Running head: Time-based versus money-based decision making under risk. Time-based versus money-based decision making

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1 Running head: Time-based versus money-based decision making under risk Time-based versus money-based decision making under risk: An experimental investigation September 2014 Anouk Festjens, KU Leuven Sabrina Bruyneel, KU Leuven Enrico Diecidue, INSEAD Siegfried Dewitte, KU Leuven Anouk Festjens is a doctoral student at the Research Center for Marketing and Consumer Science at KU Leuven, Faculty of Business and Economics, Naamsestraat 69, B-3000 Leuven, Belgium, Anouk.Festjens@kuleuven.be, Tel: Sabrina Bruyneel is Assistant Professor of Marketing at the Research Center for Marketing and Consumer Science at KU Leuven, Faculty of Business and Economics. Enrico Diecidue is Associate Professor of Decision Sciences at INSEAD. Siegfried Dewitte is Professor of Marketing at the Research Center for Marketing and Consumer Science at KU Leuven, Faculty of Business and Economics. Correspondence: Anouk Festjens. The first author is supported by a PhD fellowship of the Research Foundation Flanders (FWO). The second and fourth authors are supported by grant G N from the Research Foundation Flanders (FWO). We thank Han Bleichrodt, Pierre Chandon, and Daniel Read as well as the Consumer Behavior group at KU Leuven for helpful and valuable comments on a previous version of this paper.

2 1 Abstract This paper investigates whether individuals make similar decisions under risk when the outcomes are expressed in time versus monetary units. We address this issue by using two studies to measure individual risk preferences and prospect theory parameters (i.e., utility curvature, probability weighting, and loss aversion) for both time and money. In the first (resp., second) study we consider relatively small (resp., large) time and monetary outcomes. We find that individuals hold similar risk preferences for time and money; we also find evidence that time is money with regard to the utility curvature for gains, loss aversion, and decision weighting. However, individuals have different valuations of losing time and money. The utility function for small losses of money is more concave and variable than the utility function for small losses of time (Study 1), but the utility function for large losses of time is more concave and variable than that for large losses of money (Study 2). We argue that these results reflect a difference in the perceived slack of the respective resource. Keywords: risky decision making, prospect theory, time versus money outcomes

3 2 1. Introduction Every day, individuals make risky decisions involving time outcomes for instance, when weighing whether to take the longer, traffic-free way home (with the certainty of a 50-minute drive) or the shorter, traffic-sensitive route (with equal chances of a 40-minute or a 60-minute drive), or when deciding whether to take the longer waiting line being serviced by an experienced cashier (with the certainty of a 10-minute wait) or the shorter one serviced by an inexperienced cashier (with equal chances of a 5-minute or a 15-minute wait). Making these choices efficiently has become increasingly 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 outcomes are involved. One reason for this state of affairs may be the economic assumption that time-based decisions under risk should abide by the same principles as monetary decisions under risk (i.e., time is money ; Becker, 1965). Decisions in the money domain have long been studied (see Wakker, 2010). Yet, a growing body of psychological literature demonstrates that individuals treat time and money differently. Therefore, findings in the money domain do not 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 in time versus monetary units. Following Abdellaoui, Bleichrodt, and l Haridon (2008), we use the certainty equivalents (CEs) of two-outcome prospects to measure individual preferences for time and money under conditions of risk; the main advantage of a simple design based on CEs is that it allows for the measurement of attitudes toward risk without

4 3 imposing any particular model of choice. We also use a general model of choice under risk formalized as expressions (1) (3) to quantify psychologically meaningful parameters. In the domain of two-outcome prospects, this model generalizes expected utility and coincides with prospect theory (Tversky & Kahneman, 1992), original prospect theory (Kahneman & Tversky, 1979), RAM/TAX models (Birnbaum, 2008), Viscusi s (1989) prospective reference theory, and Gul s (1991) disappointment aversion theory. We use the shorthand PT when referring to this descriptive prospect theory, which can parsimoniously describe decisions under risk and capture risk attitudes using psychologically meaningful parameters (Wakker, 2010). These attributes are especially relevant for our purposes, since we attempt to illuminate decision processes in a relatively understudied domain. Our results show that, without committing to any specific model of choice, individuals hold similar risk preferences for time 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 contexts. Yet we also find evidence that time is not money : the utility function for losses differs across time- and money-based contexts. That is, the utility function for small money losses is more concave and variable than the utility function for small time 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 moneybased decision making, we describe the model-free measurement of risk preferences as well as the prospect theory parameters for time and money outcomes. Next we report the results of our

5 4 two studies, and we conclude with a discussion of our results. 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 ) and hence 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 whether alternatives are described using monetary units or time units. The ability of consumers to buy time-saving products and services may also have contributed to the widespread belief that time can be expressed in monetary equivalents (Bivens & Volker, 1986; Graham, 1981). For instance, consumers buy products that increase efficiency (e.g., organizational tools), enhance productivity (e.g., technology), and extend life (e.g., fitness and health products). Contrary to the economic literature, research in psychology suggests that people treat time and money differently (Leclerc et al., 1995; Lee, Lee & Zauberman, 2014; Mogilner, 2010). For instance, Soman (2001) demonstrates that past expenditures (i.e., sunk costs) are given less weight when contemplating the investment of time than of money. Saini and Monga (2008) find that quick-and-easy heuristics are used more in the context of time-based than monetary decisions. Okada and Hoch (2004) show that, when individuals pay in time rather than money, they are more 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 slack is more pronounced for time than for money (i.e., individuals have relatively lower expectations of having more money a

6 5 month from now than today). The observed differences in time-based versus money-based decision making are primarily explained by the value of time being more ambiguous than the value of money (Leclerc et al., 1995; 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 is often 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 money in the long run, this is probably not the case in the short run. With regard to the distant future, the value of time is more ambiguous than the value of money because future plans are vague and can be easily moved around. In the immediate future, however, the value of time may be even less ambiguous than the value of money because immediate plans are concrete and difficult to move around. These psychological findings show that individuals treat time and money differently, but the literature has not clarified exactly how these two resources differ. In sum, there are two conflicting views regarding the possibility that time- and moneybased decision making are similar. Standard economics assumes that time is money ; from this perspective, decisions should not vary as a function of whether alternatives are described in time or rather in monetary terms. In contrast, psychological literature assumes that time is not money and predicts that preferences should vary depending on whether alternatives are expressed in time or monetary units. The aim of this paper is to investigate whether time is money when individuals make decisions under risk. Toward that end, we will use a robust and tractable method to measure

