward (holding constant base hazard rate).

“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 interpurchase time, on the first card).”

The goal-gradient effect extends to the domain of quantity decisions.

“With this empirical application, we were able not only to replicate the finding of goal-motivated acceleration in visit rates (in the context of Web site rather than café visits) but also to extend the goal-gradient effect to the domain of quantity decisions and effort persistence.”

Shorter goal distance led members to visit a song-rating Web site more frequently.

“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 frequently, rate more songs during each visit, and persist longer in the rating effort.”

In a field experiment, customers who received a 12-stamp card with two preexisting bonus stamps completed the ten required coffee purchases faster than customers who received a regular 10-stamp card.

“One test of this hypothesis involved a field experiment, in which customers who received a 12-stamp card with two preexisting bonus stamps completed the ten required coffee purchases faster than customers who received a regular 10-stamp card.”

For incomplete certificates, we found deceleration (b1 = .7, p < .1; b2 = .01, p > .9).

“Consistent with the analysis of the incomplete cards in the café RP, we found deceleration ( b 1 = .7, p &lt; .1; b 2 = .01, p &gt; .9).”

These effects were replicated in the context of the Jaboom music-rating program.

“We replicated these effects in the context of the Jaboom music-rating program.”

As members approached the 51-song goal, they rated more songs in later visits.

“Consistent with the goal-gradient hypothesis, as members approached the 51-song goal, they rated more songs in later visits.”

There was a quadratic effect (p < .01) indicating a diminishing rate of acceleration.

“There was also a quadratic effect ( p &lt; .01) that indicated a diminishing rate of acceleration.”

The GDM captured three forms of goal gradients: increased persistence, rate, and quantity of effort closer to the reward threshold.

“Extending the GDM . Using a common measure of goal distance (d t ) 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.”

In the Jaboom music-rating program, goal-motivated acceleration in visit rates was replicated in a Web site context (rather than café visits).

“With this empirical application, we were able not only to replicate the finding of goal-motivated acceleration in visit rates (in the context of Web site rather than café visits) but also to extend the goal-gradient effect to the domain of quantity decisions and effort persistence.”

A majority (17% or 80/473) of all visit terminations occurred at d_itq = 1.0.

“Figure 7 illustrates these results and shows that a majority (17% or 80/473) of all visit terminations occurred at d itq = 1.0.”

Failure to persist in the effort stream and fulfill the requirements was associated with weaker acceleration and even deceleration.

“Relatedly, failure to persist in the effort stream and fulfill the requirements was associated with weaker acceleration and even deceleration.”

There was a negative effect of the number of certificates already earned during the same visit (p < .01).

“In addition, we found a negative effect of the number of certificates already earned during the same visit ( p &lt; .01), consistent with satiation or fatigue.”

Analysis of participants' entire sequence of ratings (including ratings that did not eventually lead to reward) revealed significant goal gradients.

“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.”

Significant goal gradients were found even after accounting for unobserved heterogeneity and controlling for time trends in visit and song-rating frequencies.

“We found significant goal gradients even after we accounted for unobserved heterogeneity and statistically controlled for time trends in visit and song-rating frequencies.”

There was no difference in feeling valence between experimental and control respondents (t = .2, n.s.).

“Importantly, there was no difference in feeling valence between experimental and control respondents (t = .2, n.s.).”

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).

“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 &lt; .05).”

We found a negative linear goal-distance parameter (p < .01), indicating that members rated more songs per visit when they were closer to the goal.

“Consistent with the goal-gradient hypothesis, we found a negative linear goal-distance parameter ( p &lt; .01; see Table 4) that indicated that members rated more songs per visit when they were closer to the goal.”

In an observational study, customers who participated in the RP (vs. nonparticipants) were more likely to leave a tip (21% vs. 3%; p < .01).

“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 &lt; .05), chat for a few minutes with café employees (26% versus 7%; p &lt; .05), say 'thank you' (95% versus 87%; n.s.), and leave a tip (21% versus 3%; p &lt; .01).”

The effect of first-card individual-level acceleration on earning a second reward was in the hypothesized direction (b = -.5, Wald χ2 = 5.3; p < .05).

