Intertemporal Decision-Making: Economic andCognitive Perspectives

Davide Dragone�

FIRST VERSION 15/3/2006THIS VERSION 1/6/2007

Abstract

Intertemporal decision-making is a fundamental issue in the study ofindividual behavior. In this paper I review the economic approach to in-tertemporal decision-making by considering the behavioral assumptionsthat are implied by the Exponential and the Hyperbolic discounting mod-els. Both approaches focus on how people evaluate utility �ows over time.However, there is evidence showing that there also exist cognitive con-straints that do not change the evaluation of utility over time and yetthey a¤ect the intertemporal behavior of people. This evidence suggeststhat a cognitive perspective can be useful for improving our understandingof intertemporal decision-making

Keywords: Intertemporal decision-making, Exponential discounting,Hyperbolic discounting, Cognitive constraints, Fatigue.

JEL: D01, D90

1 Introduction

In Economics, intertemporal choice is generally treated within the preference-based approach. According to this approach, intertemporal individual decisionsdepend on the way people make trade-o¤s between costs and bene�ts occur-ring at di¤erent points in time. The decision about whether to sign a contractfor a job, for example, depends on how a person evaluates the e¤ects of be-ing employed on both present and future well-being. On one hand, there arethe bene�ts of working, which include the satisfaction the person can get fromthat job and the commodities that the wage allows to buy. On the other hand,

�Department of Economics, University of Bologna, Strada Maggiore 45, 40125, Bologna,Italy; e-mail: davide.dragone@unibo.it

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accepting a job implies bearing some costs which depend on the e¤ort that isrequired to provide a good performance, to organize the time according to thejob schedule, to respect hierarchies and procedures. Moreover, working requiresrenouncing to leisure time that a person may want to devote to some other activ-ity. The individual intertemporal preferences summarize how an agent evaluatesall these costs and bene�ts. Clearly, the fact that they do not occur simulta-neously, but they are distributed over time, can play a relevant role. In somecases, it is possible that an individual only evaluates the overall net di¤erencebetween costs and bene�ts, regardless of their intertemporal distribution. Thismeans that time is a neutral factor, so that the decision the person takes isjust the solution of a static problem. In other cases time plays a major role.For example, the agent may be impatient and value future bene�ts less thanpresent ones; or the passing of time changes the evaluation previously given tothe available alternatives, eventually inducing a person to change her mind andto prefer today what will be disliked tomorrow.

In this paper I review the two most successful approaches to intertemporaldecision-making: the Exponential Discounting model and the Hyperbolic Dis-counting model. The two approaches maintain the same theoretical structure:people choose according to their preferences, the evaluation of an alternative de-pends on the sum of costs and bene�ts it determines over time, distant bene�tsare less desirable, everything else equal, than closer ones. The main di¤erencebetween the two approaches concerns the way people evaluate the outcomes overtime. Accordingly, an exponential discounter never changes her mind, so thatshe always does what she has planned to do. An hyperbolic discounter, on theother hand, is much more myopic, and the opportunities of getting instantaneousgrati�cation can lead her to change her mind and to contradict what she hadplanned to do. In other words, an hyperbolic agent can be time-inconsistent andshe can be driven by the temptation of the present. For example, she can im-pulsively purchase an expensive good even if she knows she should save money,or she can decide to eat a tempting dessert even if she is on diet.

Psychology and Cognitive Psychology have observed that intertemporal be-havior is not only a¤ected by the way people evaluate outcomes over time.Empirical evidence from Cognitive Psychology shows that there exist cognitivemechanisms that are involved when people implement a given plan of actionand that can signi�cantly impact on the intertemporal behavior of people. Forexample, the evidence shows that the performance of people in prolonged tasksrequiring complex cognition (e.g. making decisions, adhering to a saving plan ormaintaining attention on a given task) degrades over time as a consequence ofthe accumulation of fatigue. This implies that exerting cognitive e¤ort does notsimply yield disutility, as it is commonly assumed in the economic literature,but it has endogenous consequences on the performance on subsequent tasks

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requiring e¤ort exertion. A consequence of this cognitive perspective is, for ex-ample, that people �nd themselves unable to adhere to a given plan of behaviornot because they cannot, in general, resist to the temptation of, say, spendingimpulsively or eating a forbidden food, but because they cannot persist in doingso over a prolonged time-horizon.Introducing cognitive constraints and the accumulation of fatigue in the

study of dynamic decision-making problem can be helpful in understanding theway people behave over time. Such a cognitive perspective does not substitutethe standard preference-based approach that is used in the economic litera-ture, rather it can complement it. Indeed, while the focus of the literatureon intertemporal decision-making has been mainly concerned on how costs andbene�ts over time enter the utility function of the decision-maker, a cognitiveperspective allows to take into account that there exist endogenous constraintson the intertemporal behavior of the decision-maker that are due to the speci�cway the mind works. In particular, I claim that taking also these dynamics inconsideration is recommendable when studying a decision-making environmentin which a prolonged cognitive e¤ort is required.

The paper is structured as follows. In the following section I describe thestandard theoretical framework that is used in the economic literature: the Ex-ponential Discounting model. I identify some of the features that characterize itin order to make explicit that this is not a general model for studying intertem-poral preferences and that adopting it means assuming that the decision-makerevaluates costs and bene�ts according to very speci�c hypothesis. In Section 3the Hyperbolic Discounting model is described and some of the extensions thathave been proposed in the last ten years are presented. As it turns out, none ofthe two models is good or bad; rather they assume di¤erent properties on theway people make intertemporal trade-o¤s and, consequently, in the way theybehave over time. In Section 4 I introduce the idea that, beyond the speci�cassumptions on the intertemporal preferences of the decision-maker, there ex-ist cognitive dynamics that a¤ect the way people behave over time. The factthat providing e¤ort over time is fatiguing, justi�es the introduction of cogni-tive constraints in the intertemporal decision-making problem. The e¤ect ofthese endogenous constraints is as signi�cant as a budget constraint is, and ig-noring it when it is binding can lead the researcher to study an intertemporaldecision-making problem whose solution may be not feasible.

2 Exponential discounting and dynamic consis-tency

In Economics the standard theoretical framework for studying decision-makingis based on the assumption that the decision-maker is endowed with preferences

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over the available alternatives and that these preferences are rational, a technicalconcept that requires the set of preferences to be complete and transitive. Thesuccess of the rational choice paradigm is largely due to its analytical tractabilityand to its normative implications in terms of individual welfare. Moreover,it proves to be a �exible approach, since it allows to use a single theoreticalframework for a wide range of applications.

According to this methodology, Economics studies intertemporal decision-making as an extension of the standard preference-based approach. The maindi¤erence with respect to a static decisional problem is that the commoditiesto be chosen are indexed by time as one of the many characteristics de�ningthem. More speci�cally, the standard microeconomic approach to intertempo-ral consumer behavior assumes that the choice objects are consumption paths(ct; :::; cT ) that the economic actor can enjoy in time. Given a set of feasiblealternatives (represented by alternative consumption paths), the decision-makerchooses according to her intertemporal preferences, conventionally assumed tobe rational and continuous. This allows for the construction of an intertemporalutility function that represents them, so that the intertemporal problem can besolved by using the familiar tools of utility maximization.

In 1937 Samuelson proposed a speci�c intertemporal utility function thatevaluates a given consumption stream as the discounted sum of the per-periodutilities that an agent enjoys over time. In a discrete time environment thismeans that the individual preferences over the intertemporal outcomes can berepresented by the following functional form1 :

U t(ct; :::; cT ) =

T�tXk=0

�ku(ct+k), (1)

where (ct; :::; cT ) is the consumption path and each element ct+k 2 RL+ of thepath represents the consumption vector that is available at time t + k (L isthe dimension of the consumption vector). U t(�) represents the intertemporalpreference, expressed at time t; for this path of consumption, u(�) is the per-period utility function and � � 1 is a discount factor that represents all thepsychological factors that in�uence the evaluation of future utilities as a functionof the time distance k. The time horizon T can be either a �nite or in�nitenumber.

This function, known as the Exponential Discounting (ED) function, com-putes the present value of a consumption stream in a way that closely resembles

1Samuelson�s original proposal concerns a continuous-time problem in which the intertem-poral utility function is written as U =

R T0 e�atu(xt)dt; where x is money income per unit-

time and a a constant discount rate. For expositional reasons here I focus on a discrete-timedecision-making environment with no uncertainty and full information.

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the �nancial computation of the present value of a stream of payments. Due toits simplicity and tractability it has soon become, and still is, the standard toolfor studying intertemporal choice both at a micro and macro level and, indeed,this is the functional form that the majority of students of Economics are taughtto use to model decisions over time.Despite its large use in the economic literature, little concern is generally

paid to the fact that the ED function implies speci�c assumptions on the waypeople evaluate outcomes over time. In particular, it is noteworthy observingthat both Samuelson (1937), who �rst proposed the ED model, and Koopmans(1960), that provided an axiomatic foundation for it, explicitly required theintertemporal preferences of the decision maker (and the intertemporal utilityfunction representing them) to maintain "a certain persistency over time�2 . Todo so, Koopmans (1960) postulates the existence of stationary time preferences,so that the evaluation of the available alternatives does not depend on the calen-dar time in which it is elicited3 . This requirement allows to simplify the notationand the computations by eliminating the time index of the intertemporal utilityfunction in (1) and simply set,

U t(ct; :::; cT ) = U(ct; :::; cT ): (2)

Given stationarity (and no interdependence between consumption experiencedin di¤erent periods), the stationary intertemporal preferences represented bythe ED function are also dynamically consistent. This means that the prefer-ences expressed in any period t will be con�rmed, given the same alternativesand information, in the following periods: for any pair of consumption paths(ct; ct+1; : : : ; cT ) and (ct; c0t+1; : : : ; c

0T ), it must be:

U t(ct; ct+1; : : : ; cT ) � U t(ct; c0t+1; : : : ; c0T )() (3)

U t+1(ct+1; : : : ; cT ) � U t+1(c0t+1; : : : ; c0T ),8t:

The property of dynamic consistency is particularly helpful because it impliesthat there will be no change of preferences as the agent gets older, and that thealternatives that are preferred at a certain time t are still preferred at t+ 14 .

A consequence of the stationarity assumption is the following. Consider aplanning/implementation problem in which the agent has to make two sequen-tial choices: one in period t (the planning phase) and the other in period t+ 1

2Koopmans (1960:287); but see also Samuelson (1937:155).3Formally, Koopmans (1960) requires the intertemporal utility function to be such that

U(ct; ct+1; ::; cT ) � U(ct; c0t+1; :::c0T ) i¤ U(ct+1; ::; cT ) � U(c0t+1; :::c

0T ), so that stationarity

allows confronting only the parts of the two consumption paths beginning in period T + 1.4Note that stationarity of the intertemporal utility function implies dynamic consistency,

but the opposite is not necessarily true, see Mas-Colell et al. (1995) and references therein.

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(the implementation phase). At time t the decision-maker elaborates a con-sumption plan by choosing between two alternative consumption streams, c andc0; according to her intertemporal utility function. Assume that the choice madein period t does not force the economic actor to implement it so that, regardlessof the plan that has been chosen as optimal at time t, at time t + 1 the agentcan freely reconsider what she considers optimal from the new time perspective.Then the implication of dynamic consistent preferences is that, given the samealternatives and information, in period t+1 the agent will faithfully implementthe plan that was assessed as optimal at time t. In other words no "changeof mind" should be observed because the path of choices that was preferred attime t will still be the preferred one in the subsequent periods.From this perspective the passing of time adds nothing to the solution ob-

tained at time t = 0, meaning that the intertemporal decision-making problemstudied by using an ED function is, essentially, a static problem that can besolved in an arbitrary moment. Indeed this is the standard practice in the eco-nomic literature where the evaluation of the desirability of a consumption pathis studied in only one point in time (generally at time t = 0) with no concernfor checking whether such evaluation will be con�rmed in future periods5 .

