Intertemporal preferences of individual and collective decision-makers

Abstract

This thesis contributes to theoretical modelling of time preferences of individual and collective decision-makers. In the context of an individual decision-maker we study two problems: axiomatization of time preferences and the effect of delay on the ranking of sequences of dated outcomes. In the context of a group of decision-makers we investigate the problem of aggregation of time preferences. First, we provide a new axiomatic foundation for exponential, quasi-hyperbolic and semi-hyperbolic discounting when preferences are expressed over streams of consumption lotteries. The key advantage of our axiomatic system is its simplicity and its use of a common framework for finite and infinite time horizons. Second, we analyse preferences with the property that the ranking of two sequences of dated outcomes can switch from one strict ranking to the opposite at most once as a function of some common delay -- the "one-switch" property of Bell [12]. We demonstrate that time preferences satisfy the one-switch property if and only if the discount function is either the sum of exponentials or linear times exponential. This is a revision of Bell's result [12], who claimed that the only discount functions compatible with the one-switch property are sums of exponentials. We also show that linear times exponential discount functions exhibit increasing impatience in the sense of Takeuchi [77]. To the best of our knowledge, linear times exponential discount functions have not been used in the context of time preference before. Finally, we study the problem of aggregating time preferences when individual time preferences exhibit decreasing impatience. If decision-makers have the same level of decreasing impatience, our result proves that the aggregate discount function is strictly more decreasingly impatient than each of individual discount functions. This is a generalization of Prelec's and Jackson and Yariv's results on the aggregation of discount functions [46, 63]. We also analyse the situation in which the aggregation problem arises because of some uncertainty about the discount function. In this context we prove the analogue of Weitzman's influential result [81], showing that if a decision-maker is uncertain about her hyperbolic discount rate, then long-term costs and benefits will be discounted at a hyperbolic discount rate which is the probability-weighted harmonic mean of the possible hyperbolic discount rates.