“The effect of the first-card individual-level acceleration estimate for the member was in the hypothesized direction ( b = -.5, Wald χ 2 = 5.3; p &lt; .05).”

In an observational study, customers who participated in the RP (vs. nonparticipants) were more likely to say 'thank you' (95% vs. 87%; n.s.).

“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 &lt; .05), chat for a few minutes with café employees (26% versus 7%; p &lt; .05), say 'thank you' (95% versus 87%; n.s.), and leave a tip (21% versus 3%; p &lt; .01).”

Members of a café RP accelerated their coffee purchases as they progressed toward earning a free coffee.

“We found that members of a café RP accelerated their coffee purchases as they progressed toward earning a free coffee.”

Shorter goal distance led members to rate more songs during each visit.

“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 frequently, rate more songs during each visit, and persist longer in the rating effort.”

The rate of acceleration diminished, as indicated by the negative quadratic goal-distance parameter (p < .01).

“Consistent with Hull's (1934) findings with rats and our results of the café RP, the rate of acceleration diminished, as indicated by the negative quadratic goal-distance parameter ( p &lt; .01).”

• cites Hull's (1934) sourceNot checked — no full text of the source

Customers accelerate toward rewards in terms of timing, quantity, and persistence of effort.

“Not only do customers accelerate toward rewards (in terms of timing, quantity, and persistence of effort), but their acceleration also predicts loyalty and future engagement with similar goals.”

In an unpublished study, respondents in the near-reward condition were more likely than those in the distant-reward condition to accept the promotional offer (56% vs. 38%, χ2 = 10.7; p < .001).

“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%, χ 2 = 10.7; p &lt; .001).”

Acceleration predicts loyalty and future engagement with similar goals.

“Not only do customers accelerate toward rewards (in terms of timing, quantity, and persistence of effort), but their acceleration also predicts loyalty and future engagement with similar goals.”

We observe goal-motivated acceleration after accounting for weekly sales and other time-varying covariates.

“we observe goalmotivated acceleration after accounting for weekly sales and other time-varying covariates”

We find a majority of accelerators after accounting for unobserved heterogeneity in both the hazard rate and the tendency to accelerate.

“we find a majority of accelerators after accounting for unobserved heterogeneity in both the hazard rate and the tendency to accelerate.”

Process experiments show that the illusionary goal progress effect cannot be explained by rival accounts, such as sunk cost.

“Process experiments show that the illusionary goal progress effect cannot be explained by rival accounts, such as sunk cost.”

Using statistical and experimental controls, the authors rule out alternative explanations for the observed goal gradients.

“using statistical and experimental controls, the authors rule out alternative explanations for the observed goal gradients”

The observed purchase and effort acceleration cannot be explained by habituation, expiration concerns, other time-trend effects, or heterogeneity bias.

“The observed purchase and effort acceleration cannot be explained by habituation, expiration concerns, other time-trend effects, or heterogeneity bias.”

In the field experiment, the experimental group started with a lower proportion of original distance remaining to the goal than did the control group (d_t+2 = .83 and d_t = 1.0, respectively).

“the experimental group started with a lower proportion of original distance remaining to the goal than did the control group (i.e., d t +2 = .83 and d t = 1.0, respectively).”

In the process test, the control and experimental groups faced identical effort requirements (r - n_t = eight pizza meals).

“Thus, whereas the control and the experimental groups faced identical effort requirements (i.e., r - n t = eight pizza meals)”

It is difficult to interpret noninstrumental behaviors and physiological measurements as evidence supporting or refuting the goal-gradient hypothesis.

“As Heilizer (1977) details, it is difficult to interpret noninstrumental behaviors and physiological measurements as evidence supporting (or refuting) the goal-gradient hypothesis.”

• cites Heilizer 1977 sourceNot checked — no full text of the source

Goal motivation is influenced by the perceived rather than by the real progress toward the goal, all else being equal.

“Thus, we posit that, all else being equal, goal motivation is influenced by the perceived rather than by the real progress toward the goal.”

This implies that in a typical month, on average, members purchased two more coffees than they would have without an RP in order to earn one free coffee.

