Pre-commitment and flexibility in a time decisionexperiment

Marco Casari

Published online: 11 February 2009# Springer Science + Business Media, LLC 2009

Abstract An agent with dynamically inconsistent preferences may deviate from herplan of action as the future draws near. An exponential discounter may do exactlythe same when facing an uncertain future. Through an experiment we comparepreference-based vs. uncertainty-based explanations for choice reversal over time byeliciting choices for pre-commitment and flexibility. Evidence of widespreadcommitment favors a preference-based explanation.

Keywords Experiments . Intertemporal choices . Dynamic consistency .

Commitment . Flexibility . Uncertainty

JEL Classification C91 . D90 . D81

J Risk Uncertain (2009) 38:117–141DOI 10.1007/s11166-009-9061-5

This study was initiated when visiting the Autònoma University of Barcelona, Spain. Discussions withHoward Rachlin have been particularly valuable. Earlier versions of this manuscript have also benefitedfrom the comments of Alberto Bisin, Jordi Brandts, Gabriele Camera, Colin Camerer, Gary Charness,Pierre Courtois, Guillaume Frechette, David Laibson, Dan Levin, Rosella Nicolini, Charlie Plott, ArnoRiedl, Kip Viscusi, and of participants at seminars at Kyoto Sangyo University, University of Maastricht,University of Venezia, New York University, Capua Workshop in Behavioral Economics, the AutònomaUniversity of Barcelona, Purdue University, and at the ESA meeting in Montreal. All remaining errors aremine. Henrik Nordin and Ricardo Flores provided valuable research assistance. Many thanks to AuroraGallego and Nikos Georgantis for letting me use the LEE (Laboratori d’Economia Experimental) of theUniversidad Jaume I of Castellon, Spain, and to Juan Gómez Pérez for the technical help. The financialsupport from an EU Marie Curie Fellowship and the Russell Sage Foundation (grant #: 98-04-05) isgratefully acknowledged. Any opinions, findings, and conclusions or recommendations in this material arethose of the author and do not necessarily reflect the views of the European Commission or of the RusselSage Foundation.

M. Casari (*)Department of Economics, University of Bologna, Piazza Scaravilli 2, 40126 Bologna, Italye-mail: marco.casari@unibo.it

In a medical study, pregnant women were asked 1 month before delivery whetherthey preferred to have anesthesia during labor. The anesthesia would offer immediatepain relief but would also expose the newborn to a small risk of long-term sideeffects. Most women preferred to avoid anesthesia. Despite their earlier statements,during active labor many did choose anesthesia over pain (Christensen-Szalanski1984). Had they had a choice 1 month prior to delivery, would they have signed astatement committing to withhold anesthesia? Or, would they have been willing topay to have the opportunity during labor to change their previous choice?

This paper provides experimental evidence regarding similar types of decisions,but in situations involving money. Intertemporal decisions have recently receivedconsiderable attention from behavioral economists (for a review, see Frederick et al.2002). We provide and discuss new empirical evidence regarding preferences forpre-commitment and flexibility, which is important to discriminate betweencompeting models of time discounting.

Typically, empirical studies focus on subjects’ discount rate for short and longtime horizons:

(a) Would you prefer $100 in 2 days or $110 in 2 months?(b) Would you prefer $100 in 1 year and 2 days or $110 in 1 year and 2 months?

Most participants in experiments prefer $100 in 2 days in (a), and then reversetheir choice by preferring $110 in 2 months in (b). In line with this finding, in ourstudy about 65% of participants reversed their choices over time. Under thecanonical exponential discounting model, such choices are interpreted as timeinconsistent behavior (Thaler 1981; Benzion et al. 1989; Loewenstein 1987;Chapman 1996).1 Scholars have attributed this choice reversal to discount ratesdeclining for longer time horizons and put forward alternative discounting functions(Kirby 1997; Ainslie 1992; Ainslie and Haendel 1983). The present study does nottest for the best functional form of discounting but investigates what type of motivecauses choice reversal.2 To this end, we elicit preferences for pre-commitment:

(c) Would you prefer $109 in 1 year and 2 months, or being able to choose 1 yearfrom today, between $100 in 2 days or $110 in 2 months?

If a subject that previously reversed her choice now prefers $109 in 1 year and2 months, she reveals a strict preference for commitment, i.e. to restrict her futurechoice set.3

Understanding whether decision makers are willing to pay to restrict their choiceset is relevant for several reasons. First, if time-inconsistent agents will improve theirwelfare through commitment, then the practical impact of time inconsistency may be

1 Harrison et al. (2002) and Rubinstein (2003) and others have questioned this finding. Pender (1996)explains it through a seasonality effect. Notice that when choices are defined over sets of outcomes andnot over single outcomes, choice reversal can originate from dynamically consistent preferences (Gul andPesendorfer 2001).2 For a comparison among alternative discounting functions see Benhabib et al. (2006) and Tanaka et al.(2005).3 Strotz (1955) introduced the expression “strategy for pre-commitment.” In this paper we will use pre-commitment and commitment interchangeably.

118 J Risk Uncertain (2009) 38:117–141

quite limited. Given voluntary commitment, policy makers’ roles would simply be toensure that time-inconsistent agents have access to cheap commitment options. Onthe contrary, if agents are unaware of their inconsistency (naïve), they will notvoluntarily commit (Strotz 1955; O’Donoghue and Rabin 1999). In this case,optimal policies may call for strict constraints on choice sets.4 Although theimplications of naïveté or sophistication are profound, the behavioral evidence is stillquite limited (Ashraf et al. 2006; Ariely and Wertenbroch 2002; DellaVigna andMalmendier 2006; Benartzi and Thaler 2004). The first contribution of this paper isto present empirical evidence on the degree to which the preference for commitmentis common. Second, while choice reversal over time may originate from inconsistenttime preferences, it may also be the result of uncertainty about future outcomes.Halevy (2008) is a recent contribution in this direction. In the example aboutpregnant women, both issues may be at work. On one hand, choice reversal may bedue to the temptation to ask for anesthesia that arises while experiencing pain. Givensuch a preference-based explanation, commitment could be an appealing option forthe decision-maker. An alternative explanation for choice reversal may be ignoranceabout the future level of pain. Only during labor does a woman realize the level ofpain, and only then can she make an informed choice about whether or not to takeanesthesia.5 Under this uncertainty-based explanation, commitment is never a goodoption. Far from being optimal, committing can prevent a decision-maker fromrevising a decision in light of new, relevant information. Actually, in the presence ofuncertainty, there may be a strict preference for flexibility, i.e. for a larger choice set.

We also elicited a person’s preference for flexibility:

(d) Would you prefer $111 in 1 year and 2 months, or being able to choose 1 yearfrom today, between $100 in 2 days or $110 in 2 months?

A novel aspect of this study is that subjects faced both commitment and flexibilitychoices. Hence, we were able to classify subjects into those that preferredcommitment, those that preferred flexibility, and those that were “in-between.” Wereport that about 60% of those who reversed their choice did commit. Moreover, thelower the cost of commitment the more subjects chose to commit. Interestingly,certain smoking habits were correlated with reversing choices and selectingcommitment. This evidence provides direct support for a preference-basedexplanation of choice reversal over time.

Among those who reversed their choices, 14% preferred flexibility and 26% were“in-between.” The minority of subjects who preferred flexibility suggests twoqualifications for the earlier conclusion in favor of a preference-based explanation.On one hand, this evidence rules out that the presence of uncertainty was the onlymotive for choice reversal over time. On the other hand, it shows that uncertainty

4 However, the welfare implications of commitment are not clear-cut. For one, by committing, an agentforgoes the value of flexibility. Moreover, it is sometimes unclear how to use the agent’s preferences forwelfare comparisons. In Gul and Pesendorfer (2001) the welfare criterion is clear: the agent “isunambiguously better off when ex ante undesirable temptations are no longer available.”5 Evidence is mixed on this point (Christensen-Szalanski 1984). In a follow-up interview 1monthpostpartum, many women regretted their choice and expressed their preference to avoid using anesthesia(support for the preference-based explanation). Women at their first childbirth experience were more likelyto reverse their choice than the average (support for the uncertainty-based explanation).

