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Time in Economics, part II

Temporal Discounting, Emotions and Agency

Escompte temporel, émotions et agentivité
Pierre Livet
p. 191-200


De quel type sont les émotions qui pourraient être les causes de l’escompte temporel et de sa courbe hyperboloïde? Il ne s’agit pas de la catégorie générale des émotions anticipatrices « viscérales » (Loewenstein et Lerner), mais de la catégorie plus spécifique des émotions reliées à l’agentivité (les « émotions anticipatrices entraînant l’action »). L’incohérence temporelle - la préférence pour l’option la plus proche dans le temps, ou son contraire, la « préférence négative » (Loewenstein et Prelec) – peuvent être reliées à la possibilité ou impossibilité pour l’agent d’intégrer les différentes options de différentes dates dans un même programme d’action. On discutera aussi d’autres propositions d’explication : une perception logarithmique du temps – Takahashi – ou une relation entre l’impatience et les émotions positives – Geoffard et Lucchini.

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  • 1 Rubinstein’s procedural explanation (2003) will be mentioned later.

1Since Ainslie (1974, 1992) has proposed a hyperbolic curve—instead of the exponential curve that ensures inter-temporal consistency—in order to describe the temporal discount bias, economists (and physicists) have focused their researches on the type of curve that fits the data of experimental psychologists. Loewenstein and Prelec (1992) suggested also a generalized hyberbolic function. Laibson (1997) proposed a discrete quasi hyperbolic function—steeper in the first period, smoother in the following ones. Green and Myerson (1995, 2004) as well as Rachlin (2006) proposed also hyperboloid models (for a comparison, McKerchar, Green, Myerson, 2010).1

2A hyperboloid model is coherent with the data, but is not by itself an explanation. What psychological factors could explain the skewed curve? Loewenstein and Lerner (2003) suggested that the main factors are “anticipatory influences” on emotions: the anticipation of the future emotions that a reward is expected to raise in the future influences our immediate emotions (Loewenstein and Lerner, 2003, 621). But they did not tell in detail how this effect of anticipatory emotions explains the temporal discounting bias. One problem is that we can feel anticipatory emotions both about outcomes in a remote future and in a closer one. Loewenstein supposes that “visceral influences” like emotions could be the cause of preferring a smaller but immediate reward to a more remote bigger one. Loewenstein and Lerner appeal to appetites such as hunger and sexual desire and assume that “the mere expectation of an imminent reward seems to trigger appetitive mechanisms at the most basic level of the brain’s reward system” (Loewenstein and Lerner, 2003, 625). But the quasi hyperbolic function, as well as hyperboloid ones, is steeper during the whole first year- this suggests that the same mechanism is at work in this period- and a year seems too long for these basic appetitive mechanisms.

3Loewenstein and Prelec (1991) had also shown a reverse fact: the same person who prefers a good dinner sooner rather than later, may prefer an indifferent dinner followed by a good one, to the good one followed by an indifferent one (Loewenstein and Prelec, 1991, 351). Here, people are able to resist the appetitive mechanisms. The authors attributed this pattern of choice to “the sensitivity of time preference to the sequence frame”—this is more a description of the problem than an explanation. Geoffard and Lucchini (2010) addressed the problem of the negative time preference and related it to impatience. I will discuss this hypothesis.

4Takahashi et al. (2008) and Han and Takahashi (2012) claimed that the main factor is that our perception of time follows a logarithmic function, giving less importance to differences of time in the remote than in the near future. I will discuss the experimental validation of this claim.

  • 2 A perspective that I share with Geoffard and Lucchini: see Livet (2010).

5In this paper, I will describe emotional processes that can explain both the usual temporal discounting bias and the negative time preference. I will reframe the notion of “anticipatory emotion” in a different perspective2 than the one of Loewenstein and Lerner. I will make a distinction between emotions related to dynamics of action (driving anticipating emotions, DAE) and emotions related to purely evaluative representations (representational anticipatory emotions, RAE). I will take into account the relation between our experience of time, our sense of agency and our experience of impatience.

1. Discussion of Two Models

6Why not to reduce the problem of temporal discounting to the influence of a logarithmic perception of time, as claimed by Han, Takahashi et al. (2008, 2012)? The idea is seducing, because here the curve gives an explanation of the experiments, as it represents the variation of the perception of time. Participants had to choose between two options: obtaining the same gain (or loss) either immediately or with a delay. At first, the intervals between the different delays were short ones, but as the delay became larger, the intervals increased in a non-linear way: 1 week, 2 weeks, 1 month, 6 months, 1 year, 5 years, 25 years. Participants indicated, for each delay, how they placed it on a line of 180mm.