“The 20% (.7 day) decrease in average interpurchase times from the first to the last stamp on the card implies that in a typical month, on average, members purchased two more coffees than they would have without an RP in order to earn one free coffee.”

In the café RP, members accelerated their coffee purchases as they got closer to earning a free coffee.

“This result supports H 1 and demonstrates that members accelerated their coffee purchases as they got closer to earning a free coffee.”

• Also stated in: § Alternative Explanations · p. 9 · hedged

  “Consistent with the goal-gradient hypothesis (H 1 ), the findings from the café RP indicate that customers accelerated their purchases as a function of smaller goal distance.”

The modeling approach accounts for unobserved heterogeneity (individual differences in base purchase rates and acceleration tendencies).

“Our modeling approach also enables us to account for unobserved heterogeneity (i.e., individual differences in base purchase rates and acceleration tendencies).”

• AssumptionThe authors state this as an assumption: Each day is a potential purchase occasion, except for days on which the café is closed.

The interpurchase times on the transparent cards steadily increased as customers neared the nonreinforced (unrewarded) completion of the card.

“The interpurchase times on the transparent cards steadily increased as customers neared the nonreinforced (unrewarded) completion of the card.”

Illusionary goal progress led to faster completion of the reward requirement.

“Consistent with H 2 , the results indicate that illusionary goal progress led to faster completion of the reward requirement.”

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.

“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.”

• AssumptionRests on an assumption: Members from whom buyback cards were bought exhibited a lack of goal motivation.

This longer circulation suggests that without the intervention, such buyback cards would have resulted in 'breakage' (i.e., nonredeemed stamps or cards).

“which suggests that without our intervention, such buyback cards would have resulted in 'breakage' (i.e., nonredeemed stamps or cards).”

This pattern suggests that, unlike redeemers, buyback customers do not accelerate their purchases as a function of progress toward the reward.

“This pattern suggests that, unlike redeemers, buyback customers do not accelerate their purchases as a function of progress toward the reward.”

The analysis of the transparent cards supports the notion that the purchase acceleration found in the main data set was driven by goal motivation rather than by time-trend effects or habituation.

“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 timetrend effects or habituation.”

All results are replicated when excluding from the analyses the subsequent cards of members who redeemed more than one card.

“All the results are replicated when we exclude from the analyses the subsequent cards of members who redeemed more than one card.”

In the field experiment, the two groups faced identical effort requirements when joining the program (r - n_t = accumulating 10 coffee purchases).

“Thus, although the two groups faced identical effort requirements when joining the program (i.e., r n t = accumulating 10 coffee purchases)”

We ruled out several alternative explanations for the observed purchase acceleration using an experimental control (transparent cards) and statistical controls.

“We ruled out several alternative explanations for the observed purchase acceleration using an experimental control (i.e., the transparent cards) and statistical controls.”

Prior theorization about human motivation, affect, and cognition supports the relevance of the goal-gradient hypothesis for the human psychology of rewards.

“In summary, prior theorization about human motivation, affect, and cognition supports the relevance of the goal-gradient hypothesis for the human psychology of rewards.”

• AssumptionRests on an assumption: The implications of the goal-gradient hypothesis for human behavior and decision making are understudied.

The negative quadratic parameter implies a diminishing rate of acceleration.

“Consistent with the goalgradient curve in Figure 3, the negative quadratic parameter b 2 ( p &lt; .01) implies a diminishing rate of acceleration.”

When we ran the models without latent-class segmentation, all of the results still held.

“when we ran the models without latent-class segmentation, all of the results still held.”

• AssumptionThe authors state this as an assumption: Each day is a potential purchase occasion, except for days on which the café is closed.

The limited research conducted with humans used mostly physiological measurements that were noninstrumental for goal achievement.

“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.”

• cites Heilizer 1977 sourceNot checked — no full text of the source

Single-visit certificates must be excluded from analyses of intervisit times because they do not permit testing for acceleration or deceleration.

“Although such single-visit certificates arguably signify strong goal motivation, they must be excluded from the analyses of intervisit times because they do not permit testing for acceleration (or deceleration).”

