An agent with dynamically inconsistent preferences may deviate from her plan of action as the future draws near. An exponential discounter may do exactly the same when facing an uncertain future. Through an experiment we compare preference-based vs. uncertainty-based explanations for choice reversal over time by eliciting choices for pre-commitment and flexibility. Evidence of widespread commitment favors a preference-based explanation.
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Harrison et al. (2002) and Rubinstein (2003) and others have questioned this finding. Pender (1996) explains it through a seasonality effect. Notice that when choices are defined over sets of outcomes and not over single outcomes, choice reversal can originate from dynamically consistent preferences (Gul and Pesendorfer 2001).
Strotz (1955) introduced the expression “strategy for pre-commitment.” In this paper we will use pre-commitment and commitment interchangeably.
However, the welfare implications of commitment are not clear-cut. For one, by committing, an agent forgoes the value of flexibility. Moreover, it is sometimes unclear how to use the agent’s preferences for welfare comparisons. In Gul and Pesendorfer (2001) the welfare criterion is clear: the agent “is unambiguously better off when ex ante undesirable temptations are no longer available.”
Evidence is mixed on this point (Christensen-Szalanski 1984). In a follow-up interview 1month postpartum, many women regretted their choice and expressed their preference to avoid using anesthesia (support for the preference-based explanation). Women at their first childbirth experience were more likely to reverse their choice than the average (support for the uncertainty-based explanation).
Six sessions were run between April 26 and April 28, 2004. The actual last payment took place on May 30, 2005. Recruitment was done through announcements in classes. Half of the subjects were women and a large majority was comprised of economics or business majors. Basic statistics on the sample composition are in Table 6 in the “Appendix”.
Unless a subject has a discount factor of one, hence is perfectly patient, there always exists a long enough delay to induce the switch in favor of the sooner-smaller reward.
Although the number of decisions in parts one and two could vary across participants, there was no advantage for someone to finish earlier because that would not have changed the time the person could leave the room. In part one, the elicited maximum wait D* was 276 days. In part two, the elicited front-end delay was between 7 and 395 days. The elicited furthest possible time of payment in the experiment was 611 days.
If payment fell on Saturday, Sunday, or an official holiday the delay was automatically adjusted either backward or forward to make it easy for subjects to cash the reward. The summer period (July 25–September 5) was excluded, as well as Christmas vacations (December 22–January 6) and several other national or local festive days (for example October 9 and 12, November 1, December 6 and 8, February 27, March 19, May 1, June 29). Classes ran up to May 28, and then there were exams up to June 30. The university was closed in August. About 90% of the subjects’ families lived in the university town or in the region (Valencia province). More details on the procedure can be found in Casari (2006).
It was explained that only replies arriving within two days before or after the specified day would be considered valid. Almost all of the responses were received on the specified day. The response rate was 64.1%.
A payment of 5.61€ ($6.68) per person was given right after the session. It included a 3€ show-up fee (2€ in the first two sessions) and a performance-based fee for some correct answers in the questionnaire, as explained in the result session. Another component is discussed in footnote 21. The exchange rate at the time of the experiment was 1€ = $1.19.
All post-session payments were carried out by the personnel affiliated with the Jaume I University Laboratory of Experimental Economics (LEE). These personnel teach in the department of economics and conducted experiments and payments in previous experiments, so they were familiar to the subjects. Only the persons selected for the large payments had the burden of returning to collect money.
The envelope was stored in the laboratory, and any participant could ask to have it opened when all decisions and payments had been completed, which was several months later. This procedure gave credibility to the promise of a later payment while maintaining an incentive for all subjects to send the follow-up email. When the date of payment approached, the selected person was privately contacted to arrange an appointment for the payment day.
Complete instructions are available upon request to the author. Elicitation of risk attitudes closely followed the procedure of Holt and Laury (2002) and results are not reported here. Random draws and lottery payments were carried out at the end of the session.
Under an uncertainty scenario, an exponential discounter who reverses her choices over time will never commit, hence becoming observationally equivalent to a naïve agent.
This experiment offered an investment technology. If the yields of the investment were better than the market rate, subjects may have simply borrowed from the field and invested in the lab. If such trading took place, the revealed experimental choices would show an upper bound in willingness to wait defined by the market borrowing rate. Results did not reflect this upper bound because our subjects had a rather limited access to credit markets. More details in Casari (2006, 2008) and a general discussion in Cubitt and Read (2007).
In the transition from part one to part two, seven subjects experienced software problems and 23 subjects exhibited erratic behavior. Example: a subject ends part one confirming her choice for SS; on the first decision of part two she chooses LL, hence showing choice reversal. Yet, she then chooses SS, then LL again, and eventually ends up confirming LL, i.e. a consistent choice.
There is no systematic correlation between being hard-to-classify and being inconsistent in risk attitude choices, getting all compound interest questions wrong, having a low admission score to college (nota de selectividad), or not sending an email. These results come from an unreported probit regression.
In Table 3, col. (2) regressors are dropped by the statistical package Stata with the message that it “predicts success perfectly.” This event is informative about the relation between the regressor and the dependent variable. More precisely, when the subject is willing to wait less than 7 days for the larger reward in part one, it is always the case that the subject reversed her choice in part two.
