Journal of Economic Psychology 50 (2015) 52–72

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Journal of Economic Psychology

journal homepage: www.elsevier .com/ locate / joep

Time-based versus money-based decision making under risk:An experimental investigation q

http://dx.doi.org/10.1016/j.joep.2015.07.0030167-4870/� 2015 Elsevier B.V. All rights reserved.

q The first author is supported by a Ph.D. fellowship of the Research Foundation – Flanders (FWO). The second and fourth authors are suppResearch Foundation – Flanders (FWO), grant G.0472.09N.⇑ Corresponding author. Tel.: +32 16 37 37 04.

E-mail address: Anouk.Festjens@kuleuven.be (A. Festjens).

Anouk Festjens a,⇑, Sabrina Bruyneel a, Enrico Diecidue b, Siegfried Dewitte a

a Behavioral Engineering Research Centre, Faculty of Economics and Business, KU Leuven, Naamsestraat 69, 3000 Leuven, Belgiumb INSEAD, Boulevard de Constance, 77305 Fontainebleau, France

a r t i c l e i n f o

Article history:Received 2 January 2015Received in revised form 22 June 2015Accepted 22 July 2015Available online 30 July 2015

JEL classification:39002300

PsycINFO classification:C91D81

Keywords:Time vs. moneyProspect theoryRisk preferences

a b s t r a c t

This paper investigates whether individuals make similar decisions under risk when theoutcomes are expressed in time versus monetary units. We address this issue in twostudies measuring individual risk preferences and prospect theory parameters (i.e., utilitycurvature, probability weighting, and loss aversion) for both time and money. In the first(resp., second) study we consider relatively small (resp., large) time and monetaryoutcomes. We find that individuals hold similar risk preferences for time and money; wealso find evidence that ‘‘time is money’’ with regard to the utility curvature for gains, lossaversion, and decision weighting. However, individuals have different valuations of losingtime and money. The utility function for small losses of money is more concave and vari-able than the utility function for small losses of time (Study 1), but the utility function forlarge losses of time is more concave and variable than that for large losses of money (Study2). We argue that these results reflect a difference in the perceived slack of the respectiveresource.

� 2015 Elsevier B.V. All rights reserved.

1. Introduction

Every day, individuals make risky decisions involving time outcomes, i.e. gains and losses of time—for instance, whenweighing whether to take the longer, traffic-free way home (with the certainty of a 50-min drive) or the shorter,traffic-sensitive route (with equal chances of a 40-min or a 60-min drive), or when deciding whether to take the longerwaiting line being serviced by an experienced cashier (with the certainty of a 10-min wait) or the shorter one serviced byan inexperienced cashier (with equal chances of a 5-min or a 15-min wait). Making these choices efficiently has becomeincreasingly important in societies where more and more individuals experience ‘‘time poverty’’ (Leclerc, Schmitt, &Dubé, 1995). For many, time is not just a scarce resource, it is the scarce resource.

Despite the importance of time in daily life, we have a limited understanding of decision making when risky time out-comes are involved. One reason for this state of affairs may be the economic assumption that time-based decisions underrisk should abide by the same principles as monetary decisions under risk (i.e., ‘‘time is money’’; Becker, 1965). Yet, a grow-ing body of psychological literature demonstrates that individuals treat time and money differently. Therefore, findings in

orted by

A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72 53

the money domain do not always translate perfectly to the time domain (Leclerc et al., 1995; Okada & Hoch, 2004; Saini &Monga, 2008; Soman, 2001; Zauberman & Lynch, 2005).

In this paper we explore whether individuals make decisions under risk similarly when the outcomes are expressed intime versus monetary units. The current research thus considers time as an outcome (gain/loss) that a person receives inrisky choice (and not as a duration that a person needs to wait in intertemporal choice). Following Abdellaoui, Bleichrodt,and l’Haridon (2008), we use the certainty equivalents (CEs) of two-outcome prospects to measure individual preferencesfor time and money under conditions of risk. The main advantage of a simple design based on CEs is that it allows for themeasurement of attitudes toward risk without imposing any particular model of choice. Yet, in a next step, we also useProspect Theory (PT, Tversky & Kahneman, 1992) to parsimoniously capture risk attitudes using psychologically meaningfulparameters (Wakker, 2010). This is especially relevant for our purposes, since we attempt to illuminate decision processes ina relatively understudied domain.

Our results show that, without committing to any specific model of choice, individuals hold similar risk preferences fortime and money. When assuming PT, we further obtain individual information on the utility function, probability weighting,and loss aversion. We find additional evidence for the claim that ‘‘time is money’’—in particular, the utility function for gains,the loss aversion coefficient, and decision weights in the gain and loss domains do not differ across time and monetary con-texts. Yet we also find evidence that ‘‘time is not money’’: the utility function for losses differs across time- and money-basedcontexts. That is, the utility function for small money losses is more concave and variable than the utility function for smalltime losses, whereas the utility function for time is more concave and variable than the one for money when stakes are large.

The paper proceeds as follows. After reviewing the literature on time- versus money-based decision making, we describethe model-free measurement of risk preferences as well as the PT parameters for time and money outcomes. Next we reportthe results of our two studies, and we conclude with a discussion of our results.

2. Time-based versus money-based decision making under risk

In economic theory, it is assumed that the value of time can be derived from the value of money (i.e., ‘‘time is money’’) andhence that time-based decisions under risk should abide by the same principles as monetary decisions under risk (Becker,1965). The implication of this assumption is that individuals will make the same choice regardless of whether alternativesare described using monetary units or time units.

Contrary to the economic literature, research in psychology suggests that people treat time and money differently (Leclercet al., 1995). For instance, Soman (2001) demonstrates that past expenditures (i.e., sunk costs) are given less weight whencontemplating the investment of time than of money. Saini and Monga (2008) find that quick-and-easy heuristics are usedmore in the context of time-based than monetary decisions. Okada and Hoch (2004) show that, when individuals pay in timerather than money, they are willing to pay more for high-risk-high return gambles (that are expressed in monetary terms).Zauberman and Lynch (2005) show that individuals expect slack for time to be greater in the future than in the present (i.e.,individuals expect to have more spare time a month from now than today) and, moreover, that this expected growth of slackis more pronounced for time than for money (i.e., individuals have relatively lower expectations of having more money amonth from now than today).

The observed differences in time-based versus money-based decision making are primarily explained by the value of timebeing more ‘‘ambiguous’’ than the value of money (Okada & Hoch, 2004; Saini & Monga, 2008; Soman, 2001). Unlike money,which can be stored and is unambiguous (a dollar is a dollar in all circumstances), the value of time is perishable, malleable,and impossible to determine precisely. The use of time may well vary from one situation to another; the value of time isoften determined ad hoc because it depends on characteristics of the individual and the situation. Zauberman and Lynch(2005) expand on this explanation by stating that, although the value of time is more ambiguous than the value of moneyin the long run, this is probably not the case in the short run. With regard to the distant future, the value of time is moreambiguous than the value of money because future plans are vague and can be easily moved around. In the immediatefuture, however, the value of time may be even less ambiguous than the value of money because immediate plans are con-crete and difficult to move around. These psychological findings show that individuals treat time and money differently, butthe literature has not clarified exactly how these two resources differ.

In sum, there are two conflicting views regarding the possibility that time- and money-based decision making are similar.Standard economics assumes that ‘‘time is money’’ and psychological literature assumes that ‘‘time is not money’’. The aim ofthis paper is to investigate whether ‘‘time is money’’ when individuals make decisions under risk. Toward that end, we willuse a robust and tractable method to measure individual preferences under risk both for time and for equivalent monetaryamounts. A key advantage of this method is that it offers a systematic approach to studying the components that underliedecision making under risk (i.e., utility, probability weighting, and loss aversion). More specifically, we shall first obtain amodel-free measure of an individual’s risk preferences for time and money outcomes (in the form of CEs of severaltwo-outcome prospects). Next we obtain information—at the individual level—about the PT parameters on which such amodel-free measure is based (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992). We are then able to address thequestion of whether ‘‘time is money’’ with respect to each PT component separately. For example, individuals may be equallyoptimistic about the chance of obtaining a specific time or monetary outcome (decision weights are equal across resources)but nonetheless value the outcomes differently (utility functions differ across resources).

54 A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72

2.1. Previous research on risk attitudes for time versus money outcomes

The estimation of the PT parameters for time (vs. money) outcomes offers additional insights compared to studies that arelimited to the investigation of the model-free risk attitudes for time (vs. money) outcomes (Kroll & Vogt, 2008; Leclerc et al.,1995; Weber & Milliman, 1997; Zushi, Curlo, & Thomas, 2009). In one study that focused on the time versus money compar-ison, Leclerc et al. (1995) for instance found that participants were more risk averse for time than for monetary losses. Thatis, participants were presented with two different scenarios, one for time and one for money. The first scenario askedwhether they would prefer (a) having to wait 60 min for sure or (b) having a 50% chance of waiting 30 min and a 50% chanceof waiting 90 min. No other information was given. The second scenario asked whether they would prefer (a) having a cer-tain loss of $10 or (b) having a 50% chance of losing $5 and a 50% chance of losing $15. (The conversion rate was determinedby an independent sample upfront.) Results showed that participants were more risk averse for time (47% preferred optionb) than for money outcomes (70% preferred option b).