The stationarity and time consistency requirements seem to be reasonableover limited spans of time, but they are harder to justify in a more generaldecision-making environment. Our intuition, indeed, would suggest that inmany cases people change the evaluation of the available alternatives as timegoes by. Strotz (1955/6) shows that the standard economic approach does notresult in a loss of generality only because of the special properties of the in-tertemporal utility function in (1). More speci�cally, he shows that the repre-sentation of intertemporal preferences according to the ED function cannot beconsidered a neutral assumption, since it is equivalent to assume that an agenthas consistent preferences.The work by Strotz focuses on the relevance of the exponential discounting

function �k in determining this property. In order to do so, Strotz (1955/6) con-siders a dynamic optimization problem in which the agent reconsiders, in everyperiod t + k; the most desirable consumption plan according to the followingintertemporal utility function,

U t(ct; :::; cT ) =T�tXk=0

D(k)u(ct+k); (4)

5According to the stationarity requirement in Mas-Colell et al. (1995:734) the per-periodutilities are always discounted with reference to time t = 0, so that the intertemporal utilityfunction has the special form U(c0; :::; cT ) =

PTk=0 �

ku(ck). In this case dynamic consistencyis tautologically true, since the consumption streams are evaluated only with respect to a�xed date (time t = 0 ).

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in which D(k) is a generic discount function applied to u(ct+k)6 . Such a form ismore general than the ED function in (1) because it does not impose a speci�cform to the discounting function and, consequently, the intertemporal prefer-ences U t(�) expressed at time t can, eventually, depend on the moment in whichthey are elicited.Note also that, according to this utility function, time can in�uence the

individual intertemporal preferences through two di¤erent channels. The �rstone is the time-distance between the future date t+k and the present date t, as itis indicated in the discount function D(k). The second one is the calendar datet+ k of future consumption, as indicated by u(ct+k). In the standard economicapproach to intertemporal choice this distinction between time-distance andcalendar date is often lost because the date t is �xed and only the time-delay kmatters7

By considering a dynamic optimization problem using the function in (4)and the usual budget constraint, Strotz (1955/6) shows that the evaluationof an optimal consumption plan at time t does not necessarily coincide withthe evaluation assessed at a generic t + k. More speci�cally, he shows that anecessary and su¢ cient condition to behave consistently with the previous planis for D(k) to be equal to �k; with � a constant number. This means that theonly stationary discount function that generates dynamic consistency, accordingto the function in (4), is the exponential discounting function that is usuallyadopted in the economic literature on intertemporal choice. In all the othercases the evaluations assessed at a generic time t change as time goes on, sothat the individual can �nd it optimal to behave di¤erently than planned8 .

To get an intuition of why this property holds consider a situation in which,given a constant baseline consumption c in all periods, an individual is indi¤erentbetween adding x units to consumption at time t + k and y units at a latertime t + k + h (with y > x)9 . Consider a generic discounting function thatdepends only on the time-distance between the moment in which consumptionis available and the moment in which the preferences are elicited. Indi¤erencebetween adding x units of consumption at time t+h and y units at time t+h+kimplies:

D(t+h)u(c+x)+D(t+h+ k)u(c) = D(t+h)u(c)+D(t+h+ k)u(c+ y): (5)

6Strotz (1955/6)�s original paper concerns a continuous-time environment in which theindividual can also enjoy the memory of past consumption. For expositional reasons, only adiscrete-time environment is considered, ignoring past consumption.

7See, for example, Mas-Colell et al. (1995).8Note that saying that preferences change as a function of time does not mean that a prefer-

ence reversal always occurs. Thus non stationary preferences may induce an time inconsistentbehavior as well as consistent behavior.

9Loewenstein and Prelec (1992).

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Dividing by D(t+ h) yields

u(c+ x)� u(c) = D(t+ h+ k)

D(t+ h)[u(c+ y)� u(c)]: (6)

In general, the ratio D(t+h+k)D(t+h) depends on t; h and k: Nevertheless, the intertem-

poral preferences of the agent will be consistent over time if and only if suchratio depends uniquely on h, the time distance between the two consumptionadjustments. Such a condition is veri�ed only when D(�) is an exponentialfunction, so that only in the speci�c case given by the ED function in (1) thedecision-maker will behave consistently with her plans.To see it, let t = 0; k = 1 and h = 1. Then the equation in (6) can be written

as:u(c+ x)� u(c)u(c+ y)� u(c) =

D(2)

D(1): (7)

Suppose now that h = 2, so that:

u(c+ x)� u(c)u(c+ y)� u(c) =

D(3)

D(2): (8)

This impliesD(2)

D(1)=D(3)

D(2); (9)

i.e. the discount function must be such that the two ratios are constant. This istrue only if D(�) is an exponential function and the discount factor is constant.In fact:

D(k + 1) =u(c+ x)� u(c)u(c+ y)� u(c)D(k) and (10)

D(k + 2) =u(c+ x)� u(c)u(c+ y)� u(c)D(k + 1) (11)

= (u(c+ x)� u(c)u(c+ y)� u(c) )

2D(k): (12)

By recursive substitution

D(k + 2) = (u(c+ x)� u(c)u(c+ y)� u(c) )

k+2D(0);8k: (13)

Letting u(c+x)�u(c)u(c+y)�u(c) = � and normalizing D(0) to 1 yields

D(k) = �k; (14)

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so thatD(2)

D(1)=D(3)

D(2)= �. (15)

The result obtained by Strotz (1955/6) is particularly important because itholds even when the decision-making environment is riskless and the optimalpaths are evaluated given full and complete information. Moreover, as Strotzobserves, from a dynamic perspective this �change of tastes�has nothing to dowith a violation of rationality since �to continue to obey a �xed consumptionplan just because it was optimal when viewed at an earlier date is not ratio-nal if that plan is not the optimal one at the present date�10 . An interestingfact is that, in his seminal work, Samuelson (1937) was aware of the propertyhighlighted by Strotz when he observed that "[c]ontemplation of our particu-lar equations [the ED function] will reveal that the results are unchanged evenif the individual always discounts from the existing point of time, rather thanfrom the beginning of the period. He will still make at each instant the samedecision with respect to the expenditure as he would have if at the beginning ofthe period he were to decide on his expenditure for the whole period�11 . Sucha property was clearly welcome when, in 1937, there was the need of settingsome benchmark for studying the evaluation of streams of utility over time.Nevertheless, after twenty years Strotz (1955/6) shows that the representationof intertemporal preferences according to the ED function cannot be considereda neutral assumption since it is equivalent to assume that an agent has con-sistent preferences. Moreover, such a consistency property is fragile, becauseany modi�cation of the familiar exponential discounting function is enough toinduce a divergence between planning a sequence of choices and implementingsuch a plan.

Strotz�s contribution has inspired an interesting research literature aimed at�nding, testing and calibrating non-exponential discounting functions that seemto �t the real-life behavior of people better than the standard ED function, themost famous being the introduction of a hyperbolic (or quasi-hyperbolic) dis-counting function. As in Strotz, in such literature most of the features of the EDfunction are maintained: the intertemporal utility function depends on the sumof per-period utilities and all the attention is concentrated on studying the spe-ci�c discounting function D(k) to use. I will focus on these contributions in Sec-tion 3. Before doing so, in the next subsection I want to highlight the fact thatthe ED model imposes speci�c restrictions on the preferences of the decision-maker that are often ignored when modeling intertemporal decision-making. Inorder to do so I will split the ED function in its three main components: theper-period utility function u(ct+k); the discounting function �k and the sum-mation operator

PT�tk=0 that aggregates the discounted per-period utilities into

10Strotz (1955/6:169,170).11Samuelson (1937:160).

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the intertemporal utility function U t(�). The properties I concentrate on are nothidden features, indeed they were explicitly postulated in the axiomatization oftime preferences proposed by Koopmans in 1960. Nevertheless, it is noteworthyobserving that their introduction was mainly a technical issue, and that neitherSamuelson (1937) nor Koopmans (1960) have ever claimed that they are psycho-logically plausible. They are useful because they allow obtaining a very simpleand tractable intertemporal utility function but, as I will observe in the nextsection, the price to be paid for such simplicity is a restriction of the domain ofapplication of the ED model to individual choice. As a consequence, despite itsbroad use in the economic theory, the ED model cannot be considered a generalor neutral model for describing how people evaluate intertemporal utility overtime.

2.1 Utility, discounting and aggregation

In this subsection I split the exponential discounting model in its main compo-nents in order to make clear some of the restrictions on individual behavior thatthis model postulates. I �rst focus on the per-period utility function u(ct+k) toobserve that the stationarity of the intertemporal preferences (the "persistence"that Koopmans, 1960, required) critically depends on how people evaluate con-sumption at any point in time. I then move to the discounting function to conveythe message that postulating that future outcomes are evaluated according toa constant discount factor is an assumption that the empirical studies on in-dividual decision-making do not con�rm. Finally, I consider the role of thesummation operator and its separability properties.

The per-period utility function u(ct+k)12 represents the utility that an indi-vidual can get from the consumption vector available at time t+ k. Consistentwith the standard assumptions of no satiation and decreasing marginal utility,it is assumed to be strictly increasing and concave. A notable feature is that,in most of the cases, not only the intertemporal utility function U(ct:::; cT ),but also the per-period utility function u(ct+k) is assumed to be stationary, im-plying that the consumption vector ct+k always generates the same utility. Inother words, not only the preferences over consumption pro�les do not dependon calendar time, as assumed by Koopmans (1960), but also the way peopleevaluate the single consumption vector is not a¤ected by the passing of time.This property is generally retained for analytical convenience, but it does nothave a global descriptive validity because it means that there is no evolutionin tastes, a condition that is contradicted in at least two important domains ofindividual behavior: addiction13 and cultural education.12Or, in a continuous-time environment, the instantaneous utility function.13On addictive behavior see, for example, O�Donoghue and Rabin (1999a, 2000). See also

Loewenstein and Angner (in press) for a discussion of di¤erent sources of preference change.

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An additional, non negligible property of the per-period utility function isthe absence of intertemporal complementarities. This feature is shared by themajority of the intertemporal utility functions that have been proposed in theeconomic literature14 and it is explicitly postulated by Koopmans (1960). Nev-ertheless, as both Samuelson and Koopmans admit, there is no compelling ra-tionale for such assumption15 .The absence of interdependencies over time means that a person�s well-being

in a given period is independent of her consumption in any other period. In otherwords the marginal rate of substitution between consumption in period k and k0

is independent from consumption in any other period k00, an assumption that,as Frederick et al. (2002) observe, is quite restrictive because it implies that "aperson�s preference between an Italian and Thai restaurant tonight should notdepend on whether she had Italian last night, nor whether she expects to have ittomorrow"16 . Furthermore the absence of intertemporal complementarities im-plies that there is no concern for the distribution of utility over time, a conclusionthat is contradicted if people have preferences over pro�les of consumption17 ,and that the individual preferences are not a¤ected by the consumption pathsin periods in which consumption is identical in the two pro�les. This propertyis analytically helpful to compare alternative utility �ows because it means thatthey are to be evaluated only with reference to their relative di¤erences (as donein the previous subsection to illustrate Strotz�s argument). Anyway, as Mas-Colell et al. (1995) observe, the plausibility of this assumption may criticallydepend on the length of the time period that is considered, and it is strained ifthe length of the period is very short.

