Marzilli Ericson, White, and Cohen (2015) on Simple Discounting Heuristics

Keith M. Marzilli Ericson, John Myles White, and Jonathan D. Cohen, “Money Earlier or Later? Simple Heuristics Explain Intertemporal Choices Better than Delay Discounting.” NBER Working Paper No. w20948, February 2015.

• A series of “Money Earlier or Later” (MEL) choice problems are given to 1000 participants on Amazon’s Mechanical Turk service. Each MEL problem asks a person to choose between a Small-Early option (x1, t1), where x1 is the amount of money to be received t1 time periods from now, and a Large Late option (x2, t2); the names of the options recognize that x1<x2, and t1<t2. So, are you willing to wait until time t2 (instead of t1) to receive a larger payment of x2 (instead of the smaller but earlier payment of x1)?

• Problems with existing models of discount rates are what motivate this experiment. We have already seen why exponential discounting is inconsistent with common choice behavior. But even hyperbolic or quasi-hyperbolic discounting, though they can generate a present bias, cannot explain the magnitude effect, where multiplying up the dollar amounts by a common factor leads to lower revealed discount rates: a person who will take $10 today instead of $13 a week from now (often) will not take $1000 today instead of $1300 one week from now.

• The authors propose that in MEL problems, people employ rules of thumb, heuristics, so they call their model the ITCH model, for Intertemporal Choice Heuristics. In the ITCH models, the four factors that people employ to make their decision are the absolute (x2-x1) and relative ((x2-x1)/(x1+x2)/2) differences in monetary amounts and, the absolute (t2-t1) and relative ((t2-t1)/(t1+t2)/2) time delays. These four factors are combined via a weighted sum, which turns out to be fairly stable across individuals and “frames” for the MEL problems. The use of average time and delay in determining relative changes provides a sort of reference point interpretation to the heuristic.

• ITCH explains decreasing impatience (with time) and the absolute magnitude effect: If both the early and late options are delayed by a week, the relative time delay falls, so the use of a lower discount rate results. Alternatively, increasing the stakes proportionally increases the absolute payoff, and again, a lower discount rate will be chosen by the heuristics.

• Calibration of the model on a subset of the data shows that relative money is a much larger factor than absolute money, whereas relative and absolute time have similar weights. (But the time periods were rather paltry, and were presented always in absolute form, so a different approach could raise the decision weight of the relative time component.)

• In predicting the out-of-sample data, the ITCH model out-performs all the tested alternatives such as exponential discounting or quasi-hyperbolic discounting.

• So, perhaps people do not have “a” discount rate, but rather, use some rules of thumb to make intertemporal trade-offs.