Abstract
We investigate the predictive power of survey-elicited time preferences. The discount factor elicited from choice experiments using real payments predicts various health, energy, and financial outcomes, including overall self-reported health, smoking, installing energy-efficient lighting, and credit card balance. Allowing for time-inconsistent preferences, both the long-run and present-bias discount factors (δ and β) are also significantly associated in the expected direction with several outcomes. We consider several hypotheses regarding the strength of the association between discount factors and outcomes, such as salience of the outcome or liquidity constraints.
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Von Gaudecker et al. (2011) perform a similar analysis but looking at risk, not time, preferences.
A related prediction is found in the model of willpower in Bénabou and Tirole (2004).
The time periods were the same as those used in Meier and Sprenger (2010). We adjusted the dollar values of the payments downward to reflect our budget (and rounded each to the nearest dollar integer).
The probabilities and dollar values are taken from Andersen et al. (2008).
Ferecatu and Önçüler (2016) provide an alternative methodology for estimating time and risk preferences, based on a hierarchical Bayesian methodology.
An alternative and somewhat simpler way to calculate discount factors is employed by Meier and Sprenger (2010). They calculate a monthly discount factor for each of the three payout time pairs; call these δ0,1, δ0,6, and δ6,7. (That is, δ0,1 is the discount factor calculated using the respondent’s answer to the MPL questions about payoffs now vs. one month from now.) The arithmetic mean of all three of these discount factors is δ avg ; this assumes time-consistent discounting. They allow for time-inconsistent discounting by noting that a respondent can have a different value for δ0,1 and δ6,7. If δ0,1<δ6,7, then consumers are present-biased. The present bias discount factor is β qh =δ0,1/δ6,7 and the long-run discount factor δ qh =δ6,7. A caveat of using this method is that it drops observations for respondents failing to respond to one or more questions, as well as those with inconsistency in their responses, whereas our MLE method retains some of these individuals. Also, the present bias discount factors δ qh and β qh are calculated using just the red and blue blocks. Another methodology for calculating discount factors is to assume that a respondent was indifferent at any observed switching point; however, this method requires strong assumptions about whether to use the first or last switching point if a respondent leaves a question blank or exhibits multiple switches. Our results are robust to using these alternate calculation methods. An alternative strategy is to require that respondents only have at most one switching point by imposing that requirement in the survey, rather than asking about each pair separately; this is the method taken in, e.g., Tanaka et al. (2010).
The payout questions include the time preference questions described here and the lottery questions asked to elicit risk preferences, described above.
For some subjects who exhibited multiple switching points (violating preference monotonicity), our MLE method returned implausibly large or small discounting parameters. We exclude subjects with fitted values of δ qh < 0.45, β qh < 0.25, or β qh > 2.5, which drops 8% of respondents.
For examples, see Ioannou and Sadeh (2016), Meier and Sprenger (2010), and Frederick et al. (2002). The discount factors are low (discount rates are high) relative to studies that use alternative elicitation methods, such as convex time budgets (Andreoni and Sprenger 2012a) or Bayesian methods (Ferecatu and Önçüler 2016).
That survey is available at: http://www.cdc.gov/brfss/.
We considered separate models for smoking status and cigarettes per day among smokers, but the sample size in the regression containing only smokers was too small to obtain meaningful precision. We therefore are unable to disentangle whether effects of time preference on smoking occur along the extensive or intensive margins.
That survey is available at: http://www.eia.gov/consumption/residential/. Additional questions were taken from the survey designed for Attari et al. (2010).
Other health, energy, and financial variables were asked of respondents, although regression results are not reported here. The entire survey, including the questions not used in this study, is in Appendix B.
The questions are: “How patient are you in general?”, “How strong is your willpower/ability to control your impulses?”, “How difficult is it for you to avoid eating a snack food you enjoy (e.g. chocolate chip cookies, ice cream, potato chips) if it is easily available, even if you are not hungry?”
We calculated this health-related discount factor by assuming that a consumer was indifferent at the mid-point between the first observed switching row. For respondents that never switched, but for example always chose drug B, we assumed the respondent was indifferent at the most extreme delayed row. Eighty-two percent of subjects exhibited zero or one switch for these migraine questions. Note that this methodology implicitly assumes a linear utility function for health-related outcomes.
In question 2, the intuitive answer is 100 min, but the correct answer is 5 min. In question 3, the intuitive answer is 24 days, but the correct answer is 47 days.