J Risk Uncertain (2009) 38:117–141 119

about future states was a relevant motive for some people. Finally, the subjectscharacterized as “in-between” did not clearly select either commitment or flexibility.Under a preference-based explanation, these subjects are considered “naïve” becausethey fell into temptation but were unaware of it. Being in the “in-between” categorywas also correlated with having lower intellectual abilities. In conclusion, accordingto our estimates, most subjects were “sophisticated” and not “naïve.”

The paper is structured as follows. Section 1 outlines the experimental designemployed, while Section 2 puts forward some theoretical predictions of uncertainty-based and preference-based models. Section 3 presents the results. Section 4 is aliterature survey. Conclusions follow in Section 5.

1 Experimental design and procedures

We studied the time preferences of 120 subjects recruited from the undergraduatepopulation of Jaume I University of Castellon, Spain.6 Each subject faced a series ofchoices between a smaller-sooner payment (SS) and a larger-later (LL) payment withdelays between 2 days and 22 months. Choices were divided into three parts: a firstpart to measure impatience, a second part to detect choice reversal, and a third part toassess preferences for commitment and flexibility. The procedures for parts one andtwo share similarities with the titration procedure used in Mazur (1987) and Kirbyand Herrnstein (1995). In all parts special attention was given to equalize the implicitcosts among alternative options. For instance, no option involved an immediatepayment, so subjects had to return to the lab to cash rewards no matter what thechoice was.

In part one, each decision had four parameters: the amount of the two possiblepayments and their delays. Both payment amounts were held constant throughout theprocedure at 100€ and 110€. The goal of part one was to elicit an approximate measureof impatience D* by fixing the delay of the smaller-sooner payment at 2 days, SS=(100€, 2 days), and varying the delay D of the larger-later payment, LL=(110€, D),up and down until the subject was approaching indifference between the twopayments. The main reason for eliciting D* was not to accurately estimateimpatience but to be able to individually calibrate choices in parts two and three.An example will clarify the procedure of part one. Consider a subject who selectsLL=(110€, 10 days) over SS=(100€, 2 days), but chooses SS over LL=(110€,17 days). In this example the point of the switch from LL to SS narrows down thesubject’s indifference point between the two options to a delay in between 10 and17 days. We take D*=17 as our measure of impatience, i.e. the waiting time in daysfor LL in that decision where the subject switches from LL to SS.7 To minimizetrembling hand mistakes, following the switch, one or two additional decisions were

6 Six sessions were run between April 26 and April 28, 2004. The actual last payment took place on May30, 2005. Recruitment was done through announcements in classes. Half of the subjects were women anda large majority was comprised of economics or business majors. Basic statistics on the samplecomposition are in Table 6 in the “Appendix”.7 Unless a subject has a discount factor of one, hence is perfectly patient, there always exists a longenough delay to induce the switch in favor of the sooner-smaller reward.

120 J Risk Uncertain (2009) 38:117–141

prompted with longer delays D, and answers had to confirm the switch for part oneto stop. Moreover, a list of all part-one decisions was presented and each one of themcould be changed before moving to part two.

In part two, subjects faced a series of decisions with a front-end delay (FED)added to both rewards SS and LL in order to detect possible choice reversals (Figs. 1and 2). The smaller-sooner reward maintained a consistent delay of FED+2 days andthe larger-later reward maintained a delay of FED+D* days, which ensuredthroughout part two that the waiting time difference between SS and LL wasconstant. The remaining parameters of the decisions were unchanged. This designincreased the chances to detect the presence of choice reversal patterns. To continuewith the example, part two would open with a decision with a FED of 7 daysbetween SS=(100€, 9 days) versus LL=(110€, 24 days). Assume that in thisopening decision the subject chose SS. Then the following choice would be (100€,16 days) versus (110€, 31 days). If the subject kept choosing SS, the FED wouldbecome progressively longer. If, instead, at this point a subject chose LL, suchchoice was the hint of a choice reversal. Following this switch from SS to LL, one ortwo additional decisions were prompted with longer FED delays, and the subject hadto confirm the switch in order for part two to stop. In case the choice reversal wasconfirmed, we define FED*, which in the example is 14 days, as the shortest front-end delay that induced the subject to reverse her choice from SS to LL. Theprocedure stopped in any case when the front-end delay FED exceeded 395 days.8

Finally, a list of all part two decisions was presented, and each one of them could bechanged before moving to part three. Throughout the experiment, particular care wastaken to avoid calendar effects, i.e. the inability or unwillingness to cash the rewardon a particular day because of events such as birthdays, examinations, or travelingout of town.9

SS: (100€, FED+2 days)

FED = Front-end delay

LL: (110€, FED+D days)

Decision

during the session

Fig. 1 Willingness to waitin parts one and two of theexperiment

8 Although the number of decisions in parts one and two could vary across participants, there was noadvantage for someone to finish earlier because that would not have changed the time the person couldleave the room. In part one, the elicited maximum wait D* was 276 days. In part two, the elicited front-end delay was between 7 and 395 days. The elicited furthest possible time of payment in the experimentwas 611 days.9 If payment fell on Saturday, Sunday, or an official holiday the delay was automatically adjusted eitherbackward or forward to make it easy for subjects to cash the reward. The summer period (July 25–September 5) was excluded, as well as Christmas vacations (December 22–January 6) and several othernational or local festive days (for example October 9 and 12, November 1, December 6 and 8, February27, March 19, May 1, June 29). Classes ran up to May 28, and then there were exams up to June 30. Theuniversity was closed in August. About 90% of the subjects’ families lived in the university town or in theregion (Valencia province). More details on the procedure can be found in Casari (2006).

J Risk Uncertain (2009) 38:117–141 121

Part three included eleven decisions aimed at measuring preferences forcommitment and flexibility (Table 1). These choices had two peculiarities. First,instead of only two alternative payments, each decision could involve either three orfour. Second, each decision comprised two choices that took place on two separatedays: one on the day of the experimental session and the other through email at alater date, sometimes months later. Part three gives interesting insights especially forthose subjects who reversed their choices.

In part three, a subject could either commit immediately to the larger-later reward{LL} or postpone the choice between a larger-later reward and a smaller-soonerreward, {LL, SS} (Table 1, decision 5). The commitment strictly eliminated thepossibility of later choosing another option: in particular, once made, it irreversiblyruled out the possibility at a future date to opt for SS. On the contrary, postponingthe choice allowed a subject to wait exactly FED* days and send an email stating apreference for either LL or SS.10 Amount and delays of payments were structured ina way to resemble decisions already made in parts one and two. In particular, in thelab a subject faced SS=(100€, FED*+2) versus LL=(110€, FED*+D*). Rememberthat the subject faced the same decision in part two, and those who reversed theirchoices chose LL. The subject could commit to LL and would need to send an emailafter FED* days. As an alternative, she could postpone the choice and, after havingwaited FED* days, she could send an email choosing between SS=(100€, 2) versusLL=(110€, D*). Remember that the subject faced this same decision in part one andchose SS. A commitment for LL at the time of the lab session reveals an awarenessof the future temptation to choose SS.

Part three included several variants of the choice above where a cost was addedeither to the restricted set {LL} or to the larger set {SS, LL} in terms of a lowerpayment amount or a longer delay. In one case, strict commitment was available forfree (decision 5), and in the other two cases it was available for the cost in terms of amodified restricted set {LL′}. In decision 7, LL′ offered a lower amount than LLwhile in decision 10 LL′ exhibited a longer delay than LL.