Weber and Milliman (1997) also reported risk aversion for time losses and found risk seeking for time gains (they did notstudy money outcomes). Their conclusions were based on participants’ responses to lottery equivalence questions such as:‘‘Please provide the probability q that would make you indifferent between lottery A that gives you a q% chance on a trainthat arrives 40 min faster (slower) than scheduled (but also a 1 � q% chance on a train that arrives as scheduled), and lotteryB that gives you an 80% chance on a train that arrives 15 min faster (slower) than scheduled (but also a 20% chance on a trainthat arrives at the scheduled time)’’. In contrast, Kroll and Vogt (2008) reported that people were risk seeking for time losses.They conducted one (incentivized) experiment where participants were repeatedly (10 times) asked to choose between twolotteries that were expressed in waiting time (ranging from 5 to 60 min). Option a (vs. option b) always offered less risk butalso a higher sure waiting time. Also Zushi et al. (2009) found risk seeking for time losses. In two experiments, they adaptedthe experimental design of Leclerc et al. (1995) in that time losses (gains) referred to being later (earlier) than scheduled(e.g., ‘‘Your class starts at 4:00 and you need to decide which train to take. Which option do you prefer (a) train A: you willarrive at 4:20 or (b) train b: 50% chance that you will arrive at 4:05 and 50% chance that you will arrive at 4:35’’). Their rea-soning was that people typically expect variations in waiting times such that the time losses used in Leclerc et al. (1995)were not perceived as actual losses. By explicitly taking the schedule as the reference point, Zushi et al. (2009) found that72% (32%) of participants preferred the risky option B when the outcomes were framed as losses (gains).

Together, these papers show that the few results with regard to risk preferences for time outcomes are mixed. This maybe a consequence of differences in elicitation procedure (e.g., one-shot choice vs. series of choices; choices vs. probabilityestimates), the choice of the reference point (e.g., time losses as mere waiting times vs. time losses as being behind on sched-ule), or the particularities of the decision context (e.g., time outcomes as gains and losses in commuting time vs. incontext-free settings). The current research adds to the research on risk preference in the time domain in several ways.First, we focus on the comparison of risk preferences for time versus monetary outcomes. The study of monetary outcomeshas dominated the decision science literature. We want to test whether the findings in the money domain are transferrableto the time domain. Second, we explicitly define time outcomes as gains and losses relative to an expected duration. A wait of60 min (cf., option A in Leclerc et al., 1995) may not be perceived as an actual loss when scheduled and expected upfront.Also, we investigate risk preferences in both loss and gain domain and focus on a series of risky choices (instead of basingourselves on one choice only; for more information on the robustness of our elicitation procedure see Section 3.2). Finally,we move beyond the study of model-free risk preferences and also estimate the underlying PT risk components, namely util-ity, probability weighting, and loss aversion.

We are aware of one study that elicits the PT components for time and monetary outcomes (Abdellaoui & Kemel, 2014).The study consisted in two stages: the first stage covered the time domain and the second one the money domain. In eachstage, participants were presented with a series of binary choices between a sure consequence and a two-outcome prospect(e.g., time: A = win 15 min for sure or B = having a 50% chance to win 30 min and a 50% chance to win 0 min; money: A = win€600 for sure or B = having a 50% chance to win €1200 and a 50% chance to win €0). The outcomes in the time domainreferred to leaving the two-hour experimental session earlier (gains) or later (losses) than expected. The outcomes in themonetary domain referred to financial gains and losses that would be added to or subtracted from participants’ total wealth.Based on participants’ responses in the two stages, the PT components for both time and money were estimated. The authorsfound that in the time domain there was less concave utility, less loss aversion, more optimism for gains, and more pes-simism for losses than in the money domain. Our study differs from the research of Abdellaoui and Kemel (2014) in severalimportant ways. First, unlike Abdellaoui and Kemel (2014) who compare the PT components of small time prospects againstthose of large monetary prospects (using a conversion rate of €1200 = 60 min), we keep the size of the stakes constant fortime and monetary resources (i.e., €12 = 60 min for the small stake studies and €1500 = 1 month for the large stake studies).This feature of our approach is important because previous research found that the size of the stakes heavily influences thePT parameters. High stakes have for instance been shown to lead to more loss aversion (Ert & Erev, 2013; Harinck, Van-Dijk,Van-Beest, & Mersmann, 2007), general risk aversion (Holt & Laury, 2002; Weber & Chapman, 2005), and utility curvature(Wakker & Deneffe, 1996). Our design thus allows for making a clean comparison between small (time and monetary) out-comes at the one hand and large (time and monetary) outcomes on the other hand. Second, unlike Abdellaoui and Kemel(2014) who compare the PT components of expectation-referenced time prospects (the reference point is the expectedtwo-hour duration of the experiment) against those of wealth-referenced monetary prospects (the reference point is the cur-rent wealth rather than the expected payout of the experiment), we keep the reference constant for time and monetary

A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72 55

resources in the current research (i.e., expected duration/payout of the experiment in experiment 1 and expected duration/-cost of a hypothetical task in experiment 2). This feature of our approach is important because previous research argued thatthe choice of the specific reference point may have a substantial impact on the PT parameters (for a review of the argumentssee Wakker, 2010, p. 247).

In sum, although there are some previous studies that investigate the model-free risk preferences (Leclerc et al., 1995)and the PT parameters (Abdellaoui & Kemel, 2014) for time versus monetary outcomes, we contribute to this research topicin several important ways. That is, we use a robust and validated elicitation method to measure risk preferences and the PTparameters for time versus money, and we acknowledge that the results may vary with the size of the stakes. In the nextsection, we introduce a descriptive theory to model preferences under risk. We also describe the experimental method usedto measure risk preferences for time and money.

3. Measuring preferences

3.1. A descriptive theory for modeling preferences under risk

Prospect theory (PT) is the most popular descriptive theory for decision making under risk (Kahneman & Tversky, 1979;Tversky & Kahneman, 1992). The main descriptive features of PT can be summarized as follows. The theory acknowledgesthat individuals are more sensitive to changes than to absolute states and that outcomes are thus coded as gains and lossesrelative to a reference point. This aspect is especially relevant for our study because other authors have shown that referencepoints play a key role in the valuation of time (e.g., Kumar, Kalwani, & Dada, 1997). Another assumption of PT is that ‘‘lossesloom larger than gains’’—a phenomenon known as loss aversion. The importance not only of changes but also of loss aversionis captured by an utility function that is defined over gains and losses yet is steeper for the latter. Following Köbberling andWakker (2005), we assume that utility U is composed of a basic utility u (which reflects the value of outcomes) and of lossaversion (which reflects the different evaluation of gains and losses). Thus:

UðxÞ ¼uðxÞ if x P 0;kuðxÞ if x < 0;

�ð1Þ

here k is the loss aversion parameter. PT further acknowledges that each individual has a subjective perception of probability,which is captured by decision weights. Small probabilities are typically overestimated, whereas moderate and large proba-bilities tend to be underestimated. In PT, these tendencies are represented by a probability weighting function. Under PT notonly utility curvature but also probability weighting and loss aversion contribute to overall risk attitude (Kahneman &Tversky, 1979; Qiu & Steiger, 2011). Using PT as our descriptive theory allows us to explore thoroughly the underlying struc-ture of risky decision making.

Formally, consider a binary prospect (x, p; y), which means receiving outcome x with probability p and receiving outcomey otherwise. Under PT, individuals evaluate such prospects as follows:

pþðpÞ � uðxÞ þ ð1� pþðpÞÞ � uðyÞ for gains ðx P y P 0Þ; ð2Þ

p�ðpÞ � uðxÞ þ ð1� p�ðpÞÞ � uðyÞ for losses ðx 6 y 6 0Þ; ð3Þ

pþðpÞ � uðxÞ þ kðp�ð1� pÞ � uðyÞÞ for mixed outcomes ðx > 0 > yÞ: ð4Þ

Here uð�Þ is a utility function, p+/� are the decision weights attached to the outcomes, and k is the loss aversion coefficient.

3.2. Measurement of preferences under risk assuming PT

Abdellaoui, Bleichrodt, and l’Haridon (2008) introduced a tractable and robust method for measuring individual prefer-ences under risk for monetary outcomes. We shall use this methodology also for time outcomes, i.e. gains and losses of time.The method is based on repeated elicitation of certainty equivalents (CEs) of two outcome prospects of the form (x, p; y). Itconsists of three steps: eliciting the CEs of six prospects with pure gain outcomes; eliciting the CEs of six prospects with pureloss outcomes; and eliciting the maximum losses that individuals are willing to bear as regards prospects with mixedoutcomes.

Consider, for example, eliciting the CE of a pure gain prospect (x, p; y) with x P y P 0. The CE is obtained through a seriesof binary choices. A choice-based procedure has been shown to lead to fewer inconsistencies than asking for the indifferencedirectly (Attema & Brouwer, 2013; Bostic, Herrnstein, & Luce, 1990). In each choice, an individual is faced with two prospects(or options) labeled A and B, where prospect A is always riskless (see Fig. A1 in Appendix A). As an example in the context oftime gains, individuals must choose between leaving the experiment 15 min earlier than planned for certain (option A) orinstead participating in a two-outcome gamble that gives them a 50% chance of leaving the experiment 30 min earlier thanplanned and a 50% chance of leaving at the planned time (option B); we formalize this latter option by writing(x, p; y) = (+30 min, ½; 0 min). Depending on the choices that are made, the value of the sure option changes in a bisectionprocess and comes closer to the CE of the prospect after each iteration (see Appendix B for an example). Starting values for

56 A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72

the iterations were chosen in such a way that prospects had equal expected value. There were exactly six iterations in eachbisection process. The CE is the sure time gain that would make individuals indifferent with regard to the risky prospect(CE � (x, p; y)).

The CE of a loss prospect is obtained similarly. Suppose we seek the CE of a loss prospect x 6 y 6 0 in (x, p; y). In that case,individuals would be asked to choose between leaving the experiment 15 min later than planned for sure or participating ina two-outcome prospect that gives them a 50% chance of leaving the experiment 30 min later than planned and a 50% chanceof leaving at the planned time: (�30 min, ½; 0 min); see Fig. A2. Depending on their choices, the value of the sure optionchanges with each iteration and comes closer to the CE of the prospect.