Table 3, col. (2). A smoker who never tried to quit is always reversing her choice. See also the previous footnote.
The money may be spent long after it was received. The experimenter knows the time of the payments but not the time of the actual consumption. There were cues that the upcoming weekend constituted that moment for many participants. While the timing of actual consumption is crucial to estimate discount rates, less stringent conditions are needed for the purpose of studying commitment and flexibility. The delay between payment and consumption can be positive and can be different between SS and LL.
The score is 100 for a subject who chose flexibility in one or more decisions and never committed (E). The score is 0 when there was no choice for flexibility (A and C). When some choices were for commitment and some for flexibility, the overall propensity was established by balancing the fraction of choices in both directions. A higher fraction of flexibility choices than for commitment suggests a propensity for flexibility (D) and the difference defines the commitment score. If the opposite is true, the flexibility score is 0 (B).
In Table 4, col. (2) a regressor is dropped by the statistical package Stata with the message that it “predicts failure perfectly.” When the subject is a smoker who never tried to quit, it is never the case that the subject is in the flexibility category E.
In the first column of Table 5, the net present values are derived after calibrating a hyperbolic discounting model. For each subject who reversed her choices, there is one parameter to estimate, k. The calibration employed the four choices coming from the decision immediately preceding and the one immediately following the SS/LL switch in parts one and two of the experiment. Each choice provided either a lower or an upper bound for k. Our estimate for k is the average of the minimum upper bound and the maximum lower bound. The calibration of the quasi-hyperbolic model in the second column employs the above, four choices to estimate two parameters, β and δ. First, δ is estimated as the average of the values from the two choices in part two. This δ is used for estimating β from the two choices in part one (average). A delay of up to 2 days is considered present for this calibration of the model.
For each question, there was a list of six possible answers: (S) If your initial capital was 1,000 euros, what is your final capital after 6 years at 5% interest rate? €1,340, 50.0% of answers were correct; (T) If your final capital in 10 years will be 10,000 euros with 8% interest rate, what is your initial capital? €4,630, 35.8% correct; (U) If your initial capital was 500 euros and your final capital after 5 years is 1,000 euros, what is the interest rate? 15%, 40.0% correct. A hand calculator was provided. Out of 120 participants, 45.8% all wrong answers.
In part one, just one randomly selected decision was paid. Hence, the longer the sequence of decisions, the worse was the expected payment in terms of delay. As a consequence, there was a slight incentive to reveal a lower willingness to wait than the true one.
For the lower bound: (A’ + B’ + D’) = 35 subjects and (A’ + B’ + C’ + D’) = 64 subjects, hence 54.7%. In the uncertainty scenario, dynamically inconsistent subjects may sometimes want to choose for flexibility, which is why categories B, B’, D, and D’ are included in the calculations. Another possible lower bound, (A’ + (A − A’)/2) = 37, which includes half of the subjects that may have chosen to commit at no cost simply because they were indifferent (naïve subjects are indifferent regarding committing or not in the certainty scenario). For the upper bound: (A + B + D − C/2) = 52 subjects and (A + B + C + D) = 67, hence 77.6%. See Result 2 and Fig. 4.
There was no correlation between choice reversal and low intellectual skills. When controlling for other factors, neither being able to compute compound interest nor having a low admission score to college were significant in explaining choice reversal (Table 3).
In the questionnaire, we did a simple elicitation of the perceived additional risk associated with the later reward. This measurement of risk did not ultimately correlate with choice reversal, commitment, nor flexibility.
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This study was initiated when visiting the Autònoma University of Barcelona, Spain. Discussions with Howard Rachlin have been particularly valuable. Earlier versions of this manuscript have also benefited from the comments of Alberto Bisin, Jordi Brandts, Gabriele Camera, Colin Camerer, Gary Charness, Pierre Courtois, Guillaume Frechette, David Laibson, Dan Levin, Rosella Nicolini, Charlie Plott, Arno Riedl, Kip Viscusi, and of participants at seminars at Kyoto Sangyo University, University of Maastricht, University of Venezia, New York University, Capua Workshop in Behavioral Economics, the Autònoma University of Barcelona, Purdue University, and at the ESA meeting in Montreal. All remaining errors are mine. Henrik Nordin and Ricardo Flores provided valuable research assistance. Many thanks to Aurora Gallego and Nikos Georgantis for letting me use the LEE (Laboratori d’Economia Experimental) of the Universidad Jaume I of Castellon, Spain, and to Juan Gómez Pérez for the technical help. The financial support from an EU Marie Curie Fellowship and the Russell Sage Foundation (grant #: 98-04-05) is gratefully acknowledged. Any opinions, findings, and conclusions or recommendations in this material are those of the author and do not necessarily reflect the views of the European Commission or of the Russel Sage Foundation.
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Casari, M. Pre-commitment and flexibility in a time decision experiment. J Risk Uncertain 38, 117–141 (2009). https://doi.org/10.1007/s11166-009-9061-5
- Intertemporal choices
- Dynamic consistency