We also studied soft commitment using choices with four alternative rewards SS,SS′, LL, LL′. In the lab a subject selected one of the two sets, {SS, LL} or {SS′, LL′},and in a later email she chose an option within the set already selected (Fig. 3). In threecases LL′ = LL and SS′ offered either a lower amount (decisions 1 and 2) or a longer

Decision Later decision

during the session by email

LL (110€, FED*+D*)

LL’ (110€, FED* +D*)

SS (100€, FED* +2)

SS’ (98€, FED* +2)

Fig. 2 Soft commitment in de-cision 1 (Table 1)

10 It was explained that only replies arriving within two days before or after the specified day would beconsidered valid. Almost all of the responses were received on the specified day. The response rate was64.1%.

122 J Risk Uncertain (2009) 38:117–141

Tab

le1

Decisions

regardingcommitm

entandflexibility

intheexperiment

OptionA

OptionB

%choicesforop

tionBa

Sooner-sm

allerreward,

SS

Larger-laterreward,

LL

Sooner-sm

allerreward,

SS′

Larger-laterreward,

LL′

Delay,t

Amou

nt,€

Delay,t

Amou

nt,€

Delay,t

Amou

nt,€

Delay,t

Amou

nt,€

Softcommitm

ent

1.Monetarycost,low

FED*+2

100

FED*+D*

110

FED*+2

100−2

FED*+D*

110

12.8

2.Monetarycost,high

FED*+2

100

FED*+D*

110

FED*+2

100−6

FED*+D*

110

7.7

3.Monetarycost,high

FED*+2

100

FED*+D*

110

FED*+2

100−6

FED*+D*

110−2

10.2

4.Tim

ecost,low

FED*+2

100

FED*+D*

110

FED*+2+5(a)

100

FED*+D*

110

17.9

Strictcommitm

ent

5.Nocost

FED*+2

100

FED*+D*

110

FED*+D*

110

61.5

7.Monetarycost,low

FED*+2

100

FED*+D*

110

FED*+D*

110−2

17.9

10.Tim

ecost,low

FED*+2

100

FED*+D*

110

FED*+D*+2(b)

110

23.1

Flexibility

6.Monetarygain,low

FED*+2

100

FED*+D*

110−2

FED*+D*

110

87.2

8.Monetarygain,low

FED*+2

100−2

FED*+D*

110−2

FED*+D*

110

96.1

9.Tim

egain,low

FED*+2

100

FED*+D*+2(b)

110

FED*+D*

110

82.0

11.Tim

egain,low

FED*+2+5(c)

100

FED*+D*+5(d)

110

FED*+D*

110

89.7

Notes:In

partthreeof

theexperiment,subjectsfacedeleven

choices.Eachlin

ein

thetabledescribesachoice

betweenop

tionAandop

tionB.S

omeop

tions

includeafollo

w-up

decision

betweenasooner-smallerreward(SS)andalarger-laterreward(LL).D*Delay

indays

that

was

elicitedin

parton

e,FED*individu

alfron

t-enddelayin

days

elicitedin

parttwo.

For

“calendar”

reasonstheactualdelayof

rewards

may

have

been

differentforsomesubjects.D

elaysin

days

may

have

been

(a)5or

7;(b)2,

3,4;

46foron

esubject;

(c)between1and7;

0fortwosubjects;(d)5,

6,7,

andforfive

subjectsitwas

either

46or

50.In

nocase

was

thelaterrewardat

anearlierdate

than

theearlierreward.

Two

additio

naldecisionsweremadeaftertheeleven

listedabov

e;they

areno

treported

becausethey

areno

trelevant

forthepresentanalyses,12

:SS=(FED*+2,

100−5),LL=

(FED*+D*,

110),SS′=(FED*+2,

110−6)

and13

:SS=(FED*+2+2,

100),LL=(FED*+D*+2,

110),LL′=(FED*+D*+2,

110)

aBased

only

onsubjectswho

didreversetheirchoices(N

=78

)

J Risk Uncertain (2009) 38:117–141 123

delay (decision 4). In another case SS′ offered a substantially lower amount than SSand LL′ offered a slightly lower amount than LL (decision 3).

Finally, there were four choices regarding flexibility. These decisions wereformally similar to those pertaining to strict commitment (Fig. 3), but instead ofpaying a cost to restrict the choice set, a subject had to pay a cost to make it wider.More precisely, option LL involved a monetary cost (decisions 6 and 8) or a delaycost (decisions 9 and 11) with respect to option LL′.

The payments related to choices over time were never immediate. Subjects had tocome back at a future date at least 2 days after the session. Payments were made incash, hence no trip to a bank was necessary.11 For choices in part one, only oneparticipant per session received a large, delayed payment. There were 20 participantsin each session. A volunteer randomly drew a number out of a bag immediately atthe end of the session to select one of the lucky persons. The selected personreceived a signed letter on university letterhead promising a later payment of 100€ or110€. The exact date and amount of the actual payment reflected one of the subject’schoices in part one of the experiment. The choice paid out was selected through asecond random draw.12

For choices in parts two and three, the computer randomly selected one otherperson per session for a large payment between 94€ and 110€ and randomly selectedone choice in part two or part three. His or her name and the selected decision werenot immediately revealed to the participants. Instead, along with all participants’contact information, the name was placed in an envelope that was then sealed infront of them and signed by two subjects.13 Only the subjects who emailed theirfollow-up choices were eligible to receive this second large payment. In particular, achoice for commitment did not save the cost of sending an email at the pre-specified

Decision Later decision

during the session by email

LL (110€, FED*+D*)

LL’ (108€, FED* +D*+k)

t0

t1

SS (100€, FED* +2) Fig. 3 Strict commitment indecision 7 (Table 1)

11 A payment of 5.61€ ($6.68) per person was given right after the session. It included a 3€ show-up fee (2€in the first two sessions) and a performance-based fee for some correct answers in the questionnaire, asexplained in the result session. Another component is discussed in footnote 21. The exchange rate at the timeof the experiment was 1€ = $1.19.12 All post-session payments were carried out by the personnel affiliated with the Jaume I UniversityLaboratory of Experimental Economics (LEE). These personnel teach in the department of economics andconducted experiments and payments in previous experiments, so they were familiar to the subjects. Onlythe persons selected for the large payments had the burden of returning to collect money.13 The envelope was stored in the laboratory, and any participant could ask to have it opened when alldecisions and payments had been completed, which was several months later. This procedure gavecredibility to the promise of a later payment while maintaining an incentive for all subjects to send thefollow-up email. When the date of payment approached, the selected person was privately contacted toarrange an appointment for the payment day.

124 J Risk Uncertain (2009) 38:117–141

date, because a lack of a confirmation message would have precluded participationin the draw for the payment.

Subjects were seated at computer terminals and separated by partitions.Instructions were distributed and read aloud. First, instructions for a risk attitudetask were read and the corresponding decisions taken with pen and paper.14 Then,time choice instructions were read and the corresponding decisions were made viacomputers. Finally, a questionnaire was distributed. No communication amongsubjects was allowed. Including instruction and reading time, a session lastedbetween 2 and 2.5 h. Overall, the average payment per subject was 16.06€ ($19.11).

2 Predictions

This section outlines the predictions of alternative models of time discounting andputs forward five statements that provide guidelines to interpret the experimentalresults. The key question is what explains choice reversal. According to apreference-based explanation, an agent reverses her choice over time because shehas present-biased preferences, instead of exponential time preferences. Accordingto an uncertainty-based explanation, an agent reverses her choice over time becausefuture promises carry an implicit risk of default that is characterized by a declininghazard rate; alternatively, there may exist other forms of risk or uncertainty aboutaspects of the decisional situation, with similar consequences.15 The remaining partof this section will clarify these two explanations, which are not mutually exclusive.

With few exceptions, the empirical literature has discussed time preferenceswithin a “certainty” scenario, where there is neither risk nor uncertainty at futuredates about (a) actually receiving the reward, (b) the wealth position of the agent, (c)the agent’s preferences, and (d) other aspects of the decisional situation. We nowillustrate the predictions on choice reversal, commitment, and flexibility for anexponential and a hyperbolic discounter under a certainty and an uncertaintyscenario (Table 2). The “uncertainty” scenario is the most general situation.

