Estimating representations of time preferences and models of probabilistic intertemporal choice on experimental data

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.     

At the nexus of risk and time preferences: An experimental investigation

Although many economic decisions involve choices between uncertain outcomes occurring at different times, most theoretical and empirical work restricts attention to one dimension or another. In this paper, we investigate whether both risk and time preferences can be represented by a single parameter. We collect experimental data to estimate models which allows for a disentanglement of risk and time preferences. Results reveal that the discounted expected utility model assumption, that risk and time preferences can be explained by a single parameter, is not supported by the data. The model estimates imply people prefer to delay the resolution of risky outcomes.     

Preference for gradual resolution of uncertainty

Analyses of preference for the timing of uncertainty resolution usually assumes all uncertainty to resolve in one point in time. More realistically, uncertainty should be modelled to resolve gradually over time. Kreps and Porteus (1978) have introduced an axiomatically based model of time preference which can explain preferences for gradual uncertainty resolution. This paper presents an experimental test of the Kreps-Porteus model. We derive implications of the model relating preferences for gradual and one-time resolving lotteries. Our data do not support the Kreps-Porteus model but show that some of the behaviour observed may be explained by similarity heuristics.     

Indecisiveness aversion and preference for commitment

We present an axiomatic model of preferences over menus that is motivated by three assumptions. First, the decision maker is uncertain ex ante (i.e., at the time of choosing a menu) about her ex post (i.e., at the time of choosing an option within her chosen menu) preferences over options, and she anticipates that this subjective uncertainty will not resolve before the ex post stage. Second, she is averse to ex post indecisiveness (i.e., to having to choose between options that she cannot rank with certainty). Third, when evaluating a menu she discards options that are dominated (i.e., inferior to another option whatever her ex post preferences may be) and restricts attention to the undominated ones. Under these assumptions, the decision maker has a preference for commitment in the sense of preferring menus with fewer undominated alternatives. We derive a representation in which the decision maker’s uncertainty about her ex post preferences is captured by means of a subjective state space, which in turn determines which options are undominated in a given menu, and in which the decision maker fears, whenever indecisive, to choose an option that will turn out to be the worst (undominated) one according to the realization of her ex post preferences.     

The Aversion to the Sequential Resolution of Uncertainty

This paper sets forth and offers an explanation for preferences for the form of the timing of resolution of uncertainty; namely for uncertainty to be resolved all at one time rather than sequentially. The explanation is based on a weakening of the independence axiom, in particular on the notion of disappointment aversion developed in Gul's (1991) axiomatic model of preferences. Implications of this aversion are discussed for issues in finance, intertemporal decision making under uncertainty, high stakes risky situations and consumer self-regulation. The analysis encourages a formulation of preferences over all attributes of interest to the decision maker, including psychological satisfaction.     

Welfare analysis under uncertainty

This article extends Bergsonian welfare analysis to an environment of uncertainty where preferences are not expected utility and may even be state-inconsistent. Given state-inconsistent preferences, the familiar notion of ex ante efficiency is also state-inconsistent. Other efficiency and welfare concepts achieve state consistency by ignoring entirely the prospective preferences of consumers. The framework developed in this article allows welfare judgments to be state-consistent while respecting prospective and conditional preferences. The theory is called inclusive welfare. An application to optimum insurance subsidies illustrates the practical use of the concept.     

Viewing the future through a warped lens: Why uncertainty generates hyperbolic discounting

A large body of experimental research has demonstrated that, on average, people violate the axioms of expected utility theory as well as of discounted utility theory. In particular, aggregate behavior is best characterized by probability distortions and hyperbolic discounting. But is it the same people who are prone to these behaviors? Based on an experiment with salient monetary incentives we demonstrate that there is a strong and significant relationship between greater departures from linear probability weighting and the degree of decreasing discount rates at the level of individual behavior. We argue that this relationship can be rationalized by the uncertainty inherent in any future event, linking discounting behavior directly to risk preferences. Consequently, decreasing discount rates may be generated by people’s proneness to probability distortions.     

Schur convexity,quasi-convexity and preference for early resolution of uncertainty

This paper deals with decision makers who choose among information systems. It shows that the properties of Schur convexity and of quasi-convexity are equivalent, even when general preferences are considered. Since Schur convexity is closely related to having a willingness to accept information and since quasi-convexity is closely related to having a preference for early resolution of the uncertainty about which information system prevails, then it follows that the equivalence implies that decision makers prefer more information to less if, and only if, they prefer early resolution of uncertainty to later resolution.     