7 6 individual preferences under risk both for time and for equivalent monetary amounts. A key advantage of this method is that it offers a systematic approach to studying the components that underlie decision making under risk (i.e., utility, probability weighting, and loss aversion). More specifically, we shall first obtain a model-free measure of an individual s risk preferences for time and money outcomes (in the form of CEs of several two-outcome prospects). Next we obtain information at the individual level about the PT parameters on which such a modelfree measure is based (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992). We are then able to address the question of whether time is money with respect to each prospect theory component separately. For example, individuals may be equally optimistic 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). In the next section, we introduce a descriptive theory to model preferences under risk. We also describe the experimental method used to measure risk preferences for time and money. 2. Measuring preferences 2.1. A descriptive theory for modeling preferences under risk Consider a binary prospect (x, p; y), which means receiving outcome x with probability p and receiving outcome y otherwise. Under a general model of choice, individuals evaluate such prospects as follows: ( ( p) u( x)) ((1 ( p)) u( y)) for gains ( x y 0) ; (1) ( ( p) u( x)) ((1 ( p)) u( y)) for losses ( x y 0) ; (2) ( ( p) u( x)) ( ( p) u( y)) for mixed outcomes ( x 0 y). (3) Here u() is a utility function, π +/ are the decision weights attached to the outcomes, and λ is the

8 7 loss aversion coefficient. For the binary prospects in our studies, this general model which was introduced by Luce (1991) coincides with prospect theory (Tversky & Kahneman, 1992), original prospect theory (Kahneman & Tversky, 1979), RAM/TAX models (Birnbaum, 2008), Viscusi s (1989) prospective reference theory, and Gul s (1991) disappointment aversion theory. Most importantly, this model includes expected utility as special case and resolves a large body of its empirical shortcomings (see Starmer, 2000). Prospect theory is a well-established descriptive theory for monetary decision making under risk (Kahneman & Tversky, 1979; Luce & Fishburn, 1991; Tversky & Kahneman, 1992). Prospect theory is mathematically and psychologically founded (Wakker, 2010), and its tractable form allows for a fairly straightforward estimate of its parameters (utility, decision weights, loss aversion). The main descriptive features of PT can be summarized as follows. First, the theory acknowledges that individuals are more sensitive to changes than to absolute states and that outcomes are thus coded as gains and losses relative to a reference point. This aspect is especially relevant for our study because other authors have shown that reference points play a key role in the valuation of time (Antonides, Verhoef & Van Aalst, 2002; Janakiraman, Meyer & Hoch, 2011; Kumar, Kalwani & Dada, 1997). Another assumption of PT is that losses loom larger than gains a phenomenon known as loss aversion. The importance not only of changes but also of loss aversion is captured by a monotonically increasing utility function that is defined over gains and losses yet is steeper for the latter. Following Köbberling and Wakker (2005), we assume that utility U is composed of a basic utility u (which reflects the value of outcomes) and of loss aversion (which reflects the different evaluation of gains and losses). Thus: u( x) if x 0, U( x) u( x) if x 0; (4) here λ is the loss aversion parameter. Prospect theory further acknowledges that each individual

9 8 has a subjective perception of probability, which is captured by decision weights. Small probabilities are typically overestimated, whereas moderate and large probabilities tend to be underestimated. In PT, these tendencies are represented by a probability weighting function. Of particular importance for our research is prospect theory s assumption that not only utility curvature but also probability weighting and loss aversion contribute to overall risk attitude (Kahneman & Tversky, 1979; Qiu & Steiger, 2011; Toubia et al., 2013). Using PT as our descriptive theory allows us to explore thoroughly the underlying structure of risky decision making Measurement of preferences under risk assuming PT Abdellaoui et al. (2008) introduced a tractable and robust method for measuring individual preferences under risk for monetary outcomes. We shall use this methodology also for time outcomes. The method is based on repeated elicitation of certainty equivalents of two outcome prospects of the form (x, p; y). It consists of three steps: eliciting the CEs of six prospects with pure gain outcomes; eliciting the CEs of six prospects with pure loss outcomes; and eliciting the maximum losses that individuals are willing to bear as regards prospects with mixed outcomes. Consider, for example, eliciting the CE of a pure gain prospect namely, (x, p; y) with x y 0 (and with x and y varying across six two-outcome prospects; p remained constant at ½). The CE is obtained through a series of binary choices. In each choice, an individual is faced with two prospects (or options) labeled A and B, where prospect A is always riskless. As an example in the context of time, individuals must choose between leaving the experiment 15 minutes earlier than planned for certain (option A) or instead participating in a two-outcome gamble that gives them a 50% chance of leaving the experiment 30 minutes earlier than planned and a 50%

10 9 chance of leaving at the planned time (option B); we formalize this latter option by writing (x, p; y) = (+30 min, ½; 0 min) (see Figure A1 in Appendix A for a diagrammatic presentation of this scenario). Depending on the choices that are made, the value of the sure option changes in a bisection process and comes closer to the CE of the prospect after each iteration (see Appendix B for an illustrative example). Starting values for the iterations were chosen in such a way that prospects had equal expected value. There were exactly six iterations in each bisection 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 < y 0 in (x, p; y). In that case, individuals would be asked to choose between leaving the experiment 15 minutes later than planned for sure or participating in a twooutcome prospect that gives them a 50% chance of leaving the experiment 30 minutes later than planned and a 50% chance of leaving at the planned time: ( 30 min, ½; 0 min); see Figure A2. Depending on their choices, the value of the sure option changes with each iteration and comes closer to the CE of the prospect. This way of eliciting CEs allows for two different levels of analysis. First, a model-free risk measure is computed simply by comparing the CE with the expected value (EV) of the prospect. An individual is risk averse (resp., risk neutral, risk seeking) if the CE is smaller than (resp., equal to, larger than) the EV of the prospect. A second level of analysis allows us to estimate the parameters of expressions (1) (3): the curvature of the utility function, the decision weights, and the extent of loss aversion. We remark that this second level of analysis is semiparametric; thus, a parametric specification is adopted for utility but not for the decision weight. Following Abdellaoui et al. (2008), we used the six gain CEs to estimate the utility