All statements rely on the following standard assumptions. First, the instanta-neous utility ut(ct) of each agent does not change over time, i.e. ut(ct)=u(ct) for everyperiod t=0,…,T; second, the utility function increases in consumption, ∂u/∂ct>0;and, third, it is weakly concave, ∂2u/∂2ct≤0. In other words, the statements below donot rely on the instantaneous utility being linear in consumption. Consider a“certainty” scenario where the net present utility can be represented as

U0ðcÞ ¼X

t ¼ 0;...;TlðtÞuðctÞ ð1Þ

where c=(c0, c1,…,cT) is a consumption profile and l(t) is a discount function,which we normalize as l(0)=1. When an agent discounts exponentially, l(t)=δt,

14 Complete instructions are available upon request to the author. Elicitation of risk attitudes closelyfollowed the procedure of Holt and Laury (2002) and results are not reported here. Random draws andlottery payments were carried out at the end of the session.15 In Amador et al. (2006) agents expect to receive in the future relevant information regarding theirpreferences. Fernandez-Villaverde and Mukherji (2000) focus on possible shocks on income as it iscommon in the macroeconomic literature.

J Risk Uncertain (2009) 38:117–141 125

with a constant discount factor 0≤δ≤1, she will never reverse her choices (Table 2,line a). On the contrary, when the discount factor is not constant but depends on thehorizon, an agent with an established plan for a far-away future might not implementit as that future draws near (Strotz 1955). When the discount factor is smaller for short-horizon rewards than for long-horizon rewards, we refer to the agent as “present-bias.”We take hyperbolic discounting, l(t)=1/(1+k·t), with k>0, as the reference model forsuch preferences but the predictions apply more generally to many present-biasedmodels. For any hyperbolic discounter, one can construct a larger-later reward (LL)and a smaller-sooner reward (SS) that pay at a fixed, future date where today the agentprefers the LL and then, at some point in the future, the agent switches to the SS(Table 2, line b). When scholars reported empirical evidence of choice reversal overtime, it was rationalized as a preference-based phenomenon explained by hyperbolicdiscounting. This explanation is only one among many possible explanations.

Another prediction of hyperbolic discounting is that agents may be willing tocommit, i.e. given two sets of alternatives A and B choose the set B over A, whereboth set contain the same, best element, and where A is a superset of B (Akerlof1991; O’Donoghue and Rabin 2001; Gul and Pesendorfer 2001). Commitment isattractive because it removes future temptations to deviate from the established plan.The likelihood of commitment choices depends on two factors, which are nowbriefly discussed: the agent’s assessment of the extent of her future self-controlproblems and the cost of commitment. An agent is called “sophisticated” if she isaware of her future-self control problems, and “naïve” otherwise.

Statement 1. Under a preference-based explanation, a sophisticated agent whoreverses her choice over time may be willing to commit, while anaïve agent who reverses her choice over time is never willing tocommit.

A sophisticated, hyperbolic discounter may commit or not depending on the priceat which she can buy commitment. For instance, if the net present value forgone bycommitting is higher than the maximum willingness to pay to avoid temptation, thena hyperbolic discounter will not commit.

Table 2 Predictions of different models of time preferences

Any possible case ofchoice reversal? (1)

Possible willingness topay for commitment? (2)

Possible willingness topay for flexibility? (3)

Certainty scenarioa) Exponential discounting No No Nob) Hyperbolic discounting Yes Yesa NoUncertainty scenarioc) Exponential discounting Yes No Yesd) Hyperbolic discounting Yes Yesa Yes

Notes: The table does not explicitly list the quasi-hyperbolic discounting model. If a 2-day delay is stilltreated as “present” then the quasi-hyperbolic model yields similar predictions in this experiment as thehyperbolic model. If not, predictions are the same as the exponential discounting model. In this paper weassume that a delay of up to 2 days is considered “present” and so the quasi-hyperbolic and hyperbolicdiscounting models yield similar predictionsa Stands for “yes” if the agent is sophisticated and for “no” if the agent is naïve

126 J Risk Uncertain (2009) 38:117–141

Statement 2. Under a preference-based explanation, the higher the cost ofcommitment, the less frequently sophisticated agents subject totemptation will choose to commit.

In an uncertainty scenario statements 1 and 2 still hold but the above analysisbecomes richer. There exist forms of uncertainty for which choice reversals overtime can be a rational path for an exponential discounter. What uncertainty cannotexplain is why the exponential discounter chooses to pay for commitment.16 Toillustrate the effect of uncertainty, we will focus on the case of implicit default risk ofthe promise to deliver the reward. Such promise may lack credibility and the rewardmay fail to materialize entirely or arrive with delay (Benzion et al. 1989; Dasguptaand Maskin 2005). There may also be a chance of the agent being unable to cash thereward because of unforeseen logistical obstacles, such as having to leave on a businesstrip or simply losing a coupon for a spa massage. Under this uncertainty scenario, timediscounting is the product of time preferences and of the likelihood of the consumptionin a given time period, s(t). The expected net present utility can be represented as

E½U0ðcÞ� ¼X

t ¼ 0;...;TlðtÞsðtÞuðctÞ ð2Þ

Uncertainty has three important implications. First, for some probability distributionsof s(t), an exponential discounter may rationally reverse her choice over time. Considerthe following example adapted from Sozou (1998). Bob has to choose between twopromises from Jim: a promise of a cake and of a bottle of wine. Assume that Bobvalues the wine w more than the cake c, u(w)=3, u(c)=2, and that he has a belief aboutthe likelihood of actually receiving the item from Jim, which models promises withhigher delays as less credible, more precisely, s(t)=1/(1+t) where t is the delay inmonths. If Bob is risk neutral and perfectly patient, λ(t)=1 he will prefer a promise ofwine in 3 months over a promise of a cake in 2 months, 1/4 u(w)>

1/3 u(c). Yet, after2 months have passed he will reverse his choice and prefer the cake to the wine in amonth, 1/2 u(w)<u(c).

Statement 3. Both uncertainty-based and preference-based explanations canrationalize choice reversal over time.

A dynamically consistent agent may reverse her choices over time when thepromise to deliver the reward has a default risk characterized by a hazard rate, s(t),declining over time, like in the example described above. Hence, when observingchoice reversal without observing the subjective distribution of the default risk, onecan still hold the assumption that the decision-maker is an exponential discounter(Sozou 1998). Situations characterized by declining hazard rates include, forinstance, students dropping out of high school (Mortenson 1999) or start-up firmsgoing bankrupt (Bartelsman et al. 2005). It is important to notice that not any defaultrisk will produce choice reversals in our experimental setting, but just a very specificform of it. For a constant or an increasing hazard rate for s(t) of the default risk,choices of an exponential discounter should never exhibit choice reversal.

16 Under an uncertainty scenario, an exponential discounter who reverses her choices over time will nevercommit, hence becoming observationally equivalent to a naïve agent.

J Risk Uncertain (2009) 38:117–141 127

The second implication is that to reject a model of exponential discounting one needsmore than simply to observe choice reversals over time. While in a certainty scenarioexponential and hyperbolic discounting makes distinct predictions about choice reversal(Table 2, lines a and b), the two models become more difficult to distinguish in anuncertainty scenario (Table 2, lines c and d). Predictions about choices forcommitments, instead, are not qualitatively affected by the uncertainty scenario(Table 2, col. 2). Statement 4 illustrates this second, important implication of uncertainty.

Statement 4. In an uncertainty scenario, an exponential discounter who reverses herchoice over time will never commit, while a sophisticated hyperbolicdiscounter may be willing to commit.

