Intertemporal choice and competitive equilibrium

Abstract

iii 1.1.Intertemporal Choice unaffected when making a choice.Discounted utility is commonly assumed in economics.The focus of much research in psychology and economics is on the type of discounting.Samuelson (1937) considered constant discounting, also known as exponential discounting.With constant discounting a preference between two streams of outcomes does not change if all outcomes in both streams are delayed by an equal period of time.Individuals exhibiting constant discounting are said to have constant impatience.From the perspective of today, their impatience, or discounting, between today and tomorrow is not different from the impatience between March 4, 2030 and March 5, 2030.Much empirical evidence has demonstrated that humans and animals do not satisfy constant discounting (Frederick, Loewenstein, and O'Donoghue, 2002).Many studies have found that individuals are less impatient for the far future than for the near future, i.e. that they satisfy decreasing impatience.(Quasi-)hyperbolic discounting can capture decreasing impatience.Currently, quasi-hyperbolic discounting is becoming increasingly popular in applications.Hyperbolic and quasihyperbolic discounting are only two alternatives to constant discounting.Other alternatives could be thought of as well, but have not been considered in the literature.The main task in intertemporal choice today is to obtain a deeper understanding of the deviation from constant discounting and to develop appropriate alternatives.The first part of this thesis contributes to this task.In order to obtain a good understanding of the deviation from constant discounting and to develop alternatives, it is important to first understand fully what constant discounting is.Koopmans (1960Koopmans ( , 1972) ) gave a preference foundation of constant discounting that is very popular.A preference foundation is a set of conditions that fully characterize a preference model and that are easy to interpret and empirically verifiable.Thus, a preference foundation of constant discounting gives us a good insight into what constant discounting exactly implies and what it means empirically.Unfortunately, Koopmans' analysis contains some inaccuracies.Also, he does not allow for infinite economic growth in the infinite future, which is unnecessarily restrictive.Chapter 2 resolves these problems and provides, to the best of my knowledge, the first correct presentation of Koopmans' classical result.Chapter 3 introduces a measure for the deviation from constant discounting.This measure, the hyperbolic factor, quantifies the degree of decreasing impatience and proneness to choice anomalies.The hyperbolic factor is easily measurable.Thus, it gives an easy tool to identify (groups of) individuals that are prone to choice anomalies.Moreover, the hyperbolic factor provides a simple test of hyper-2 Koopmans' Constant Discounting: A Simplification and an Extension to Incorporate Economic GrowthKoopmans provided a well-known preference foundation for constant discounted utility, the most widely used model for intertemporal optimization.There were, however, some technical problems in his analysis; in particular, there was an unforeseen implication of bounded utility.Some partial resolutions have been suggested in the literature.This chapter 1 completely resolves the problems mentioned, with complete flexibility regarding the utility functions that can be used and the conceivable economic growth.It, thus, provides a complete and accessible preference foundation of constant discounted utility, and clarifies the appeal of Koopmans' intuitive axioms. The Hyperbolic Factor: a Measure of Decreasing ImpatienceMany studies have found that discounting is hyperbolic rather than constant.Hyperbolic discounting is becoming increasingly popular in economic applications.Most studies that provide evidence in favor of hyperbolic discounting either are merely qualitative or they depend on assumptions about, or parametric fittings of, utility functions.This chapter 1 provides a quantitative measure for the degree of deviation from stationarity that can overcome the problems mentioned.This measure, the hyperbolic factor, can easily be calculated from data and does not require knowledge of the utility function.Moreover, it provides simple preference foundations of the most popular discount functions.Thus, the hyperbolic factor provides an easy tool for theoretical preference foundations, critical empirical tests, and quantitative measurements of hyperbolic discounting.

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