Recent evidence on intertemporal choice suggests that decision-makers may exhibit both increasing and decreasing impatience simultaneously, called inverse-S discounting. This paper introduces trichotomic discounted utility to model inverse-S discounting. Under trichotomic discounted utility the decision-maker distinguishes between short-term delays, medium-term delays, and long-term delays. Exponential discounting holds within each category, but not necessarily across each category. We provide preference foundations for trichotomic discounted utility in the timed outcomes framework and in the consumption streams framework. The key axiom is a weakening (...) of the time consistency axiom that allows for both increasing and decreasing impatience. We also consider a weak, local version of time consistency, and show that this plausible condition is satisfied only by discount functions with exponential “pieces”. (shrink)

We conduct an experiment to investigate the degree to which deviations from exponential discounting can be accounted for by the hypothesis of hyperbolic discounting. Subjects are asked to choose between an earlier or later payoff in a series of 40 choice questions. Each question consists of a pair of monetary amounts determined by compounding a given base amount at a constant rate per period. Two bases (8 and 20 dollars), three compounding rates (low, medium and high) and three delays (2, (...) 4, and 6 weeks) are each used. There are also 2 initial periods (Today and 2 weeks) and there are two separate questionnaires, one with lower “realistic” compounding rates and the other with higher compounding rates, typical of those used in previous studies. We analyze the detailed patterns of choice in 6 groups of 6 related questions each (in which the base and rate is fixed but the initial period and delay varies), documenting the frequency of patterns consistent with exponential discounting and with hyperbolic discounting. We find that exponential discounting is the clear modal choice pattern in virtually all cases. Hyperbolic discounting is never the modal pattern (except in the sense that constant discounting is a special case of hyperbolic discounting). We also estimate a linear probability model that takes account of individual heterogeneity. The estimates show substantial increases in the probability of choosing the later option when the compounding rate increases, as one would expect. There are small, sometimes significant, increases in this probability when the delay is increased or the initial period is in the future. Such behavior is consistent with hyperbolic discounting, but can account for only a small proportion of choices. Overall, deviations from exponential discounting appear to be due to error, or to other effects not accounted for by hyperbolic discounting. Principal among these is an increase in later choices when the base is larger. (shrink)

In recent years, a disagreement has erupted between two camps of philosophers about the rationality of bias toward the near and bias toward the future. According to the traditional hybrid view, near bias is rationally impermissible, while future bias is either rationally permissible or obligatory. Time neutralists, meanwhile, argue that the hybrid view is untenable. They claim that those who reject near bias should reject both biases and embrace time neutrality. To date, experimental work has focused on future-directed near bias. (...) The primary aim of this paper is to shed light on the debate by investigating past-directed near bias. If people treat the past and future differently with respect to near bias, by being future-directed but not past-directed near biased, then this supports a particular version of the hybrid view: temporal metaphysic hybridism. If people treat the past and future the same with respect to near bias, then this supports a simple version of time neutralism, which explains both future bias and near bias in terms of the functioning of a single mechanism: the anticipatory/retrospectory mechanism. Our results undermine the claim that people are future-directed, but not past-directed, near biased, and hence do not support temporal metaphysic hybridism. They also fail to support simple time-neutralism; instead, they suggest that there are multiple mechanisms that differently shape future- and past-directed preferences. (shrink)

Some contemporary paternalists argue in favor of government interventions based on how experimental psychologists and behavioral economists have found that our behavior often diverges from what would be predicted by rational-choice models. In this article it is argued that these findings can, more specifically, be used to identify decisional trouble spots where paternalist interventions may be legitimate. It is further argued that since the epistemic legitimacy of government paternalism ultimately rests on centralized decision-making having a comparative advantage, it also depends (...) on the possibility of such interventions being governed by an ideal of evidence-based policy-making. The article asks how stringently this requirement should be understood, and to what extent government can legitimately engage in what might be called experimental policy-making of a paternalistic character. (shrink)

Experimental studies suggest that individuals exhibit more risk aversion in choices among prospects when the payment and resolution of uncertainty are immediate relative to when it is delayed. This leads to preference reversals that cannot be attributed to discounting. When data suggest that utility is time-independent, probability weighting functions, such as those used to model prospect theory preferences, can accommodate such reversals. We propose a simple descriptive model with a two-parameter probability weighting function where one of these parameters depends on (...) the time at which a prospect is resolved. The time-dependent parameter is responsible for the curvature of the probability weighting function and is regarded as an index of sensitivity towards changes in probabilities. We provide conditions that characterize increased sensitivity towards more distant probabilities; this can account for the observed relatively less risk aversion towards delayed prospects. In our framework, the discount function is unrestricted, such that the model is compatible with empirical findings of non-constant discounting. In a simple application to bargaining we illustrate when it is advantageous for an individual to advance or delay the bargaining resolution time if an opponent displays increased sensitivity towards probability changes with delay. (shrink)