The third implication of an uncertainty scenario is that an agent may exhibitpreference for flexibility. An agent with a preference for flexibility prefers any set ofalternatives to its subsets, even when two of them contain the same best element(Kreps 1979; Barberà and Grodal 2003). When some resolution of uncertainty willtake place before the time of the SS reward, an agent expects a benefit frompostponing her decision and will exhibit a preference for flexibility. As column (3)of Table 2 makes clear, not only exponential discounters but also hyperbolicdiscounters may be willing to pay for flexibility. Choices for flexibility are not directevidence against hyperbolic discounting; they are evidence that uncertainty plays animportant role in the choice between the SS and the LL rewards.

Statement 5. In a certainty scenario, neither exponential nor hyperbolic discounterswill be willing to pay for flexibility.

3 Results

We report five main results.

Result 1. About 65% of subjects reversed their choice over time.

Among the 120 subjects, the median willingness to wait for 110€ over 100€ was14 days.17 78 subjects reversed their choice when adding a front-end delay (FED).The median subject that reversed her choice did so with a FED of 42 days. Only 12subjects never reversed their choice (10%). The remaining 30 subjects were hard toclassify. Their choice patterns were difficult to interpret because of a lack ofconfirmation regarding their final choice or various switches between LL and SS.18

17 This experiment offered an investment technology. If the yields of the investment were better than themarket rate, subjects may have simply borrowed from the field and invested in the lab. If such trading tookplace, the revealed experimental choices would show an upper bound in willingness to wait defined by themarket borrowing rate. Results did not reflect this upper bound because our subjects had a rather limitedaccess to credit markets. More details in Casari (2006, 2008) and a general discussion in Cubitt and Read(2007).18 In the transition from part one to part two, seven subjects experienced software problems and 23subjects exhibited erratic behavior. Example: a subject ends part one confirming her choice for SS; on thefirst decision of part two she chooses LL, hence showing choice reversal. Yet, she then chooses SS, thenLL again, and eventually ends up confirming LL, i.e. a consistent choice.

128 J Risk Uncertain (2009) 38:117–141

Possible reasons for this erratic behavior are confusion and calendar effects. Wefound no correlation between being hard-to-classify and making mistakes in otheraspects of the experiment or having low intellectual skills.19 We attribute the erraticbehavior primarily to calendar effects.

It is possible that an even higher fraction of people would have reversed theirchoices. To begin with, no hard-to-classify subject was included in the 65% figure.Moreover, choice elicitation was limited by the time horizon given in theexperiment. Many low discounters may have eventually reversed their choice hada longer FED been proposed. This point is confirmed by the probit regressions ofTable 3, which are carried out both including and excluding the hard-to-classifysubjects. People with the longest willingness to wait (60 days or more) were lesslikely to reverse their choices, and those with the shortest willingness to wait weremore likely to reverse their choices.20

We found a relation between smoking habits and time preferences over monetaryrewards. In our sample, 60 subjects smoked at some point while 59 subjects neversmoked (habit unknown for one subject). Among the former group, 20 never tried tostop smoking. Of those who did try, 12 were successful (former smokers) while 26were not successful (habit unknown for the two remaining subjects). Table 3 shows astrong positive correlation between never having tried to stop smoking and doingchoice reversal.21

Result 2. About 60% of those who reversed their choice did commit.

Table 1 lists choices for flexibility and commitment for the 78 people who didreverse their choice. Based on those results, we conclude that 60.2% of the subjectshad preferences for commitment.22 According to Statement 4, this is evidence infavor of a preference-based explanation of choice reversal. We divided subjects intofive categories according to their choices:

A. One or more choices for commitment, never for flexibilityB. Propend for commitment, also choices for flexibilityC. Never for commitment, never for flexibilityD. Propend for flexibility, also choices for commitmentE. One or more choices for flexibility, never for commitment

19 There is no systematic correlation between being hard-to-classify and being inconsistent in risk attitudechoices, getting all compound interest questions wrong, having a low admission score to college (nota deselectividad), or not sending an email. These results come from an unreported probit regression.20 In Table 3, col. (2) regressors are dropped by the statistical package Stata with the message that it“predicts success perfectly.” This event is informative about the relation between the regressor and thedependent variable. More precisely, when the subject is willing to wait less than 7 days for the largerreward in part one, it is always the case that the subject reversed her choice in part two.21 Table 3, col. (2). A smoker who never tried to quit is always reversing her choice. See also the previousfootnote.22 The money may be spent long after it was received. The experimenter knows the time of the paymentsbut not the time of the actual consumption. There were cues that the upcoming weekend constituted thatmoment for many participants. While the timing of actual consumption is crucial to estimate discountrates, less stringent conditions are needed for the purpose of studying commitment and flexibility. Thedelay between payment and consumption can be positive and can be different between SS and LL.

J Risk Uncertain (2009) 38:117–141 129

Category assignment was based on a commitment and a flexibility score. Thecommitment score is a number between 0 and 100 based on the seven commitmentdecisions (1–5, 7, and 10) and the four flexibility decisions (6, 8, 9, and 11) ofTable 1. Such a score is 100 for a subject who committed in one or more decisionsand never chose in favor of flexibility (category A). The score is 0 when there wasnever commitment (C and E). When some choices were for commitment and somefor flexibility, the overall propensity was established by balancing the fraction ofchoices in both directions. A higher fraction of commitment choices (out of seven)than for flexibility (out of four) suggested a propensity for commitment (B) and thedifference defined the commitment score. If the opposite was true, the commitmentscore was 0 (D). Figure 4 illustrates the commitment index and the categorybreakdown.

The number of subjects classified for commitment (A=47) is fairly robust. Whenone drops one of the eleven questions used in the classification, one question at atime, the number of subjects varies between 46 and 50, with the exception of

Table 3 Probit regression results for the determinants of choice reversal

Dependent variable: 1 = subjectwho reversed her choice, 0 = all others

Full sample (1) Excluding hard-to-classify subjects (2)

The subject is willing to wait between 0 and 4extra days to obtain the larger reward

0.3010 (0.0980)b –a

The subject is willing to wait between 5 and 7extra days to obtain the larger reward

0.0393 (0.1368) –a

The subject is willing to wait between 15 and 30extra days to obtain the larger reward

0.0723 (0.1421) −0.1393 (0.1600)

The subject is willing to wait between 31 and 60extra days to obtain the larger reward

0.1746 (0.1193) −0.0740 (0.1260)

The subject is willing to wait more than 60extra days to obtain the larger reward

−0.2325 (0.1716) −0.3567 (0.2029)c

Male −0.0131 (0.1008) −0.0193 (0.0744)Credit constraints −0.0131 (0.1190) 0.0598 (0.0977)Able to compute compound interest −0.0542 (0.1123) −0.0973 (0.0957)College admission score, lowest quartile 0.0808 (0.1054) −0.0122 (0.0832)Smoker, never tried to quit −0.1519 (0.1444) –a

Smoker, tried to quit unsuccessfully 0.1046 (0.1159) −0.0936 (0.1053)Former smoker −0.1160 (0.1667) −0.2402 (0.1923)Observations (no. subjects) 120 90

Notes: The dependent variable codes whether subjects in part two reversed the choices they made in partone. More precisely, the dependent variable equals 1 if there is a choice reversal by the subject and 0otherwise. The dependent variables include part one choices and questionnaire answers. The table reportsthe marginal effects of probit regressions with standard errors reported in parentheses. The five dummyvariables “the subject is willing to wait...” are proxies for the subjects’ impatience levels and code part onechoices. The default behavior in the probit regression is an extra 8–14-day wait for obtaining the largerreward. The dummy variable “ Credit constraint” equals 1 if th self-reported chances of getting either abank loan or a credit card are less than 90%. The dummy variable “Able to compute compound interest”equals 1 if the subject correctly computed the compounded interest in three paid, multiple-choicequestions; sessions dummies are included in regression but are not reported in the Tablea Variables dropped from the regressionb Significant at 1% levelc Significant at 10%

130 J Risk Uncertain (2009) 38:117–141

question 5 that was on strict commitment without cost. Without question 5, thealternative breakdown in categories is A′=27, B′=4, C′=29, D′=4, E′=14, andhence 34.6% of subjects are classified for commitment instead of 60.2%. This largeswing may suggest that subjects were particularly sensitive to the explicit cost of thecommitment technology offered. A discussion of this point follows Result 4. Weincluded question 5 in the classification, because in an uncertainty scenariocommitment always carries the implicit costs of the forgone flexibility.