11 10 curvature and decision weight for time gains. By (1), the indifference CE ~ (x, ½; y) implies that u(ce) ( ( ) u( x)) ((1 ( )) u( y)), (5) where u() is the utility of the outcome and π + (½) is the decision weight of the probability ½. Following Köbberling and Wakker (2005), we adopted a normalized exponential specification for the utility function: x (1 e )/ if x 0 and 0, x u( x) ( e 1)/ if x 0 and 0, ux ( ) if 0 or 0. (6) The gain function is concave if 0, convex if 0, or linear if 0 (6) into equation (5) now yields. Substituting CE x y 1 e 1 1 e 1 1 e ( 2) (1 ( 2)) (7) for 1 x y y ln(( ( 2) ( e e )) e ) CE. Equation (7) can be easily estimated via the method of nonlinear least squares (i.e., with two unknown parameters, namely decision weight π + (½) and utility curvature. Measuring the utility function and decision weights for time losses is analogous to measuring them for time gains. We obtain the CE of six loss prospects, after which we derive an estimate of utility curvature β for time losses (i.e., concave if β < 0, convex if β > 0, and linear if β = 0). We also estimate the decision weight in the loss domain; that is, π (½) is obtained when we estimate the following equation, which results from substituting (6) into (2):

12 CE x y e 1 e 1 e ( 2) (1 ( 2)) (8) 1 x y y ln(( ( 2) ( e e )) e ) CE. Finally, for estimates in the mixed domain, parameters from the gain and loss domains are connected to obtain a measure of 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 this mixed-domain scenario is one in which individuals must choose between gaining or losing nothing for sure on the one hand or, on the other hand, taking a gamble with a 50% chance of leaving the experiment 10 minutes earlier than planned and a 50% chance of leaving the experiment 10 minutes later than planned: (+10 min, ½; 10 min); see Figure A3. For this estimation, the loss of the two outcome prospects was changed until indifference was reached (see Appendix B). By (3) and (4), we have u(0) ( ( ) U( G)) ( ( ) U( L)). (9) Because λ is the only unknown component in (9), its value is determined directly by solving the equation. Thus, ( ) ug ( ). ( ) ul ( ) In short, our elicitation method provides a model-free measure of risk attitude as well as the PT parameters of each individual: the utility curvature for gains ( ), decision weights for gain prospects (π + ), utility curvature for losses (β), decision weights for loss prospects (π ), and an index of loss aversion (λ). 3. The studies Two studies were conducted to measure risk preferences and the prospect theory parameters for

13 12 time and monetary outcomes. The first study deals with relatively small time and monetary outcomes (viz., time outcomes of up to 60 minutes and monetary outcomes of up to 12). We want to address small-stakes time stimuli because many decisions in daily life involve durations on the order of minutes. In this study, time gains (resp., time losses ) amount to leaving the experiment earlier (resp., later) than planned. 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 have been shown to fluctuate with outcome size (Harinck et al., 2007; Markowitz, 1952). The second study deals with relatively large time and monetary outcomes (time outcomes of up to 12 months; monetary outcomes of up to 18,000). This study uses large stakes as a test of whether Study 1 s findings are robust to changes in outcome size. Zauberman and Lynch (2005) suggest that, whereas the value of large time outcomes is more ambiguous than the value 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 (Leclerc et al., 1995; Okada & Hoch, 2004; Saini & Monga, 2008) and if the relative ambiguity of each resource type varies with the size of the stakes (Zauberman & Lynch, 2005), then we should expect stake size to play a pivotal role in our results. In order for our study design to accommodate the larger time stakes since it would be nonsensical to leave an experiment twelve months earlier or later than planned we modified the experimental context slightly. In particular: time gains (losses) now refer to finishing a large-scale hypothetical project earlier (later) than planned. To ensure that the results for large stakes are fully ascribable to the size of the stakes and not to the changed experimental context, we also tested whether the results for small stakes

14 13 (Study 1) were similar in the new experimental context. For this test, we measured whether risk preferences for small time and monetary outcomes were similar when time gains (losses) referred to finishing a small-scale hypothetical project rather than leaving the experiment earlier (later) than planned. 4. 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 time and money for each participant in the sample Participants The participants in our two-stage study were 157 undergraduate students (60 men, 97 women) ranging in age from 18 to 28 years (M = yr; SD = 3.37). Each was paid a flat fee of 20 at the end of the second session Procedure Participants came to the laboratory in groups of ten. Each participant was assigned a seat in a partially enclosed cubicle and 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 sessions was counterbalanced and had no effect on our results; this temporal separation in our preference measurements was intended to reduce both sequence effects and fatigue effects.) Once seated, participants were shown an example of a CE elicitation so that they could familiarize themselves with the task. Participants were also told that there were three rounds of tasks, one each for gains,

15 14 losses, and mixed prospects. The certainty equivalents for prospects involving pure gain outcomes were always elicited first (because output from this round served as input for the mixed round), and the order of CE elicitation for pure loss and for the mixed domain was counterbalanced. After each step there was a break during which a 3-minute nature documentary was shown. All CEs were obtained through a bisection process, as illustrated in Appendix B, that zeroed in on participants CEs. We used hypothetical payoffs: participants were asked to imagine staying in the lab longer or leaving sooner than planned, and the study actually ended as planned. Previous research indicates that using real incentives has no effect on the estimation of PT parameters (see, e.g., Abdellaoui, Baillon et al., 2011; Abdellaoui, L Haridon & Paraschiv, 2011). To measure the reliability of participants choices, we repeated elicitation of CEs for the third prospect in the domains of gains, losses, and mixed gambles for both time and money (see Section 4.4.2). We employed this reliability measure when evaluating the consistency of participants answers Stimuli Our estimation of risk preferences and of PT parameters for time gains and losses was based on the elicited CEs for six prospects in each case (see Table 1). To determine the CE of (+30 min, ½; 0 min) [ 30 min, ½; 0 min], for instance, we asked participants the following question[s]: Would you prefer to leave the experiment 15 minutes earlier [later] than planned with certainty, or instead are you prepared to gamble with a 50% chance of leaving the experiment 30 minutes earlier [later] than planned and a 50% chance of gaining [losing] nothing? The amount of the sure option was then changed via a bisection process until indifference was reached (see

