An Attentional Model of Time Discounting

Abstract: When decision makers evaluate a sequence of rewards, they may pay more attention to larger rewards and, given attention is limited, less attention to smaller rewards. They may also become less attentive to each reward when attention is spread over a longer period of time. Such reductions in attention could lead to greater discounting of the rewards' values. This paper introduces a novel theory of time discounting based on these assumptions. The resulting discount factors in the theory follow a distribution similar to the multinomial logit function. We characterize such discount factors using two approaches: one based on information maximizing exploration and the other based on the optimal discounting framework. The theory can explain a wide range of anomalies, including the hidden-zero effect, S-shaped value function, and intertemporal correlation aversion. Also, it specifies new mediators for some well-known psychological effects, such as the common difference effect, risk aversion over time lotteries, and the present bias.