  • 3 Other experiments present delays in a similar progression, but they do not argue in favour of a log (...)

7As the participants choose one location on the line for a given delay—one different delay at each presentation—they have difficulty to build a representation of the non-linearity except in favorable circumstances, for instance if the first presented delays give them information about what pairs of delays to locate at the beginning and the end of the line. The constraint of mapping without this information these different intervals and their non-linear progression on a line is precisely the kind of problem that a logarithmic function can solve. The protocol of the experiment could be suspected to induce a logarithmic relation between the different evaluations of the delays.3 The claim that logarithmic perception of time is responsible for the time discounting bias is not really validated by these experiments.

8Let us now examine Geoffard and Luchini’s paper. They assume that positive emotions increase the experienced time interval and give rise to impatience while negative emotions decrease it and give rise to anxiety. When we feel sad we underestimate duration (Angrilli et al. 1997).

9But this is not coherent with other experiments on the relation between present emotion and experienced duration (Droit-Volet and Gil, 2016). Seeing pictures of angry or fearful faces produces negative emotions but also overestimation of time—relatively to neutral faces. Seeing sad faces, as well as happy ones, produces overestimation, but of a lesser magnitude. These variations seem related with the urgency of the incentives to act that are suggested by faces. This overestimation can be contrasted with the effect discovered by Wenke and Haggard (2009): during a voluntary action, we underestimate the duration, as a relation that they call “intentional binding” makes us focus on the goal of our action.

10The reason for these differences of estimated durations may be that when we look at images, the expressions activate our tendencies to actions, but we have to inhibit them, as we cannot interact with images. As action leads us to underestimate duration, inhibition of action may lead us to overestimate it. But if the action is a step in a chain of sub-actions that have to be done in a given order, the intentional binding can be extended to the whole chain, decreasing the (over)estimation of the duration of the inhibition of the too hasty action.

11These complexities and differences, neither the link that Frijda (1986) has shown between emotions and “action readiness potentials”. Deonna and Teroni (2012) are not taken into account by Geoffard and Lucchini’s hypothesis.

2. A Methodological Problem

12In the experiments participants are asked about what option they prefer between an immediate reward A and a delayed one B (A<B). They neither really get the immediate reward, nor wait for the delayed one. Similar questions are asked, with different delays and amounts in a rather random way. One may wonder whether the previous effects (that relate emotions, actions, and experienced time) are relevant here.

  • 4 A notable exception is Rubinstein’s hypothesis that amount of time and amount of money are two fact (...)

13Nevertheless, when experimental economists have to find a psychological explanation, they have to assume that the reversal of preferences in experiments has its origin in psychological processes of the real life—in which time periods cannot be in such random order. They do not focus on cognitive processes that would be specific to the experimental conditions4, but they assume that the choice situations are similar to decision scenarios that are recognized as prototypical in our society.

14We can infer that a good explanation has to satisfy three constraints: being plausible in prototypical situations; taking into account the similarity, but also the differences between them and the experimental situations; giving an interpretation of the skewing of the slope of the discount rate function as time interval increases. This skewing suggests that two factors combine their respective influences in proportions that differ between two regions of the time line. My hypothesis is that two kinds of emotions are working here.

3. Anticipating Emotions

15Loewenstein and Lerner (2003) explanation implies a notion of “anticipatory emotions”. Emotions are related with dynamics of anticipation: occurrent emotions imply that the new situations differ from what would be the continuation of our usual dynamics. But in Loewenstein and Lerner’s framework, these anticipatory emotions may be just the effect (on our immediate emotions) of the representation of “expected emotions”, the emotions that we believe that we would feel when having outcome A or B. I call them representational anticipatory emotions (RAE). They are triggered by an evaluative comparison of the outcomes (including uncertainty). RAE cannot explain the skewed curve, the first part of which has a steeper slope.

16My hypothesis takes into account another experience of time, related to our experience of action. One main constraint of action is that it has to be done step by step in order to reach a goal. If we are tempted to jump toward the final steps, we are compelled to inhibit this tendency. Inhibition of an isolated action raises negative affects but if this action is integrated in a chain of actions, an action program oriented toward the same goal, the intentional binding decreases the negative effect of inhibition. I call “driving anticipating emotions” (DAE) these anticipating emotions related to agency and action.

  • 5 Investing the gain A would require to integrate it in an action program, the goal of which are the (...)
  • 6 This frustration effect could be related to the phenomenon of cognitive dissonance studied by Festi (...)

