Abstract
We introduce, test, and compare two auction-based methods for eliciting discount rates. In these “patience auctions”, participants bid the smallest future sum they would prefer -or- the longest time they would wait for a reward, rather than receive a smaller, immediate payoff. The most patient bidder receives the delayed reward; all others receive the immediate payoff. These auctions allow us to compare discounting when participants’ attention is focused on the temporal versus monetary dimension of delayed rewards. We find that the estimated parameters in the three most commonly used discount functions (exponential, hyperbolic, and quasi-hyperbolic) differ across these two bidding methods (time-bids vs. money-bids). Specifically, our participants tend to show more impatience under time-bids. Furthermore, we find that people are more likely to exhibit exponential (as opposed to hyperbolic) discounting and exhibit less present bias under time-bids, compared to money-bids. To our knowledge, this paper is the first to directly compare time versus money preference elicitations, within the same subjects, using an incentive-compatible mechanism.
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Notes
In fact, there is evidence that consumers may make inconsistent choices across these two normatively equivalent ways of approaching the decision to wait for a discount. Sussman and Olivola (2011; Experiment 2) asked a sample of consumers (N = 351) to indicate both their willingness to wait (in minutes) in line for a 9 % discount on a product, and the smallest discount (in percentage) on that same product for which they would be willing wait 15 min in line. Both sets of preferences were collected using multiple-binary-choice ladders (with waiting times ranging from 5 to 60 min and discounts ranging from 5 to 12 %, respectively), and all participants completed both ladders (with ladders presented in counterbalanced order and usually separated by other, unrelated questions). We reanalyzed the data from that study, focusing on the 339 participants who completed both ladders without multiple switching points and on the equivalent binary-choice question in each ladder (whether they were willing to wait 15 min for a 9 % discount on the product). Our analyses showed that Sussman and Olivola’s participants were significantly more likely to accept waiting 15 min for a 9 % discount (i.e., when the ladder varied the waiting time) than they were to accept a 9 % discount in exchange for a 15 min wait (i.e., when the ladder varied the discount size): likelihood of accepting = 87 vs. 74 %, z = 4.07, p < 0.0001. A closer look at their responses showed that 19 % of the participants reported inconsistent preferences: 16 % accepted to wait 15 min for the 9 % discount but also refused a 9 % discount for the 15 min wait; 3 % exhibited the opposite inconsistency (i.e., refusing to wait 15 min for the 9 % discount but also accepting a 9 % discount for the 15 min wait).
Research comparing decisions about spending (or earning) time versus money (as goods in their own right) has shown that people treat these two commodities very differently (Burmeister-Lamp and Schade unpublished manuscript; De Borger and Fosgerau 2008; Duxbury et al. 2005; Leclerc et al. 1995; Liu and Aaker 2008; Monga and Saini 2009; Okada and Hoch 2004; Saini and Monga 2008; Soman 2001; Soster et al. 2010; Zauberman and Lynch 2005). However, whereas these previous studies compared preferences for two different kinds of goods (money versus time), we are interested in examining how people value the same class of goods (delayed rewards) when they express their preferences along one of two different dimensions (money versus time). The fact that people approach expenditures (or earnings) of money and time differently tells us little about how their patience-levels might vary depending on whether they are focused on the monetary or temporal dimension of delayed rewards.
Our analyses revealed no order effects within either type of auction (on either the discount rate or the β parameter representing present-bias).
Overbidding has been documented in laboratory second-price auctions (Heyman et al. 2004; Kagel et al. 1987; Kagel and Levin 1993). This phenomenon could be due to a myriad of factors ranging from a failure to understand the dominant bidding strategy to “auction fever” over the possibility of “winning” (Delgado et al. 2008).
Participants could choose from several options to receive their payments: cash payments in person, check payments by mail, or direct bank transfers. Doing so helped minimize the cost to them of receiving their payments and ensured that we could pay them even if they had left campus when their payment deadlines arrived.
For a more extensive discussion of this procedure, see Frederick et al. (2002).
In contrast to the auctions, we do observe order effects with the hypothetical matching task survey. Specifically, we find a marginally significant order effect on the discount rate under money biding (when we estimate exponential and hyperbolic models, but not when we estimate quasi-hyperbolic models), such that discount rates are higher under the time-then-money ordering (compared to the money-then-time ordering). And we find a significant order effect on the discount rate under time biding (for all three discounting models), such that discount rates are again higher under the time-then-money ordering. Finally, when we estimate the quasi-hyperbolic model, we find significant order effects on the β (present-bias) parameter: under money bidding, β is larger in the money-then-time ordering; under time bidding, β is larger in the time-then-money ordering.