Hope: An empirical study of attitude toward the timing of uncertainty resolution

Hope is experienced when there is enjoyment in delaying the resolution of uncertainty. The main objective of this article is to identify the phenomenon of hope. In addition, we empirically test several axiomatic theories of temporal preferences which have implications for attitudes toward the timing of uncertainty resolution. Overall, the data support the extension of recursive expected utility specification to incorporate a weighted utility model of attitude toward future uncertainty. We find that the instances where hopefulness are more prevalent tend to be associated with a small probability of occurrence of a large gain. Interestingly, the degree of hopefulness is not correlated with risk attitude.     

Giving in the face of risk

Decisions about how to share resources with others often need to be taken under uncertainty regarding its allocational consequences. Although risk preferences are likely important, existing research is silent about how social and risk preferences interact in such situations. In this paper we provide experimental evidence on this question. In a first experiment givers are not exposed to risk while beneficiaries’ final earnings may be larger or smaller than the allocation itself, depending on the realized state of the world. In a second experiment, risk affects the earnings of givers but not of beneficiaries. We find that individuals’ risk preferences are predictive for giving in both experiments. Increased risk exposure of beneficiaries tends to decrease giving whereas increased risk exposure of givers has no effect. We propose a simple non-linear generalization of a model allowing for other-regarding preferences, ex-post and ex-ante fairness, and risk aversion. We find some support for it in our data when risk is on the beneficiaries’ side but less so when risk is on the givers’ side. Our results point to the importance of the further development of models of social preferences that also incorporate risk preferences.     

Nontransitive preferences in decision theory

Intransitive preferences have been a topic of curiosity, study, and debate over the past 40 years. Many economists and decision theorists insist on transitivity as the cornerstone of rational choice, and even in behavioral decision theory intransitivities are often attributed to faulty experiments, random or sloppy choices, poor judgment, or unexamined biases. But others see intransitive preferences as potential truths of reasoned comparisons and propose representations of preferences that accommodate intransitivities. This article offers a partial survey of models for intransitive preferences in a variety of decisional contexts. These include economic consumer theory, multiattribute utility theory, game theory, preference between time streams, and decision making under risk and uncertainty. The survey is preceded by a discussion of issues that bear on the relevance and reasonableness of intransitivity.     

The aggregation of preferences: can we ignore the past?

The article shows that a Paretian social welfare function can be history independent and time consistent only if a stringent set of conditions is verified. Individual utilities must be additive. The social welfare function must be a linear combination of these utilities. Social preferences are stationary only if, in addition, all individuals have the same constant discount rate. The results are implemented in two frameworks: deterministic dynamic choice and dynamic choice under uncertainty. The applications highlight that the conditions are unlikely to be met by individual preferences, and that they severely restrict social preferences.     

Does time inconsistency differ between gain and loss? An intra-personal comparison using a non-parametric elicitation method

Several studies on time preference have found time inconsistency in both gain and loss preferences. However, the relationship between the two within the same person remains unclear; that is, does an individual who demonstrates time inconsistency for gain outcomes do so for losses as well? This paper reports on individuals’ time inconsistency for gains and losses in a laboratory setting. To obtain a precise comparison of individuals’ time inconsistency for gains and losses, we used Rohde’s “DI (decreasing impatience)-index” (Manag Sci 65(4):1700–1716, 2018) and measured the level of time inconsistency, rather than merely identifying whether TI was present. This index represents how strongly a person exhibits present bias, and easily extends to the comparison between gain and loss preferences within the same person. Further, it allows the experiment to test for so-called future bias, which has been a focus area in recent time inconsistency literature. It is elicited through a non-parametric method, which avoids any specification errors in the analysis. Our findings are as follows: first, we found future bias in preferences for not only gains but also losses, and we confirmed that this tendency is consistent with previous findings on preferences for gains. Second, a positive correlation between time inconsistency for gains and losses was found at the individual level. Indeed, we could not find a significant difference between the two in most cases.

     

Noise and bias in eliciting preferences

In the context of eliciting preferences for decision making under risk, we analyse the features of four different elicitation methods—pairwise choice, willingness-to-pay, willingness-to-accept, and the Becker-DeGroot-Marschak mechanism—and estimate noise, bias and risk attitudes for two different preference functionals, Expected Utility and Rank-Dependent Expected Utility. It is well-known that methods differ in terms of the bias in the elicitation; it is rather less well-known that methods differ in terms of their noisiness. It has also been reported that risk attitudes are not stable across different elicitation methods. Our results suggest that elicited preferences should only be used in the context in which they were elicited, and the bias in the certainty-equivalent methods should be kept in mind when making predictions based on the elicited preferences. Moreover, conclusions should be moderated to take into account the various methods’ noise, which is generally lowest in the case of pairwise choice.     