The elicited CEs allow for two different levels of analysis. First, a model-free risk measure is computed simply by com-paring the CE with the expected value (EV) of the prospect. An individual is risk averse (resp., risk neutral, risk seeking) ifthe CE is smaller than (resp., equal to, larger than) the EV of the prospect. A second level of analysis allows us to estimatethe parameters of expressions (2)-(4): the curvature of the utility function, the decision weights, and the extent of loss aver-sion. This analysis is semiparametric: a parametric specification is adopted for utility but not for the decision weight.

Following Abdellaoui, Bleichrodt, and l’Haridon (2008), we used the six gain CEs to estimate the utility curvature anddecision weight for time gains. By (2), the indifference CE � (x, ½; y) implies that

1 Abdways. Fstakes aaversioindividu

uðCEÞ ¼ pþ 12

� �� uðxÞ

� �þ 1� pþ 1

2

� �� �� uðyÞ

� �; ð5Þ

where uð�Þ is the utility of the outcome and p+(½) is the decision weight of the probability ½. Following Köbberling andWakker (2005), we adopted a normalized exponential specification1 for the utility function:

uðxÞ ¼ð1� e�axÞ=a if x P 0 and a – 0;ðebx � 1Þ=b if x 6 0 and b – 0;uðxÞ if a ¼ 0 or b ¼ 0:

8><>: ð6Þ

The gain function is concave if a > 0, convex if a < 0, or linear if a ¼ 0. Substituting (6) into Eq. (5) now yields

1� e�aCE

a¼ pþ 1

2

� �� 1� e�ax

a

� �þ 1� pþ 1

2

� �� �� 1� eay

a

� �ð7Þ

for

CE ¼ �lnððpþ 1

2

� �� ðe�ax � e�ayÞÞ þ e�ayÞ

a:

Eq. (7) can be easily estimated via the method of nonlinear least squares (i.e., with two unknown parameters, namelydecision weight p+(½) and utility curvature a). Detailed information on the estimation procedure can be found inAppendix C.

Measuring the utility function and decision weights for time losses is analogous to measuring them for time gains. Weobtain the CE of six loss prospects, after which we derive an estimate of utility curvature b for time losses (i.e., concave ifb < 0, convex if b > 0, and linear if b = 0). We also estimate the decision weight in the loss domain; that is, p�(½) is obtainedwhen we estimate the following equation, which results from substituting (6) into (3):

ebCE � 1b

¼ p� 12

� �� ebx � 1

b

� �þ 1� p� 1

2

� �� �� eby � 1

b

� �ð8Þ

CE ¼lnððp�ð12Þ � ðebx � ebyÞÞ þ ebyÞ

b:

Finally, for estimates in the mixed domain, parameters from the gain and loss domains are connected to obtain a measureof loss aversion. We select a CE of the gain round, denoted G, and elicit the loss L for which 0 � (G, p; L). An example of thismixed-domain scenario is one in which individuals must choose between gaining or losing nothing for sure on the one handor, on the other hand, taking a gamble with a 50% chance of leaving the experiment 10 min earlier than planned and a 50%chance of leaving the experiment 10 min later than planned: (+10 min, ½; �10 min); see Fig. A3. For this estimation, the lossof the two outcome prospects was changed until indifference was reached (see Appendix B). By (4), we have

uð0Þ ¼ pþ12

� �� UðGÞ

� �þ k p�

12

� �� UðLÞ

� �: ð9Þ

ellaoui and Kemel (2014) used a power specification for utility. We believe however that an exponential specification is better in at least two importantirst, power functions exhibit extreme and implausible behavior near the reference (Wakker, 2010, p. 267). This is problematic for studies where smallre at play (e.g., time stakes in the order of 60 min). Second, the exponential specification has the additional desirable feature that k > 1 implies both loss

n according to Köbberling and Wakker’s (2005) definition and according to Kahneman and Tversky’s (1979) definition. The advantage of having anal measurement of loss aversion that is robust across two of the most popular definitions is attractive.

A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72 57

Because k is the only unknown component in (9), its value is determined directly by solving the equation. Thus,

2 See

k ¼ �pþð12Þ � uðGÞp�ð12Þ � uðLÞ

:

In short, our elicitation method provides a model-free measure of risk attitude as well as the PT parameters of each indi-vidual: the utility curvature for gains (a), decision weights for gain prospects (p+), utility curvature for losses (b), decisionweights for loss prospects (p�), and an index of loss aversion (k).

4. The studies

Two studies were conducted to measure risk preferences and the PT parameters for time and monetary outcomes. Thefirst study deals with relatively small time and monetary outcomes (time outcomes of up to 60 min and monetary outcomesof up to €12). We want to address small-stakes time stimuli because many decisions in daily life involve durations on theorder of minutes. In this study, ‘‘time gains’’ (resp., ‘‘time losses’’) amount to leaving the experiment earlier (resp., later) thanplanned. Time outcomes were converted to monetary outcomes at the average wage rate in the labor market (€12 = 60 min)so that the magnitude of each outcome type was comparable. Such comparability is important because risk preferences havebeen shown to fluctuate with outcome size (Harinck et al., 2007).

The second study deals with relatively large time and monetary outcomes (time outcomes of up to 12 months; monetaryoutcomes of up to €18000). This study uses large stakes as a test of whether Study 1’s findings are robust to changes in out-come size. Zauberman and Lynch (2005) suggest that, whereas the value of large time outcomes is more ambiguous than thevalue of large money outcomes, the value of small time outcomes is less ambiguous than the value of small money outcomes.If ambiguity is the main difference between time and monetary resources (Okada & Hoch, 2004; Saini & Monga, 2008) and ifthe relative ambiguity of each resource type varies with the size of the stakes (Zauberman & Lynch, 2005), then we shouldexpect stake size to play a pivotal role in our results. To accommodate the larger time stakes—since it would be nonsensicalto ‘‘leave an experiment’’ twelve months earlier or later than planned—we modified the experimental context slightly. Inparticular: time gains (losses) now refer to ‘‘finishing a large-scale hypothetical project’’ earlier (later) than planned. Toensure that the results for large stakes are fully ascribable to the size of the stakes and not to the changed experimental con-text, we also tested whether the results for small stakes (Study 1) were similar in the new experimental context (Study 2).

5. Study 1: small-stakes time and money outcomes

In Study 1, we use a method similar to that of Abdellaoui et al. (2008) and measure the risk preferences for money andtime units for each participant in the sample.

5.1. Participants

The participants in our two-stage study were 157 undergraduate students (97 women) ranging in age from 18 to 28 years(M = 21.68 yr; SD = 3.37). Each was paid a flat fee of €20 at the end of the second session.

5.2. Procedure

Participants came to the laboratory in groups of ten. Each participant was assigned a seat in a partially enclosed cubicleand then completed the study in private on a personal computer. The study comprised two sessions separated by one week.Risk preferences for time were measured in one session, risk preferences for money in the other. (The order of the sessionswas counterbalanced and had no effect on our results; this temporal separation in our preference measurements wasintended to reduce both sequence effects and fatigue effects.) Once seated, participants were shown an example of a CE elic-itation so that they could familiarize themselves with the task. Participants were also told that there were three rounds oftasks, one each for gains, losses, and mixed prospects. The CEs for prospects involving pure gain outcomes were always eli-cited first (because output from this round served as input for the mixed round), and the order of CE elicitation for pure lossand for the mixed domain was counterbalanced. After each round there was a break during which a 3-min nature documen-tary was shown.

All CEs were obtained through a bisection process, as illustrated in Appendix B, that zeroed in on participants’ CEs. Weused hypothetical payoffs2: participants were asked to imagine staying in the lab longer or leaving sooner than planned, andthe study actually ended as planned. To measure the reliability of participants’ choices, we repeated elicitation of CEs for thethird prospect in the domains of gains, losses, and mixed gambles for both time and money (see Section 5.4.2). We employedthis reliability measure when evaluating the consistency of participants’ answers.

Section 7.3 for an extensive motivation for the use of hypothetical payoffs.

58 A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72

5.3. Stimuli

Based on the CE of six prospects, the risk preferences and PT parameters for time [money] gains and losses were elicited.The specific prospects are depicted in Table 1. We used the bisection method to elicit the CE of the prospects. Our estimationof the loss aversion coefficient for time [money] was based on the maximum loss that participants were willing to incur infour3 mixed-outcome prospects (Table 1). In other words, we selected four times a CE of the gain round, G, and elicited the loss Lfor which 0 � (G, p; L). We thus obtained four different loss aversion coefficients per participant (i.e., one for each of the fourmixed outcome prospects). Following Abdellaoui et al. (2008), we then considered the median of these four loss aversion mea-surements as the loss aversion coefficient for that participant. The mixed outcome prospects are depicted in Table 1.

A fixed conversion rate of €12/60 min was used to convert the time stimuli into the monetary stimuli. This conversionrate reflects the wage that a student could earn in the labor market for one hour of work at the time of our study.

5.4. Results

5.4.1. OutliersTen participants (6%) were removed from the dataset because they were unwilling to risk any loss—however small—for

the possibility of a gain. For these individuals, k > 100 for time (n = 6) or for money (n = 3) or for both (n = 1).

5.4.2. Reliability checkWe assessed the reliability of participants’ answers by repeating the CE elicitation of one prospect in each of the three

rounds (domains of gains, losses, and mixed prospects). The Spearman correlations were satisfactory and ranged from .69to .96. This means that participants were generally consistent in their responses. Paired t-tests revealed, in addition, thatno systematic shifts in CEs occurred from the first to the second measurement for any of the items (|t| < 1.68 in all cases).