For decisions whose consequences accrue over time, there are several possible techniques to compute total utility. One is to discount utilities of future consequences at some appropriate rate. The second is to discount per-period certainty equivalents. And the third is to compute net present values (NPVs) of various possible streams and to then apply the utility function to these net present values. We find that the best approach is to first compute NPVs of various possible income streams and then take (...) the utility of such NPVs. We show the drawbacks of other alternative models of evaluating income streams. The article discusses the advantages of the power and logarithmic forms in the modeling of time preference. These are the only forms for which utility of income and utility of consumption are strategically equivalent. Further, these forms permit the flexibility in the choice of a time period (e.g., monthly or quarterly) without modifying the utility function, thus simplifying analysis. (shrink)

There are two kinds of time bias: near bias and future bias. While philosophers typically hold that near bias is rationally impermissible, many hold that future bias is rationally permissible. Call this normative hybridism. According to arbitrariness objections, certain patterns of preference are rationally impermissible because they are arbitrary. While arbitrariness objections have been leveled against both near bias and future bias, the kind of arbitrariness in question has been different. In this article we investigate whether there are forms of (...) arbitrariness that are common to both kinds of preferences and, hence, whether there are versions of the arbitrariness objection that are objections to both near bias and future bias. If there are, then this might go some way toward undermining normative hybridism and to defending thoroughgoing time-neutralism. (shrink)

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 :199–205, 1963, p. 201). (shrink)

Some recent arguments for paternalist government interventions have been based in empirical results in psychology and behavioral economics that would seem to show that adult human beings are far removed from the ideals of rationality presupposed by much of philosophical and economic theory. In this paper it is argued that we need to move to a different conception of human decision-making competence than the one that lies behind that common line of philosophical and economic thinking, and which actually still lies (...) in the background of some of these recent approaches to paternalist interventions. An alternative picture of human decision-making competence is outlined and four criteria for identifying areas where paternalist interventions have a basic moral and political legitimacy are then identified on the basis of this picture. (shrink)

In business settings, decision makers facing moral issues often experience the challenges of continuous changes. This dynamic process has been less examined in previous literature on moral decision making. We borrow theories on learning strategies and computational models from decision neuroscience to explain the updating and learning mechanisms underlying moral decision processes. Specifically, we present two main learning strategies: model-free learning, wherein the values of choices are updated in a trial-and-error fashion sustaining the formation of habits and model-based learning, wherein (...) the brain updates more general cognitive maps and associations, thus sustaining flexible and state-dependent behaviors. We then summarize studies explaining the neuro-computational processes of both learning strategies—the calculation of prediction errors and valuation. We conclude by emphasizing how the incorporation of dynamic aspects in moral decision making could open new avenues for understanding moral behaviors in a changing world. (shrink)

Discounted utility theory and its generalizations use discount functions for weighting utilities of outcomes received in different time periods. We propose a new simple test of convexity–concavity of discount function. This test can be used with any utility function and any preferences over risky lotteries. The data from a controlled laboratory experiment show that about one third of experimental subjects reveal a concave discount function and another one third of subjects reveal a convex discount function.

We present an experiment in which we add a common delay in a choice between two risky prospects. The results show that delay produces the same change in preferences as in the well-documented common ratio effect in risky lotteries. The added common delay acts as if the probabilities were divided by some common ratio. Moreover, we show that there is a strong magnitude effect, in the sense that the effect of delay depends on the magnitude of the outcome. The results (...) are consistent with the recently introduced probability time trade-off (PTT) model by Baucells and Heukamp. We present a parameterization of the model based on the experimental results, showing that the value function exhibits increasing relative risk aversion, the weighting function is s-shaped, and the intrinsic discount rate is decreasing. (shrink)

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 -index” :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. (shrink)

This paper presents a very simple model in which situational cues associated with a particular consumption good compel an agent—who may have otherwise been “thinking about” something else—to consider the decision to consume that good. Within this framework, it is shown how an endowment effect and a present bias can arise through a common mechanism. The analysis points to a novel, contributing role for inattention in understanding both of these behavioral anomalies while also speaking to evidence that they are often (...) cue-induced. (shrink)

This study experimentally tests our proposed extended present bias hypothesis—discount factor increases over the proximate future and eventually approaches constancy, but remains distinct from unity in the remote future. Using front-end delay and a post-dated check for payment, discount factors are elicited for three seven-day durations: between 2 and 9 days later, between 31 and 38 days later, and between 301 versus 308 days later. We find support for diminishing discounting between the proximate and intermediate comparisons, but not between the (...) intermediate and the remote comparisons. The findings validate our extended present bias hypothesis. (shrink)