17In experiments about temporal discount, getting A at t1 and getting B at t2 might have been presented as actions that belong to the same program, in which gain A is a part of gain B and enjoying the use of the A-part has to delayed to t2 in order to enjoy the global gain B.5 But in experiments the only actions are choosing A or choosing B, each action preventing the other. Seeing from t’ <near t1, choosing B implies to inhibit getting A, while still not getting anything. We still feel frustrated not to have done action A6, as long as we have not got B. These negative DAE related to inhibition are not decreased by any intentional binding. If we choose action A, the inhibition of not doing B is alleviated by having done A and got its gain. This dissymmetry of DAE, the reverse of the purely evaluative dissymmetry—gain B > A, in RAE—is only related to choices seen as conflicting actions.

18For intervals t0-t1 from around one week to around one month, the negative and asymmetric inhibition effects of DAE can be activated during a part of period t0-t1, not only for t’-t1-t2. The nearer is t1 from t0, and the longer the delay t1-t2, the stronger the effect of negative DAE. This effect is stronger than the exponential decrease of the value of B –compared to (A +interests).

19In mid-range intervals (from some weeks to one year) DAE can still be active for delayed actions, by projecting on more remote situations of action DAE that are typical for t1 near t0. But this kind of projection is limited to the time interval in which future actions can still be relevant for our agenda of action plans. Most of the times, it does not exceed one year. The influence of the projection of DAE and its decreasing diminishes progressively from t1= 1 day to t1= 1 year.

20After one year (or a bit later), the discount is stable because it depends mainly on the stable fact that the situation of choice is not in the agent’s active agenda. DAE are not sensitive to the evolution of interests of investments outside of the active agenda. The exponential function would imply a higher discount than this stable one, and the dominance of B activates RAE. The result is that in the end of the mid-range intervals, the curve that represents the evolution is progressively skewed from a curve that is more decreasing than an exponential one, toward one that is less decreasing. This appears in Laibson’s curve as an abrupt inflexion after 1 year, or between 6 months and 1 year in Takahashi’s results.

21Two of our constraints seem to be satisfied. What about the first one—explaining prototypical situations, in which people have to make a choice and to change their actions in relation with the evolution of the circumstances?

4. Analysis of a Prototypical Situation

22Let us take Ainslie’s example. Event A is an attractive party and event B is an exam. Alice decides at t0 (the day before the party) not to go to the party at t2 (tomorrow night) and prefers to be ready at t4 (the day after) for her exam. But as time goes on, the attraction of the party becomes stronger, maybe Bob invites here to the party, and at time t1 (tomorrow afternoon), she reverses her preference. Here, the goal of the party and the goal of the exam cannot be parts of the same action program.

23At time t0, thinking to the party and thinking to the future exam activates DAE and RAE. RAE raised by comparing the benefits of the party P and the exam E make her to prefer to be ready for the exam. This choice activates E-DAE, related to preparing for the exam. As the time of the party become closer, Alice may think about how she would have prepared for the party. These plans activate Party-DAE that choosing preparation for exam implies to inhibit. This inhibition is more and more costly as t2 comes nearer. A compromise is to go to the party for two hours and then to leave it at t3 in order to prepare for the exam. Two hours later, the party is very attractive, the inhibition of its P-DAE would be very frustrating, and she stays at the party.

24Waiting for the exam and preparing for it is unpleasant, mainly because it requires inhibiting the driving tendencies related to the attractiveness of the party. Inhibition is costly, raises an emotion of negative valence and leads to overestimate the time, a time during which Alice feels an unpleasant form of impatience. Inhibiting each of the projects of actions suggested by the party is more and more unpleasant, as a very simple decision—going to the party- can transform the unpleasant waiting in a pleasant one. At the party, each plan of action can be combined to the other, activating the intentional binding. By choosing to go to the party, Alice exchanges inhibition of P-DAE that induces an unpleasant form of impatience for other driving activities that induce a pleasant one. This specific way of experiencing time from an action perspective is a main dimension of DAE.

25Of course, other anticipatory emotions are active in the same time interval: expecting the success at the exam, regretting to have chosen the party and to waste time for preparing the exam and taking some rest. But in time interval (t2–t3)—during the exciting party—these emotions are mostly RAE and not DAE because Alice is involved in P-actions. The dynamic of these actions would make the inhibition suggested by E-DAE still more costly and increase the frustration of P-DAE. In time interval (t3-t4) in the morning, just before the exam, E-DAE will dominate, but it will be too late.

5. Answers to Objections: Negative Time Preference

26Two objections to this explanation can be made. 1) If A is immediate, there is no difference between Loewenstein’s “visceral emotions” and driving emotions. Answer: visceral emotions are reactions to the present new situation, but with no explicit reference to the specific constraints of the action dynamics and its experience of time that imply to inhibit tendency to action A while waiting for B. 2) If we prefer parsimony, do we really need to construct the specific category of DAE for a limited period (one day in Ainslie’s example, one year in the choice experiments)?