From a similar sensitivity analysis, it emerges that strict commitment was moreattractive than soft commitment. A classification that excludes all soft commitmentquestions reduced A from 47 to 43 people while the exclusion of all strictcommitment questions reduced A from 47 to 16. Removing the temptation of SSwas valued more than simply reducing its attractiveness.

Result 3. About 14% of those who reversed their choice were willing to pay forflexibility.

We find that 11 subjects show a preference for flexibility. Figure 4 illustrates theassignment in categories based on a flexibility score.23 According to statement 5, Result3 highlights the importance of uncertainty in the choice of at least a significant minorityof subjects. The number of subjects classified for flexibility (category E) varies betweenseven and 14 (9% and 17.9%) when one drops one of the eleven questions from Table 1used in the classification, one question at a time. The biggest impact comes fromquestion 9, where there is a small-time cost associated with flexibility. Without thatquestion, E was reduced from 11 to 7.

Table 4 presents a probit regression that examines the characteristics of subjects witha preference for flexibility. Because of the large difference made by the question oncostless commitment in the classification of subjects, regression results are presented fortwo distinct classifications: one based on all eleven Table 1 questions and another basedon ten questions only (col. 2 and 5). Smoking habits are correlated with choices for

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Flexibilityscore

Commitmentscore

A=47 B=5 C=8 D=7 E=11

Fig. 4 Classification of the sub-jects who reversed their choice.Notes: The 78 subjects whoreversed their choices over timewere sorted into five categories,A, B, C, D, and E based on thedecisions in Table 1. For in-stance, category A includes sub-jects who never chose flexibilityand who chose commitment in atleast one decision in Table 1.The classification relies on acommitment score and a flexi-bility score explained after Re-sult 2 and employed also inTable 4

23 The score is 100 for a subject who chose flexibility in one or more decisions and never committed (E). Thescore is 0 when there was no choice for flexibility (A and C).When some choices were for commitment and somefor flexibility, the overall propensity was established by balancing the fraction of choices in both directions. Ahigher fraction of flexibility choices than for commitment suggests a propensity for flexibility (D) and thedifference defines the commitment score. If the opposite is true, the flexibility score is 0 (B).

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Table 4 Probit regression results for the determinants of commitment and flexibility

Subjects’ classification

based on Table 1 choicesMain classification Classification without question 5

Dependent variable:

1=subject in the categoryindicated, 0=all others

(the figures are the no. ofsubjects in the category)

(1)

Commitment

A=47

(2)

Flexibility

E=11

(3)

No

commitment

nor

flexibility

C=8

(4)

Commitment

A’=27

(5)

Flexibility

E’=14

(6)

No

commitment

nor

flexibility

C’=29

0.128 0.959 -0.105

0.088 0.165 -0.210

The subject is willing towait between 0 and 4extra days to obtain thelarger reward (0.206) (0.118)a (0.057)c (0.211) (0.243) (0.150)

-0.192 0.775 -0.126 0.228 -0.177The subject is willing towait between 5 and 7extra days to obtain thelarger reward

(0.198) (0.264)a (0.156) (0.215) (0.157)

0.021 0.948 0.055 -0.151 0.237 0.045The subject is willing towait between 15 and30 extra days to obtainthe larger reward

(0.215) (0.107)a (0.064) (0.174) (0.244) (0.220)

0.034 -0.000 -0.160 -0.026 0.261The subject is willing towait more than 30 extradays to obtain the largerreward

(0.179) (0.000) (0.152) (0.098) (0.204)

Male -0.123 -0.000 -0.020 0.002 0.034 -0.151

(0.132) (0.000) (0.066) (0.132) (0.081) (0.132)

Credit constraints -0.147 0.000 0.039 0.115 0.097 -0.191

(0.151) (0.000) (0.060) (0.143) (0.064) (0.192)

Able to compute -0.246 0.935 -0.009 -0.124 0.448 -0.195

compound interest (0.149)c (0.073)a (0.067) (0.137) (0.163)a (0.127)

College admission score, -0.004 -0.000 0.079 -0.257 -0.098 0.374

lowest quartile (0.143) (0.000) (0.082) (0.111)b (0.057)c (0.142)a

Smoker, never tried 0.124 (d) 0.013 0.155 -0.033 -0.046

to quit (0.165) (0.102) (0.187) (0.082) (0.177)

Smoker, tried to quit 0.037 0.000 -0.065 -0.023 -0.044 -0.112

Unsuccessfully (0.154) (0.000) (0.051) (0.141) (0.069) (0.151)

Former smoker -0.044 -0.000 0.059 -0.208 -0.053 0.157

(0.247) (0.000) (0.136) (0.164) (0.087) (0.255)

Observations (no. subjects) 78 78 78 78 78 78

Notes: The dependent variable is based on the classification of subjects into categories based on commitmentand flexibility choices. More precisely, each column originates from a binary coding of Table 1 choices.Categories in columns (1)–(3) reflect those in Figure 4. Categories in columns (4)–(6) are explained in thetext after Result 2. The two classifications were included to evaluate the robustness of the results. The tablereports the marginal effects of probit regressions with standard errors reported in parentheses. Theindependent variables include part one choices and questionnaire answers and are explained in the notes toTable 3. In column (3) some categories for “The subject is willing to wait...” have been aggregated becausetoo few observations were available. Session dummies are included in regressions but are not reporteda Significant at 1% levelb Significant at 5% levelc Significant at 10% leveld Variables dropped from the regression

132 J Risk Uncertain (2009) 38:117–141

flexibility. Smokers who never tried to quit are less likely to choose for flexibility. Thereis no reason for smokers with consistent preferences to do that, although smokers whoregret their smoking habit may want to avoid situations where they are exposed to futuretemptations. Table 5 confirms that smokers who never tried to quit are relatively morelikely to commit and relatively less likely to choose for flexibility.24 The econometricmodel in Table 5 will be explained in a moment.

Result 4. The higher its cost, the less people chose to commit.

Support for Result 4 is provided in Table 5, which presents the results of probitregressions to explain whether a subject made a choice for commitment rather than forflexibility. According to statement 2, this finding is in line with a preference-basedexplanation of commitment. In Table 5 the dependent variable is 1 when option B in aline of Table 1 is chosen and is 0 otherwise. This new analysis complements Table 4 in atleast four ways. First, it includes all 11 observations for each individual and not just asummary score. Second, it does not rely on the above classification of subjects in types.Third, it estimates preferences for commitment and flexibility jointly. Fourth, itincorporates the subjects’ net present cost of commitment and flexibility by employingsubjects’ impatience levels.

The regressors dloss and dflex were constructed as follows. For each option {SS”,LL”} in Table 1, it is possible to compute how much worse is the LL” available incomparison to LL=(110€, FED*+D*). The loss is computed in terms of net presentvalues, [NPV(LL”)−NPV(LL)]/NPV(LL), based on the level of impatience that thesubject revealed in parts one and two of the experiment.

The flexibility measurement flex depends only on the relative timings of SS” andLL”. The flexibility measure is set to 0 when SS” in unavailable or has the same delayas LL” and is set to 1 when facing SS versus LL. The flexibility measurement is largerthe further apart the two rewards are from one another, f(SS”, LL”)=(D(LL”)−D(SS”))/(FED*+2). The measurement is normalized as flex=f(SS”, LL”)/f(SS, LL).

