Temporal dominance and relative patience in intertemporal choice
TL;DR: In this article, a stream of intertemporal payoffs temporarily dominates another stream Y if the cumulative payoff function of X up to any moment of time is always at least as high as that of Y; equivalently, any rank-dependent discounted utility maximizer with a strictly increasing (concave) utility function and a strictly decreasing (convex) discount function prefers X over Y.
Abstract: A stream of intertemporal payoffs X first-order (second-order) temporarily dominates another stream Y if (the area below) the cumulative payoff function of X up till any moment of time is always at least as high as that of Y; or, equivalently, any rank-dependent discounted utility maximizer with a strictly increasing (concave) utility function and a strictly decreasing (convex) discount function prefers X over Y. An individual A is relatively more patient than an individual B if, whenever B is willing to undertake some investment project, A is moreover so; or, equivalently, for any stream of payoffs, A’s present-day equivalent is at least as high as that of B; or, equivalently, A’s discount factor is at least as high as that of B and B’s utility function is “more concave” than that of A. Related concepts of absolute patience and comparative probabilistic patience are briefly discussed.
Citations
More filters
TL;DR: Rank-dependent discounted utility and its special case, the maximization of present discounted value, was found to be the best-fitting theory for about two-thirds of all subjects.
Abstract: We here estimate a number of alternatives to discounted-utility theory, such as quasi-hyperbolic discounting, generalized hyperbolic discounting, and rank-dependent discounted utility with three different models of probabilistic choice. The data come from a controlled laboratory experiment designed to reveal individual time preferences in two rounds of 100 binary-choice problems. Rank-dependent discounted utility and its special case—the maximization of present discounted value—turn out to be the best-fitting theory (for about two-thirds of all subjects). For a great majority of subjects (72%), the representation of time preferences in Luce’s choice model provides the best fit.
12 citations
TL;DR: In this paper, the authors propose a special case of the two representations, called risk-time reversal, for obtaining a special class of expected discounted utility, which is similar to assumption 2 "reversal of order in compound lotteries".
Abstract: Standard axioms of additively separable utility for choice over time and classic axioms of expected utility theory for choice under risk yield a generalized expected additively separable utility representation of risk-time preferences over probability distributions over sure streams of intertemporal outcomes. A dual approach is to use the analogues of the same axioms in a reversed order to obtain a generalized additively separable expected utility representation of time–risk preferences over intertemporal streams of probability distributions over sure outcomes. The paper proposes an additional axiom, which is called risk-time reversal, for obtaining a special case of the two representations—expected discounted utility. The axiom of risk-time reversal postulates that if a risky lottery over streams of sure intertemporal outcomes and an intertemporal stream of risky lotteries yield the same probability distribution of possible outcomes in every point in time then a decision-maker is indifferent between the two. This axiom is similar to assumption 2 “reversal of order in compound lotteries” in Anscombe and Aumann (Ann Math Stat 34(1):199–205, 1963, p. 201).
4 citations
2 citations
1 citations
TL;DR: This paper presents a microeconomic model of discrete intertemporal choice (which is equivalent to heteroscedastic probit/logit) that rules out such unlikely errors (i.e. violations of period-wise monotonicity).
1 citations
References
More filters
TL;DR: In this paper, the authors enumerate a set of discounted utility anomalies analogous to the EU anomalies and propose a model that accounts for the anomalies, as well as other intertemporal choice phenomena incompatible with DU.
Abstract: Research on decision making under uncertainly has been strongly influenced by the documentation of numerous expected utility (EU) anomalies—behaviors that violate the expected utility axioms. The relative lack of progress on the closely related topic of intertemporal choice is partly due to the absence of an analogous set of discounted utility (DU) anomalies. We enumerate a set of DU anomalies analogous to the EU anomalies and propose a model that accounts for the anomalies, as well as other intertemporal choice phenomena incompatible with DU. We discuss implications for savings behavior, estimation of discount rates, and choice framing effects.
2,208 citations
1,938 citations
TL;DR: In this article, the authors highlight the question whether second-best saving is greater or smaller than first-best savings when given future saving is non-optimal from the standpoint of the present generation.
Abstract: This chapter highlights the question whether second-best saving is greater or smaller than first-best saving when given future saving is non-optimal from the standpoint of the present generation. The chapter presents the postulation that all generations expect each succeeding generation to choose the saving ratio that is second-best in its eyes. This somewhat game-theoretic model leads to the concept of an equilibrium sequence of saving-income ratios having the property that no generation acting alone can do better and all generations act so as to warrant the expectations of the future saving ratios. The chapter presents a comparison of this equilibrium and the first-best optimum. The concept and calculation of the second-best optimum is of interest even if that analysis does not explain actual national saving because society as a whole has no notion of such an optimum.
1,367 citations
TL;DR: The main results based on exponential discounting are robust to alternative specifications such as hyperbolic discounting and have direct implications for attempts to elicit time preferences, as well as debates over the appropriate domain of the utility function when characterizing risk aversion and time consistency.
Abstract: We design experiments to jointly elicit risk and time preferences for the adult Danish population. Since subjects are generally risk averse, we find that joint elicitation provides estimates of discount rates that are significantly lower than those found in previous studies and more in line with what would be considered as a priori reasonable rates. The statistical specification relies on a theoretical framework that involves a latent trade-off between long-run optimization and short-run temptation. Estimation of this specification is undertaken using structural, maximum likelihood methods. Our main results based on exponential discounting are robust to alternative specifications such as hyperbolic discounting. These results have direct implications for attempts to elicit time preferences, as well as debates over the appropriate domain of the utility function when characterizing risk aversion and time consistency.
1,143 citations