Estimating Discount Factors within a Random Utility Theoretic Framework

Abstract

Choices involving tradeoffs of benefits and costs over time are pervasive in our everyday lives. The observation of declining discount rates in experimental settings has led many to promote hyperbolic discounting over standard exponential discounting as the preferred descriptive model of intertemporal choice. In this paper, I develop a new framework that directly models the intertemporal utility function associated with an intertemporal outcome. This random utility model produces explicit maximum likelihood estimates of the discounting parameters. The main benefit of this approach is that I am able to perform formal statistical tests of quasi-hyperbolic and hyperbolic discounting, which has not been done previously in the economics literature. I apply this estimation method to two original data sets, a stated-preference survey of cleanup options for the Minnesota River Basin and revealed-preference choices of lottery payment options, in addition to one published data set. Formal statistical tests fail to find evidence in support of hyperbolic or quasi-hyperbolic discounting. Constant (exponential) annual discount rates range from eight to eleven percent over the three data sets, which are lower than those usually found in experimental studies but consistent with interest rates found in capital markets. I propose that confounding experimental artifacts may be responsible for previous evidence in favor of hyperbolic discounting. Specifically, uncertainty in future rewards, perceived future transaction costs, and subadditive discounting may confound estimates of rates of time preference (discount rates) from previous experimental designs.

Keywords: discounting, hyperbolic, random utility, intertemporal choice

JEL Classification: D90, Q25, Q53, H43