As observed before, the standard approach to intertemporal choice exploitsthe assumptions and tools of the static rational choice theory, with the peculiar-ity that the commodities have a time index as one of the many characteristicsde�ning them. Given the stationarity of the per-period utility function and theabsence of intertemporal complementarities, in the ED function time is relevantonly with respect to the discounting part of the intertemporal utility function.In the literature three terms are often used to refer to the evaluation of out-14A notable exception are the studies on habit-formation, in which the utility from current

consumption is a¤ected by the level of past consumption. See, for example, Duesenberry(1952), Pollak (1970), Ryder, Heal (1973), Becker, Murphy (1988).15Samuelson (1957: 674) observes that "the amount of wine I drank yesterday and will drink

tomorrow can be expected to have e¤ects upon my today�s indi¤erence slope between wine andmilk�. Koopmans (1960: 292) observes: �we are willing to postulate that the particular bundleof commodities to be consumed in the �rst period has no e¤ect on the preference betweenalternative sequences of bundles in the remaining future, and conversely. One cannot claim ahigh degree of realism for such a postulate, because there is no reason why complementarityof goods could not extend over more than one time period�.16Frederick et al. (2002:10).17See Loewenstein and Prelec (1992).

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comes over time: discount function, discount rate and discount factor.18 Inorder to make clear what they refer to, consider the formulation in (4), whichis reproduce below:

U t(ct; :::; cT ) =T�tXk=0

D(k)u(ct+k):

The discount function is represented by D(k). It is the relative weight that thedecision-maker attaches to her well-being in period t + k, where k is the delaybetween the current period and the moment in which future consumption isenjoyed. In general people consider future consumption to be worth less thancurrent consumption19 . Thus D(k) is required to be decreasing in k, meaningthat the more a commodity is far in time, the less it is worth. In any case,utility is not undesirable, so that the discount function cannot be negative andD(k) � 0 for all values of k. In other words, the idea of discounting involves thefact that any consumption vector yields some positive utility, whose relevanceis inversely related to the delay horizon (the distance between the moment inwhich the agent evaluates an alternative and the moment in which she will enjoyit). Combining together these two features, for 0 < k < k0 the discount functionis assumed to satisfy the following inequalities:

0 � D(k0) � D(k) � D(0) (16)

Note that the conventional notation D(k) means that the discount function isindependent from consumption, with the consequence that the decision-makercannot have a "banana time-preference" and a di¤erent "holiday time-preference".The main advantage of this assumption is that it allows not labeling the timepreference according to the commodity that is to be evaluated: indeed, the waythe economic agents evaluate future outcomes doesn�t depend on the kind ofcommodity, but only on the utility it can provide. Yet there is a large evidenceof the fact that time preferences vary across di¤erent types of intertemporalchoices: gains are discounted more than losses, small amounts more than largeamounts, and explicit sequences of multiple outcomes are discounted di¤erentlythan outcomes considered in isolation20 .

A discount function D(k) is often described by referring to the concept ofdiscount rate and of discount factor. The discount rate in period k representsthe rate of decline in the discount function between periods k � 1 and k :

r(k) = �D(k)�D(k � 1)D(k)

: (17)

18See Laibson (2003).19For empirical evidence showing that also the opposite can hold, see Loewenstein and

Prelec (1991).20See Frederick et al. (2002:54) and references therein for more on this point.

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Clearly, the higher the discount rate r(k), the more quickly value declines withthe delay horizon.

The discount factor in period k is the ratio between the discount functionat time k and the discount function in the previous period and it is related tothe discount rate according to the following formulation:

d(k) =D(k)

D(k � 1) =1

1 + r(k)21 : (18)

In general, in the literature on intertemporal choice the discount factor d(k) isassumed to range from zero to one, with d(k) = 0 representing the case of acompletely myopic decision-maker and d(k) = 1 representing the case of equalweighting of present and future utilities: an in�nitely patient agent22 .The requirement d(k) < 1 implies time impatience, a concept that Irving

Fisher (1930) de�nes as a preference for advancing the timing of future sat-isfaction23 : if c = (ct; ct+1; :::; cT ) is a non-zero consumption stream, then theforward-shifted consumption stream c0 = (0; ct; ct+1; :::; cT ) is strictly worse thanc. This delay e¤ect may re�ect di¤erent factors. For example, delayed rewardscan be risky if the decision-maker may die before the rewards are experienced.Or the decision-maker may perceive them as more abstract than current re-wards, so that she is not able to appreciate their full impact in advance24 .Technically, the fact that d(k) < 1 is helpful in guaranteeing, when T !1,

that the (bounded) consumption path c has a �nite utility value. In the EDspeci�cation this feature ensures that the sum of the discounted per-period util-ities converges to a �nite number. As a consequence any consumption path canbe compared with the others, thus guaranteeing transitivity and completenessof the intertemporal preferences. Since these are the two properties that de�nea set of preferences as rational, such a feature is clearly desirable.

After these preliminary considerations, it should be clear that using theED model implies assuming that the discount function has the special form21As observed in Laibson (2003), for discrete-time models, we need to de�ne a discrete

grid of delay values so that k 2 f0;�; 2�; 3�; :::g and the discount function can be writtenas fD(0); D(�); D(2�); D(3�); :::g : This allows to write the generic discount rate as r(k) =�[(D(k) � D(k � �))=�]=D(k) and the discount factor as d(k) = (1=(1 + r(k)�))1=� =(D(k)=D(k ��))1=�. When we consider � = 1; we get the discount rate and discount fctoras in (17) and in (18). As the time interval becomes arbitrarily short, the discount rate andthe discount factor become, respectively, r(k) = �D0(k)=D(k) and d(k) = e�r(k):22See Frederick (1999) and Frederick et al. (2002) for a discussion on the assumption of

positive time preference (i.e. d(k) < 1). See Koopmans (1960) for a set of axioms thatjusti�es such assumption. See Loewenstein, Prelec (1991) for empirical evidence of peoplewith negative time preference (i.e. d(k) > 1) in the cases in which the savoring of an eventinduces the decision maker to prefer a postponed realization.23An alternative interpretation views the discount factor d(k) as a probability of survival

to the next period. Then U(c) is the expected value of lifetime utility.24See Frederick (1999) for a study of the normative rationale to discount the future.

13

D(k) = �k. The discount function depends, as required, on the delay horizon.Nevertheless, the exponential speci�cation implies that both the per-period dis-count rate and the discount factor are constant, since r(k) = (1=�) � 1 andd(k) = �. So a single piece of information, the discount factor �; providesenough information to compute the discount rate regardless of calendar time25 .As noted by Frederick et al. (2002), assuming constant discounting entails

an even handedness in the way a person evaluates time. It means that de-laying or accelerating two dated outcomes by a common amount should notchange preferences between the outcomes and so it is a critical feature in as-sessing the stationarity (and, consequently, the consistency) of the individualintertemporal preferences. To make this point clear with an example in a three-periods environment, consider the following consumption paths: c = (0; 0; c2)and c0 = (0; c1; 0). Given the standard ED function, at time 0 the economicactor strictly prefers c to c0 if and only if

�2u(c2) > �u(c1): (19)

If the decision-maker were given the opportunity to reconsider her plan at laterdates, she will con�rm it because, at time 1;

�u(c2) > u(c1): (20)

A di¤erent outcome would result if �0 6= �1: In such a case, at time 0 theeconomic actor prefers c to c0 if and only if

�20u(c2) > �0u(c1) or, equivalently, (21)

u(c1)

u(c2)< �0 (22)

Nevertheless, the discount factor at time 1 can be such that

�1 <u(c1)

u(c2)< �0; (23)

implying that the previous choice is not con�rmed and that (c1; 0); the con-tinuation path of c0; is preferred to (0; c2); the continuation path of c. So, ifthe discount factor changes over time, we could observe an agent that plansto consume nothing for two periods and to enjoy c2 in the third one, but thenchanges her mind as time goes on and consumes c1 in the second period.

In the last three decades, several studies, both in Economics and in Psy-chology, have been conducted in order to test whether it is correct to think to2519th and early 20th century economists were aware of the existence of many con�icting

psychological motives that in�uence intertemporal behavior. In the Exponential Discountingmodel, such variety is condensed in the discount factor �. See Frederick et al. (2002) for acritical review.

14

time preference as a unitary construct. Measuring discount rates has proved tobe controversial and, in general, the results are quite contradictory. As Fred-erick et al. (2002) observe, it seems that, despite the e¤orts, there hasn�t beenmuch methodological progress, concluding that "correlations between variousmeasures of time preference or between measures of time preference and plausi-ble real world expressions of it are modest, at best"26 . Empirically, it must beacknowledged that the measurement of time preference is technically di¢ cult.As a consequence it is not surprising that the implicit discount rates that havebeen computed, both considering the behavior of people in the lab and in the"real world", show a huge variability in the estimates. Yet one empirical regu-larity seems to emerge: the observed discount rates are not constant over time,and they appear to decline with the time horizon (or, equivalently, the discountfactor increases). This experimental evidence has suggested a modi�cation ofthe exponential discount function D(k) = �k that characterizes the ED model,and it has inspired the introduction of alternative discounting functions. Ac-cording to the result by Strotz (1955/6), such functions allow for some form ofdynamic inconsistency to emerge.

A further implication of the exponential discounting function is that, whentwo di¤erent consumption paths are to be evaluated, what matters is only theabsolute time interval separating them, and calendar time doesn�t matter. Thisproperty holds despite the fact that, apparently, in the ED model time in�uencesthe value of a given consumption vector both according to the moment in whichit will be enjoyed, as indicated by u(ct+k), and according to the delay horizon, asindicated by the discount function �k27 . To see it, consider the example providedin (5) to give the intuition for Strotz (1955/6)�s results on time consistency.Consider a constant baseline consumption c in all periods and an individualthat is indi¤erent between adding x units to consumption at time t + k and yunits at a later time t+k+h (with y > x)28 . Instead of using a generic discountfunction D(k); now assume that the agent evaluates future utilities accordingto the exponential discounting function �t. According to the ED model, theindi¤erence between the two consumption paths is equivalent to write

�t+ku(c+ x) + �t+k+hu(c) = �t+ku(c) + �t+k+hu(c+ y): (24)

Dividing by �t+k yields

u(c+ x)� u(c) = �h[u(c+ y)� u(c)]: (25)

Thus time operates only through the time distance separating the two consump-tion adjustments, as indicated by the exponent h of the discount factor. Neither

26Frederick et al. (2002:391)27See Strotz (1955/6:168).28This example builds on Loewenstein and Prelec (1992).

15

k; the delay horizon with the closer alternative, nor t, the moment in which theevaluation is made, matter. This would imply that, if a person�s preferenceswere representable according to the ED function and if this person were indif-ferent between ten apples in one week and eleven apples in two weeks (i.e. hequal to one week), she would also be indi¤erent between ten apples in one yearand eleven apples in one year and one week29 because what matters is only theabsolute time distance between the outcomes and not the time t in which theoutcomes are evaluated30 . Such conclusion has been largely investigated, andlargely contradicted, by the empirical evidence31 .