27We need, because the category of visceral emotions cannot explain the experience of Loewenstein and Prelec (1991) in “Negative time preference”: participants prefer a dinner in a Greek restaurant in a month and a dinner in a French restaurant in two months. But if only one dinner in the French restaurant is at stake, they prefer to have it in a month rather than in two months. If moved by visceral emotions with a preference for nearer future, participants would choose to go first to the French restaurant and then to the Greek one. In another inquiry participants even prefer to visit first a boring aunt the first weekend and to postpone their enjoying visit to good friends until the second weekend.

28These situations differ from the previous ones: both actions are possible, but in different orders; participants get both outcomes. These differences make possible to organize the two actions as two steps of unique program of action. Going to a first restaurant is the first step of the program, going to the second is its achievement. Inhibiting our tendency to go directly to the final step and waiting for the right time is usual in a sequence of steps that belong to the same program. The negativity of inhibition is alleviated in this case because the intentional binding of the global action reduces the subjective experience of the duration of waiting. We can activate the DAE related to the second restaurant, the final goal of the program, during the whole sequence. If an action implies successive steps, the goal is the final step and its importance is higher than the one of the steps. The goal, as a final step, has to be better than the intermediary steps. The dynamics has to increase and not decrease. We choose the French restaurant as a final goal.

29In the boring aunt example, the first step is worse than the second, not just less good. But this visit is mandatory. We prefer to see it and the associated inhibition of the other visit as related to the advancement of the goals of our action program, as a step towards a better situation, than as a pure constraint—this decreases the unpleasant overestimation of time related to inhibition. This is the case both when one visit is this weekend, and the other the next week-end, or when they are scheduled in 26 and 27 weeks from now. What counts is only the possibility to see the two visits as two parts of the same program of action (this is not the case if they are separated by 25 weeks; 48% visit their friends first).

30By contrast, when A and B are mutually exclusive options, they cannot be integrated in the same action program. When they are in the time span of our preparation for action, our active agenda, the earlier option has some advantage, but not when they are out of this range.

31It is possible to imagine experiments that might test this hypothesis of the importance of the relation of emotions and action driving perspectives. First, reformatting the classical experiment in a way that make possible to consider getting A as part of the action program, the goal of which is to enjoy the use of B, would decrease the temporal discount bias. Second, DAE’s imply that the activities and plans that are related to gains A or B are in the agent’s repertory. Suppose that A and B are facilities for activities that the agent has not in her repertory. She can imagine her satisfaction (bigger for B than for A) and feel RAE, but she cannot activate plans and routines that activate DAE. According to the hypothesis, the temporal discount bias would be smaller. We would also observe the same effect when one would have to evaluate the different temporal choices of fictitious eccentric characters.


32I hope to have shown that this analysis of the temporal discount bias gives us the opportunity to pay more attention to the importance of the dynamics of action for the relation of emotions and decision. Economists have already considered concepts such as anticipatory emotions. But they do not make the distinction between RAE and DAE. They miss the specific relation that driving emotions imply between our sense of agency and our emotions, as well as the richness of the relations between these different kinds of emotions. They do not (except Geoffard and Lucchini) pay enough attention to the relation of DAE with our experience of time as shorter or longer than the clock-time and our impatience as positive or negative.

33It would be better to examine “biased” choices as the result of the interactions between emotions as readiness to future actions and emotions as representation of future states. Instead of postulating an “experience of time “that could be studied in isolation from agency and emotions, we have to consider it as the result of their interactions.

I am greatly indebted to the anonymous reviewers, and particularly for the very detailed and helpful criticisms and suggestions of one of them. Thanks also to R. Boucekkine and S. Lucchini.

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1 Rubinstein’s procedural explanation (2003) will be mentioned later.

2 A perspective that I share with Geoffard and Lucchini: see Livet (2010).

3 Other experiments present delays in a similar progression, but they do not argue in favour of a logarithmic function!

4 A notable exception is Rubinstein’s hypothesis that amount of time and amount of money are two factors that are processed in the same way (discarding similar amounts and focussing on dissimilarity). But our subjective experiences of different durations are rather different from our comparisons between amounts of money, particularly in relation to emotions (Droit-Volet and Gil, 2016).

5 Investing the gain A would require to integrate it in an action program, the goal of which are the interests (related to the exponential discount). Is such program active in a simple choice?

6 This frustration effect could be related to the phenomenon of cognitive dissonance studied by Festinger (1957): frustration after making a choice is higher when the two options are both attractive.

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Pierre Livet

Aix Marseille Univ, CNRS, CEPERC, Aix-en-Provence, France,

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