Subjective random discounting and intertemporal choice

This paper provides an axiomatic foundation for a particular type of preference shock model called the random discounting representation where a decision maker believes that her discount factors change randomly over time. For this purpose, we formulate an infinite horizon extension of [E. Dekel, B. Lipman, A. Rustichini, Representing preferences with a unique subjective state space, Econometrica 69 (2001) 891-934], and identify the behavior that reduces all subjective uncertainties to those about future discount factors. We also show uniqueness of subjective belief about discount factors. Moreover, a behavioral comparison about preference for flexibility characterizes the condition that one's subjective belief second-order stochastically dominates the other. Finally, the resulting model is applied to a consumption-savings problem.     

Quasi-stationary cardinal utility and present bias

This note gives an axiomatic foundation for utility exhibiting quasi-geometric discounting. In addition, it introduces a wider class of utility functions satisfying weakened stationarity, called quasi-stationary utility. Both are established as von Neumann-Morgenstern utility indices in a model of risk preference.     

The intertemporal allocation of consumption,time preference,and life-history strategies

This paper studies the intertemporal allocation of consumption and time preference in both biological and economic framework. By incorporating intergenerational transfers to examine human life-history strategies, this study demonstrates that time discounting and mortality mirror the age-variation in the value of survival, which in turn depends on future reproduction and productive surplus. Consistent with empirical findings, the results suggest that our biologically endowed rate of time preference is positive, and is lowest in early adulthood, but increases thereafter. The results also offers a biological explanation for intertemporal loss aversion, indicating that time preference is higher when exchange transactions involve a reduction in current consumption than when they involve an increase in current consumption. In a broader perspective, this paper looks into the biological foundation of preferences and motivation. Establishing the foundation of preferences with biological models and incorporating the results into economic models enrich the understanding of our decision-making mechanism and behavior.     

Finite additive utility representations for preferences over menus

I characterize a finite additive utility representation for preferences over menus. The numbers of both positive and negative components in this representation are expressed explicitly in terms of preference. These expressions can be used to characterize models of temptation, perfectionism, context effects, and other phenomena.     

A simple explanation of some key time preference anomalies

Abstract Individual time discounting behaviour experimentally exhibits important anomalies that are inconsistent with the standard discounted utility model. These include the time preference reversal characteristic of hyperbolic discounting, the magnitude effect and the extreme sign effect. I propose a simple explanation of discounting that accounts for these three anomalies simultaneously, within the context of the expected utility model with uncertainty, risk aversion, and preference for precautionary saving.     

INTERTEMPORAL UTILITY SMOOTHING: THEORY AND APPLICATIONS

This paper reviews models of intertemporal choice designed to be consistent with a phenomenon called a preference for spread; that is, where a decision‐maker prefers to spread good and bad consumption evenly over time. We closely examine the notion of utility smoothing adopted in these models as a source of the preference for spread. The paper also reviews extensions of these models where a strong aversion to volatility involved in a utility sequence causes preferences to be nonmonotone. Furthermore, to gain a better understanding of the behaviour implied by these models, we apply them to the Diamond growth model.     

A behavioral characterization of plausible priors

Recent decision theories represent ambiguity via multiple priors, interpreted as alternative probabilistic models of the relevant uncertainty. This paper provides a robust behavioral foundation for this interpretation. A prior P is “plausible” if preferences over some subset of acts admit an expected utility representation with prior P, but not with any other prior Q≠P. Under suitable axioms, plausible priors can be elicited from preferences, and fully characterize them; also, probabilistic sophistication implies that there exists only one plausible prior; finally, “plausible posteriors” can be derived via Bayesian updating. Several familiar decision models are consistent with the proposed axioms.     

The α-MEU model: A comment

In Ghirardato et al. (2004) [7], Ghirardato, Macheroni and Marinacci propose a method for distinguishing between perceived ambiguity and the decision-maker?s reaction to it. They study a general class of preferences which they refer to as invariant biseparable. This class includes CEU and MEU. They axiomatize a subclass of α-MEU preferences. If attention is restricted to finite state spaces, we show that any α-MEU preference relation, satisfies GMM?s axioms if and only ifα=0 or 1, that is, the preferences must be either maxmin or maxmax. We show by example that these axioms may be satisfied when the state space is [0,1].     

Is there a daily discount rate? Evidence from the food stamp nutrition cycle

Quasi-hyperbolic discounting predicts impatience over short-run tradeoffs. I present a direct non-laboratory test of this implication using data on the nutritional intake of food stamp recipients. Caloric intake declines by 10 to 15 percent over the food stamp month, implying a significant preference for immediate consumption. These findings constitute a rejection of the permanent income hypothesis and are extremely difficult to reconcile with exponential discounting. The data support an explanation based on time preference and reject several alternative explanations, including highly elastic intertemporal substitution. I explore implications for the optimal timing of transfer payments under alternative assumptions about preferences.     

Over-savings and hyperbolic discounting

Hyperbolic discounting models are widely seen as implying that consumers do not save enough, in accordance with the observed low rates of savings of some households. This paper qualifies this view by showing that hyperbolic consumers may ‘oversave’ in the short run. The result extends to uncertainty on future income and does not depend on whether preferences are present-biased or future-biased. A generalized comparative statics analysis of self-control is introduced, and its relationship to the analysis of uncertainty on discount factors is emphasized.     

