Estimating representations of time preferences and models of probabilistic intertemporal choice on experimental data
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.
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TL;DR: In this paper, the curvature of utility elicited directly from choices over time is found to be significantly concave, but far closer to linear than that elicited under risk, and the effect of correcting discount rates for this curvature is modest.
Abstract: In both standard and behavioral theory, as well as experimental procedures to elicit time preference, it is commonly assumed that a single utility function is used to evaluate payoffs both under risk and over time. I introduce a novel experimental design to examine this assumption, by transposing the well-known Holt-Laury risk preference experiment from state-payoff space into time-dated payoff space. I find that the curvature of utility elicited directly from choices over time is significantly concave, but far closer to linear than utility elicited under risk. As a result, the effect of correcting discount rates for this curvature is modest.
25 citations
TL;DR: In this paper, the effects of alternative assumptions regarding the curvature of utility upon estimated discount rates in experimental data were examined, and it was shown that the effect of adjusting discount rates for this curvature is modest compared to assuming linear utility, and considerably less than when utility from a risk preference task is imposed.
Abstract: This paper examines the effects of alternative assumptions regarding the curvature of utility upon estimated discount rates in experimental data. To do so, it introduces a novel design to elicit time preference building upon a translation of the Holt and Laury method for risk. The results demonstrate that utility elicited directly from choice over time is significantly concave, but far closer to linear than utility elicited under risk. As a result, the effect of adjusting discount rates for this curvature is modest compared to assuming linear utility, and considerably less than when utility from a risk preference task is imposed.
10 citations
TL;DR: Analytical and experimental results indicate that exponential discounting can explain intertemporal choice behavior that was supposed to be beyond its descriptive scope if the discount factor is permitted to vary at random.
7 citations
TL;DR: In this paper, the authors generalize the classic Fechner model of probabilistic/stochastic binary choice to choice among several alternatives, including Luce's choice model, multivariate probit and deterministic preferences.
5 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
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TL;DR: In this article, the authors propose simple and directional likelihood-ratio tests for discriminating and choosing between two competing models whether the models are nonnested, overlapping or nested and whether both, one, or neither is misspecified.
Abstract: In this paper, we propose a classical approach to model selection. Using the Kullback-Leibler Information measure, we propose simple and directional likelihood-ratio tests for discriminating and choosing between two competing models whether the models are nonnested, overlapping or nested and whether both, one, or neither is misspecified. As a prerequisite, we fully characterize the asymptotic distribution of the likelihood ratio statistic under the most general conditions.
5,661 citations
TL;DR: This paper introduced a three-item Cognitive Reflection Test (CRT) as a simple measure of one type of cognitive ability, i.e., the ability or disposition to reflect on a question and resist reporting the first response that comes to mind.
Abstract: This paper introduces a three-item "Cognitive Reflection Test" (CRT) as a simple measure of one type of cognitive ability—the ability or disposition to reflect on a question and resist reporting the first response that comes to mind. The author will show that CRT scores are predictive of the types of choices that feature prominently in tests of decision-making theories, like expected utility theory and prospect theory. Indeed, the relation is sometimes so strong that the preferences themselves effectively function as expressions of cognitive ability—an empirical fact begging for a theoretical explanation. The author examines the relation between CRT scores and two important decision-making characteristics: time preference and risk preference. The CRT scores are then compared with other measures of cognitive ability or cognitive "style." The CRT scores exhibit considerable difference between men and women and the article explores how this relates to sex differences in time and risk preferences. The final section addresses the interpretation of correlations between cognitive abilities and decision-making characteristics.
3,902 citations
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
TL;DR: In this paper, individual discount rates for losses and gains were estimated from survey evidence and they were found to vary inversely with the size of the reward and the length of time to be waited.
2,141 citations