16 15 Appendix B). Our estimation of the loss aversion coefficient for time was based on the maximum loss that participants were willing to incur in four 1 mixed-outcome prospects (Table 1). In other words, we selected a CE of the gain round, G, and elicited the loss L for which 0 ~ (G, p; L). So, for example, if we wanted to determine this value for the prospect ( min, ½; min) then we would ask participants the following question: Do you prefer to gain or lose nothing with certainty or rather to gamble with a 50% chance of leaving the experiment minutes later than planned and a 50% chance of leaving the experiment minutes earlier than planned? The amount of the loss was then changed via a bisection process until indifference was reached. Table 1: Prospects, EVs, and elicited CEs (Study 1) Time prospect (min) EV Median CE Money prospect ( ) EV Median CE (+20 min, ½; 0 min) [ ] (+ 4, ½; 0) [ ] (+30 min, ½; 0 min) [ ] (+ 6, ½; 0) [ ] (+40 min, ½; 0 min) [ ] (+ 8, ½; 0) [ ] (+60 min, ½; 0 min) [ ] (+ 12, ½; 0) [ ] (+60 min, ½; +20 min) [ ] (+ 12, ½; + 4) [ ] (+60 min, ½; +40 min) [ ] (+ 12, ½; + 8) [ ] ( 20 min, ½; 0 min) [ ] ( 4, ½; 0) [ ] ( 30 min, ½; 0 min) [ ] ( 6, ½; 0) [ ] ( 40 min, ½; 0 min) [ ] ( 8, ½; 0) [ ] ( 60 min, ½; 0 min) [ ] ( 12, ½; 0) [ ] ( 60 min, ½; 20 min) [ ] ( 12, ½; 4) [ ] ( 60 min, ½; 40 min) [ ] ( 12, ½; 8) [ ] ( min, ½; min) [ ] (+ 2.34, ½; ) [ ] ( min, ½; min) [ ] (+ 3.23, ½; ) [ ] ( min, ½; min) [ ] (+ 4.19, ½; ) [ ] ( min, ½; min) [ ] (+ 6.28, ½; ) [ ] A fixed conversion rate of 12/60 minutes was used to convert the time stimuli into the 1 Four questions should suffice in light of Abdellaoui et al. s (2008) observation that the loss aversion index is stable across different mixed prospects.

17 16 monetary stimuli. This conversion rate reflects the wage that a student could earn in the labor market for one hour of work at the time of our study. Thus, time was expressed in terms of its monetary opportunity cost (Becker, 1965). Analogously to the elicitation for time outcomes, the estimation of risk preferences and PT parameters for monetary gains and losses was based on the CE of six prospects each (Table 1). To determine the CE of (+ 6, ½; 0) [ 6, ½; 0], for instance, we asked participants the following question[s]: Would you prefer to gain [lose] 3 with certainty, or are you prepared to gamble with a 50% chance of gaining [losing] 6 and a 50% chance of gaining [losing] nothing? The amount of the sure option was then changed in a bisection process until indifference was reached. Our estimation of the loss aversion coefficient for money was based on the maximum loss that participants were willing to incur in four mixedoutcome prospects (Table 1). So just as with time outcomes, we selected a CE of the gain round, G, and elicited the loss L for which 0 ~ (G, p; L). To determine this value for the prospect (+ 2.34, ½; ), for instance, we asked participants the following question: Do you prefer to gain or lose nothing with certainty or instead to gamble with a 50% chance of losing 2.34 and a 50% chance of gaining 2.34? Once again, the amount of the loss was changed in a bisection process until indifference was reached Results Outliers Ten 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, λ > 100 for time (n = 6) or for money (n = 3) or for both (n = 1).

18 Reliability check We assessed the reliability of participants answers by repeating the CE elicitation of one prospect in each of three rounds (domains of gains, losses, and mixed prospects). The Spearman correlations were satisfactory and ranged from.69 to.96. This means that participants were generally consistent in their responses. Paired t-tests revealed, in addition, that no systematic shifts in CEs occurred from the first to the second measurement for any of the items ( t < 1.68 in all cases) Model-free results Median CEs and model-free risk attitude. Table 1 shows the median CEs of the prospects; similar results were obtained for the means. After comparing the median CE with the EV of each prospect, we observed that the dominant risk pattern was one of risk seeking for gains (CE > EV for five time and money prospects) and risk aversion for losses (CE < EV for four time and money prospects). To investigate this risk pattern in more depth, we computed a model-free index of risk attitude at the participant level (see Table 2, wherein H 0 denotes the null hypothesis). 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 is considered risk averse (risk neutral, risk seeking) if RISK + is smaller than (equal to, larger than) ½ or if RISK that is, the absolute value of RISK is larger than (equal to, smaller than) ½. A one-sample Wilcoxon signed-rank test showed that participants were risk seeking for money and time gains (p <.05) but risk neutral for money and time losses (p >.05). A Wilcoxon signed-rank test for related samples showed that neither the median RISK + nor the median RISK differed across resources (p >.05

19 18 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. Table 2: Parameter estimates and risk attitudes (Study 1) α money α time β money β time π + money π + time π money π time Mean Median SD Q Q H 0 : Medians are equal p =.13, p =.00, reject H 0 p =.66, p =.16, H 0 : Distributions are equal p =.06, p =.03, reject H 0 p =.68, p =.10, λ money λ time RISK + money RISK + time RISK money RISK time Mean Median SD Q Q H 0 : Medians are equal p =.54, p =.65, p =.86, H 0 : Distributions are equal p =.68, p =.68, p =.67, Parameter estimates Parameter estimates α time/money and β time/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 local maximum was obtained). A one-sample Wilcoxon signed-rank test showed that participants had a linear utility function for both money and time gains (p >.05 in each case) but a concave utility function for both money and time losses (p <.001 in each case). A Wilcoxon signed-rank test for related samples showed

20 -60 min min min min min min min min min min min min that the median did not differ across resources (p >.05) but also that the median β was more concave for money than for time (p <.001). Figure 1 displays the median utility function for time and monetary outcomes. A Friedman s two-way ANOVA by ranks test showed that, although the distribution of did not differ across resources (p >.05), the distribution of β did (p <.05). The distribution of β time/money, which is plotted in Figure 2, gives us additional insight into this difference. Figure 2 shows that, although β time is narrowly distributed around zero (which means that many participants value time losses linearly), the distribution of β money is much more heterogeneous (i.e., variable). Figure 1: Value functions for time and money (Study 1) Conversion rate: 60 min = 12. Time Money

21 20 Figure 2: Distribution of β time/money Loss Money β money Loss Time β time Parameter estimates λ time/money. The loss aversion coefficients for time and money are given in Table 2. A one-sample Wilcoxon signed-rank test showed that participants were loss averse for both money (λ money = 2.14, p <.001) and time (λ time = 2.09, p <.001). A Wilcoxon signed-rank test for related samples showed that the median λ did not differ across resources (p >.05). A Friedman s two-way ANOVA by ranks test showed that the distribution of λ did not differ across resources (p >.05). Parameter estimates time/money and 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 overweighted 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 samples showed that neither the median π + nor the median π differed across resources (p >.05 in both cases). Also, a Friedman s two-way ANOVA by ranks test showed that neither the distribution of π + nor of π differed across resources (p >.05 in both cases) Discussion Overall, we observed that risk preferences were similar for time and monetary outcomes ( time