Imprecise probabilistic beliefs as a context for decision-making under ambiguity

Coherent imprecise probabilistic beliefs are modeled as incomplete comparative likelihood relations admitting a multiple-prior representation. Under a structural assumption of Equidivisibility, we provide an axiomatization of such relations and show uniqueness of the representation. In the second part of the paper, we formulate a behaviorally general “Likelihood Compatibility” axiom relating preferences and probabilistic beliefs and characterize its implications for the class of “invariant biseparable” preferences that includes the MEU and CEU models among others.     

An additively separable representation in the Savage framework

This paper proposes necessary and sufficient conditions for an additively separable representation of preferences in the Savage framework (where the objects of choice are acts: measurable functions from an infinite set of states to a potentially finite set of consequences). A preference relation over acts is represented by the integral over the subset of the product of the state space and the consequence space which corresponds to the act, where this integral is calculated with respect to an evaluation measure on this space. The result requires neither Savage's P3 (monotonicity) nor his P4 (weak comparative probability). Nevertheless, the representation it provides is as useful as Savage's for many economic applications.     

Developments in discounting: With special reference to future health events

Research on time preferences and discounting has two main motivations: to inform decision making by providing a basis for the comparison of future costs and benefits; to explain the influence of the future on current behaviour. This paper introduces the wide range of discount functions which have been advocated in addition to the standard constant rate exponential model. The different approaches taken to estimating the parameters of the discount function are reviewed. The issues raised by discounting in the longer term are discussed. Particular attention is given to time preferences with respect to future health events which have for a number of reasons been a fruitful area for research on time preferences. Specifically the paper examines: the distinctive issues raised when discounting future health events; the methods which have been used to discount health events; the relationship between time preferences and health-affecting behaviour.     

Expected utility theory without the completeness axiom

We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteries by means of a set of von Neumann-Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well-defined sense.     

An extension of quasi-hyperbolic discounting to continuous time

Two-Stage Exponential (TSE) discounting, the model developed here, generalises exponential discounting in a parsimonious way. It can be seen as an extension of Quasi-Hyperbolic discounting to continuous time. A TSE discounter has a constant rate of time preference before and after some threshold time; the switch point. If the switch point is expressed in calendar time, TSE discounting captures time consistent behaviour. If it is expressed in waiting time, TSE discounting captures time invariant behaviour. We provide preference foundations for all cases, showing how the switch point is derived endogenously from behaviour. We apply each case to Rubinstein's infinite-horizon, alternating-offers bargaining model.     

Risk and intertemporal substitution: Livestock portfolios and off-take among Kenyan pastoralists

Most decisions involve variability in two dimensions: uncertainty across states of nature and fluctuations over time. The stakes involved in tradeoffs between these variability dimensions are especially high for the poor who have difficulty managing and recovering from shocks. We assume Epstein and Zin recursive preferences and estimate risk aversion and intertemporal substitution as distinct preferences using data from Kenyan herders. Results suggest that the assumption implicit in additive expected utility models that relative risk aversion (RRA) is the inverse of the elasticity of intertemporal substitution (EIS) is flawed. Specifically, our RRA and EIS estimates are consistent with a preference for the early resolution of uncertainty, which we believe is driven importantly by the instrumental value of early uncertainty resolution. This same preference pattern is consistent with asset smoothing in response to a dynamic asset threshold.     

Stable schedule matching under revealed preference

Baiou and Balinski (Math. Oper. Res., 27 (2002) 485) studied schedule matching where one determines the partnerships that form and how much time they spend together, under the assumption that each agent has a ranking on all potential partners. Here we study schedule matching under more general preferences that extend the substitutable preferences in Roth (Econometrica 52 (1984) 47) by an extension of the revealed preference approach in Alkan (Econom. Theory 19 (2002) 737). We give a generalization of the Gale-Shapley algorithm and show that some familiar properties of ordinary stable matchings continue to hold. Our main result is that, when preferences satisfy an additional property called size monotonicity, stable matchings are a lattice under the joint preferences of all agents on each side and have other interesting structural properties.     

Decreasing Impatience: A Criterion for Non‐stationary Time Preference and "Hyperbolic" Discounting

Despite recent interest in hyperbolic discounting, there has been little discussion of exactly what property of time preferences is instantiated by hyperbolic or quasi‐hyperbolic functional forms. The paper revives an earlier proposal in Prelec (1989) that the key property is Pratt–Arrow convexity of the log of the discount function, which corresponds to decreasing impatience(DI) at the level of preferences. DI provides a natural criterion for assessing the severity of departure from stationarity in that greater DI is equivalent to more choices of dominated options in two‐stage decision problems, as well as greater convexity of the log of the discount function. Inefficient choices may arise as intentional precommitments, or as unintended reversals of preference by “naïve” agents.     

To be consumed with moderation

We study the optimal behavior of a hyperbolic discounting agent who has incomplete information about his own preferences and can only learn them through consumption. We show that, even if moderate current consumption and moderate future consumption always dominates abstinence, the agent may optimally decide not to consume as a commitment device against inefficient learning that would lead to future excesses. This provides a rationale for why smokers, gamblers or compulsive buyers stick to second-best personal rules of behavior - such as “abstinence” - without invoking standard habit formation arguments. We also study how urges modify the strategy of the individual.     

Ambiguity,data and preferences for information – A case-based approach

We model decision making under ambiguity based on available data. Decision makers express preferences over actions and data sets. We derive an α-max–min representation of preferences, in which beliefs combine objective characteristics of the data (number and frequency of observations) with subjective features of the decision maker (similarity of observations and perceived ambiguity). We identify the subjectively perceived ambiguity and separate it into ambiguity due to a limited number of observations and ambiguity due to data heterogeneity. The special case of no ambiguity provides a behavioral foundation for beliefs as similarity-weighted frequencies as in Billot et al. (2005) [3].