The last feature of the ED function I want to address is the additive formthat aggregates the discounted per-period utility over the time horizon. Thisform of intertemporal aggregation was explicitly considered by Samuelson (1937)that required the intertemporal utility function to be given by "the sum of allfuture utilities, reduced to comparable magnitudes by suitable time discount-ing"32 . Given the speci�c assumptions on the stationarity of the per-periodutility function and the exponential discounting function, additivity turns outto imply two separability properties that make the intertemporal utility functionparticularly tractable33 . The �rst property is that, for any period t; preferenceson the consumption path that begins in period � + 1 (with � > t) are inde-pendent from past consumption path (i.e. consumption enjoyed between t and�). In utility terms this is easy to see because

PT�tk=�+1 �

ku(ct+k) does not de-pend on the path of past consumption (ct; ct+1;:::; c� ). The second separabilityproperty is that the ordering on consumption paths from t to � is independentfrom future consumption paths, so that

P�k=0 �

ku(ct+k) is independent fromE[(c�+1; :::; cT )]

34 .Combined together, these separability properties of the ED are very helpful

to recursively express the intertemporal utility function as the sum of currentutility u(ct) and of the discounted utility �ow that the decision-maker will getfrom the continuation consumption path starting at t+ 1 : (ct+1;:::; cT ). To seeit consider c = (ct; ct+1;:::; c� ; :::; cT ); to be evaluated at time t: According tothe ED function, the preferences for this path can be represented as:

U(ct; :::; cT ) =XT�t

k=0�ku(ct+k):

29Thaler (1981).30See Loewenstein and Prelec (1992).31See, for example, Loewenstein and Thaler (1989), Loewenstein and Prelec (1992, 1993).32Samuelson (1937:156).33See Mas-Colell et al. (1995).34 In turn, these separability properties imply additivity in the form Ut(ct; :::; cT ) =PT�tk=0 ut+k(ct+k), the general form of the ED function in which the discounting function

is embedded in the per-period utility term; for a proof see Blackhorby et al. (1987).

16

Given the additive form, the above expression can also be expressed as:

U(ct; :::; cT ) = u(ct) + �XT�t

k=1�k�1u(ct+k) (26)

= u(ct) + �XT�t�1

s=0�su(ct+s+1); (27)

which in turn implies

U(ct; :::; cT ) = u(ct) + �U(ct+1; :::; cT ): (28)

The expression in (28) shows that the ED function can be de�ned in recur-sive terms, a property that is particularly useful when studying the dynamicproperties of intertemporal decision-making. Given this formulation, it is alsoimmediately clear that the marginal rate of substitution between current andfuture utility equals the discount factor �; that such factor does not depend ontime and that it is independent from the levels of current and future utility35 .

Note that, even if the ED represents the intertemporal preferences over con-sumption paths of a single consumer, the recursive formulation in (28) allowsfor a multi-agent interpretation. Accordingly, the sum of the (discounted) per-period utilities that the decision-maker gets from period t to T can be seen asthe sum of the utilities u(ct+k) that a sequence of identical decision-makers,each living one single period, enjoys from t to T: In this context, the discountfactor � represents how much the agent at time t cares about the utility of fu-ture agents as a function of the delay horizon. In other words, the discountfactor would represent the degree of inter-agent altruism, and the expressionU t(ct; :::; cT ) =

PT�tk=0 �

ku(ct+k) represents the total well being enjoyed by thealtruistic decision-maker living in period t. This multi-agent interpretation hasbeen used both at a macro and micro level. In the �rst case, u(ct) representsthe well-being of a whole generation of individuals, and U t(c) is the aggregateutility of the "dynasty", a sequence of generations, beginning in period t. Fromthis perspective the recursive form of the intertemporal utility function in (28)expresses the overall utility of an altruistic generation t by separately consider-ing its own per-period utility and the next generations�. At a micro level thesequence of decision-makers living one single period can be considered as thesequence of the time-t incarnations of the decision-maker. Thus a single agentcan be thought of as a "multiple self". At time t every self, like the generationsin the previous interpretation, enjoys u(ct) and, if � 6= 0, she also cares aboutthe well-being of the future selves. Again, given the recursive form, the overallutility for self-t can be computed by just considering her well-being and theutility of the next self.The additivity property of the ED function, though plausible, seems to be

contradicted by the evidence on choice bracketing36 . Bracketing is a behavioral35See Koopmans (1960) for a generalization of the ED model in a recursive utility model.36See, for example, Loewenstein, Prelec (1993), Read, Loewenstein and Rabin (1999).

17

concept that incorporates the idea that people do not maximize a global utilityfunction, but rather partition reality in little pieces, i.e. brackets, and thatthey use such special "lens" to focus only on some aspects of the alternatives toevaluate. When bracketing is relevant, dynamic inconsistencies can be observedeven if the agent discounts future utilities exponentially because, as time goeson, the relevant information that is used to evaluate the available alternativeschanges.

3 Hyperbolic discounting and dynamic inconsis-tency

In the previous section I have presented some of the properties and behavioralfeatures implied by the ED model. In particular I have shown that the speci�cassumptions on the per-period utility function, on the discount function andon the aggregation of future discounted utilities imply that the decision-makeralways behaves consistently over time. This consistency property is explicitlyrequired in the construction of the ED model and it is largely exploited inthe economic literature to simplify the computations and to yield analyticallytractable models. Nevertheless it doesn�t seem to be a good description of theway people evaluate alternative streams of consumption.Over the last twenty years a growing literature in Experimental Economics

has documented various anomalies that reduce the descriptive power of the EDmodel. In particular, there is robust evidence on the fact that people behavedi¤erently than planned, and that their intertemporal choices are not rational-izable in terms of an exponential discount function.In many cases a dynamic inconsistent behavior is attributed to the existence

of some contingent "temptation" that has enhanced impulsivity and has induceda deviation from the desirable behavior. Particularly relevant in this directionis the evidence on impulsive purchasing on which the marketing literature hasfocused since the early �fties. As Vohs and Faber (2007:537) observe, "modernWestern societies provide ever-increasing opportunities for impulse spending.[...] Developments in technology as cash machines, shop at home television pro-grams, and Internet shopping now render urges to act immediately and buyaround the clock highly di¢ cult to resist". The consequences of impulsive pur-chasing are relevant: "the ratio of household debt to disposable income in theUnited States is at an all-time high and continues to climb (Federal Reserve2003; Federal Reserve Bank of Cleveland 1997), impulse purchasing being ahefty chunk of spending (Bellenger, Robertson, and Hirschman 1978)"37 . Ina similar vein, in Italy a recent research has remarked that 90% of the con-sumers periodically makes impulsive purchases and, when interviewed about

37Vohs and Faber (2007,537)

18

the issue, two out of �ve people de�ne themselves as impulsive shoppers38 .Similar evidence of inconsistent behavior is documented in choices concerningdieting, exercising, procrastination and health care, as well as undersaving (thereverse side of the evidence on impulsive buying) where several surveys havedocumented systematic deviations from the behavior that was recognized to bethe normative reference39 . The common feature of these surveys is that therespondents believe they should be saving more for retirement, but they admitthey are doing little to do so. In other words they recognize that there is a needof planning a certain path of behavior and they are aware of the best courseof action they should take but then, for some reason, they �nd themselves notdoing what they know they should do.

The observed plan-implementation gap is obviously a form of dynamic in-consistency which should not occur if people�s preferences were represented bythe ED intertemporal utility function. The empirical evidence has been ex-plained in di¤erent ways. In Economics, the most popular explanation suggeststhat people behave inconsistently because they do not discount future utilitiesexponentially. This approach has been �rst suggested by Strotz (1955/6) that,in his theoretical work on dynamic utility maximization, observes that there isno apparent reason for using an exponential discount function, unless one wantsto circumscribe his attention on a decision-maker that is dynamically consistentby assumption. More generally, he suggests that "special attention" should begiven to a discount function overweighting proximate utility relative to distantone40 . In other words, a kind of hyper-myopic discount function that makes thetrade-o¤ between instantaneous and delayed utility particularly favorable to theformer.Strotz�s intuition is corroborated by the experimental evidence. In the last

years, in fact, an increasing number of works have observed that people seem tobe very patient when choices involve costs and bene�ts that are far in time,but they are very impatient when they come closer. More speci�cally, theexperimental evidence suggests that the actual discount function declines ata greater rate in the short run than in the long run, so that delaying a short-run reward by a few days reduces the value of the reward more (in percentageterms) than delaying a long-run reward by a few days41 . This evidence hasbeen reproduced both by psychologists and economists in several experimentsinvolving a wide variety of rewards including money, durable goods, fruit juice,sweets, video rentals, relief from noxious noise, and access to video games42 .38See Caritas Italiana and Fondazione Zancan (Eds.) (2004).39See Angeletos et al. (2001), Thaler and Benartzi (2004) and references therein.40Strotz (1955/6:177).41The �rst tests on intertemporal choice revealing non-exponential discounting emerged

from studies on animal behavior, see Chung, Herrnstein (1967) and Ainslie (1991). Thaler(1981) was the �rst to empirically test that hypothesis on human subjects.42See Angeletos et al. (2001).

19

When the researchers estimate the shape of the discount function basedon the choices made by the experimental subjects, the estimates are betterapproximated by hyperbolic discount functions than by exponential ones43 . Asseen in the previous section, the latter implies a constant discount rate; theformers, on the other hand, exhibit discount rates that decrease as the delayhorizon increases44 . In other words the hyperbolic shape implies that peoplemake relatively far-sighted decisions when planning in advance, but they makerelatively short-sighted decisions when costs and bene�ts are immediate.

In a discrete-time decision-making environment a functional form that cap-tures the qualitative properties of the hyperbolic discount function is the Quasi-Hyperbolic Discounting function45 . This function assumes that the agent dis-counts future utilities according to the following sequence:�

1; ��; ��2; ��3:::

(29)

The quasi-hyperbolic form approximates the hyperbolic function with two pa-rameters, � and �; that are assumed to be less or equal to one. The � parameterexponentially discounts all future periods (as in the ED model) while �, thatdetermines the immediacy e¤ect, uniformly discounts all future periods, but notthe current one. For � < 1 the future utilities are over-discounted with respectto current utility and the short-run discount rate exceeds the long-run discountrate, while for � = 1 we are back to the standard exponential discount function.Combined with the intertemporal utility function in (4), the quasi-hyperbolicspeci�cation requires:

U t(c) = u(ct) + ��u(ct+1) + :::+ ��Tu(cT ) (30)

= u(ct) + �XT

k=t+1�ku(ck): (31)

The speci�c functional form of the quasi-hyperbolic discount function impliestwo di¤erent ways of making intertemporal trade-o¤s. The �rst one concerns

43 In the economic literature, the hyperbolic discount function was suggested for the �rsttime by the psychologist Ainslie (1991). Alternative explanations to the same evidence havebeen proposed; Rubinstein (2001), for example, shows that the observed evidence is consistentwith a speci�c form of procedural rationality, Thaler and Shefrin (1981) explain it in terms ofa dual economic man and Gul and Pesendorfer (2001) rationalize the evidence by consideringpreferences over sets of actions.44See Prelec (2005) for an attempt to sum up the observed evidence in terms decreasing

impatience of the intertemporal preferences.45Proposed by Laibson (1997), the same functional form was �rst suggested by Phelps and

Pollak (1968) to model intergenerational time preferences. As Laibson (2003) observes, "thequasi-hyperbolic discount function is only �hyperbolic� in the sense that it captures the keyqualitative property of the hyperbolic functions: a faster rate of decline in the short-runthan in the long-run". Alternative names in the literature refer to a �present-biased� or a�quasi-geometric" discount function.