While the validity of the random-lottery incentive system (paying all participants according to one randomly selected choice) has received strong empirical support (Beattie and Loomes 1997; Cubitt et al. 1998; Hey and Lee 2005a, b; Lee 2008; Starmer and Sugden 1991), the validity of paying a random subset of participants according to their choices is less well established (see Baltussen et al. 2012). The few tests of this latter method have found that it biases preferences by lowering risk aversion (Baltussen et al. 2012).
Recently, a working paper by David Eil has come to our attention. He utilizes a multiple-choice method (involving a series of binary choices between smaller payoffs today and larger payoffs in the future) to identify switching points in subject’s preferences (in order to estimate their implied discounting parameters). He directly compares time preferences when the delay vs. amount of the future payoff is systematically varied. However, it should be noted that his experiment was conducted in May 2010, whereas ours was carried out in the fall of 2007, our results were first presented (at a major conference) in 2007, and the first complete draft of our manuscript had been written by 2009.
Note that our manipulation is within-bidder, and therefore controls for bidder-specific fixed effects (including risk attitudes and beliefs about the distribution of other bidders’ risk and time preferences).
Testing this assumption is left to future work.
We can also check whether revenue equivalence holds between the first- and second-price money-bid auctions. Here we define “revenue” as the amount given to the “winner” of the money-bid auction at the delayed date instead of $10 in the present. A Mann–Whitney test comparing revenues from the first-price money-bid auctions and revenues from the second-price money-bid auctions yields p value = 0.057. Note that numerous previous experiments have found lack of revenue equivalence between first- and second-price auctions (Kagel 1995). The predicted revenue equivalence hinges on the assumption that bidders are risk-neutral, so any lack of revenue equivalence found here could be attributed to non-risk-neutrality or to a number of other possible factors.
These model parameters were estimated using data from all subjects with estimable parameters, not just those for whom the model represented the best fit according to the BIC.
These results are consistent with those obtained by Eil (unpublished manuscript), who finds that eliciting time preferences through a multiple-choice method in which the delay of the future payoff is systematically varied (to identify a switching point) yields more impatience and less present bias than a multiple-choice method in which the amount of the future payoff is varied instead. However, whereas Eil finds evidence of future bias (i.e., β > 1, see also Takeuchi 2011) under the “time” multiple-choice method, we find lower or no present bias with time bids, but not future bias.
We also fitted a model specification with a free θ (hyperbolicity) parameter (such that θ = 1 produced the exponential and θ = 2 produced the standard hyperbolic function; see Benhabib et al. 2010), and found that the estimated θ is lower and closer to 1 for time bids (compared to money bids) under all three elicitation procedures. Specifically, the θ parameter ranged from 1.1 to 1.8 for time bids, and from 2.5 to 3.4 for money bids. Thus, people seem to be less hyperbolic (i.e., more exponential) when they bid time, whereas they seem to be “supra”-hyperbolic (θ > 2) when they bid money.
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Acknowledgments
We would like to thank Abhijit Banerji, Roland Benabou, Colin Camerer, John Doyle, Jacob Goeree, Jens Großer, David Hardisty, Joel Huber, Eric J. Johnson, Nobuo Koida, Alexey Kushnir, Graham Loomes, J.V. Meenakshi, Daniel Mochon, C. Dan Myers, Thomas Palfrey, Uliana Popova Makarov, Ganna Pogrebna, Eldar Shafir, Rohini Somanathan, Dean Spears, Peter Wakker, and four anonymous reviewers (including one from the Russell Sage Foundation) for their helpful comments and suggestions. We also received helpful feedback from participants of SJDM 2007, BDRM 2008, Yale Whitebox 2008, ACR 2008, ESA 2008, SJDM 2008, SCP 2009, SPUDM 2009, the DR@W seminar at the University of Warwick, the ECO seminar at the University of East Anglia, and the Center for Development Economics seminar at the Delhi School of Economics. We are especially indebted to Chris Crabbe, who did a spectacular job programming the experiment. This research was generously funded by a grant from the Russell Sage Foundation’s small grants program in Behavioral Economics and an award from the Society for Judgment and Decision Making.
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Olivola, C.Y., Wang, S.W. Patience auctions: the impact of time vs. money bidding on elicited discount rates. Exp Econ 19, 864–885 (2016). https://doi.org/10.1007/s10683-015-9472-x
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DOI: https://doi.org/10.1007/s10683-015-9472-x