5.4.3. Model-free resultsMedian CEs and model-free risk attitude. Table 1 shows the median CEs of the prospects; similar results were obtained for

the means. To gain insight in individual risk preferences, we computed a model-free index of risk attitude at the participantlevel (see Table 2). To obtain this index, we first normalized the 32 prospects and corresponding CEs (i.e., (CE � y)/(x � y));we then averaged these normalized scores over the six gain prospects (RISK+) and six loss prospects (RISK�). A participant isconsidered risk averse (risk neutral, risk seeking) if RISK+ is smaller than (equal to, larger than) ½ or if |RISK�| is larger than(equal to, smaller than) ½. A one-sample Wilcoxon signed-rank test showed that participants were risk seeking for moneyand time gains (p < .05) but risk neutral for money and time losses (p > .05). A Wilcoxon signed-rank test for related samplesshowed that neither the median RISK+ nor the median RISK� differed across resources (p > .05 in both cases). A Friedman’stwo-way ANOVA by ranks test showed that neither the distribution of RISK+ (p > .05) nor the distribution of RISK� (p > .05)differed across resources.

5.4.4. Parameter estimatesParameter estimates atime/money and btime/money. The utility curvatures for time and monetary outcomes are given in Table 2.

Our analyses ensured that the error associated with these parameter estimates was minimal (i.e., a global rather than a localmaximum was obtained). A one-sample Wilcoxon signed-rank test showed that participants had a linear utility function forboth money and time gains (p > .05 in each case) but a concave utility function for both money and time losses (p < .001 ineach case). A Wilcoxon signed-rank test for related samples showed that the median a did not differ across resources(p > .05) but also that the median b was more concave for money than for time (p < .001).

Fig. 1 displays the median utility function for time and monetary outcomes. A Friedman’s two-way ANOVA by ranks testshowed that, although the distribution of a did not differ across resources (p > .05), the distribution of b did (p < .05). Thedistribution of btime/money, which is plotted in Fig. 2, gives us additional insight into this difference. Fig. 2 shows that, althoughbtime is narrowly distributed around zero (which means that many participants value time losses linearly), the distribution ofbmoney is much more heterogeneous.

Parameter estimates ktime/money. The loss aversion coefficients for time and money are given in Table 2. A one-sampleWilcoxon signed-rank test showed that participants were loss averse for both money (kmoney = 2.14, p < .001) and time(ktime = 2.09, p < .001). A Wilcoxon signed-rank test for related samples showed that the median k did not differ acrossresources (p > .05). A Friedman’s two-way ANOVA by ranks test showed that the distribution of k did not differ acrossresources (p > .05).

Parameter estimates pþtime=money and p�time=money. The decision weights for time and money outcomes are also given in

Table 2. A one-sample Wilcoxon signed-rank test showed that participants overestimated the probability of winning time(p < .01) and money (p < .01) but underestimated the probability of losing time (p < .001) and money (p < .001).Participants were thus optimistic with respect to both gains and losses. Another Wilcoxon signed-rank test for related sam-ples showed that neither the median p+ nor the median p� differed across resources (p > .05 in each case). Also, a Friedman’s

3 Four questions should suffice in light of Abdellaoui et al.’s (2008) observation that the loss aversion index is stable across different mixed prospects.

Table 1Prospects, EVs, and elicited CEs (Study 1).

Time prospect (min) |EV| |Median CE| Money prospect (€) |EV| |Median CE|

(+20 min, ½; 0 min) 10 12.03 [9.53–15.47] (+€4, ½; 0) 2 2.34 [1.91–2.91](+30 min, ½; 0 min) 15 17.58 [13.83–23.20] (+€6, ½; 0) 3 3.23 [2.86–4.64](+40 min, ½; 0 min) 20 21.56 [16.56–25.94] (+€8, ½; 0) 4 4.19 [3.69–4.81](+60 min, ½; 0 min) 30 31.41 [23.91–38.91] (+€12, ½; 0) 6 6.28 [4.97–7.78](+60 min, ½; +20 min) 40 40.94 [34.06–44.06] (+€12, ½; +€4) 8 8.19 [6.81–8.81](+60 min, ½; +40 min) 50 49.53 [44.53–52.03] (+€12, ½; +€8) 10 9.91 [8.91–10.16]

(�20 min, ½; 0 min) 10 10.78 [9.22–12.97] (�€4, ½; 0) 2 2.09 [1.84–2.59](�30 min, ½; 0 min) 15 16.17 [13.83–19.45] (�€6, ½; 0) 3 3.23 [2.86–3.98](�40 min, ½; 0 min) 20 21.56 [16.56–25.94] (�€8, ½; 0) 4 4.31 [3.81–4.81](�60 min, ½; 0 min) 30 32.34 [28.59–39.84] (�€12, ½; 0) 6 6.28 [5.72–7.78](�60 min, ½; �20 min) 40 39.06 [33.44–41.56] (�€12, ½; �€4) 8 7.69 [6.19–8.19](�60 min, ½; �40 min) 50 47.97 [44.22–50.47] (�€12, ½; �€8) 10 9.59 [8.19–10.09]

(+12.03 min, ½; �__ min) 0 7.35 [4.61–13.11] (+€2.34, ½; �€__) 0 1.54 [0.75–2.53](+17.58 min, ½; �__ min) 0 10.43 [5.47–14.48] (+€3.23, ½; �€__) 0 2.10 [0.94–3.29](+21.56 min, ½; �__ min) 0 10.90 [5.93–18.17] (+€4.19, ½; �€__) 0 2.09 [1.00–3.99](+31.41 min, ½; �__ min) 0 13.25 [7.38–22.49] (+€6.28, ½; �€__) 0 2.93 [1.43–5.79]

Table 2Parameter estimates and risk attitudes (Study 1).

amoney atime bmoney btime p+money p+

time p�money p�time

Mean 0.034 0.007 �0.13 �0.022 0.547 0.562 0.429 0.407Median 0.022 0.002 �0.049 �0.022 0.546 0.534 0.454 0.423SD 0.377 0.145 0.426 0.100 0.215 0.215 0.177 0.182Q25 �0.081 �0.017 �0.181 �0.048 0.402 0.429 0.333 0.277Q75 0.165 0.033 0.014 0.000 0.693 0.729 0.535 0.523H0: Medians are equal p = .13, retain H0 p = .00, reject H0 p = .66, retain H0 p = .16, retain H0

H0: Distributions are equal p = .06, retain H0 p = .03, reject H0 p = .68, retain H0 p = .10, retain H0

kmoney ktime RISK+money RISK+

time RISK�money RISK�time

Mean 4.891 4.305 0.526 0.538 0.495 0.488Median 2.088 2.143 0.523 0.529 0.508 0.510SD 11.375 6.162 0.141 0.166 0.113 0.137Q25 1.073 1.281 0.427 0.417 0.432 0.411Q75 3.895 3.965 0.625 0.646 0.563 0.576H0: Medians are equal p = .54, retain H0 p = .65, retain H0 p = .86, retain H0

H0: Distributions are equal p = .68, retain H0 p = .68, retain H0 p = .67, retain H0

A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72 59

two-way ANOVA by ranks test showed that neither the distribution of p+ nor of p� differed across resources (p > .05 in eachcase).

5.5. Discussion

In Study 1 involving small stakes, we observed that risk preferences were similar for time and money. In addition, resultsshowed that neither the utility function for gains (a), the decision weights for gains and losses (p+/�), nor the loss aversioncoefficient (k) differed across resource contexts. However, the utility function for time losses (btime) was more linear andhomogeneous than was the utility function for money losses (bmoney).

6. Study 2: risk preferences for small and large time and money outcomes

Our second study deals with relatively large time and monetary outcomes. We changed the size of the outcomes to testwhether the results of Study 1 could be extended to the case of larger stakes. We expected the size of the stakes to play a keyrole because it has been argued that differences between time and money are mainly driven by differences in ambiguity(Leclerc et al., 1995; Okada & Hoch, 2004; Saini & Monga, 2008), and also that time is more ambiguous than money whenthe outcomes are large but not when they are small (Zauberman & Lynch, 2005). To accommodate for the larger stakes, wemodified the experimental context: time outcomes now reference to finishing a large-scale project earlier or later thanplanned (rather than leaving the experimental session earlier or later than planned). We ensured that the results for largestakes are fully ascribable to the size of those stakes (and not to the change in experimental context) by testing for whetherthe results for small stakes are robust to that change.

Fig. 1. Value functions for time and money (Study 1).

60 A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72

6.1. Participants

128 students (68 women) ranging in age from 18 to 27 years (M = 20.77 yr; SD = 1.79) participated in Study 2. Each par-ticipant received a flat fee at the end of the second session.

6.2. Procedure

One group of participants (n = 80, 41 women) received questions with large time and monetary outcomes. This allowstesting whether the results of Study 1 can be extended to large stakes. A second group of participants (n = 48, 27 women)received questions with small time and monetary outcomes. This allows testing whether the results of Study 1 hold inanother experimental setting (finishing a hypothetical project earlier or later than planned rather than leaving the experi-ment earlier or later than planned).

The same procedure as in Study 1 was implemented to measure the CEs for the large-stakes prospects. Thus, this‘‘large-stake’’ part of the study consisted of two stages (time versus money; the order of the stages was counterbalancedand did not affect the results) of three rounds each (gain, loss, and mixed outcomes; the order of the loss and mixed roundwas counterbalanced); as before, we used hypothetical payoffs (Booij & Van de Kuilen, 2009). Prior to giving participants an

Loss Money – βmoney Loss Time – β�me

01020304050

01020304050

Fig. 2. Distribution of btime vs money (Study 1).

A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72 61

example of a CE question, we asked them to imagine engaging in an important large-scale project that might keep them busyfor a considerable amount of time [that might cost them a considerable amount of money]. We also told them that, owing toseveral circumstances, the project may finish earlier or last longer [may cost less or more] than expected. We said that wewere interested in how they would deal with risk regarding the end date [the costs] of the project. The small-stakes proce-dure was exactly the same—except for the scale of the project (cf. infra).

6.3. Stimuli

We used essentially the same procedure as in Study 1 to obtain the CEs of several large-stakes prospects. The only mod-ifications were in (i) the prospect values (we used those given in Table 4) and (ii) the experimental context. In the case ofgains, for example, we asked: ‘‘Would you prefer that the project ends 3 months earlier [costs €4500 less] than planned withcertainty, or would you rather gamble with taking a 50% chance that the project ends 6 months earlier [costs €9000 less] thanplanned and a 50% chance that the projects ends at the planned time [costs as much as planned]?’’. A fixed conversion rate of€1500/1 month was used to convert the time stimuli into the monetary stimuli.