22 21 is money ). In addition, our measurement method allowed us to study the underlying components of these risk preferences (i.e., utility curvature, decision weights, and loss aversion). Results showed that neither the utility function for gains ( ), the decision weights for gains and losses (π +/ ), nor the loss aversion coefficient (λ) differed across resource contexts. However, the utility function for time losses (β time ) was more linear and homogeneous than was the utility function for money losses (β money ). 5. 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 test whether the results of Study 1 could be extended to the case of larger stakes. We expected the size of the stakes to play a key role 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 when the outcomes are large but not when they are small (Zauberman & Lynch, 2005). To accommodate for the larger stakes, we modified the experimental context: time outcomes now reference finishing a large-scale project earlier or later than planned (rather than leaving the experimental session earlier or later than planned). We ensured that the results for large stakes are fully ascribable to the size of those stakes (and not to the change in experimental context) by testing for whether the results for small stakes are robust to that change. In sum: the first part of Study 2 elicited risk preferences for large time and monetary outcomes (i.e., up to 12 months and 18,000) in one group of participants; the second part elicited risk preferences for small time and monetary outcomes (i.e., up to 60 minutes and 12, cf. Study 1) in another group of participants. In both parts, time outcomes referred to finishing a project earlier or later than

23 22 planned rather than to leaving an experiment earlier or later than planned Participants Study 2 involved 128 students (of whom 68 were women) ranging in age from 18 to 27 years (M = yr; SD = 1.79). Each participant received a flat fee at the end of the study Procedure To test whether the results of Study 1 could be extended to large stakes, one group of participants (n = 80, of whom 41 were women) received CE questions about large time and monetary outcomes. To test whether the results of Study 1 are the same in another experimental setting (finishing a hypothetical project earlier or later than planned rather than leaving the experiment earlier or later than planned), another group of participants (n = 48, of whom 27 were women) received CE questions about small time and monetary outcomes. The same procedure as in Study 1 was implemented to measure the CEs for the largestakes prospects. Thus, this part of the study consisted of two stages (time versus money; the order of the stages was counterbalanced and did not affect the results) of three rounds each (gain, loss, and mixed outcomes; the order of the loss and mixed round was counterbalanced); as before, we used hypothetical payoffs. Prior to giving participants an example of a CE question, we asked them to imagine engaging in an important large-scale project that might keep them busy for a considerable amount of time [that might cost them a considerable amount of money]. We also told them that, owing to several circumstances, the project may finish earlier or last longer [may cost less or more] than expected. We said that we were interested in how they would deal with risk regarding the end date [the costs] of the project. The small-stakes procedure was

24 23 exactly the same except for the scale of the project Stimuli We used essentially the same procedure as in Study 1 to obtain the CEs of several large-stakes prospects. The only modifications were in (i) the prospect values (we use those given in Table 4) and (ii) the experimental context. In the case of gains, for example, we asked: Would you prefer that the project ends 3 months earlier [costs 4,500 less] than planned with certainty, or would you rather gamble with taking a 50% chance that the project ends 6 months earlier [costs 9,000 less] than planned and a 50% chance that the projects ends at the planned time [costs as much as planned]? The stimuli for small stakes were identical to those in Study 1 (Table 3). The context of the CE questions for small stakes resembled that for large stakes in that time outcomes referred to finishing a hypothetical project earlier or later than expected. For instance, with regard to the gains domain we might ask the following question: Would you prefer that the project ends 15 minutes earlier [costs 3 less] than planned with certainty, or are you prepared to gamble with a 50% chance that the project ends 30 minutes earlier [costs 6 less] than planned and a 50% chance that the projects ends at the planned time [costs as much as planned]? 5.4. Results Outliers Four 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

25 24 participants, λ > 100 for either time (n = 1) or money (n = 3). Twelve participants (15%) 2 were removed from the dataset for large stakes because they were unwilling to trade a loss no matter how small for the chance of a gain. For these individuals, λ > 100 for time (n = 1) or for money (n = 10) or for both (n = 1) Model-free results Small 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. After comparing the median CE with the EV of each prospect in Table 3, we observed that the dominant risk pattern was that of risk seeking for gains (CE > EV for five time and money prospects) and risk aversion for losses (CE < EV for four time and money prospects). As in Study 1, we sought additional insight into participants risk preferences by computing a model-free index of risk attitude at the participant level (see Table 5 in Section 5.4.3). 3 A participant is 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 money gains (p <.05) but risk neutral for time gains (p >.05), money losses (p >.05), and time losses (p >.05). A Wilcoxon signed-rank test showed that neither the median RISK + nor the median RISK differed across resources (p >.05 in both cases). A Friedman s 2 This percentage may seem high but is comparable to Abdellaoui et al. (2008), who excluded 12.5% of their participants. The percentage of outliers for large stakes (15%) is higher than that for small stakes (8.3%), which is consistent with findings of Harinck et al. (2007) showing that loss aversion is more pronounced for large than for small stakes. The number of participants exhibiting λ > 100 is also more pronounced for large money outcomes (n = 10) than for large time outcomes (n = 1), which seems in line with a slack interpretation of our results (see Section 6). 3 We averaged only five (instead of six) normalized CEs for money gains because the CE information was missing for prospect (+ 12, ½; + 8). This shortcoming resulted from a programming error: that prospect was never displayed to participants during the course of their tasks. Hence we obtained no information on the CE of this particular prospect, which also made it impossible to estimate any PT parameters for small monetary gains. However, that estimation is not essential for our current purposes.

26 25 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 results replicate Study 1 s findings. RISK time, these Table 3: Prospects, 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) [ ] (+ 4, ½; 0) [ ] (+30 min, ½; 0 min) [ ] (+ 6, ½; 0) [ ] (+40 min, ½; 0 min) [ ] (+ 8, ½; 0) [ ] (+60 min, ½; 0 min) [ ] (+ 12, ½; 0) [ ] (+60 min, ½; +20 min) [ ] (+ 12, ½; + 4) [ ] (+60 min, ½; +40min) [ ] (+ 12, ½; + 8) ( 20 min, ½; 0 min) [ ] ( 4, ½; 0) [ ] ( 30min, ½; 0 min) [ ] ( 6, ½; 0) [ ] ( 40min, ½; 0 min) [ ] ( 8, ½; 0) [ ] ( 60min, ½; 0 min) [ ] ( 12, ½; 0) [ ] ( 60min, ½; 20 min) [ ] ( 12, ½; 4) [ ] ( 60min, ½; 40 min) [ ] ( 12, ½; 8) [ ] ( min, ½; min) [ ] (+ 2.41, ½; ) [ ] ( min, ½; min) [ ] (+ 3.42, ½; ) [ ] ( min, ½; min) [ ] (+ 4.31, ½; ) [ ] ( min, ½; min) [ ] (+ 6.28, ½; ) [ ] Large stakes: Median CEs and model-free risk attitude. Table 4 shows the median CEs of the 32 large-stakes prospects; similar results were obtained for the means. After comparing the median CE with the EV of each prospect, we observed that the dominant risk pattern was one of risk aversion both for gains (CE < EV for five time and money prospects) and for losses (CE < EV for four time and money prospects). For additional insight into risk preferences, we used the same procedure as in Study 1 to compute a model-free index of risk attitude at the participant level (see Table 6 in Section 5.4.3). A participant is 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 neutral for