The negative effect of certificates already earned is consistent with satiation or fatigue.

“In addition, we found a negative effect of the number of certificates already earned during the same visit ( p &lt; .01), consistent with satiation or fatigue.”

Postreward resetting rules out learning and other time-trend effects.

“The finding of postreward resetting is a key corollary of the goalgradient 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 survivor) rival account.”

Given postreward resetting, the results cannot be explained as a simple continuation of the increased purchase rates of accelerators.

“Given the previously reported findings of postreward resetting, our results cannot be explained as a simple continuation of the increased purchase rates of accelerators.”

These results are inconsistent with the sunk-cost alternative explanation.

“These results are inconsistent with the sunk-cost alternative explanation.”

• AssumptionRests on an assumption: The two stamps due to the respondent's own purchase effort in the sunk-cost condition are perceived as a sunk cost.

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 experimental and the control respondents.

“Because the sunkcost 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 experimental and the control respondents.”

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 (d_t = n_t/r).

“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., d t = n t /r).”

The manipulation of illusionary goal progress used in the field experiment and the current test was designed not to affect respondents' idiosyncratic fit with the RP.

“we deliberately used a manipulation of illusionary goal progress that we did not expect to affect respondents' idiosyncratic fit with the RP.”

The effect of illusionary goal progress is inconsistent with the rational accounts of purchase acceleration (cost-benefit and time-discounting explanations).

“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 results of the café RP imply that to earn one free coffee, customers bought two more coffees than they would have otherwise.

“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.”

These observational results suggest that goal striving is intrinsically motivating beyond extrinsic rewards.

“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.”

The Type I Tobit model captures the underlying motivation to rate songs while taking into account the 51-song constraint per certificate.

“This approach enables us to capture the underlying motivation to rate songs, while taking into account the constraint of 51 songs per certificate.”

The effect of illusionary goal progress provides direct support for the proposition that psychological goal distance (d_t) is a key determinant of achievement motivation and willingness to invest effort.

“The effect of illusionary goal progress provides direct support for our proposition that psychological goal distance (d t ) is a key determinant of achievement motivation and willingness to invest effort.”

• AssumptionRests on an assumption: The two free bonus stamps in the experimental conditions create the perception of illusionary goal progress.

Postreward resetting rules out a self-selection (or survivor) rival account.

“The finding of postreward resetting is a key corollary of the goalgradient 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 survivor) rival account.”

Individual differences in the goal gradient capture variations in the motivation to earn free rewards.

“We posited that individual differences in the goal gradient capture variations in the motivation to earn free rewards.”

Applying a regression to censored data leads to biased parameter estimates.

“because applying a regression to censored data leads to biased parameter estimates (Breen 1996)”

• cites Breen 1996Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Postreward resetting demonstrates that effort expenditure is a function of goal distance.

“The finding of postreward resetting is a key corollary of the goalgradient 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 survivor) rival account.”

RP members who exhibit enhanced acceleration possess a stronger motivation to earn free rewards (e.g., due to a higher achievement motivation).

“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).”

Self-selection is inconsistent with the analysis of participants' entire sequence of ratings.

“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.”

The finding that both segments demonstrate acceleration is inconsistent with the heterogeneity bias rival account.

“The finding that both segments demonstrate acceleration is inconsistent with the heterogeneity bias rival account.”

The findings provide converging evidence for the impact and importance of goal gradients in the human psychology of rewards.

“Based on a wide range of empirical and modeling approaches, the findings we report in this article provide converging evidence for the impact and importance of goal gradients in the human psychology of rewards.”

Compared with nonmembers of the RP, members may be willing to pay a price premium or forgo convenience, particularly when they near a program goal.

“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.”

People working toward future rewards accelerate their effort as they near the reward goal.

“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.”

Goal proximity increases customers' responsiveness to credit-earning promotions and offers.

“The findings suggest that goal proximity increases customers' responsiveness to credit-earning promotions and offers.”

The own- and cross-price elasticities of the RP sponsor are lower for members who are closer to the program's goals.

“It suggests that the ownand cross-price elasticities of the RP sponsor are lower for members who are closer to the program's goals.”