The stimuli for small stakes were identical to those in Study 1 (Table 3). The context of the CE questions for small stakesresembled that for large stakes in that time [money] outcomes referred to finishing a hypothetical project earlier or laterthan expected [costing less or more than expected] (e.g., ‘‘Would you prefer that the project ends 15 min earlier [costs €3less] than planned with certainty, or are you prepared to gamble with a 50% chance that the project ends 30 min earlier[costs €6 less] than planned and a 50% chance that the projects ends at the planned time [costs as much as planned]?’’).(Note that a fixed conversion rate of €12/60 min was used to convert the time stimuli into the monetary stimuli.)

6.4. Results

6.4.1. OutliersFour participants (8.3%) were removed from the dataset for small stakes because they were not willing to trade any loss

for a gain, irrespective of how small the loss was; so for these participants, k > 100 for either time (n = 1) or money (n = 3).Twelve participants (15%) were removed from the dataset for large stakes because they were unwilling to trade a loss—nomatter how small—for the chance of a gain. For these individuals, k > 100 for time (n = 1) or for money (n = 10) or for both(n = 1).

6.4.2. Model-free resultsSmall stakes: Median CEs and model-free risk attitude. Table 3 reports the median CEs of the small-stakes prospects; similar

results were obtained for the means. To obtain insight in individual risk preferences, we computed a model-free index of riskattitude at the participant level (see RISK+/� in Table 5 in Section 5.4.3).4 A one-sample Wilcoxon signed-rank test showed thatparticipants were risk seeking for money gains (p < .05) but risk neutral for time gains (p > .05), money losses (p > .05), and timelosses (p > .05). A Wilcoxon signed-rank test showed that neither the median RISK+ nor the median RISK� differed acrossresources (p > .05 in both cases). A Friedman’s two-way ANOVA by ranks test showed that neither the distribution of RISK+

(p > .05) nor the distribution of RISK� (p > .05) differed across resources. Except for the value of RISKþtime, these results replicateStudy 1’s findings.

Large stakes: Median CEs and model-free risk attitude. Table 4 shows the median CEs of the 32 large-stakes prospects; sim-ilar results were obtained for the means. To obtain insight in individual risk preferences, we computed a model-free index ofrisk attitude at the participant level (see RISK+/� in Table 6 in Section 5.4.3). A one-sample Wilcoxon signed-rank test showedthat participants were risk neutral for both money and time gains and losses (all p > .05). A Wilcoxon signed-rank testshowed further that neither the median RISK+ nor the median RISK� differed across resources (p > .05 in both cases). AFriedman’s two-way ANOVA by ranks test showed that neither the distribution of RISK+ nor that of RISK� differed acrossresources (p > .05 in both cases).

6.4.3. Parameter estimatesSmall stakes: Parameter estimates atime and btime/money. The utility curvatures for time and monetary outcomes are given in

Table 5. A one-sample Wilcoxon signed-rank test showed that participants had a linear utility function for time gains(p > .05) but a concave utility function for both time losses (p < .001) and money losses (p < .001). A Wilcoxon signed-ranktest for related samples showed that the median b was more concave for money than for time (p < .01; see Fig. 3), replicatingthe results of Study 1. A Friedman’s two-way ANOVA by ranks test showed that the distribution of b differed across resources(p < .01). Fig. 4 confirms that, although btime is narrowly distributed around zero, the distribution of bmoney is much moreheterogeneous (cf. Study 1).

4 We averaged only five (instead of six) normalized CEs for money gains because the CE information was missing for prospect (+€12, ½; +€8). Thisshortcoming resulted from a programming error: that prospect was never displayed to participants during the course of their tasks. Hence we obtained noinformation on the CE of this particular prospect, which also made it impossible to estimate any PT parameters for small monetary gains. However, thatestimation is not essential for our current purposes.

Table 3Prospects, EVs, and elicited CEs for small stakes (Study 2).

Small time prospects (minutes) |EV| |Median CE| Small money prospects (€) |EV| |Median CE|

(+20 min, ½; 0 min) 10 12.03 [8.28–15.23] (+€4, ½; 0) 2 2.41 [1.91–2.91](+30 min, ½; 0 min) 15 15.70 [13.83–23.20] (+€6, ½; 0) 3 3.23 [2.86–3.98](+40 min, ½; 0 min) 20 21.56 [16.56–25.47] (+€8, ½; 0) 4 4.31 [3.81–4.81](+60 min, ½; 0 min) 30 31.41 [23.91–38.91] (+€12, ½; 0) 6 6.28 [5.58–7.22](+60 min, ½; +20 min) 40 40.94 [36.09–44.06] (+€12, ½; +€4) 8 8.19 [7.81–8.28](+60 min, ½; +40 min) 50 49.38 [44.53–51.48] (+€12, ½; +€8) – –

(�20 min, ½; 0 min) 10 10.47 [8.05–12.97] (�€4, ½; 0) 2 2.09 [1.61–2.55](�30 min, ½; 0 min) 15 15.70 [14.30–19.10] (�€6, ½; 0) 3 3.23 [2.86–3.89](�40 min, ½; 0 min) 20 22.50 [19.06–25.94] (�€8, ½; 0) 4 4.25 [3.81–4.81](�60 min, ½; 0 min) 30 33.75 [28.59–38.91] (�€12, ½; 0) 6 6.38 [5.86–7.22](�60 min, ½; �20 min) 40 35.94 [29.06–40.94] (�€12, ½; �€4) 8 7.81 [6.19–8.19](�60 min, ½; �40 min) 50 49.22 [42.34–50.47] (�€12, ½; �€8) 10 9.03 [8.45–9.91]

(+12.03 min, ½; �__ min) 0 9.98 [5.73–12.19] (+€2.41, ½; �€__) 0 1.82 [0.89–3.13](+15.70 min, ½; �__ min) 0 11.02 [7.61–14.97] (+€3.42, ½; �€__) 0 2.23 [1.36–3.36](+21.56 min, ½; �__ min) 0 12.03 [8.28–15.23] (+€4.31, ½; �€__) 0 2.41 [1.91–2.91](+31.41 min, ½; �__ min) 0 15.70 [13.83–23.20] (+€6.28, ½; �€__) 0 3.23 [2.86–3.98]

Table 4Prospects, EVs, and elicited CEs for large stakes (Study 2).

Large time prospects (months) |EV| |Median CE| Large money prospects (€) |EV| |Median CE|

(+4 months, ½; 0 months) 2 1.91 [1.36–2.84] (+€6000, ½; 0) 3000 2859.38 [2015.63–3210.94](+6 months, ½; 0 months) 3 2.86 [2.18–3.98] (+€9000, ½; 0) 4500 4289.06 [3023.44–4851.56](+8 months, ½; 0 months) 4 3.81 [2.81–4.81] (+€12000, ½; 0) 6000 5718.75 [4078.13–7031.25](+12 months, ½; 0 months) 6 5.72 [4.78–7.92] (+€18000, ½; 0) 9000 8578.125 [6046.88–10546.88](+12 months, ½; +4 months) 8 8.19 [6.81–8.81] (+€18000, ½; +€6000) 12,000 12281.25 [10031.25–13640.63](+12 months, ½; +8 months) 10 9.91 [8.91–10.09] (+€18000, ½; +€12000) 15,000 14859.38 [13359.38–15984.38]

(�4 months, ½; 0 months) 2 2.25 [1.91–2.64] (�€6000, ½; 0) 3000 3140.63 [2484.38–3890.625](�6 months, ½; 0 months) 3 3.23 [2.86–4.55] (�€9000, ½; 0) 4500 4710.94 [3726.56–5273.44](�8 months, ½; 0 months) 4 4.31 [3.81–5.09] (�€12000, ½; 0) 6000 6281.25 [5531.25–7781.25](�12 months, ½; 0 months) 6 6.47 [5.72–7.97] (�€18000, ½; 0) 9000 9421.88 [7453.13–13640.63](�12 months, ½; �4 months) 8 7.81 [5.91–8.19] (�€18000, ½; �€6000) 12,000 11718.75 [9328.13–12421.88](�12 months, ½; �8 months) 10 9.63 [8.91–10.09] (�€18000, ½; �€12000) 15,000 14390.63 [13359.38–15140.63]

(+1.91 months, ½; �__ months) 0 1.17 [0.43–2.05] (+€2859.38, ½; �€__) 0 1581.30 [550.05–2697.51](+2.86 months, ½; �__ months) 0 1.42 [0.68–2.67] (+€4289.06, ½; �€__) 0 2134.64 [789.92–3455.20](+3.81 months, ½; �__ months) 0 1.97 [0.90–3.24] (+€5718.75, ½; �€__) 0 2931.15 [971.92–4735.84](+5.72 months, ½; �__ months) 0 2.76 [1.15–4.68] (+€8718.75, ½; �€__) 0 3823.24 [1149.17–5962.28]

Table 5Parameter estimates and risk attitudes for small stakes (Study 2).

amoney atime bmoney btime p+money p+

time p�money p�time

Mean – 0.010 �0.046 �0.043 – 0.529 0.414 0.369Median – 0.000 �0.104 �0.014 – 0.529 0.413 0.360SD – 0.124 0.416 0.107 – 0.242 0.151 0.184Q25 – �0.026 �0.164 �0.065 – 0.382 0.322 0.183Q75 – 0.038 �0.030 0.004 – 0.707 0.524 0.523H0: Medians are equal – p = .01, reject H0 – p = .36, retain H0