Table 5 employs two different discounting models to compute the net present value ofthe loss and temptation measurements. The calibration of these discounting models wascarried out to roughly scale the cost of commitment and flexibility given the wideindividual differences in willingness to wait. The aim of the calibration was not toprecisely assess individual impatience levels. Because such calibration relies on theassumption that utility is linear in money, two different specifications are used to check forrobustness, one with a hyperbolic and one with quasi-hyperbolic discounting.25

24 In Table 4, col. (2) a regressor is dropped by the statistical package Stata with the message that it“predicts failure perfectly.” When the subject is a smoker who never tried to quit, it is never the case thatthe subject is in the flexibility category E.25 In the first column of Table 5, the net present values are derived after calibrating a hyperbolic discountingmodel. For each subject who reversed her choices, there is one parameter to estimate, k. The calibration employedthe four choices coming from the decision immediately preceding and the one immediately following the SS/LLswitch in parts one and two of the experiment. Each choice provided either a lower or an upper bound for k. Ourestimate for k is the average of the minimum upper bound and the maximum lower bound. The calibration ofthe quasi-hyperbolic model in the second column employs the above, four choices to estimate two parameters, βand δ. First, δ is estimated as the average of the values from the two choices in part two. This δ is used forestimating β from the two choices in part one (average). A delay of up to 2 days is considered present for thiscalibration of the model.

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The regressors include the relative loss of the commitment option in comparisonto the alternative (dloss equals loss for option B minus loss for option A) and therelative flexibility (dflex equals flex for option B minus flex for option A). Results inTable 5 are in the expected direction; they are in line with the findings of Table 4 andare robust to the specific discounting model employed. The positive coefficient ondloss suggests that the larger the loss on B the less B choices were observed. Thenegative coefficient for dflex suggests that relative to more flexibility of A, fewer Bchoices were observed. Moreover, when question 5 is removed from the regressionsof Table 5, the above results do not change. Moreover, subjects that answeredcorrectly to all three compound interest questions committed significantly less thanthe others. Each correct answer paid fifty cents.26 As Table 4 clarifies, this result isdriven by a strong demand for flexibility from subjects who answered correctly.Interestingly, “smokers who never tried to quit” commit more than others.

We now do a short digression on the experimental procedure. The design adoptedfor this study presented both advantages and drawbacks. The procedures of part oneand part two elicited accurately the minimum front-end delay that induced choicereversal, subject by subject. As individuals’ willingness to wait and to reversechoices were widely different, this calibration was extremely useful for detectingpreferences for commitment. Moreover, the procedure stopped after a reasonablemaximum delay and did not force choice reversal on subjects.

Table 5 Probit regression results on single choices for commitment vs. flexibility

Dependent variable: 1 = choice for option B0 = choice for option A (Table 1)

Hyperbolicdiscounting

Quasi-hyperbolicdiscounting

Dflex −0.4951 (0.0640)a −0.6425 (0.0557)a

Dloss 19.0512 (2.0361)a 4.1720 (1.1146)a

Male 0.0290 (0.0517) 0.0232 (0.0405)Credit constraints −0.0438 (0.0770) −0.0310 (0.0636)Able to compute compound interest −0.1969 (0.0661)a −0.1560 (0.0529)a

College admission score, lowest quartile 0.0340 (0.0515) 0.0277 (0.0419)Smoker, never tried to quit 0.1171 (0.0635)b 0.1399 (0.0483)a

Smoker, tried to quit unsuccessfully −0.0614 (0.0780) 0.0663 (0.0641)Former smoker −0.0791 (0.0644) −0.0254 (0.0636)No. observations 858 858No. subjects 78 78

Notes: The table reports the marginal effects of a Probit regression with robust standard errors inparentheses (clusters on individuals). For each individual the regression considers the eleven choices listedin Table 1. The dependent variables include the relative loss for option B versus option A in terms of netpresent value (dloss), the relative date flexibility associated with option B versus option A (dflex), andquestionnaire answers. More details are in the text after Result 4. Sessions dummies included in regressionbut not reported in the table. See also notes to Table 3a Significant at 1% levelb Significant at 10%

26 For each question, there was a list of six possible answers: (S) If your initial capital was 1,000 euros,what is your final capital after 6 years at 5% interest rate? €1,340, 50.0% of answers were correct; (T) Ifyour final capital in 10 years will be 10,000 euros with 8% interest rate, what is your initial capital?€4,630, 35.8% correct; (U) If your initial capital was 500 euros and your final capital after 5 years is 1,000euros, what is the interest rate? 15%, 40.0% correct. A hand calculator was provided. Out of 120participants, 45.8% all wrong answers.

134 J Risk Uncertain (2009) 38:117–141

A drawback of the design was the possibility that subjects manipulated the procedure.Because earlier choices were employed to generate future decisional situations, a subjectcould have lied in the earlier parts of the experiment in order to be prompted with morefavorable future choices. More precisely, in our design an exponential discounter had anincentive to reveal a lower willingness to wait, to reverse her preferences, and not tocommit.27 This required that the subject knew how the algorithm generated decisions,which was not explained in the instructions nor asked about by any subject. It shouldbe noted that if the adopted design had biased results it would be against expressingpreferences for commitment. Hence, the fraction of subjects committing (Result 2)should be interpreted as a lower-bound for the true preferences for commitment, whichstrengthens the support for preference-based models.

Result 5. Under the assumption that subjects reversed their choices because of theirpreferences, at least half of them were sophisticated and not naïve.

If everyone engaging in choice reversal was subject to temptation, with theexception of those paying for flexibility (category E or E′), the data can be employedto estimate the fraction of sophisticated subjects following statement 1. An upperbound estimate of 77.6% of sophisticated subjects results from the categorybreakdown based on all Table 1 questions and considers all those who reversedtheir choices and then engaged in some costly or free commitment. A lower boundestimate of 54.7% comes from the alternative category breakdown. The lowerbound estimate excludes the question on costless commitment (no. 5 in Table 1)and counts all those who reversed their choices and then engaged in some costlycommitment.28

Warner and Pleeter (2001) found that impatience is correlated with lowintellectual skills. Constructing future scenarios for decision-making is a cognitivelydemanding task, and people with lower intellectual skills may focus more on thepresent. Our results are coherent with this perspective. We find that the intellectualability of subjects is correlated with commitment and flexibility behavior. We adopttwo measures of skill. First is the admission score to college (i.e. nota deselectividad, similar to SAT), which was self-reported by 91% of the participants.In Tables 4 and 5 it is coded as a dummy variable with a 1-value for subjects in thelowest quartile of our sample and 0 otherwise. Second is the ability to computecompounded interest that was measured in the questionnaire. The ability score was 1if a subject answered correctly three numerical questions (29.1% of sample). Underthe conjecture that the higher the skills the better is the ability to deal with futurescenarios, some interesting interpretations of the empirical findings may result.

27 In part one, just one randomly selected decision was paid. Hence, the longer the sequence of decisions,the worse was the expected payment in terms of delay. As a consequence, there was a slight incentive toreveal a lower willingness to wait than the true one.

28 For the lower bound: (A’+B’+D’)=35 subjects and (A’+B’+C’+D’)=64 subjects, hence 54.7%. In theuncertainty scenario, dynamically inconsistent subjects may sometimes want to choose for flexibility,which is why categories B, B’, D, and D’ are included in the calculations. Another possible lower bound,(A’+(A−A’)/2)=37, which includes half of the subjects that may have chosen to commit at no cost simplybecause they were indifferent (naïve subjects are indifferent regarding committing or not in the certaintyscenario). For the upper bound: (A+B+D−C/2)=52 subjects and (A+B+C+D)=67, hence 77.6%. SeeResult 2 and Fig. 4.

J Risk Uncertain (2009) 38:117–141 135

Subjects expressing a preference for flexibility (category E) had higher intellectualabilities (Table 4) as measured by both proxies. A correct computation of compoundinterest correlates with significantly more choices for flexibility (col. 2 and 5). Lowadmission scores correlates with less frequent choice for flexibility (col.2).