20

the comparison between present and future utility. In such a case the agent issubject to some kind of hyper-myopia that overvalues the present and creates abias toward accepting immediate opportunities of grati�cation and postponingimmediate costs. In fact the evaluation would be done by comparing

u(ct) and ��ku(ck): (32)

In the second case the comparison concerns two future utilities. Then the Quasi-Hyperbolic agent makes trade-o¤s as an Exponential Discounting agent does.Indeed, when confronting two delayed rewards the immediacy premium � dividesout and the ratio of the discounted future utilities is only determined by theabsolute time distance between the two alternatives, so that

��s+ku(cs+k) � ��ku(ck)() (33)

�k � u(ck)

u(cs+k)(34)

The consequence of this function is that, consistent with the evidence46 , a quasi-hyperbolic agent is able to correctly make a far-sighted optimal plan becausethe occurrence of costs and bene�ts is far, but she will �nd herself subject tothe present bias, the temptation of getting immediate grati�cation, when theyare close in time.

Assuming that an agent possesses (quasi-)hyperbolic preferences implies thatshe is subject to a tendency to postpone immediate costs and to accelerateimmediate bene�ts, a behavior called procrastination. To see it, consider thefollowing case adapted from Akerlof (1991) in which an agent has to choose whenexercising. Assume that exercising at time t has an immediate cost c = 6 and,at time t+1; a certain delayed bene�t b = 8. The agent has a linear per-periodutility function u(ct) = ct and her intertemporal preferences are represented bya quasi-hyperbolic discount function. Assume � = 1

2 and � = 1. The agent isconsidering 3 possible alternatives: a) (1; 0): exercise today and rest tomorrow,b) (0; 1): rest today and exercise tomorrow, c) (0; 0): never exercise. If theagent decides to exercise today, she gets

option a) U(1; 0) = �6 + 12(8) = �2; (35)

while the value of waiting today and exercising tomorrow is

option b) U(0; 1) = 0 +1

2(�6 + 8) = 1: (36)

Never exercising is not as good as waiting and exercising tomorrow, since

option c) U(0; 0) = 0: (37)46See, for example, Benzion, Rapoport and Yagil (1989)

21

As a consequence, at time 0 the economic actor prefers option (b): restingtoday and exercising tomorrow. In a static environment, this would not be abig issue. Nevertheless, in a dynamic environment, if the alternatives are thesame the passing of time would simply reproduce the same choice set, so thattomorrow the agent will again choose to (rationally!) postpone exercising to thefollowing day. The consequence is that she will keep on procrastinating and wewill observe the agent behaving according to option c) yielding (0; 0): Notably,this is the option that, from the time-0 perspective, was the least preferred bythe agent.

The case of procrastination captures a tension that many decision-makersexperience in real life: when distant, a certain project seems desirable, butas the moment of implementing it gets closer, the same project may becomeincreasingly unappealing and it is preferable to postpone it to a new tomorrow.A similar behavioral pattern is very common and it can be observed, for example,in those that decide to quit smoking "from the next cigarette", or that decide tostart an aggressive saving plan starting next year, or those that decide they needto diet from tomorrow, while they �nish the delicious dessert they are eating.

The intuitive appealing of the quasi-hyperbolic discount functions explainsits application in the economic literature to a wide range of self-regulation prob-lems including procrastination, credit card spending and drug addiction47 . Inall these cases, the evaluation of utility streams is better represented by somekind of hyperbolic discount function. As the previous example has shown, thisdiscounting function can induce the economic actor to make choices that, whenjudged from a distant perspective, are not desirable. In such a case the agent,like Ulysses, could desire to tie his hands before the sirens begin to sing. Inother words, the agent can �nd it optimal to make use of some external pre-commitment device that makes it impossible, or very costly, to deviate from theplan of action that has been chosen at time 0:The idea of precommitment devices as means to enforce a speci�c solution

in a sequential decision-making environment is easily representable by exploit-ing the additive form of the intertemporal discounting model, a form that, asshown in the previous section, allows for a multi-agent interpretation. Accord-ingly, the intertemporal utility function of a single agent can be interpreted asthe sum of the current utility and the discounted future utilities enjoyed by thefuture incarnations (selves) of the decision-maker over time. Given the sequen-tial structure of the interaction between the di¤erent players, the present selfplays as a leader in a Stackelberg game and she can impose to the future selvesthe optimal course of actions by modifying the sets of available alternatives48 . If

47See Angeletos et al. (2001) and references therein.48See Prelec (1989), Schelling (1992), Strotz (1956), Thaler and Shefrin (1981), Wertenbroch

(1998) and Gul and Pesendorfer (2001).

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each of these selves is assumed to possess (quasi)hyperbolic preferences accord-ing to (31), each of them will make impatient decisions whenever they involveimmediate costs and bene�ts, but she will be patient if these choices involvecosts and bene�ts that will be borne by the future selves. As a consequence, theQuasi-Hyperbolic Discount model predicts that the decision-maker gives in topresent temptation (�let me enjoy this last cigarette, for tomorrow I will quit!�)and that she will constrain the future selves, whenever it is feasible, in order toeliminate the possibility of facing an irresistible temptation in the future (�I amrunning out of cigarettes, but I don�t want to buy a new box for tomorrow�).The importance of precommitment devices is supported by a large literature

on binding behaviors. Health retreats where some types of food are not available,saving in non-interest bearing Christmas clubs, or buying small packages ofcigarettes in order to reduce consumption49 can all be seen as precommitmentactions that people use to voluntary bind their future behavior and resist futuretemptations50 .

To be feasible, a precommitment strategy requires at least two assumptionsto be satis�ed:

1. precommitment devices must be feasible and economically a¤ordable forthe present self;

2. the present self must be sophisticated enough to foresee the failure of thefuture selves in implementing a plan that she considers optimal at presenttime.

The last assumption is, indeed, a critical feature that can explain why peo-ple, though being tempted by the present, are able to implement long-termplans. Concerning this issue Strotz (1955/6) and Pollack (1968) discuss twoextreme alternatives. At one extreme a person could be completely naïve, sothat she is not aware of the fact that her future preferences will change as timegoes on. Since she doesn�t correctly foresee her future behavior, she will not useany precommitment device and the sequence of choices that will be observedis likely to be dynamically inconsistent at every point in time. At the otherextreme a person could be fully sophisticated and correctly predict how prefer-ences will change through time. This kind of person would, therefore, be willingto precommit in order to constraint the future selves to behave according to thesequence of behaviors that is optimal from the present-date perspective.As observed by Frederick et al. (2002), the degree of sophistication vs.

naïveté has important consequences for public policies. Indeed, if people arenaïve, policies should be aimed at providing information and education to the

49See Wertenbroch (1998).50Elster (1979, 1986).

23

inconsistent consumers ("smoking may provoke cancer") or providing incentivesfor people to use commitment devices even if they don�t recognize the need forthem. If people are su¢ ciently sophisticated a good policy should, instead, pro-vide people with commitment devices that can be cheaply set, but are expensiveto overcome51 .

Actual research focusing on the assumption that the agents have hyperbolicpreferences has tried to estimate the degree of awareness of people by inferringit from the market demand for precommitment devices. The evidence suggeststhat people are, in general, sophisticated enough to foresee their dynamic in-consistency and that they have a preference for costly precommitment, also ina context of perfect information and no uncertainty. This result is consistentwith the existing survey data. In the domain of consumer choice Wertenbroch(1998) shows, by using both experimental and �eld data, that people are willingto forgo quantity discounts on goods that they may be tempted to overcon-sume, e¤ectively paying a �self-control premium� to implement a precommit-ment strategy of rationing their potential consumption of such �vices.� In thedomain of medical testing Trope and Fishbach (2000) allow the participants toset the magnitude of self-imposed penalties for failing to undergo small, un-pleasant medical procedures. Their results showed that the participants usedthese penalties strategically as precommitment devices, setting higher penaltiesfor more averse procedures. Similar results are showed by Della Vigna and Mal-mendier (2004) with reference to health clubs and by Read et al. (1999) withreference to �high-brow�and �low-brow�movies.As Ariely and Wertenbroch (2002) show, the attempts to impose restrictions

on oneself are helpful in correcting the tendency to be inconsistent, but some-times they are not enough to guarantee a good performance and so they are onlypartially successful. This may be due to the fact that people (assuming thatthey discount the future according to some hyperbolic function) are only par-tially naïve, so that they are aware they will have problems in implementing agiven behavioral plan, but underestimate the magnitude of the inconsistency52 .In this direction, in the last 10 years several studies have investigated, both the-oretically and empirically, the relevance of informational and awareness issues.Between them it is noteworthy mentioning the contribution by Bénabou andTirole (2004) in which the awareness issue is enriched by the assumption thatagents have imperfect memory.

3.1 Exogenous temptation costs and �xed personality traits

The stream of literature based on the assumption that people discount the fu-ture hyperbolically improves, in terms of descriptive realism, the ED model: it

51For a policy proposal to increase employee saving, see Thaler and Benartzi (2004).52Loewenstein, O�Donoghue, and Rabin (2000).

24

better �ts the real life and laboratory evidence, and it is comforted by introspec-tion. As noted, the theoretical framework is the same as the ED, and the onlydi¤erence between the two approaches is the kind of discount function that thedecision-maker is assumed to use. The exponential approach assumes that thediscount rate is constant and that it doesn�t depend on time. As a consequencepeople behave consistently because dynamically consistent are their intertem-poral preferences. The hyperbolic approach, instead, assumes that people�spreferences can be represented by intertemporal utility functions with decreas-ing discount rates, so that they overweight the present relative to the future. Asa consequence this approach to intertemporal choice implies that a hyperbolicagent is likely to procrastinate and to systematically change her mind as timegoes on.In both cases it is the "type" of agent that determines whether she will be

able to implement a previously chosen plan, given the temptation of the present.To make this clear, consider the model proposed by Bénabou and Tirole (2001)in which they study the behavior of a quasi-hyperbolic agent that has to choosebetween two alternatives. The agent can chose in two consecutive periods. Inperiod t = 0 she makes a plan: she decides what would be optimal from thetime-0 perspective. In period t = 1 she reconsiders the available options andchooses which alternative to implement. Since the �ow payo¤s associated to thetwo alternatives are enjoyed at time 0; 1 and 2, the choice implemented at time1 determines also the payo¤ at time 2. The alternatives are the following:

d = (0;�c;B) and e = (0; 0; b); (38)

with b < B. The choice of d implies an immediate cost in period t = 1 andit yields a large delayed bene�t in the following period, while choice e yieldsno immediate cost in period t = 1 and a small bene�t in the following period.From time t = 1 perspective, option d can be interpreted as the choice of savingtoday to consume tomorrow, giving up an immediate earning to invest in humancapital, spending time and e¤ort today to build trust and relational capital andso on. Option e, instead, involves no cost -no foregone utility due to giving upsome consumption today, to spend some time studying, to go to a social eventor be kind with people-, and it simply yields a little future payo¤.The agent discounts the future according to the (�; �) quasi-hyperbolic spec-

i�cation in (31). For simplicity let � = 1 and � < 1. In the planning phase (attime 0) the agent prefers d to e if c < B � b and, when the plan is to be imple-mented at time 1, she will still prefer d to e if and only if c� < B � b. The termc=� thus captures the intensity of the temptation c relative to the individualability, indicated by �; to withstand discomfort and delay grati�cation. Fromthis perspective, � is to be literally interpreted as willpower : if the agent is pow-erful enough in terms of will, she will implement the long-run plan, otherwiseshe will succumb to instantaneous grati�cation. Indeed, given c

� , three casescan occur:

25

1. c < c� < B � b: the decision-maker prefers d to e both at time t = 0 and

t = 1; in such a case the agent is time consistent;

2. B � b < c < c� : the decision-maker prefers e to d both at time t = 0 and

t = 1; also in this case the behavior will be consistent;

3. c < B � b < c� : in such a case the decision-maker prefers d to e at t = 0

but she will reverse her preference and, at t = 1, she chooses e:

Considering cases 1 and 3, it is possible to identify a threshold value �̂ = cB�b

distinguishing consistent (� > �̂) from inconsistent (� < �̂) agents. Indeed,given a preference, at time 0; for alternative d (which occurs if c < B � b), theagents with a su¢ ciently high � will always be able to implement the plan thatwas chosen before (case 1), while those with a low � will always give up (case3).