H0: Distributions are equal – p = .00, reject H0 – p = .23, retain H0

kmoney ktime RISK+money RISK+

time RISK�money RISK�time

Mean – 7.434 0.549 0.521 0.474 0.483Median – 1.611 0.555 0.512 0.482 0.504SD – 11.665 0.115 0.159 0.099 0.116Q25 – .689 0.467 0.424 0.438 0.424Q75 – 10.826 0.627 0.651 0.533 0.557H0: Medians are equal – p = .29, retain H0 p = 1.00, retain H0

H0: Distributions are equal – p = .55, retain H0 p = .29, retain H0

62 A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72

Large stakes: Parameter estimates atime/money and btime/money. The utility curvatures for time and monetary outcomes aregiven in Table 6. A one-sample Wilcoxon signed-rank test showed that participants had a linear utility function for bothmoney gains and time gains (p > .05 in each case) but a concave utility function for both money losses and time losses

Table 6Parameter estimates and risk attitudes for large stakes (Study 2).

amoney atime bmoney btime p+money p+

time p�money p�time

Mean 0.000 0.540 0.000 �0.222 0.484 0.480 0.399 0.429Median 0.000 0.007 0.000 �0.050 0.453 0.482 0.417 0.451SD 0.001 3.971 0.000 0.668 0.223 0.260 0.183 0.202Q25 0.000 �0.183 0.000 �0.188 0.324 0.275 0.275 0.295Q75 0.000 0.160 0.000 0.026 0.625 0.630 0.493 0.544H0: Medians are equal p = .85, retain H0 p = .00, reject H0 p = .89, retain H0 p = .34, retain H0

H0: Distributions are equal p = .81, retain H0 p = .02, reject H0 p = .63, retain H0 p = .10, retain H0

kmoney ktime RISK+money RISK+

time RISK�money RISK�time

Mean 5.994 4.36 0.468 0.502 0.489 0.512Median 2.083 1.709 0.460 0.473 0.486 0.520SD 12.007 8.435 0.160 0.184 0.129 0.132Q25 1.105 .828 0.378 0.383 0.405 0.446Q75 5.05 4.138 0.602 0.587 0.562 0.573H0: Medians are equal p = .58, retain H0 p = .22, retain H0 p = .12, retain H0

H0: Distributions are equal p = .81, retain H0 p = .71, retain H0 p = .11, retain H0

Fig. 3. Value functions for small time and money stakes (Study 2).

Small Loss Money – βmoney Small Loss Time – β�me

0

5

10

15

0

5

10

15

Fig. 4. Distribution of btime vs money for small stakes (Study 2).

A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72 63

64 A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72

(p < .01 in each case). A Wilcoxon signed-rank test for related samples showed that the median a did not differ acrossresources (p > .05) but also that the median b was more concave for time than for money (p < .01; see Fig. 5). AFriedman’s two-way ANOVA by ranks test showed that although the distribution of a did not differ across resources(p > .05), the distribution of b did (p < .05). The graphs in Fig. 6 show that, although bmoney is narrowly distributed aroundzero, the distribution of btime is much more heterogeneous. This pattern of findings is the opposite of what we observedfor small stakes.

Small stakes: Parameter estimate ktime. The loss aversion coefficient for time is given in Table 5. A one-sample Wilcoxonsigned-rank test showed that participants were loss averse for time (ktime = 1.61, p < .001; cf. Study 1).

Large stakes: Parameter estimates ktime/money. The loss aversion coefficients for time and money are given in Table 6. Aone-sample Wilcoxon signed-rank test showed that participants were loss averse for both money (kmoney = 2.08, p < .001)and time (ktime = 1.71, p < .001). A Wilcoxon signed-rank test for related samples showed that the median k did not differacross resources (p > .05). A Friedman’s two-way ANOVA by ranks test showed that the distribution of k did not differ acrossresources (p > .05).

Small stakes: Parameter estimates pþtime and p�time=money. The decision weights for time and monetary outcomes are given inTable 5. A one-sample Wilcoxon signed-rank test showed that participants could well approximate the probability of win-ning time (p > .05); however, participants underestimated the probability of losing either time or money (p < .001 in bothcases). Another Wilcoxon signed-rank test for related samples showed that the median p� did not differ across resources(p > .05). A Friedman’s two-way ANOVA by ranks test showed also that the distribution of p� did not differ across resources(p > .05). Except for the value of pþtime, these results replicate the findings of Study 1.

Large stakes: Parameter estimates pþtime=money and p�time=money. The decision weights for time and monetary outcomes aregiven in Table 6. A one-sample Wilcoxon signed-rank test showed that participants could well approximate probabilitiesof winning time and of winning money (p > .05 in both cases) but that they underestimated the probability of losing time(p < .01) and of losing money (p < .001). Another Wilcoxon signed-rank test for related samples showed that neither the med-ian p+ nor the median p� differed across resources (p > .05 in both cases). A Friedman’s two-way ANOVA by ranks test furthershowed that neither the distribution of p+ (p > .05) nor the distribution of p� (p > .05) differed across resources.

6.5. Discussion

Consistent with Study 1’s results for small stakes, Study 2 showed that individual risk preferences, decision weights, lossaversion, and utility functions for gains were similar for large time and monetary outcomes. Yet in contrast to the results forsmall stakes, we found that the utility function for large money losses is less (rather than more) concave and variable than isthe utility function for large time losses. These findings indicate that the utility function for losses differs between these tworesources and that the nature of this difference may depend on the size of the stakes.

7. General discussion

Should I opt for the 50-min traffic-free way home, or should I rather gamble on the shorter but traffic-sensitive route witha 50–50 chance of driving 40 min or 60 min? This research investigates whether time-based decisions under risk are made inthe same way as monetary decisions under risk. By eliciting the CEs of two-outcome prospects, we obtain model-freeinsights into individual risk-taking behavior for time- and monetary outcomes. These CEs are then used to estimate thePT parameters for time and money. We find that individuals hold similar risk preferences for time and money, which impliesthat a similar decision will be made whether our example’s options are expressed in gasoline costs or in minutes spent driv-ing. Likewise, we find evidence that ‘‘time is money’’ in the context of loss aversion (ktime = kmoney), decision weighting

(pþ=�time ¼ pþ=�money), and the utility function for gains (atime ¼ amoney). However, we find that individuals value time and monetarylosses differently (btime – bmoney). Whereas the utility function for small money losses is more concave and heterogeneousthan the utility function for small time losses (Study 1), this pattern reverses when the stakes are large. For large losses,the utility function for time is more concave and heterogeneous than the one for money (Study 2). As the effects of outcomemagnitude (small versus large stakes) and resource context (time versus money) are cleanly disentangled in the current setof studies, we are thus able to provide thorough insights into how individuals make decisions under risk for time versusmonetary outcomes.

7.1. The utility function and loss aversion

We find that individuals are equally loss averse for time and money (ktime ¼ kmoney and D(ktime) = D(kmoney)), value timeand monetary gains similarly (atime ¼ amoney and D(atime) = D(amoney)), and value time and monetary losses differently(btime – bmoney and D(btime) – D(bmoney)). It is our view that this pattern of findings can be explained by the effect of ‘‘slack’’in the respective resource domain. We start by focusing on how slack can explain differences in the loss domain. Recall thatthe utility function for large money losses is less concave and variable than the one for large time losses. Zauberman andLynch (2005) find that, whereas individuals perceive more time slack in the long term (than in the short term) to complete

Fig. 5. Value functions for large time and money stakes (Study 2).

A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72 65

several tasks, the same cannot be said of money. That is, individuals believe they will have more time—but not more money—in a few months’ time. Individuals are thus poor at anticipating future competition for their time (but not for their money).For instance, Spiller and Lynch (2009) find that even though participants underestimate the time needed to finish their hol-iday gift shopping (i.e., ‘‘planning fallacy’’), they do not underestimate the money spent on that shopping. Individuals thusseem to perceive that they have more slack in the domain of large-scale time projects than in the domain of large-scalemoney projects. That individuals underestimate the competition among their large-scale time projects may reflect the dif-ficulty of imagining what, exactly, will happen in the long-term or anticipating the precise steps needed to complete a task.This dynamic is captured by the notion that time’s value is more ambiguous than the value of money (Okada & Hoch, 2004).All things considered, we believe that the difference in slack (i.e., more slack for large time than for large money outcomes)may explain why large time losses are less painful than large money losses—a pattern that is consistent with the utility func-tion for large time losses being more concave than the one for large money losses (Fig. 7, left panel). The difference in slackmay likewise possibly explain why the utility function for large time losses is more heterogeneous than the one for largemoney losses. Individuals seem to have more difficulty imagining competition among their large time than among their largemoney projects, so the error or variance in the valuation of large time losses may be greater than in the case of large moneylosses.

In the short term, however, individuals do not see themselves as having time slack (Zauberman & Lynch, 2005).Short-term projects compete strongly for time, and individuals often feel as if they are ‘‘running out of time’’. Some studieshave even suggested that the perceived slack for small projects may actually be lower in the time domain than in the money

Large Loss Money – βmoney Large Loss Time – β�me

01020304050

01020304050

Fig. 6. Distribution of btime vs money for large stakes (Study 2).

Fig. 7. Effects of stakes (large vs. small) and resource (time vs. money).

66 A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72

domain. In the first place, Okada and Hoch (2004) document that individuals believe small money shortages can easily beabsorbed (e.g., by borrowing money; cf. using a credit card) but that small time shortages are more difficult to absorb (sincetime can be neither saved nor borrowed). Time losses often interfere with the execution of other salient projects. Putotherwise, money is more fungible than time, which may lead to individuals perceiving more competition among small timeprojects than among small monetary projects.

