The illusion of progress

This month’s Capital Ideas, published by the University of Chicago Graduate School of Business, features work done by our colleague Oleg Urminsky on the relationship between rewards and human efforts and motivations. The classic work on this puzzle was conducted in the 1930s by psychologist Clark Hull who noticed that rats ran faster as they moved closer to food. (Food they could see on a straight runway, that is.) Sensing the propinquity of the reward, the rats worked harder to obtain it. Hull called this phenomenon the “goal-gradient” hypothesis.

Urminsky, along with Ran Kivetz of Columbia University and Yuhuang Zheng of Fordham University, turned their attention to customer reward programs to further study Hull’s hypothesis, by analyzing how the distance to a final reward affected customers’ purchasing decisions.

The first experiment looked at coffee purchases by customers who participated in a coffee rewards program at a café located within the campus of a large university. Customers were offered a card that would let them earn one free coffee after buying ten coffees. To keep track of the timing of purchases, a participant’s card was stamped after each purchase.

As participants in the rewards program accumulated more stamps on their cards, the authors observed that the average length of time before the next coffee purchase decreased. Members bought that next coffee sooner the closer they were to getting a free one. In fact, the average time between purchases accelerated by about 20 percent from the first to the last stamp on the card. In other words, members purchased two more coffees in the time it took to complete the card than they would have if they hadn’t accelerated their purchases.

Even after controlling for various time trends that might affect the results, such as the weekly number of issued stamps (some weeks experience brisker sales than others) and the end of spring classes (when some students graduate), the authors found that customers bought coffees more frequently as they progressed toward their reward. On the other hand, those who were issued “transparent” cards that tracked the purchases but were not eligible for a free coffee did not speed up their consumption as they approached their tenth coffee. The same is true for customers who did not complete their cards, presumably lacking motivation to do so.

(The full article from Capital Ideas is here; the full academic version is here.)

The authors argue that the key determinant of goal motivation is the proportion of original distance remaining to the goal, an idea they refer to as “the illusion of progress.” Work by behavioral economists over the past few decades also sheds some insight into the empirical findings of rewards programs – namely that individuals’ value functions are non-linear. The intuition behind this theory is found in Richard Zeckhauser’s Russian roulette example.

Suppose you are compelled to play a round, but have the option of purchasing the removal of one bullet from a six bullet revolver. You would probably pay more money to reduce the number of bullets from one to zero or from six to five, than you would to reduce the number from four to three. The non-linear value function for coffee may be different than for bullets, but the general idea is that customers consider the last few cups of coffee a great deal since they are paying the same price as they did for earlier cups and will soon receive a free cup of joe.

Standard behavioral economic theory works from presumption that the objective difference to a reward is what matters. The authors here think that relative distance is what leads people to speed up their purchases. So a 12-stamp card with two bonus stamps will nudge people to faster coffee purchases than an empty 10-stamp card because people will feel as if they’ve already made some progress (two coffees worth!) and are closer to their goal. The authors found that customers complete the 10-stamp card in 15.6 days compared with only 12.7 days for the 12-stamp card with two bonus stamps.