The critical feature of this model is that both c and � are exogenously deter-mined, so that no dynamic aspect concerning the evolution of their ratio is takeninto account. Nevertheless, such a static approach to study the intertemporalbehavior of people receives only partial support by the empirical evidence. Insome decisional environments it is indeed true that the mere presence of a largeimmediate cost c (or, equivalently, an instantaneous grati�cation opportunity)is enough to induce the individual to deviate from the previously assessed plan.It is the case, for example, of addiction and dependencies from substances inwhich the cravings due to abstinence can be so intense that the individual alonecannot stick to the ex-ante optimal plan of quitting with drugs53 . Nevertheless,as a large literature in psychology shows, in other cases this is less justi�able.People are indeed subject to a present bias, but this does not necessarily drivethem to succumb to it. For example, they are able to behave consistently byusing external precommitment devices, or by using internal commitment devicessuch as personal rules54 .These mechanisms have been substantially ignored by the economic litera-

ture55 but they have received much attention in other social disciplines. Thepsychologists Herman and Polivy (2003), for example, observe that in the caseof dieters "[i]t is not quite accurate to explain the breakdown of restraint solelyin terms of the presence of the food. [...] It�s always a question of how ourmental apparatus cope with the "threat", and not a simple matter of the foodinexorably driving us to eat"56 . Emotions and visceral factors, for example, play53See, for example, O�Donoghue and Rabin (1999a, 2000).54See, for example, Houston, Wegner (1995) and Baumeister, Vohs (2003, 2004) and, in

the context of consumption/saving decisions, Benhabib and Bisin (2005); see also Hock andLoewenstein (1991) for a contribution on self-control strategies.55For exceptions, see Thaler, Shefrin (1981), Loewenstein and O�Donoghue (2004), Benhabib

and Bisin (2005).56Herman, Polivy (2003).

26

a relevant role in inducing deviations from the diet57 . Moreover these factorsdo not have the same incidence on people. Negative emotions and distress havebeen shown to have a di¤erential e¤ect on dieters and nondieters: distress in-hibits eating in the latter group, but it increases eating in the former. So, unlessit is shown that all dieters are weak-types and all nondieters are strong-types,this evidence would suggest that prior inhibitions interact with emotional dis-tress in in�uencing the way people behave58 . Such interaction is not taken intoaccount either in the exponential nor in the hyperbolic discount model, and itsuggests that the predictions about the behavior of people cannot be only basedon �xed individual attributes (which in Psychology are generally referred to aspersonality traits) because the history of past choices can be relevant.As Vohs and Faber (2007) observe, focusing on the notion of a given type

of intertemporal preferences without taking into account other factors obscuresthe fact that virtually everyone engages in inconsistent actions at some timeand that even identi�ed �impulsive decision-makers� resist the temptation ofthe present at various times. In other words, focusing only on the individualpropensity to impulsivity (which corresponds, in the quasi-hyperbolic notation,to the value of �), hides that also situational and cognitive factors have a strongin�uence on the way people engage in impulsive actions or successfully restrainthis impulse59 : even in cases where a present bias is easily observable, thebehavior of people is much more �exible and articulated than it is generallyconsidered in the economic literature. For example, some people respect theirplans for some time, then they deviate (eventually exceeding, as it is the case ofbinging behavior), then they come back to the original track; in other situationsthey resist to big temptations for a long time, but then they suddenly give in toa much smaller temptation. As the cognitive literature on self-regulation shows,part of this evidence can be explained by referring not just to the way peoplemake intertemporal trade-o¤s, but also to the way the mind works. This requiresconsidering that the cognitive dynamics of decision-making can constraint theintertemporal behavior of the decision-maker even if they do not directly yieldcosts or bene�ts to the agent.

57Emotional factors are relevant in in�uencing behavior also in environments where timeinconsistency is not at stake. See Lerner, Small and Loewenstein (2004) for an empirical studyon the in�uence of emotional reactions (speci�cally: sadness and disgust) on the willingnessto pay and to accept of people.58 Ibid.59See Mischel and Shoda (1998).

27

4 A complementary approach: the role of cog-nition and fatigue

In the previous sections I have analyzed how the economic literature has ap-proached intertemporal decision-making by reviewing the two most popular ap-proaches that have been proposed: the Exponential Discounting and the Hy-perbolic Discounting model. A common feature of this literature is that it ismainly focused on how people evaluate costs and bene�ts over time, and thusit stresses the need to determine which intertemporal utility function better �tsthe empirical evidence on the intertemporal behavior of people.In this section I want to introduce a complementary perspective for studying

intertemporal behavior and that, instead of investigating how people make in-tertemporal trade-o¤s, focuses on the cognitive constraints that may be bindingwhen performing prolonged complex cognitive tasks. This category includes allthe activities that require the individual to pay attention and to exert cogni-tive e¤ort, such as maintaining vigilance on the job, making decisions, solvingproblems and exerting self-regulation. Clearly, each of these activities yieldscosts and bene�ts that are distributed over time and that can be di¤erentlyevaluated by the decision-maker. Nevertheless I want also to emphasize the factthat performing this kind of activities is fatiguing and that the accumulation offatigue can signi�cantly impair the performance in subsequent tasks. In otherwords, when a prolonged e¤ort exertion is required over time there may existan intertemporal trade-o¤ between current performance and accumulation offatigue.

To illustrate this point, consider the case of dieting. A diet can be de�nedas a behavioral plan aimed at maintaining one person�s caloric intake within aprede�ned quota. Adhering to a diet requires making intertemporal trade-o¤sbetween costs and bene�ts over time and it turns out to be the most commonself-regulated behavior in contemporary Western society. Moreover, when a per-son decides to be on diet, succumbing to appetizing food represents an easilyidenti�able form of dynamic inconsistency. These features have made dietingthe most used example to explain dynamic inconsistent behavior in intertempo-ral decision-making. Indeed there is substantial evidence that long-term weightloss is extremely di¢ cult to achieve, as most people who try to regulate theireating fail. One possible reason is that dieters must exert some e¤ort to over-ride feelings of hunger (perhaps by focusing on long-term weight-loss goals) astemptations occur. Accordingly, some intertemporal decision-making modelstake into account the disutility of resisting to temptation into the preferencesof the decision-maker60 . Nevertheless the empirical evidence shows that manyfailures in self-regulation are not due to the cost of resisting to a single temp-

60See, for example, Loewenstein and O�Donoghue (2004).

28

tation, but to the inability to resist to a sequence of temptations over time. Inother words, at the beginning people are often able to strictly adhere to a diet,but then they �nd it di¢ cult to do it successfully over prolonged time-horizons.Cognitive psychology explains this evidence by considering the fact that dieting,as all complex cognitive activities, requires the exertion of e¤ort and that ex-erting prolonged e¤ort over time is fatiguing. The consequence is that exertingcontinuous e¤ort over time can seriously impact on performance. This impliesthat, beyond the disutility cost of exerting e¤ort, there are also the indirect,endogenous costs due to the fact that a person cannot exert high-levels of e¤ortfor a long time, with the consequence that providing a high performance todaycan lead to a reduced performance tomorrow.Vohs and Heatherton (2000), for example, have tested the behavioral con-

sequences of e¤ortful self-regulation in individuals that chronically control fortheir dietary habits. Their results show that the two activities negatively impactand that less ability to self-regulate results. In a similar vein Muraven et al.(1999) observe that "coping with stress had aftere¤ects that encompass a vari-ety of self-regulatory breakdowns (e.g. in eating patterns, substance abuse oremotional control); coping with emotional distress shows similar patterns; andcontinued exertion of self-control, as in many successive trials on a vigilancetask, shows consistent patterns of gradual deterioration"61 . Further evidenceindicates that inhibition in one domain exerts a generalized e¤ect on behaviorsin other domains, provided that these behaviors involve high-level cognition andexertion of cognitive e¤ort. This result is consistent with the experiments byVohs and Heatherton (2003) in which they show that the e¤ects of cognitive fa-tigue are speci�c only to high-level cognitive tasks. Indeed, activities requiringsimple information processing like visual perception and association are unaf-fected by fatigue, while decreases in performance have been recorded in relationto the complexity of the task to be completed. These results seem to be robustacross a variety of di¤erent cognitive tasks. A possible explanation is that allthese activities require drawing on some kind of limited resource, as if therewere a single capacity or dimension underlying the wide variety of cognitiveactivities that a person can perform. With an interesting analogy, the capacityto perform cognitive tasks has been compared to a muscle that gets fatiguedafter use and then requires rest62 . In particular, an implication of the cognitivedepletion hypothesis is that a person may fail to successfully exert cognitive

61Muraven et al. (1999:447)62As Muraven, Tice and Baumeister (1998:775) observe: "This is roughly the di¤erence

between attention and muscular strength: both may be limited, but one�s quantity of availableattention returns to full as soon as current demands on it cease, whereas muscular exertionis followed by a period of reduced capacity. [...] Eventually, with su¢ cient rest, regulatorystrength should return to its previous level, but in the short term the person should have areduced capacity for self-regulation". For a similar point see also Mischel (1996), Baumeister,Bratslavsky, Muraven, Tice (1998), Vohs, Heatherton (2000), Schmeichel, Vohs, Baumeister(2003), Vohs, Faber (2004).

29

e¤ort not because she systematically lacks the ability to perform it, but becauseshe is fatigued and she may temporally �nd herself not having enough resourcesto perform it63 .

5 Conclusions

In this paper I review some features of the economic approach to intertem-poral decision-making by considering the speci�c assumptions that both theExponential and the Hyperbolic discounting models imply. Both approachesfocus on how people evaluate utility over time. The Exponential Discountingmodel assumes that intertemporal preferences are time consistent, so that whatis considered to be optimal at a certain point in time is still optimal in anyother moment. The Hyperbolic Discounting model assumes that the evalua-tion of utility depends on calendar time, so that time inconsistent behavior canemerge.The recent evidence on dynamic inconsistent behavior and failures in self-

control has stimulated a lively stream of research and several studies have beendedicated to understanding and calibrating the intertemporal discount functionthat best �ts the observed behavior. Other studies have instead focused on theinformation and awareness issues linked to the existence of myopic preferences,and they have suggested speci�c strategies, such as the use of precommitmentdevices, in order to correct the tendency of people to deviate from plans ofbehavior that they had previously assessed as optimal.Other disciplines, like marketing and cognitive psychology, have also ob-

served that there exist cognitive constraints that do not a¤ect the evaluationof utility over time and yet they a¤ect the behavior of people. The empiricalevidence thus provides an alternative perspective for understanding the behav-ior of people over time. However, the idea that there exist cognitive constraintsthat in�uence the intertemporal behavior of a decision-maker does not competewith the standard economic approach to intertemporal decision-making. Indeed,the cognitive perspective I propose simply wants to point out that there existshadow costs of cognition that can be helpful in explaining part of the empiricalevidence that has been collected on behaviors requiring to exert prolonged e¤ortover time. For example, it can be useful to study the optimal path of choicesthat optimize the ability of people to stay concentrated on the job, comply withtasks requiring prolonged attention and work e¢ ciently, or the ability to exertself-control over time.63See Dragone (2006) for a model of intertemporal decision-making with endogenous cog-

nitive costs.