Second, Zauberman and Lynch (2005) suggest that (i) the perceived slack in the domain of large time outcomes is largerthan the perceived slack in the domain of large money outcomes, (ii) the perceived slack in the domain of large time out-comes is much larger than the perceived slack in the domain of small time outcomes,5 and (iii) the perceived slack in thedomain of large money outcomes is equal to the perceived slack in the domain of small money outcomes. Together, these con-siderations hint at the possibility that, when the stakes are small, perceived slack may be greater in the money than in the timedomain. This difference in slack (i.e., more slack for small money outcomes than for small time outcomes) may explain whysmall time losses are more painful than small money losses. That pattern is consistent with a more concave utility functionfor small money losses than for small time losses (Fig. 7, right panel). Similarly, we believe that the difference in slack mayexplain why the utility function for small money losses is more variable than the utility function for small time losses. If indi-viduals perceive that they have more slack for their small monetary (vs. time) outcomes and hence seem to have more difficultyimagining competition for their small monetary (vs. time) outcomes, then the error or variance in the valuation of small money(vs. time) losses is likely to be higher.

We now focus on the question of why these differences in perceived slack are not reflected in a ‘‘resource (time versusmoney) by stake (small versus large stakes)’’ effect on the utility function for gains. In other words: Why doesatime ¼ amoney for both small stakes and large stakes? One possible explanation is that gains and losses are fundamentallydifferent in the sense that losses interfere with scheduled activities or purchases whereas gains do not. For instance, time(monetary) losses—as when a seminar takes 30 min longer than expected (car repairs cost $500 more than expected)—aretypically disruptive of the affected individual’s schedule (budget) in the sense that some salient and scheduled activities(purchases) may then become impossible: the individual may be too late to catch a train (unable to afford a new washingmachine). Such interference in schedules (budgets) is likely to be worse when there is no slack—that is, for small time out-comes and for large monetary outcomes. The valuation of unexpected time (monetary) losses thus depends on the salience ofactivities (purchases) that the individual must forgo. In contrast, time or monetary gains are utilized for activities (purchases)that were not scheduled (budgeted) in advance. These new activities (purchases) are likely to be less salient than those for-gone owing to losses (Prelec & Loewenstein, 1998). We believe, then, that the amount of slack in the schedule or budgetexerts more influence on the valuation of losses (since they might interfere with scheduled activities or purchases) thanon the valuation of gains (since they do not interfere with scheduled activities or purchases).

We thus believe that the slack argument is much more important for losses than for gains. That said, we did observe adirectional ‘‘resource by stake’’ effect on the utility function for gains that is consistent with the slack explanation. To bespecific, we found that gaining small time outcomes tends to be more pleasurable than gaining small money outcomes(which is consistent with the idea that people perceive less slack for small time vs. money outcomes; see Fig. 1) and thatgaining large money outcomes tends to be more pleasurable than gaining large time outcomes (which is consistent withthe idea that people perceive less slack for large money vs. time outcomes; see Fig. 5). We believe that these tendencieson the utility function for gains combined with the significant ‘‘resource by stake’’ effects on the utility function for lossesmay explain why no effects on the loss aversion coefficient were observed (or why ktime ¼ kmoney). To understand thisbetter, consider that the loss aversion coefficient captures how much more painful losing is relative to gaining(e.g., ktime small stakes = ‘‘Pain of losing small time outcome X’’/‘‘Pleasure of gaining small time outcome X’’). For small [large] stakes,we argue that the slack for time is smaller [larger] than the slack for money and that this implies that the pain of losing timeis higher [lower] than the pain of losing money but also that the pleasure of gaining time is somewhat higher [lower] than

5 This is also consistent with the observation that the planning fallacy is more pronounced for long-term than for short-term projects (Spiller & Lynch, 2009).

A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72 67

the pleasure of gaining money. The reasoning that slack influences both components of the loss aversion ratio to some extent(and in the same direction) may dampen a possible ‘‘resource by stake’’ effect on the loss aversion coefficient.6 We call forfuture research to explore this further.

7.2. Hypothetical choices versus real incentives

The current research uses hypothetical (instead of real) time and monetary payoffs. There has been extensive debate inthe literature about whether offering real or hypothetical payoffs yields better or more reliable data. Camerer and Hogarth(1999) review numerous studies that have addressed the role of incentives in measurements of risk attitudes and that oftenfind mixed results. In general, real incentives do seem to reduce data variability (Camerer & Hogarth, 1999), and increase riskaversion (e.g. Holt & Laury, 2002; Weber, Shafir, & Blais, 2004) compared to hypothetical incentives. However, several studiesshowed that the latter difference is small if tasks are cognitively easy, such as when making direct choices between prospects(cf., the choices in our studies; Beattie & Loomes, 1997; Camerer & Hogarth, 1999). Also relevant is that Abdellaoui and Kemel(2014) investigated whether implementing real incentives influences risk preferences for time outcomes in specific. That is,the authors conducted a similar experiment as ours but divided their time sample into two subsets: the first subset of par-ticipants faced hypothetical time payoffs and the second one faced real time incentives. Results showed no differences inresults between both subsets.

Given our aim to compare resources and stake sizes as well as the fact that previous literature did not offer a compellingreason to use incentives in a research setting like ours, two considerations based on internal validity concerns led us todecide to use non-incentivized procedures. First, the use of incentives in our studies would have induced a confoundbetween incentives and resources (time and money) (Abdellaoui & Kemel, 2014; Kemel & Travers, 2015). For one thing,the implementation of real monetary losses requires the provision of a prior monetary endowment (because of ethical rea-sons) and therefore leads to the possibility that participants integrate the loss outcome and perceive it as a non-gain (and notas an actual loss). Yet, the implementation of real time losses does not require such a prior endowment (cf., Abdellaoui &Kemel, 2014; Kroll, Morgenstern, Neumann, Schosser, & Vogt, 2014; Kroll & Vogt, 2008). In the recent experiment ofAbdellaoui and Kemel (2014) for example, participants were told beforehand that the experiment would last approximately2 h (but that it could also be 1 or 3, depending on whether they gained or lost time). Time losses designated an actual waittime in the lab with no amusing/useful things like computers or mobile phones available. Other research in the time domainused similar incentive schemes for time (Kroll & Vogt, 2008; Kroll et al., 2014).7 These examples show that real time losses donot require a prior endowment and it is therefore implausible that participants perceive time losses as non-gains (as they dowith monetary losses). To summarize, the implementation of real incentives produces differences in loss prospects that arenot only attributable to the resource context (time vs. money) but also to the necessity to provide a prior endowment (lossesperceived as non-gains vs. actual losses).

Second, using incentives in our studies would have induced a confound between incentive and stake size (e.g., Abdellaouiet al., 2008; Booij & Van de Kuilen, 2009). Whereas implementing real incentives for small stakes can be done quite easily, itis much more problematic for large stake prospects (up to €18000 and 12 months). As one of the main objectives of thisresearch is to have a clean comparison between the PT parameters for small versus large time and money stakes, incentiviz-ing the small stakes but not the large ones would confound the results. That is, implementation of real incentives (for smallstakes only) would produce differences that are not only attributable to the stake sizes (large vs. small) but also to whetheror not the decisions are incentivised.

In sum, we had good reasons to use hypothetical payoffs in our studies, and want to point out that even though it may stillbe possible that the use of hypothetical payoffs influences the absolute levels of risk preferences and PT parameters, webelieve that the differences we observed between btime and bmoney are fully ascribable to the resource context (time vs.money); they do not reflect the specifics of the elicitation procedure because the same procedure was used for both timeand monetary outcomes.

7.3. Relation to intertemporal decision-making

This paper deals with decision making under risk and focuses on risks of which the outcomes are expressed in time units.We nevertheless acknowledge that one confound of our research is that the timing of the resolution of the outcome dependson the outcome itself. To give an example, it is possible that participants reframed a prospect of leaving a two-hour exper-iment 30 min [15 min] earlier than planned as a situation where the outcome (of leaving the experiment) is delayed for90 min [105 min] (at least at the start of the experiment). One concern, therefore, could be that we are tapping into people’sintertemporal preferences rather than into their time risk preferences. We believe however that this concern is largely alle-viated by the experimental setup of Study 2. Unlike the cover story of Study 1, the one of Study 2 did not articulate the

6 Note that loss aversion is directionally smaller for small monetary (k = 2.09) versus time (k = 2.14) outcomes but larger for large monetary (k = 2.08) versustime (k = 1.71) outcomes. These numbers are consistent with this reasoning.

7 Kroll and Vogt (2008) incentivized an experiment that required participants to indicate their preference between two risk prospects that were expressed interms of waiting time. Depending on their choices participants had to wait for a certain amount of time in an experimental cabin after completing theexperimental tasks without communication devices or books.

68 A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72

reference duration for the hypothetical project, making a reformulation of the prospects in terms of delay difficult. To bespecific, we asked participants in Study 2 to imagine that they had to undertake a small-scale [large-scale] project and thatthis project would take X months. The fact that the results for small stakes of Study 2 replicated the results of Study 1 sup-ports our reasoning that we are tapping into people’s risk preferences (rather than their intertemporal preferences).

A related concern is that the effects of outcome magnitude (small versus large stakes) and outcome timing (now versusdelayed) on the PT parameters could be confounded. Whereas the small outcomes of Study 1 resolve within a window ofknown time commitments (e.g., finishing the experiment 30 min earlier than expected), the large outcomes of Study 2resolve in the future (e.g., finishing a large-scale project 2 months earlier than expected). As a counterargument, however,we point out that even though the effect of operating in the window of known time commitments is less likely to play a rolein the small stake conditions of Study 2 where the reference is more abstract (compared to Study 1), we find similar results inboth studies. Nevertheless, future research could further unravel the effects of outcome magnitude versus outcome resolu-tion by using CE questions involving small stake gambles that resolve in the future, such as: ‘‘Which option would you pre-fer? Gaining 15 min in 4 months for sure or participating in a gamble with a 50% chance of gaining 30 min in 4 months and a50% chance of not gaining time in 4 months’’.