Process fairness,outcome fairness,and dynamic consistency: Experimental evidence for risk and ambiguity

Literature on fairness preferences distinguishes between outcome fairness, concerning the final allocation of payoffs, and process fairness, concerning the expected allocation of payoffs. It is not obvious, however, whether process fairness can consistently be implemented. Once uncertainty is resolved and outcomes are determined, the ex-ante procedurally fair decision maker may become consequentialist ex-post, and reconsider her choice on the basis of the observed outcomes. We present experimental evidence on dynamic consistency of social preferences under both known risk and ambiguity. A significant share of people subscribe to process fairness both before and after the resolution of uncertainty.     

Resource allocation and project selection: Control of r & d under dynamic process of data improvement

This paper deals with the problem of optimal control of R&D. The fundamental aspects of this problem are viewed as: uncertainty about economic parameters of new technology (or new activity, e.g. a search for new oil fields) explored by a group of parallel projects attempting to make advances in this technology as well as improve economic data; allocation of investments among rival projects under a given total budget; timing of the ultimate selection of new technology (activity) according to the most successful project. The process of data improvement (PDI) is described as a (random) process of reducing the intervals of uncertainty, the rate of data improvement being controlled, in effect, by the investment policy. A stationary dynamic model with infinite horizon of planning and with the criterion of total discounted costs is developed. The model is carefully investigated from the economic point of view, and some new effects are discovered. It is demonstrated that uncertainty may be the source of additional gain; the bigger the initial uncertainty, the bigger the gain may be under optimal control. This effect is based on PDI, the economic background of which is presented as multiplication of the expected gain over time, which is typical for the classical macromodels of economics.Optimal continuous control is constructed at every time moment, and answers to two main questions are given:(1) either to prolong R & D or to make ultimate selection of one project, (2) how to allocate resources among the rival projects in the case of R&D prolongation. The last question is answered on the basis of profitability indices that relate efficiencies of PDI for particular projects to the costs of information.     

Intertemporal choice under timing risk: An experimental approach

This paper investigates how individuals evaluate delayed outcomes with risky realization times. Under the discounted expected utility (DEU) model, such evaluations depend only on intertemporal preferences. We obtain several testable hypotheses using the DEU model as a benchmark and test these hypotheses in three experiments. In general, our results show that the DEU model is a poor predictor of intertemporal choice behavior under timing risk. We found that individuals are averse to timing risk and that they evaluate timing lotteries in a rank-dependent fashion. The main driver of timing risk aversion is nothing but probabilistic risk aversion that stems from the nonlinear treatment of probabilities.     

A variational model of preference under uncertainty

A familiar example devised by Daniel Ellsberg to highlight the effects of event ambiguity on preferences is transformed to separate aleatory uncertainty (chance) from epistemic uncertainty. The transformation leads to a lottery acts model whose states involve epistemic uncertainty; aleatory uncertainty enters into the statedependent lotteries. The model proposes von Neumann-Morgenstern utility for lotteries, additive subjective probability for states, and the use of across-states standard deviation weighted by a coefficient of aversion to variability to account for departures from Anscombe-Aumann subjective expected utility. Properties of the model are investigated and a partial axiomatization is provided.     

Intentional time inconsistency

We propose a theoretical model to explain the usage of time-inconsistent behavior as a strategy to exploit others when reputation and trust have secondary effects on the economic outcome. We consider two agents with time-consistent preferences exploiting common resources. Supposing that an agent is believed to have time-inconsistent preferences with probability p,  we analyze whether she uses this misinformation when she has the opportunity to use it. Using the model originally provided by Levhari and Mirman (Bell J Econ 11(1):322–334, 1980), we determine the optimal degree of present bias that the agent would like to have while pretending to have time-inconsistent preferences and we provide the range of present-bias parameter under which deceiving is optimal. Moreover, by allowing the constant relative risk aversion class of utility form, we characterize the distinction between pretending to be naive and sophisticated.

     

Ellsberg paradox: Ambiguity and complexity aversions compared

We present a simple model where preferences with complexity aversion, rather than ambiguity aversion, resolve the Ellsberg paradox. We test our theory using laboratory experiments where subjects choose among lotteries that “range” from a simple risky lottery, through risky but more complex lotteries, to one similar to Ellsberg’s ambiguity urn. Our model ranks lotteries according to their complexity and makes different—at times contrasting—predictions than most models of ambiguity in response to manipulations of prizes. The results support that complexity aversion preferences play an important and separate role from beliefs with ambiguity aversion in explaining behavior under uncertainty.