27 26 both money and time gains (p >.05) as well as for both money and time losses (p >.05). A Wilcoxon signed-rank test showed further that neither the median RISK + nor the median RISK differed across resources (p >.05 in both cases). A Friedman s two-way ANOVA by ranks test showed that neither the distribution of RISK + nor that of RISK differed across resources (p >.05 in both cases). Table 4: Prospects, 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) [ ] (+ 6000, ½; 0) [ ] (+6 months, ½; 0 months) [ ] (+ 9000, ½; 0) [ ] (+8 months, ½; 0 months) [ ] ( , ½; 0) [ ] (+12 months, ½; 0 months) [ ] ( , ½; 0) [ ] (+12 months, ½; +4 months) [ ] ( , ½; ) [ ] (+12 months, ½; +8 months) [ ] ( , ½; ) [ ] ( 4 months, ½; 0 months) [ ] (+ 6000, ½; 0) [ ] ( 6 months, ½; 0 months) [ ] (+ 9000, ½; 0) [ ] ( 8 months, ½; 0 months) [ ] ( , ½; 0) [ ] ( 12 months, ½; 0 months) [ ] ( , ½; 0) [ ] ( 12 months, ½; 4 months) [ ] ( , ½; ) [ ] ( 12 months, ½; 8 months) [ ] ( , ½; ) [ ] (+1.91 months, ½; months) [ ] ( , ½; ) [ ] (+2.86 months, ½; months) [ ] ( , ½; ) [ ] (+3.81 months, ½; months) [ ] ( , ½; ) [ ] (+5.72 months, ½; months) [ ] ( , ½; ) [ ] Parameter estimates Small stakes: Parameter estimates α time and β time/money. The utility curvatures for time and monetary outcomes are given in Table 5. (As detailed in footnote 3, a programming error prevented our estimating money.) 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-rank test for related samples showed that the median β was more concave for money than for time (p <.01; see

28 27 Figure 3), replicating the results of Study 1. A Friedman s two-way ANOVA by ranks test showed that the distribution of β differed across resources (p <.01). Figure 4 confirms that, although β time is narrowly distributed around zero, the distribution of β money is much more heterogeneous (cf. Study 1). Table 5: Parameter estimates and risk attitudes for small stakes (Study 2) α money α time β money β time π + money π + time π money π time Mean Median SD Q Q H 0 : Medians are equal H 0 : Distributions are equal p =.01, reject H 0 p =.00, reject H 0 λ money λ time RISK + money RISK + time RISK money RISK time Mean Median SD Q Q H 0 : Medians are equal H 0 : Distributions are equal p =.29, p =.55, p = 1.00, p =.29, p =.36, p =.23,

29 -60 min min min min min min min min min min min min Figure 3: Value functions for small time and money stakes (Study 2) Conversion rate: 60 min = 12 Time Money Figure 4: Distribution of β time/money for small stakes 15 Small Loss Money β money 15 Small Loss Time β time Large stakes: Parameter estimates α time/money and β time/money. The utility curvatures for time and monetary outcomes are given in Table 6. A one-sample Wilcoxon signed-rank test

30 29 showed that participants had a linear utility function for both money gains and time gains (p >.05 in each case) but a concave utility function for both money losses and time losses (p <.01 in each case). A Wilcoxon signed-rank test for related samples showed that the median did not differ across resources (p >.05) but also that the median β was more concave for time than for money (p <.01; see Figure 5). A Friedman s two-way ANOVA by ranks test showed that although the distribution of did not differ across resources (p >.05), the distribution of β did (p <.05). The graphs in Figure 6 show that, although β money is narrowly distributed around zero, the distribution of β time is much more heterogeneous. This pattern of findings is the opposite of what we observed for small stakes. Table 6: Parameter estimates and risk attitudes for large stakes (Study 2) α money α time β money β time π + money π + time π money π time Mean Median SD Q Q H 0 : Medians are equal H 0 : Distributions are equal p =.85, p =.81, p =.00, reject H 0 p =.02, reject H 0 p =.89, p =.63, λ money λ time RISK + money RISK + time RISK money RISK time Mean Median SD Q Q p =.34, p =.10, H 0 : Medians are equal p =.58, p =.22, p =.12, H 0 : Distributions are equal p =.81, p =.71, p =.11,

31 -12 months months months months months months months months months months months months Figure 5: Value functions for large time and money stakes (Study 2) Conversion rate: 1 month = 1.5. Euros are expressed in thousands. time money Figure 6: Distribution of β time/money for large stakes Large Loss Money β money Large Loss Time β time

32 31 Small stakes: Parameter estimate λ time. The loss aversion coefficient for time is given in Table 5. A one-sample Wilcoxon signed-rank test showed that participants were loss averse for time (λ time = 1.61, p <.001; cf. Study 1). We were unable to estimate λ money because of a programming error (see footnote 3). Large stakes: Parameter estimates λ time/money. The loss aversion coefficients for time and money are given in Table 6. A one-sample Wilcoxon signed-rank test showed that participants were loss averse for both money (λ money = 2.08, p <.001) and time (λ time = 1.71, p <.001). A Wilcoxon signed-rank test for related samples showed that the median λ did not differ across resources (p >.05). A Friedman s two-way ANOVA by ranks test showed that the distribution of λ did not differ across resources (p >.05). Small stakes: Parameter estimates time and time/money.the decision weights for time- and monetary outcomes are given in Table 5. A one-sample Wilcoxon signed-rank test showed that participants could well approximate the probability of winning time (p >.05); however, participants underestimated the probability of losing either time or money (p <.001 in both cases). As explained previously, a programming error prevented us from estimating money. Another Wilcoxon signed-rank test for related samples showed that the median π did not differ across resources (p >.05). A Friedman s two-way ANOVA by ranks test showed also that the distribution of π did not differ across resources (p >.05). Except for the value of results replicate the findings of Study 1. time, these Large stakes: Parameter estimates time/money and time/money. The decision weights for time and monetary outcomes are given in Table 6. A one-sample Wilcoxon signed-rank test showed that participants could well approximate probabilities of winning time and of winning money (p >.05 in both cases) but that they underestimated the probability of losing time (p <.01) and of