7.4. Interdependence versus tractability

The semi-parametric method of Abdellaoui et al. (2008) provides a measurement of the utility function that is not inde-pendent of the measurement of the decision weights. One implication of this interdependence is that the resulting exponen-tial coefficients (a, b) are correlated with the decision weights (p+, p�) for each of the domains (gain vs. loss) and resourcecontexts (time vs. money).8 We acknowledge that this is a shortcoming that decreases the robustness of our measurementmethod (Abdellaoui et al., 2008), certainly compared to the ‘‘trade-off method’’ (Wakker & Deneffe, 1996) which is the onlymethod to date that allows for an independent measurement of the two components (Qiu & Steiger, 2011). However, ourmethod (Abdellaoui et al., 2008) outperforms the trade-off method in several other important ways. First, it minimizes the cog-nitive burden for participants as it only requires a minimal number of CE measurements and as it is not built on a comparisonbetween two risky prospects (which is used in step 1 of the trade-off method, and is generally thought to be more difficult thanthe choice between one sure versus one risky option; Abdellaoui et al., 2008). Second, it is not susceptible to error propagationas the different certainty equivalents are not linked. These two advantages increase the robustness of the semi-parametricmethod of Abdellaoui et al. (2008) (compared to the trade-off method) and simultaneously highlight the need for developinga measurement method that combines the advantage of measuring decision weights and utility independently, and of not put-ting too much cognitive burden on participants. We call upon further research to further optimize the measurement methodsused in decision analyses.

7.5. Comparison to previous research on PT parameters in monetary and nonmonetary contexts

Previous literature dedicated to eliciting risk preferences and PT components for large, symmetric monetary prospectstypically found the following: (1) risk aversion for gains and risk seeking or risk neutrality for losses, (2) concave utilityfor gains and convex or concave utility for losses, (3) underestimation of the chance to win and also of the chance to lose,and (4) loss aversion (Abdellaoui, Bleichrodt, & Paraschiv, 2007; Abdellaoui et al., 2008; Booij & Van de Kuilen, 2009;Tversky & Kahneman, 1992). Comparing these results with our findings for large monetary outcomes reveals much similarityin the domain of losses. Yet for gains we observe more risk neutrality, less utility curvature, and less probability weightingthan reported in previous studies.9 Our experimental design differed from those studies in an important way: we used com-puterized tasks—rather than individual interviews—to collect the data. This allowed us to investigate risk preferences for a largesample of participants, and it also reduced social desirability concerns (Richman, Kiesler, Weisband, & Drasgow, 1999).Computerized tasks may however lead to lower levels of attention. Hence we urge future research to investigate the effectof (not) using individual interviews on absolute risk preferences and parameters. Note that our studies also differed from someprevious studies with regard to the use of hypothetical payoffs (rather than real incentives; for more explanation on this issuesee Section 7.2).

Our research also contributes to the understanding of how PT’s parameters behave in a nonmonetary context. In additionto Abdellaoui and Kemel (2014), discussed in Section 2, and some papers in the health domain (Attema, Brouwer, &l’Haridon, 2013; Bleichrodt & Pinto, 2000), the decision-making literature has been dominated by the study of monetary out-comes (Wakker, 2010). However, there are some attempts relating PT to emotional outcomes. Our results show that individ-

uals are equally optimistic about achieving a specific time versus monetary outcome (pþ=�time ¼ pþ=�money). The implication is thatoptimism seems not domain specific—which runs counter to studies showing that decision weighting is strongly dependent

8 For Study 1: CORR (atime, p+time) = .56; CORR (btime, p�time) = .59 and CORR (amoney, p+

money) = .64; CORR (bmoney, p�money) = .68. For Study 2 – Small stakes:CORR (atime, p+

time) = .63; CORR (btime, p�time) = .58 and CORR (amoney, p+money) = .66; CORR (bmoney, p�money) = .71. For Study 2 – Large stakes: CORR (atime,

p+time) = .63; CORR (btime, p�time) = .58 and CORR (amoney, p+

money) = .66; CORR (bmoney, p�money) = .71.9 For large monetary outcomes, we observe that 33.80% has a pattern of risk aversion for gains and risk seeking for losses; 26.50% has a pattern of risk

aversion for gains and for losses. Also for large money stakes, we observe that 19.10% shows concave utility for gains and convex utility for losses; 33.80% has apattern of concave utility for gains and for losses.

Fig. A1. Illustration of the task in the gain domain.

Fig. A2. Illustration of the task in the loss domain.

A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72 69

on the outcomes of those decisions. For instance, Rottenstreich and Hsee (2001) find that the valuation of prospects is muchless sensitive to the likelihood of their occurring (i.e., but more to the mere possibility of occurring) when the outcome isemotional (‘‘getting a painful electric shock’’) than when the outcome is purely financial; hence these researchers attributethe domain specificity of probability weighting to the outcomes’ level of ‘‘emotionality’’. But McGraw, Shafir, and Todorov(2010) challenge that conclusion by arguing that the probabilities of the aforementioned monetary and nonmonetary pro-spects were weighted differently because of fundamental differences in evaluation mode. That is, monetary prospectsinvolve numeric amounts that can be combined in a straightforward way with probabilities to yield at least an approximate‘‘expectation’’ of value (e.g., the CE of an 84% chance of winning $60 is easy to calculate); in contrast, nonmonetary outcomesare typically not numeric and do not lend themselves to easy combination with the associated probabilities (the CE of an 84%chance of receiving a dozen red roses is difficult to calculate). Thus the difference between high- and low-probability pro-spects is far more pronounced for monetary than for nonmonetary outcomes. Our result that the decision weights for timeand money are similar may be explained by relying on this latter set of findings. Much as with monetary prospects, timeprospects involve numeric amounts that can be easily combined with probabilities to obtain an approximate expectationof value.

Fig. A3. Illustration of the task in the mixed domain.

Table B1Example iteration processes in the gain round.

Iteration Choices offered to elicit the CE

1 +15 min versus (+30 min, ½; 0 min)2 +7.5 min versus (+30 min, ½; 0 min)3 +11.25 min versus (+30 min, ½; 0 min)4 +9.375 min versus (+30 min, ½; 0 min)5 +10.313 min versus (+30 min, ½; 0 min)6 +9.844 min versus (+30 min, ½; 0 min)

CE (10.313 + 9.844)/2 = 10.079 min

Table B2Example iteration processes in the mixed round.

Iteration Choices offered to elicit the CE

1 0 min versus (+10.079 min, ½; �10.079 min)2 0 min versus (+10.079 min, ½; �5.039 min)3 0 min versus (+10.079 min, ½; �7.559 min)4 0 min versus (+10.079 min, ½; �6.299 min)5 0 min versus (+10.079 min, ½; �6.929 min)6 0 min versus (+10.079 min, ½; �6.614 min)

CE (6.929 + 6.614)/2 = 6.772 min

Table C1An example of the restructured dataset that was imported in SAS�.

Participant number Prospect ID CE x y

171757 1 2859,375 6000 0171757 2 4289,063 9000 0171757 3 5531,25 12,000 0171757 4 8296,875 18,000 0171757 5 13781,25 18,000 6000171757 6 13359,38 18,000 12,000181623 1 1359,375 6000 0181623 2 3023,438 9000 0181623 3 4031,25 12,000 0181623 4 6046,875 18,000 0181623 5 12281,25 18,000 6000181623 6 14765,63 18,000 12,000. . . . . . . . . . . . . . .

70 A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72

Fig. C1. An example of the SAS code.

A. Festjens et al. / Journal of Economic Psychology 50 (2015) 52–72 71

8. Conclusion

The aim of this research was to investigate whether individuals make decisions under risk similarly when the outcomesare expressed in time versus monetary units. We found that individuals hold similar risk preferences for time and money:individuals will arrive at a similar decision regardless of whether the risky alternatives are expressed in time or monetaryterms. We also found evidence that ‘‘time is money’’ with respect to the utility curvature for gains, the loss aversion coef-ficient, and decision weighting for both gains and losses. However, we found that individuals value time and monetary lossesdifferently; small time losses seem to be more painful than small money losses, but this pattern is reversed when the stakesare large. Our findings can be condensed as follows: time-based decision making under risk resembles money-based decisionmaking under risk except for the valuation of losses.

Acknowledgements

We thank Han Bleichrodt, Pierre Chandon, and Daniel Read and four anonymous reviewers for their helpful and valuablecomments on a previous version of this paper.

Appendix A. Illustration of the task presented to participants

See Figs. A1–A3

Appendix B. Illustration of our bisection process

Concrete illustrations of the bisection process—by which we zero in on individuals’ CEs—are offered by Tables B1 and B2,where boldface type signifies the preferred options. Starting values in the iterations were chosen such that prospects hadequal expected value. Depending on the choices made, the certain outcome (or, in the mixed round, the loss) was increasedor decreased five times. The size of the change was always half the size of the change in the previous question. Thus a typicalsequence might be as follows: from iteration 1 to iteration 2, (15 min/2) = 7.5-min change; iteration 2 to 3, (7.5 min/2) =3.75-min change; iteration 3 to 4, (3.75 min/2) = 1.875-min change; iteration 4 to 5, (1.875 min/2) = 0.9375-min change.This process yielded an interval within which the CE should lie, and the midpoint of that interval was taken as the CE.

Appendix C. SAS code for estimating the PT parameters

This appendix provides a concrete illustration of the procedure that was used to estimate the PT parameters for largemonetary gains. To be specific, the raw dataset was first restructured such that: (1) each row represented a CE observationfor the corresponding prospect (x, p; y) with p = ½ and (2) each of the six CE observations were grouped per participant num-ber. See Table C1 for a concrete illustration of the restructured dataset. The restructured dataset was then imported into thestatistical software package SAS� and a nonlinear estimation procedure was used to estimate the PT parameters (i.e., in thiscase: a and p+) at the participant level. See Fig. C1 for the specific SAS code. The procedure incorporated a ‘‘grid search’’ todetermine the optimal starting values for both parameters (which guarantees the attainment of a global optimum). Theoutput of this procedure was a new dataset with a row for each participant displaying his or hers individual estimates ofa and p+.

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