30

6 Bibliographic references

References

[1] Ainslie, George (1975). �Specious Reward: A Behavioral Theory of Im-pulsiveness and Impulse Control.�Psychological Bulletin, 82(4), 463-96.

[2] Ainslie, George (1991). "Derivation of "Rational" Economic Behavior fromHyperbolic Discount Curves." American Economic Review, 81(2), 334-40.

[3] Ainslie, George (1992). Picoeconomics : The Strategic Interaction of Suc-cessive Motivational States Within the Person. (Studies in Rationality andSocial Change). Cambridge University Press.

[4] Ainslie, George and Nick Haslam (1992). �Hyperbolic Discounting,� inChoice over Time. George Loewenstein and Jon Elster eds., Russell SageFoundation, 57-92.

[5] Ainslie, George and Richard J. Herrnstein (1981). �Preference Reversaland Delayed Reinforcement.�Animal Learning and Behavior, 9(4), 476-82.

[6] Ainslie, George (2001). Breakdown of Will. Cambridge, England: Cam-bridge University Press.

[7] Akerlof, George A. (1991). "Procrastination and Obedience". AmericanEconomic Review, 81(2), 1-19.

[8] Ameriks, John, Andrew Caplin, John Leahy, Tom Tyler (2004).MeasuringSelf-Control. NBER working paper 10514.

[9] Angeletos, George-Marios, David Laibson, Andrea Repetto, Jeremy To-bacman, and Stephen Weinberg (2001). �The Hyperbolic ConsumptionModel: Calibration, Simulation, and Empirical Evaluation.� Journal ofEconomic Perspectives, 15(3), 47-68.

[10] Ariely, Daniel and Ziv Carmon (2003). �Preferences Over Sequences ofOutcomes,�in Time and Decision: Economic and Psychological Perspec-tives on Intertemporal Choice. George Loewenstein, Daniel Read, and RoyBaumeister eds., Russell Sage Foundation Press.

[11] Ariely, Daniel and Klaus Wertenbroch (2001). �Procrastination, Deadlinesand Performance,�Insead, Working Paper 2001/09/Mkt.

[12] Bargh, John A. (1996). "Automaticity in Social Psychology", In So-cial Psychology: Handbook of Basic Principles. E.T. Higgins and A.W.Kruglanski eds., 169-183. Guilford.

31

[13] Baumeister, Roy F. (2002). "Yielding to Temptation: Self-Control Fail-ure, Impulsive Purchasing and Consumer Behavior." Journal of ConsumerResearch, 28, 670-676.

[14] Baumeister, Roy F. (2003). "Ego Depletion and Self-Regulation Failure: AResource Model of Self-Control." Alcoholism: Clinical and ExperimentalResearch , 27(2), 281-284.

[15] Baumeister, Roy E., Ellen Bratslavsky, Mark Muraven, and Dianne M.Tice (1998). "Ego Depletion: Is the Active Self a Limited Resource?"Journal of Personality and Social Psychology, 74(5), 1252-1265.

[16] Baumeister, Roy F., Julie J. Exline (1999). "Virtue, Personality and So-cial Relations: Self-Control as the Moral Muscle," Journal of Personality,67(6), 1165-1194.

[17] Baumeister, Roy F., Todd F. Heatherton, and Diane M. Tice (1994).Losing Control: How and Why People Fail at Self-Regulation. AcademicPress.

[18] Baumeister, Roy F. and Kathleen D. Vohs (2003). �Willpower, Choice,and Self-Control,� in George Loewenstein, Daniel Read and Roy F.Baumeister, eds., Time and Decision: Economic and Psychological Per-spectives on Intertemporal Choice. Russell Sage Foundation, 201-216.

[19] Baumeister, Roy F. and Kathleen D. Vohs (2004). Willpower. mimeo

[20] Baumeister, Roy F. and Kathleen D. Vohs (2004). Handbook of Self-Regulation: Research, Theory, and Applications. Guilford.

[21] Becker, Gary, and K. Murphy (1988). �A Theory of Rational Addiction,�Journal of Political Economy, 96, 675-700.

[22] Bénabou, Roland and Marek Pycia (2002). �Dynamic Inconsistency andSelf-Control: A Planner-Doer Interpretation.�Economics Letters, 77, 419-424.

[23] Bénabou, Roland and Jean Tirole (2002). �Self-Con�dence and PersonalMotivation,�Quarterly Journal of Economics, 117(3), 871-915.

[24] Bénabou, Roland and Jean Tirole (2000b). �Self-Con�dence and SocialInteractions, �NBER Working Paper 7585.

[25] Bénabou, Roland and Jean Tirole (2000c). �Self-con�dence: Intrapersonalstrategies�, Princeton University Discussion Paper 209, Princeton.

[26] Bénabou, Roland and Jean Tirole (2004). �Willpower and Personal Rules,Journal of Political Economy, 112, 848-887.

32

[27] Benhabib, Jesse and Alberto Bisin (2004). �Modeling Internal Com-mitment Mechanisms and Self-Control: A Neuroeconomics Approach toConsumption-Saving Decisions,�mimeo.

[28] Benartzi, Shlomo and Richard H. Thaler (2004). "Save More Tomorrow:Using Behavioral Economics to Increase Employee Saving", Journal ofPolitical Economy, 112(1), S164-S187.

[29] Benzion, Uri, Amnon Rapoport and Joseph Yagil (1989). �Discount RatesInferred from Decisions: An Experimental Study,�Management Science,35(3), 270-284.

[30] Bernheim, B. Douglas and Antonio Rangel (2002). �Addiction and Cue-Conditioned Cognitive Processes.�NBER working paper #9329.

[31] Blackhorby C., D.Primont, P.Russel (1978). Duality, Separability andFunctional Structure: Theory and Economic Applications, Amsterdam:North Holland.

[32] Boekaerts, Monique , Paul R. Pintrich and Moshe Zeider (2000). Handbookof Self-Regulation. Academic Press.

[33] Caillaud, Bernard, Daniel Cohen and Bruno Jullien (2000). �Toward aTheory of Self-Restraint,�CERAS mimeo.

[34] Camerer, Colin and George Loewenstein (2004). Behavioral Economics:Past, Present, Future. mimeo.

[35] Camerer, Colin, George Loewenstein, and Drazen Prelec (2003). �Neuroe-conomics: How Neuroscience Can Inform Economics.�Mimeo, CarnegieMellon University.

[36] Carrillo, Juan (1998). �Self-Control, Moderate Consumption and Crav-ing,�CEPR DP 2017, mimeo, ULB.

[37] Carrillo, Juan and Thomas Mariotti (2000). �Strategic Ignorance as aSelf-Disciplining Device,�Review of Economic Studies, 67(3), 529-544.

[38] Caritas Italiana e Fondazione Zancan (eds.) (2004). "Vuoti a Perdere:Rapporto 2004 su Esclusione Sociale e Cittadinanza Incompiuta, Fel-trinelli.

[39] Chaiken, Shelly and Trope Yaacov (eds.) (1999). Dual-Process Theoriesin Social Psychology, Guilford Press, New York.

[40] Connolly, Terry, Hal Arkes and Kenneth R. Hammond (2000). Judgmentand Decision Making: An Interdisciplinary Reader. Cambridge UniversityPress.

33

[41] Conlisk, John (1996). �Why Bounded Rationality?�Journal of EconomicLiterature, 34, 669-700.

[42] Damasio, Antonio R. (1994). Descartes�Error: Emotion, Reason, and theHuman Brain. G.P. Putnam.

[43] DellaVigna, Stefano and Ulrike Malmendier (2003). �Overestimating Self-Control: Evidence From the Health Club Industry,� Stanford GSB Re-search Paper 1800.

[44] Duesenberry, James (1952). Income, Saving, and the Theory of ConsumerBehavior. Cambridge, MA: Harvard University Press.

[45] Dragone, Davide (2007). Endogenous Attention Costs and IntertemporalDecision-Making, working paper DSE 570-2006, Alma Mater Studiorum-Bologna.

[46] Elster, Jon (1979). Ulysses and the Sirens: Studies in Rationality andIrrationality. Cambridge University Press.

[47] Elster, Jon (1986). The Multiple Self. Cambridge University Press.

[48] Fisher, Irving (1930). The Theory of Interest. New York: MacMillan.

[49] Frederick, Shane (1999). �Discounting, Time Preference, and Identity.�Ph.D. Thesis. Department of Social & Decision Sciences. Carnegie MellonUniversity.

[50] Frederick, Shane, George Loewenstein and Ted O�Donoghue (2002). "TimeDiscounting and Time Preference: A Critical Review," Journal of Eco-nomic Literature, 40(2), 351-401.

[51] Fudenberg D., David Levine (2005), �A Dual-Self Model of Impulse Con-trol�, working paper.

[52] Glass, D. C., Singer, J. E., & Friedman, L. N. (1969). "Psychic Cost ofAdaptation to an Environmental Stressor". Journal of Personality andSocial Psychology, 12, 200-210

[53] Goldstein, William and Robin Hogarth (1997). Research on Judgment andDecision Making: Currents, Connections, and Controversies. CambridgeUniversity Press.

[54] Gul, Faruk and Wolfgang Pesendorfer (2001). �Temptation and Self Con-trol,�Econometrica, 69, 1403-1436.

[55] Gul, Faruk and Wolfgang Pesendorfer (2004). �Self-Control and the The-ory of Consumption,�Econometrica, 72(1), 119-58.

34

[56] Herman, C. Peter and Janet Polivy (2003). �Dieting as an Exercise inBehavioral Economics,�in George Loewenstein, Daniel Read and Roy F.Baumeister, eds., Time and Decision: Economic and Psychological Per-spectives on Intertemporal Choice. New York: Russell Sage Foundation,459-489.

[57] Herrnstein, Richard and Drezen Prelec (1992). �A Theory of Addiction,�in G. Loewenstein and J. Elster, eds., Choice over Time, Russell SageFoundation.

[58] Hertwig, Ralph and Andreas Ortmann (2001). "Experimental Practices inEconomics: A Methodological Challenge for Psychologists?" Behavioraland Brain Sciences, 24, 383�451.

[59] Hoch, Stephen J. and George Loewenstein (1991). "Time-InconsistentPreferences and Consumer Self-Control," Journal of Consumer Research.17, 492-507.

[60] Hogarth, Robin and Melvin Reder (1987). "Editor�s Comments: Perspec-tives from Economics and Psychology," The Journal of Business, 59, S185-S207.

[61] Houston, Christopher and Daniel Wegner M. (1995). Mental Control. InA. S. R. Manstead & M. Hewstone (Eds.), The Blackwell Encyclopedia ofSocial Psychology, 379-381.

[62] Kahneman, Daniel and Amos Tversky (2000). Choices, Values, andFrames. Cambridge University Press.

[63] Keren, Gideon (1996). "Perspective on Behavioral Decision Making: SomeCritical Notes," Organizational Behavior and Human Decision Making,65(3), 169�178.

