Magnitude effects and decreasing impatience in temporal discounting: Models, evidence, and applications

Many factors influence how individuals discount future payouts. A robust factor is the magnitude effect, whereby a small payout is discounted more than a larger one. But when individuals are confronted with more than one future payout, what drives the magnitude effect? Using a ceteris paribus design, we find that the discount rate decreases with the sum of cash flows and the highest cash flow. We also consider a separable model with cash-flow specific discount rates, but find mixed support for it. We also observe decreasing impatience, and propose various parametric models to predict present equivalents. To test these models out-of-sample, we design a retention bonus whose goal is to keep employees as highly motivated as possible during an extended period of time. All models that account for magnitude effect do a good out-of-sample job, whereas the models that merely account for decreasing impatience do not. Thus, our research can aid individuals, managers, and regulatory agencies better predict how individuals perceive financial offerings.