33 32 losing money (p <.001). Another Wilcoxon signed-rank test for related samples showed that neither the median π + nor the median π differed across resources (p >.05 in both cases). A Friedman s two-way ANOVA by ranks test further showed that neither the distribution of π + (p >.05) nor the distribution of π (p >.05) differed across resources Discussion The aim of Study 2 was to test whether our findings for small time and monetary outcomes could be extended to large time and monetary outcomes. Consistent with Study 1 s results for small stakes, we found that individuals risk preferences, decision weights, loss aversion, and utility functions for gains were similar for large time and monetary outcomes. Yet in contrast to the results for small stakes, we found that the utility function for large money losses is less (rather than more) concave and variable than is the utility function for large time losses. These findings indicate that the utility function for losses differs between these two resources and that the nature of this difference depends on the size of the stakes. 6. General discussion Should I opt for the 50-minute traffic-free way home, or should I rather gamble on the shorter but traffic-sensitive route with a chance of driving 40 minutes or 60 minutes? This research investigates whether time-based decisions under risk are made in the same way as monetary decisions under risk. By eliciting the CEs of two-outcome prospects, we obtain modelfree insights into individual risk-taking behavior for time- and monetary outcomes. These CEs are then used to estimate the following prospect theory parameters for time and money: utility curvature (, ), probability weighting (π +, π ), and loss aversion (λ). We find that individuals

34 33 hold similar risk preferences for time and money, which implies that a similar decision will be made whether our example s options are expressed in gasoline costs or in minutes spent driving. Likewise, we find evidence that time is money in the context of loss aversion (λ time = λ money ), decision weighting ( ), and the utility function for gains ( time money ). However, / / time money we find that individuals value time and monetary losses differently ( time money ). Whereas the utility function for small money losses is more concave and heterogeneous than 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) The utility function We find that individuals value time and monetary gains similarly ( time money and SD( ) SD( ) time money ) yet value time and monetary losses differently ( time money and SD( ) SD( ) ). It is our view that this pattern of findings can be explained by the effect time money of slack in the respective resource domain. We start by focusing on how slack can explain differences in the loss domain. Recall that we have demonstrated that, whereas the utility function for small money losses is more concave and variable than the one for small time losses, the utility function for large money losses is less concave and variable than the one for large time losses. Zauberman and Lynch (2005) find that, whereas individuals perceive more time slack in the long term (than in the short term) to complete several tasks, the same cannot be said of money. That is, individuals believe they will have much more time but not much more money in a few months time. Individuals are thus poor at anticipating future competition for their time (but not for their money). This finding is consistent with evidence on the so-called

35 34 planning fallacy (Kahneman & Tversky, 1977; Spiller & Lynch, 2009). That is, individuals seem to underestimate the time but not the money that they will need to complete large-scale projects. For instance, Spiller and Lynch (2009) find that even though participants underestimate the time needed to finish their holiday gift shopping, they do not underestimate the money spent on that shopping. Individuals thus seem to perceive that they have more slack in the domain of largescale time projects than in the domain of large-scale money projects. That individuals underestimate the competition among their large-scale time projects may reflect the difficulty 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 function for large time losses being more concave than the one for large money losses (Figure 7, left panel). The difference in slack might likewise explain why the utility function for large time losses is more heterogeneous than the one for large money losses. Individuals seem to have more difficulty imagining competition among their large time than for their money projects, so the error or variance in the valuation of large time losses may be greater than in the case of large money losses.

36 35 Figure 7: Effects of stakes (large vs. small) and resource (time vs. money) on the utility function for losses LARGE LOSS (months) SMALL LOSS (minutes) Time Money PAIN Time Money PAIN 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 studies have even suggested that the perceived slack for small projects may actually be lower in the time domain than in the money domain. In the first place, Okada and Hoch (2004) document that individuals believe small money shortages can easily be absorbed (e.g., by borrowing money; cf. using a credit card) but that small time shortages are more difficult to absorb (since time can be neither saved nor borrowed). Time losses often interfere with the execution of other salient projects. Put otherwise, money is more fungible than time, which may lead to individuals perceiving more competition among small time projects than among small monetary projects. Second, Zauberman and Lynch (2005) suggest that (i) the perceived slack in the domain of large time outcomes is larger than the perceived slack in the domain of large money outcomes, (ii) the perceived slack in the domain of large time outcomes is much larger than the perceived

37 36 slack in the domain of small time outcomes, 4 and (iii) the perceived slack in the domain of large money outcomes is equal to the perceived slack in the domain of for small money outcomes. Together, these considerations hint at the possibility that, when the stakes are small, perceived slack may be greater in the money than in the time domain. This difference in slack (i.e., more slack for small money outcomes than for small time outcomes) could explain why small time losses are more painful than small money losses. That pattern is consistent with a more concave utility function for small money losses than for small time losses (Figure 7, right panel). Similarly, we believe that the difference in slack may explain why the utility function for small money losses is more variable than the utility function for small time losses. If individuals perceive that they have more slack for their small monetary (vs. time) outcomes and hence seem to have more difficulty imagining the 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 versus money) by stake (small versus large stakes) effect on the utility function for gains. In other words: Why does time money for both small stakes and large stakes? One possible explanation is that gains and losses are fundamentally different 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 minutes longer than expected (car repairs cost $500 more than expected) are typically 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 washing machine). Such interference in schedules (budgets) is likely to be worse when there is no slack 4 This is also consistent with the observation that the planning fallacy is more pronounced for long-term than for short-term projects (Forsyth & Burt, 2008; Spiller & Lynch, 2009).