[64] Koopmans, Tjalling C. (1960). �Stationary Ordinal Utility and Impa-tience.�Econometrica, 28, 287-309.

[65] Laibson, David (1997). �Golden Eggs and Hyperbolic Discounting.�Quar-terly Journal of Economics, 112, 443-477.

[66] Laibson, D. (2003). Intertemporal Decision Making in Encyclopedia ofCognitive Science, London: Nature Publishing Group.

[67] Loewenstein, George (1987). �Anticipation and the Valuation of DelayedConsumption.�Economic Journal, 97, 666- 84.

[68] Loewenstein, George (1988). �Frames of Mind in Intertemporal Choice.�Management Science, 34, 200-214.

35

[69] Loewenstein, George (1996). �Out of Control: Visceral in�uences on Be-havior.�Organizational Behavior and Human Decision Processes, 65, 272-92.

[70] Loewenstein, George (1999). �A Visceral Account of Addiction,� in Get-ting Hooked: Rationality and Addiction. Jon Elster and Ole-Jorgen Skogeds. Cambridge, England: Cambridge University Press, 235-64.

[71] Loewenstein, George (2000a). �Willpower: A Decision-Theorist�s Perspec-tive.�Law and Philosophy, 19, 51-76.

[72] Loewenstein, George (2000b). �Emotions in Economic Theory and Eco-nomic Behavior.�American Economic Review: Papers and Proceedings,90, 426-32.

[73] Loewenstein, George and Eric Angner (2002). "Predicting and IndulgingChanging Preferences". In G. Loewenstein, D. Read, and R. Baumeister(Eds.) Time and Decision: Economic and Psychological Perspectives onIntertemporal Choice. New York: Russell Sage Foundation Press.

[74] Loewenstein, George and Drazen Prelec (1991). �Negative Time Prefer-ence.�American Economic Review, 81, 347-52.

[75] Loewenstein, George and Drazen Prelec (1992). �Anomalies in Intertem-poral Choice: Evidence and an Interpretation.�Quarterly Journal of Eco-nomics, May, 573-97.

[76] Loewenstein, George and Drazen Prelec (1993). �Preferences for Sequencesof Outcomes.�Psychological Review, 100(1), 91-108.

[77] Loewenstein, George and Jennifer Lerner (2002). �The Role of A¤ect inDecision Making,�in The Handbook of A¤ection Science.

[78] Loewenstein, George and Ted O�Donoghue (2004). "Animal Spirits: Af-fective and Deliberative Processes in Economic Behavior." mimeo.

[79] Loewenstein, George, Ted O�Donoghue, and Matthew Rabin (2003). "Pro-jection Bias in Predicting Future Utility". Quarterly Journal of Eco-nomics, 118(4), 1209-48.

[80] Loewenstein, George and Richard H.Thaler (1989). "IntertemporalChoice". Journal of Economic Perspectives, 3(4), 181-193.

[81] Mas-Colell, Andreu, Michael D. Whinston and Jerry Green (1995). Mi-croeconomic Theory. Oxford University Press.

36

[82] McClure, Samuel M., David Laibson, George Loewenstein, Jonathan D.Cohen (2004). "Separate Neural Systems Value Immediate and DelayedMonetary Rewards". Science, 306(5695), 503 - 507.

[83] McIntosh, Donald (1969). The Foundations of Human Society, U. ChicagoPress.

[84] Metcalfe, Janet and Walter Mischel (1999). �A Hot/Cool-System Analysisof Delay of Grati�cation: Dynamics of Willpower.�Psychological Review,106(1), 3-19.

[85] Mischel, Walter (1996). "From Good Intentions to Willpower". In P. M.Gollwitzer & J. A. Bargh (Eds.), The Psychology of Action: Linking Cog-nition and Motivation to Behavior, New York: Guilford Press, 197-218.

[86] Mischel, Walter, Ozlem Ayduk, and Rodolfo Mendoza-Denton (2003).�Sustaining Delay of Grati�cation over Time: A Hot-Cool Systems Per-spective,� in George Loewenstein, Daniel Read and Roy F. Baumeister,eds., Time and Decision: Economic and Psychological Perspectives onIntertemporal Choice. New York: Russell Sage Foundation, 175-200.

[87] Mischel, Walter, Ebbe B. Ebbesen, and Antonette Zeiss (1972). �Cogni-tive and Attentional Mechanisms in Delay of Grati�cation.� Journal ofPersonality and Social Pychology, 21(2), 204-218.

[88] Moore, Don and George Loewenstein (2004). "Self-Interest, Automaticity,and the Psychology of Con�ict of Interest," Social Justice Research, 17(2),189-202.

[89] Muraven, Mark R. and Roy F. Baumeister (2000). "Self-Regulation andDepletion of Limited Resources: Does Self-Control Resemble a Muscle?"Psychological Bulletin, 126, 247-259.

[90] Muraven, Mark, Roy F. Baumeister and Dianne M. Tice (1999). "Longi-tudinal Improvement of Self-Regulation through Practice: Building Self-Control Strengh through Repeated Exercise." Journal of Social Psychol-ogy, 139(4), 446-457.

[91] Muraven, Mark, Dianne M. Tice and Roy F. Baumeister (1998). Self-Control as Limited Resource: Regulatory Depletion Patterns. Journal ofPersonality and Social Psychology, 74(3), 774-789.

[92] Murtagh, Anne M. and Susan A. Todd (2004). "Self-Regulation: A Chal-lenge to the Strength Model." Journal of Articles in Support of the NullHypothesis, 3(1), 19-51.

37

[93] O�Donoghue, Ted and Matthew Rabin (1999a). �Addiction and Self-Control,�in Addiction: Entries and Exits. Jon Elster ed. New York: Rus-sell Sage Foundation, 169-206.

[94] O�Donoghue, Ted and Matthew Rabin (1999b). �Doing it Now or Later.�American Economic Review, 89(1), 103-24.

[95] O�Donoghue, Ted and Matthew Rabin (1999c). �Incentives for Procrasti-nators.�Quarterly Journal of Economics, 114(3), 769-816.

[96] O�Donoghue, Ted and Matthew Rabin (1999d). �Procrastination inPreparing for Retirement,�in Behavioral Dimensions of Retirement Eco-nomics. Henry Aaron, ed. Brookings Institution Press & Russell SageFoundation, 125-156.

[97] O�Donoghue, Ted and Matthew Rabin (2000). �Addiction and Present-Biased Preferences.�Cornell University and U.C. Berkeley, mimeo.

[98] O�Donoghue, Ted and Matthew Rabin (2001). �Choice and Procrastina-tion.�Quarterly Journal of Economics, 116(1), 121-60.

[99] O�Donoghue, Ted and Matthew Rabin (2003). �Self-Awareness and Self-Control,� in Time and Decision: Economic and Psychological Perspec-tives on Intertemporal Choice. George Loewenstein, Daniel Read, and RoyBaumeister eds. New York: Russell Sage Foundation Press.

[100] Phelps, Edmund S. and Robert A. Pollak (1970). "On Second Best Na-tional Saving and Game-Equilibrium Growth". Review of Economic Stud-ies, XXXV, 185-199.

[101] Pollak, Robert A. (1970). �Habit Formation and Dynamic Demand Func-tions.�Journal of Political Economy, 78(4), 745-63.

[102] Prelec, Drazen (1989). �Decreasing Impatience: De�nition and Conse-quences.�Working paper 90-015, Harvard Business School, Boston, MA.

[103] Prelec, Drazen (2004). �Decreasing Impatience: A Criterion for Non-Stationary Time Preference and �Hyperbolic�Discounting.�ScandinavianJournal of Economics, 106(3), 511-532.

[104] Rabin, Matthew (1996). "Psychology and Economics". University of Cal-ifornia �Berkeley, mimeo.

[105] Rook, Dennis W. (1987). �The Buying Impulse.� Journal of ConsumerResearch, 14, 189-199.

[106] Rook, Dennis, W. and Robert J. Fisher (1995). �Normative In�uences onImpulsive Buying Behavior". Journal of Consumer Research, 22, 305-313.

38

[107] Rubinstein, Ariel (2001). �Is it �Economics and Psychology�?: The Caseof Hyperbolic Discounting,�http://www.princeton.edu/~ariel/delta3.pdf.

[108] Samuelson, Paul (1937). �A Note on Measurement of Utility.�Review ofEconomic Studies, 4, 155-61.

[109] Schelling, Thomas C. (1978). �Egonomics, or the Art of Self-Management.�American Economic Review, Papers and Proceedings, 68,290-294.

[110] Schelling, Thomas C. (1984). �Self-Command in Practice, in Policy, andin a Theory of Rational Choice.�American Economic Review, 74(2), 1-11.

[111] Shiv, Baba and Alexander Fedorikhin (1999). �Heart and Mind in Con�ict:The Interplay of A¤ect and Cognition in Consumer Decision Making.�Journal of Consumer Research, 26, 278-292.

[112] Schmeichel, Brandon J., Kathleen D. Vohs and Roy F. Baumeister (2003)."Intellectual Performance and Ego Depletion: Role of the Self in LogicalReasoning and Other Information Processing". Journal of Personality andSocial Psychology, 85(1), 33-46.

[113] Strotz, R. H. (1955-1956). �Myopia and Inconsistency in Dynamic UtililtyMaximization.�Review of Economic Studies, 23(3), 165-80.

[114] Thaler, Richard H. (1999). �Mental Accounting Matters.�Journal of Be-havioral Decision Making, 12, 183-206.

[115] Thaler, Richard H. (1981) �Some Empirical Evidence on Dynamic Incon-sistency.�Economic Letters, 8, 201-07.

[116] Thaler, Richard H. and Shlomo Benartzi (2004). "Save More Tomorrow: Using Behavioral Economics to Increase Employee Saving." Journal ofPolitical Economy, 112(1). S164-S187.

[117] Thaler, Richard H. and Hersh M. Shefrin (1981). �An Economic Theoryof Self-Control.�Journal of Political Economy, 89(2), 392-410.

[118] Vohs, K. D., Roy F. Baumeister, Jean M. Twenge, Brandon Schmeichel,Dianne Tice and Jennifer Crocker (2004). "Decision Fatigue Exhausts Self-Regulatory Resources � but So Does Accommodating to Unchosen Alter-natives". mimeo.

[119] Vohs, Kathleen D. and Todd F. Heatherton (2000). "Self-Regulatory Fail-ure: A Resource-Depletion Approach". Psychological Science, 11(3), 249-254.

39

[120] Vohs, Kathleen. D. and Ronald J. Faber (2007). "Spent Resources: Self-Regulatory Resource Availability A¤ects Impulse Buying," Journal ofConsumer Research, 33(4), 537-547.

[121] Wegner, Daniel M. (1989). White Bears and Other Unwanted Thoughts:Suppression, Obsession, and the Psychology of Mental Control.Viking/Penguin.

[122] Wegner, Daniel M. (1994). "Ironic Processes for Mental Control." Psycho-logical Review, 101, 34-52.

[123] Wertenbroch, Klaus and Ziv Carmon (1997). "Dynamic Preference Main-tenance." Marketing Letters, 8(1), 145-152.

[124] Wertenbroch, Klaus (1998). �Consumption Self-Control by Rationing Pur-chase Quantities of Virtues and Vice,�Marketing Science, 17(4), 317�337.

[125] Wertenbroch, Klaus (2001). "Self-Rationing: Self-Control in ConsumerChoice." Insead, Working Paper 2001/63/Mkt.

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