Age and income are the only control variables with a non-trivial number of missing values (3.3% and 5% of the sample, respectively). The results are robust (with occasionally slightly less significance) to simply dropping observations with any missing demographic variables or creating missing value dummy variables and including these observations. For the continuous variables that are modeled as a series of dummies (e.g. age and income), we impute by first running linear regressions for the continuous measure and then discretizing the predicted value by rounding to the nearest applicable unit (e.g. year of age, dollar of income).
We do not include CRT score as a control in the main specification because it likely depends at least partly on time preference. Adding it might therefore “control away” part of the causal effect of time preference. We acknowledge, though, that similar arguments could be made for some of the covariates we do include—namely education and income. It is therefore reassuring that including CRT score is of little consequence for the results.
The results are generally similar using linear regressions, though the average marginal effects are often more precisely estimated by the non-linear models.
Results are similar for regressions where the dependent variable is BMI or severe obesity (BMI ≥ 35).
There are 66 respondents for whom the information required to calculate BMI is unavailable. Of those, all of them fail to report their weight, compared to just 25 who fail to report height.
The results are robust to many other measures of smoking, including an indicator for being a regular smoker or for having smoked at least 100 cigarettes in one’s life. Results are similar but less significant for some other drinking measures, including number of drinks per week. We focus on binge drinking because moderate alcohol consumption is not necessarily unhealthy.
The negative (though insignificant) association between δ and sunscreen use might occur because more patient people are less likely to be out in the sun at all, and therefore less often use sunscreen. The positive coefficient for the seat belt regressions is consistent with our expectations and it is mirrored by a slightly larger coefficient on β qh . An alternate hypothesis is that more patient people are less likely to wear a seat belt since they may drive more slowly or safely and not feel the need to wear one. The correlation we find could also be explained by aversion to being caught and fined, since this is a relatively easily detected violation.
By contrast, Newell and Siikamäki (2015) find that elicited discount factors (not allowing for quasi-hyperbolic discounting) are significantly correlated with energy-efficiency investment decisions. Their study differs from ours in a number of ways that may influence the results. First, their elicited time preferences are calculated from a series of hypothetical money trade-off questions, rather than our MPL questions that can accommodate quasi-hyperbolic preferences and in which actual (non-hypothetical) payouts are made to a random subset of respondents. Second, their energy-efficiency outcome variable is based on responses to a hypothetical choice experiment over water heater purchases, rather than actual energy-efficiency purchases. Their robust, significant results combined with our less strong results may suggest that present bias can sever the link between planned energy-efficiency investments (as measured in their hypothetical water heater purchases) and actual investments.
However, Meier and Sprenger (2010) find a correlation between credit card balance and an indicator for present bias at either the 5% or 1% level depending on the specification. Their sample consists of primarily low- to moderate-income individuals whereas ours is representative of the overall population, which may explain the difference.
In the main specifications in Tables 4 through 7, there are 41 statistically significant (at least the 10% level) coefficients, and in Appendix Tables A5 through A8 that number drops to 34, while the sample size for most of the regressions drops from about 800 to about 600 observations. Of the 41 coefficients that were statistically significant in our main results, the magnitudes actually increase for 25 of them after imposing the sample restriction, suggesting that the reduced statistical significance is merely the result of the smaller sample size.
For instance, a Bonferroni correction would mean multiplying the p-value for our most highly significant result by 30, which strikes us as excessively cautious for a relatively small-scale survey. The procedure from Holm (1979) is also very conservative.
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Acknowledgements
We thank Will Mautz and Camden Sweed for valuable research assistance, Georgia State University, the University of North Carolina at Greensboro, and the Harvard Center for Risk Analysis for funding, Darren Lubotsky for providing his code to implement the multiple proxies procedure, and Allen Bellas and conference and seminar participants at UNCG, GSU, Georgia Tech, the Federal Trade Commission, the Midwest Economics Association meetings, and the Harvard Center For Risk Analysis’s March 2014 “Risk, Perception, and Response” conference for helpful comments. Ruhm thanks the University of Virginia Bankard Fund for partial financial support. The views expressed in this article are those of the authors and do not necessarily reflect those of the Federal Trade Commission.
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Bradford, D., Courtemanche, C., Heutel, G. et al. Time preferences and consumer behavior. J Risk Uncertain 55, 119–145 (2017). https://doi.org/10.1007/s11166-018-9272-8
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DOI: https://doi.org/10.1007/s11166-018-9272-8