38 37 that is, for small time outcomes and for large monetary outcomes. The valuation of unexpected time (monetary) losses thus depends on the salience of activities (purchases) that the individual most 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 forgone owing to losses (Prelec & Loewenstein, 1998; Tversky & Kahneman, 1991). Furthermore, the valuation of these new activities (purchases) seems not to depend on the amount of slack in the previously made schedule (budget). We believe, then, that the amount of slack in the schedule or budget exerts more influence on the valuation of losses (since they might interfere with scheduled activities or purchases) than on the valuation of gains (since they do not interfere with scheduled activities or purchases). In short, we argue that differences in slack underlie the observed pattern of findings. Perceived slack is greater for large time outcomes than for large money outcomes, so large time losses are less painful than large money losses (i.e., utility is more concave for time than for money when the stakes are high). Perceived slack is less for small time outcomes than for small money outcomes, so small time losses are more painful than small money losses (i.e., utility is more concave for money than for time when the stakes are low). However, the amount of slack does not affect the valuation of gains because unexpected windfalls do not interfere with scheduled activities or purchases Comparison to previous research on PT parameters in nonmonetary contexts We observe that individuals are equally optimistic about achieving a specific time versus monetary outcome ( / / time money ). The implication is that optimism is not domain specific which runs counter to studies showing that decision weighting is strongly dependent on the

39 38 outcomes of those decisions. For instance, Rottenstreich and Hsee (2001) find that the valuation of prospects is much less sensitive to the likelihood of their occurring (i.e., but more to the mere possibility of occurring) when the outcome is emotional ( meeting and kissing your favorite movie star or getting a painful electric shock ) than when the outcome is purely financial; hence these researchers attribute the domain specificity of probability weighting to the outcomes level of emotionality. But challenging that conclusion is the research of McGraw, Shafir, and Todorov (2010), who argue that the probabilities of the aforementioned monetary and nonmonetary prospects were weighted differently because of fundamental differences in evaluation mode. That is, monetary prospects involve 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 outcomes are 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 prospects is far more pronounced for monetary than for nonmonetary outcomes. Our result that the decision weights for time and money are similar may be explained by relying on this latter set of findings. Much as with monetary prospects, time prospects involve numeric amounts that can be easily combined with probabilities to obtain an approximate expectation of value. This research thus contributes to our understanding of how prospect theory s parameters behave in a nonmonetary context. Aside from the previously cited research on probability weighting with emotional outcomes and some papers in the health domain, the decision-making literature has been dominated by the study of monetary outcomes (Wakker, 2010). However, there is a recent paper that elicits all the PT components (utility, probability weighting, and loss

40 39 aversion) for prospects expressed in time versus monetary outcomes (Abdellaoui & Kemel, 2014). This study finds less-concave utility and less loss aversion for time than for money; it also finds that individuals are more optimistic about winning time than money. However, the authors compare PT components of small time prospects against those of large monetary prospects (while using a conversion rate of 1,200 = 60 minutes). That is unlike our experimental design, which keeps the size of the stakes constant for time and monetary resources (i.e., 12 = 60 minutes for small stakes and 1,500 = 1 month for large stakes). This feature of our approach proved to be important in that we observed various effects attributable to the size of the stakes. Our experimental design augments the study of Abdellaoui and Kemel (2014) by disentangling the effects of stake size and resource context (i.e., time versus money) Limitations and future research Previous literature dedicated to eliciting risk preferences and PT components for large, symmetric monetary prospects typically found the following: (1) risk aversion for gains and risk seeking or risk neutrality for losses, (2) concave utility for 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, 2000; Abdellaoui et al., 2008; Abdellaoui et al., 2013; Abdellaoui, Bleichrodt & Paraschiv, 2007; Tversky & Kahneman, 1992). Comparing these results with our findings for large monetary outcomes reveals much similarity in the domain of losses. Yet for gains we observe more risk neutrality, less utility curvature, and less probability weighting than reported in previous studies. 5 Our experimental design differed from those studies in an 5 Note that for large monetary outcomes, if participants are classified according to their risk preferences, 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. In the case of classification according to utility curvature, we observe that 19.10% shows

41 40 important way: we used computerized tasks rather than individual interviews to collect the data. This allowed us to investigate risk preferences for a large group of participants, and it also reduced social desirability concerns. Computerized tasks may however lead to lower levels of attention. Hence we urge future research to investigate the effect of (not) using individual interviews on absolute risk preferences and parameters. Our studies also differed from some previous studies with regard to the use of hypothetical payoffs (rather than real incentives). Although the large majority of previous studies shows that using hypothetical payoffs has no effect on risk preferences and PT parameters (e.g., Abdellaoui, Baillon et al., 2011; Abdellaoui, L Haridon & Paraschiv, 2011), it remains possible that the hypothetical payoffs nonetheless influenced our results. Notwithstanding the possible effects of computerized tasks and hypothetical payoffs on the absolute levels of risk preferences and PT parameters, we believe that the observed differences between β time and β money are fully ascribable to the resource context; they do not reflect the specifics of the elicitation procedure because the same procedure was used for both time and monetary outcomes. Further research is needed also to test whether time-based decision making is similar to monetary decision making under conditions of ambiguity. In our two studies we looked at how individuals assess time outcomes that have a known probability of occurring (i.e., we looked at decisions under risk). For example, we studied decisions such as when deciding whether to take the longer, traffic-free way home (with the certainty of a 50-minute drive) or the shorter, trafficsensitive route (with a 50% chance of a 60-minute drive but also a 50% chance of only a 40- minute drive). Of course, in real life it is rare for the precise probabilities of outcomes to be known either for time or for money. Real-life decisions typically must be made in ambiguous concave utility for gains and convex utility for losses; 33.80% has a pattern of concave utility for gains and for losses.

42 41 circumstances, by which we mean that outcome probabilities are not known and cannot be readily calculated using available information. There is considerable empirical evidence that individuals are ambiguity averse in the money domain (Camerer & Weber, 1992). In other words, people prefer a known probability of winning over an unknown probability of winning even when the known probability is low and the unknown probability could be a guarantee of winning. Yet we are not aware of any studies addressing whether individuals are ambiguity averse in the time domain or comparing the extent of ambiguity aversion with regard to time versus monetary outcomes. This gap in the literature is surprising when one considers that the greater ambiguity associated with time s value is often identified as the key difference between time and monetary resources (Okada & Hoch, 2004; Saini & Monga, 2008; Soman, 2001). We call for further research to address this issue. 7. Conclusion The aim of this research was to investigate whether individuals make decisions under risk similarly when the outcomes are expressed in time versus monetary units. Our method provided individual information on risk preferences for time and money without committing to a specific choice model. Under the assumptions of prospect theory, we also obtained information on individuals utility curvatures, decision weighting, and loss aversion for both time and monetary outcomes. In line with received economic wisdom, 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 monetary terms. We also found evidence that time is money with respect to the utility curvature for gains, the loss aversion coefficient, and decision weighting for both gains and losses. However, we found that individuals value time

43 42 and monetary losses differently; small time losses seem to be more painful than small money losses, but this pattern is reversed when the stakes are large (i.e., large money losses seem to be more painful than large time losses). Our findings can be condensed as follows: time-based decision making under risk resembles money-based decision making under risk except for the valuation of losses.

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47 46 Appendix A: Illustration of the task presented to participants Figure A1: Illustration of the task in the gain domain Figure A2: Illustration of the task in the loss domain

48 Figure A3: Illustration of the task in the mixed domain 47