Interestingly, subjects who never chose commitment or flexibility (category C) had alower intellectual ability than others.29 These participants reversed their choice butnever committed or paid for flexibility. The classification based on costly commitment(col. 6) shows a significant correlation to being in the lower quartile of the admissionscore. This finding suggests that at least some subjects were naïve hyperbolicdiscounters and not exponential discounters under the uncertainty scenario.

Evidence from Table 4 also suggests that subjects with a preference for commitment(category A) had average skills. In one specification, those in the lower quartile ofadmission scores were significantly less likely to commit (col. 4) while in anotherspecification the top performers in terms of compound interest were less likely tocommit (col. 1).

4 Literature review

The focus of this paper is on commitment and flexibility in decisions over time.Through commitment an agent restricts the range of future choices and throughflexibility expands it (Rachlin 2000). We are not aware of any study jointlyanalyzing choices for commitment and flexibility. Most of the field studies oncommitment lack the controls of experiments and most of the experimental studiesare carried out with animals. DellaVigna and Malmendier (2006) show how peopleenroll in health-club memberships but do not visit the club regularly, and thereforepay more than a per-visit fee. Benartzi and Thaler (2004) look at a program thatallows workers to commit in advance to allocating a portion of their future salaryincreases toward retirement savings and report an increased saving rate for thosewho did commit versus those who did not commit. Ariely and Wertenbroch (2002)report that students in executive education programs who rely on self-imposeddeadlines earned better grades than those who did not. In a field experiment,Ashraf et al. (2006) report that women who did choice reversal over time inhypothetical questions were more likely to open a bank account with features thatrestricted access to their funds for a period of time. Most of the experimentalstudies on commitment were performed with animals. Rachlin and Green (1972)studied how hungry pigeons can make a decision to strictly commit or not based onchoices for different amounts of food with delays of seconds. If they do notcommit, they can later choose between a smaller-sooner reward or a larger-laterreward. If they commit, only the larger-later reward is available. Many pigeons docommit. Similar results were found by Ainslie (1974), Navarick and Fantino(1976), and Ainslie and Herrnstein (1981). In addition, Green and Rachlin (1996)report frequent choices for soft commitment among pigeons. Soft commitment

29 There was no correlation between choice reversal and low intellectual skills. When controlling for otherfactors, neither being able to compute compound interest nor having a low admission score to college weresignificant in explaining choice reversal (Table 3).

136 J Risk Uncertain (2009) 38:117–141

allowed pigeons to choose later between a smaller-sooner reward plus punishmentor a larger-later reward.

We have found only three experimental studies that deal with commitment where(a) participants were human beings, (b) participants were compensated, and (c)compensations took place with a real time delay. Solnick et al. (1980) explorechoices over sequences of a few minutes of irritating noise and study choice reversaland commitment. In Millar and Navarick (1984) and Fernandez-Villaverde andMukherji (2000) participants were required to play a few hours of video-gameswithin a fixed date and could chose the day in which to play the video-games. Theyfind little evidence of commitment strategies.

In the literature at least three classes of motives were mentioned to explain choicereversal: preference-based motives, the presence of uncertainties, or the use ofprocedural rules in decision-making. A crucial dimension where such models differis in their predictions over preferences for commitment.

Important preference-based models of choice reversal are hyperbolic discount-ing (Chung and Herrnstein 1967; Mazur 1987), quasi-hyperbolic discounting(Phelps and Pollak 1968; Laibson 1997), multiple selves (Thaler and Shefrin 1981;Fundenberg and Levine 2006), and, more recently, neuroeconomics models(Bernheim and Rangel 2004). Preference-based models generally allow for thepossibility that an agent can prefer to commit, provided the decision maker isaware of her self-control problems (Strotz 1955; Elster 1979; Akerlof 1991;O’Donoghue and Rabin 1999). General axiomatizations of choice reversals as apreference-based phenomenon are presented in Gul and Pesendorfer (2001) and Okand Masatlioglu (2003).

In the second class of models, agents have exponential time preferences and theexplanation for choice reversal is uncertainty-based. In all such models, commitmentis never optimal. In Sozou (1998), the decision maker is uncertain about her abilityto cash in the reward. Azfar (1999) and Halevy (2008) have extended these resultsfurther. In Dasgupta and Maskin (2005) choice reversal may come from waitingcosts and uncertainty over the actual timing of the reward. Preference-based anduncertainty-based models are not mutually exclusive.

Finally, in the third class of models, the available options are compared,attribute-by-attribute, following a specific procedure. An instance of such modelsis Read (2001), who argues that diminishing discount rates originate fromsubadditive discounting and not from diminishing impatience. Others includeRubinstein (2003) and Leland (2002), which propose an approach based onsimilarity relations. According to these models, subjects should express nopreference for commitment.

5 Conclusions

Behavioral economists have recently questioned the validity of exponentialdiscounting as a descriptive model of intertemporal choices (Ainslie and Haendel1983; Benzion et al. 1989; Chapman 1996; Pender 1996; Thaler 1981). This paperinvestigates why many subjects reverse their choices over time, which is a majoranomaly reported in time-decision experiments and replicated also in this study

J Risk Uncertain (2009) 38:117–141 137

(Result 1). To explain this anomaly, scholars have put forward models of non-exponential time preferences (Chung and Herrnstein 1967; Mazur 1987; Phelps andPollak 1968; Laibson 1997; Thaler and Shefrin 1981; Fundenberg and Levine 2006;Bernheim and Rangel 2004). Other scholars have questioned such preference-basedexplanations, and put forward uncertainty-based ones that interpret choice reversal asthe rational consequence of exponential discounters deciding under some forms ofrisk or uncertainty (Sozou 1998; Azfar 1999; Fernandez-Villaverde and Mukherji2000; Dasgupta and Maskin 2005; Halevy 2008).

We carried out an experimental study with monetary rewards offered and paidwith an actual time delay and where participants had opportunities to commit or optfor flexibility. Through revealed preferences for commitment or flexibility one canshed light on whether choice reversal is a preference-based or an uncertainty-basedphenomenon. There are three main contributions.

First, for many participants the explanation of choice reversal over time ispreference-based. This conclusion comes from widespread choices in favor ofcommitment (Result 2), which uncertainty-based explanations instead rule out(Statement 4). This evidence is compatible with many functional forms of present-biased preferences, including hyperbolic discounting.

Second, the demand for commitment was substantial and price-responsive. About60% of those who reversed their choice were classified as preferring commitment,which is the willingness to restrict the size of the choice set available in the future.Commitment always carries an implicit cost due to the uncertainty of the future. Asthe explicit cost increased, the frequency of commitment declined (Result 4), astheory would suggest (Statement 2). Moreover, some people were subject totemptation but unaware of it (naïve) and hence not willing to commit. We conjecturethat only a minority of subjects was naïve (Result 5).

Third, uncertainty was a relevant concern in intertemporal decisions becausesome subjects preferred flexibility, which is the willingness to incur a cost toenlarge the choice set available in the future. About 14% of those who reversedtheir choice were willing to pay for flexibility (Result 3). In a scenario withoutuncertainty there would be no reason to strictly prefer flexibility (Statement 5).Uncertainty-based explanations, though, can be hard to falsify directly becausethe observer could always rationalize any discount function invoking anunobserved subjective belief about risk. Our empirical tests exploited thepredictions about choices on sets of alternatives. An additional route could be toelicit beliefs directly.30

In this study we find substantial support for preference-based explanations.However, given that they are not mutually exclusive, a better model to describeintertemporal choices eventually may need to include elements from bothpreference-based and uncertainty-based explanations.

30 In the questionnaire, we did a simple elicitation of the perceived additional risk associated with the laterreward. This measurement of risk did not ultimately correlate with choice reversal, commitment, norflexibility.

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Appendix

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Table 6 Summary statistics

Mean (standard deviation) Full sample Only those who reversed their choice

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