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How soon is now? Evidence of present bias from convex time budget experiments

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Abstract

We conduct a laboratory experiment in Kenya in which we elicit time and risk preference parameters from 494 participants, using convex time budgets and tightly controlling for transaction costs. Using the Kenyan mobile money system M-Pesa to make real-time transfers to subjects’ phones , we vary whether same-day payments are made immediately after the experimental session or at the close of the business day. We find strong evidence of present bias, with estimates of the present bias parameter ranging from 0.902 to 0.924—but only when same-day payments are made immediately after the experiment.

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Notes

  1. In other words, consumption that occurs t periods in the future is discounted by a factor \(\delta ^t\), where \(\delta \le 1\) and does not vary over time. See Frederick et al. (2002) for an overview of the development of discounted utility model and its use in economics.

  2. In the discounted utility model, agents care more about immediate payments than about payments that occur k days in the future, but only as much as they care more about payments at time t than payments at time \(t+k\).

  3. Within psychology, the most widely used model of present bias is the modified hyperbola (Kirby 1997). In that model, utility takes the form: \(U(c_{t})=\frac{1}{1+kt}u(c_{t})\).

  4. Harrison et al. (2013) have criticized the CTB task for relying on corner choices in identifying present bias. This criticism is orthogonal to our goal in the present paper, which is to compare the degree of present bias across immediate and end-of-day treatments. In addition, in contrast to previous findings, our subjects choose mostly interior allocations.

  5. Other studies in a similar vein involve even greater delays. For example, in Giné et al. (2017), the soonest payments occur 1 day after decisions are made. In Carvalho et al. (2016), checks are mailed on the day decisions are made, so they arrive at least 1 day later.

  6. Augenblick et al. (2015) is an important exception: they deliver cash payments at the end of their experimental sessions, and report more limited evidence of present bias over money than over effort. However, their findings do suggest at least a modest degree of present bias over money. Specifically, their subjects allocate 38.1% (SE: 1.73) of the budget to the sooner payment date for monetary decisions not involving today, and 41% (SE: 1.34) for decisions involving today. The difference of 2.1 percentage points is marginally significant (p value 0.07) in their sample of 75 subjects. As discussed further below, the magnitude of the difference is quite similar to the difference of 2.8 percentage points observed in our study.

  7. Thaler (1981) first observed that subjects tend to appear more patient when making intertemporal tradeoffs involving larger stakes. More recently, Sun and Potters (2016) show that changes in stakes impact the estimated degree of impatience (i.e. the exponential discount factor) but not the degree of present bias. Daily expenditure is the best benchmark for stake size because income in our setting is lumpy.

  8. In our sample, 59.7% of chosen allocations are interior, and only 11.9% of subjects always choose corner solutions (which would be consistent with either risk neutrality or arbitrage). The pattern of behavior among our adult subjects stands in marked contrast to the patterns observed in several recent studies of university students in the United States and Europe. For example, Augenblick et al. (2015) report that only 14% of CTB decisions over money payouts are interior and 61% of their student subjects (in the U.S.) always choose corner solutions, while Sun and Potters (2016) report that 30% of chosen monetary allocations are interior and 37% of student subjects (in the Netherlands) always choose corner solutions. Interestingly, our results line up with those of Giné et al. (2017), who report that only 16.5% of CTB decisions by Malawian farmers are at corners (they do not report the proportion of subjects who never choose an interior allocation). Though comparisons across studies are inherently speculative, the pattern of evidence appears to suggest that adult subjects in low-income countries (Kenya and Malawi) are less likely to behave in a manner consistent with arbitrage than student subjects in wealthy countries (the U.S. and the Netherlands).

  9. These budgets are equivalent to approximately 4.08 and 6.12 USD, respectively. These endowments are large in purchasing power terms: the median level of daily expenditures in our sample is 146 Kenyan shillings (1.49 USD)

  10. At the end of the CTB portion of the experiment, subjects completed a standard Multiple Price List (MPL) task that included 24 decision problems. One of the 72 decision problems was randomly selected to determine experimental payouts. See Charness et al. (2016) for discussion of the consequences of paying for a single randomly-selected decision problem.

  11. As Andreoni and Sprenger (2012a) discuss, splitting the show-up fee across the two payment dates is critical to the research design. Haushofer (2014) presents a theoretical model suggesting that a mental cost of keeping track of time-dated payments may act as an additional (cognitive) transaction cost, pushing subjects toward corner solutions and immediate payments when the show-up fee is paid (in its entirety) on the day of the experiment. However, this cost would apply to both payment dates in our setting because half of the show-up fee is paid on each payment date. Thus, if any transaction cost enters as an additively separable (from money/consumption utility) term in the utility function, it should not impact allocation decisions at all (because choosing a corner solution would not reduce the amount received on either date to 0, so subjects would still incur the transaction costs associated with each of the two dated payments). Alternatively, if the transaction cost enters as a reduction in money utility that is larger for delayed payments, allocations to the earlier payment date should be lower when the earliest payments are immediate, since utility is (weakly) concave. Taken together with stated beliefs about the likelihood that payments will arrive on time (and subjects’ experience with the Busara lab’s reliability), it is quite unlikely that differential transaction could explain behavior in our experiment.

  12. No experimental sessions were held on Fridays or weekends to avoid any potential end-of-week effects. When considering a potential date for a session, we verified that no payment dates associated with that (potential) session fell on holidays or other days likely to lead to foreseeable changes in the desire for cash on hand (for example, the day when school fees are due). We test whether later payment dates are associated with individual needs for ready cash in Sect. 5.2.

  13. M-Pesa withdrawals can be made at any one of many M-Pesa agents in Nairobi, typically located in shops or kiosks. There are numerous M-Pesa agents in the immediate vicinity of the Busara Center, and also in the informal settlements where participants live. For example, as of 2011, Safaricom reported that there were 150 active M-Pesa agents in the single square-mile Kibera slum neighborhood, and there were at least 100 in the smaller Kawangware neighborhood. Many of these agents are open late into the night. Our payments were made before 6:00 PM, ensuring that participants were able to withdraw the money on the day of the study if they wished.

  14. Because subjects had experience receiving mobile money payments from the Busara Center via M-Pesa, there is little reason to be concerned that they doubted that their payments would arrive on time. When asked (at the end of the experiment) whether they thought that both of their experimental payments would arrive on time, 98% of subjects answered in the affirmative.

  15. In Table A2 of the Online Appendix, we show that observable characteristics are comparable across experimental treatments. The notable exception is that subjects assigned to the immediate payment treatment appear less likely to be liquidity-constrained than those assigned to the end-of-day payment treatment. Of course, if behaviors that appear present-biased were actually driven by liquidity constraints, this imbalance would predict greater present bias in the end-of-day payment treatment than in the immediate payment treatment.

  16. Sessions were conducted over two years: 2015 and 2016. Immediate payment sessions were conducted in both 2015 and 2016, while all end-of-day payment sessions were held in 2016.

  17. In CTB experiments where the budget size is denominated in terms of the later payment date (so that the maximum later payment is fixed as the interest rate changes), this is often referred to as “monotonicity” (Andreoni and Sprenger 2012a) or “demand monotonicity” (Chakraborty et al. 2017). We adopt the terminology used by Giné et al. (2017) since, like them, we use an early-valued convex time budget.

  18. See Choi et al. (2007b) for discussion.

  19. CDFs of the budget fraction allocated to the earlier payment date are presented in Online Appendix Figure A2.

  20. As discussed above, the magnitude of this reduced form effect is comparable to that observed by Augenblick et al. (2015).

  21. To facilitate comparisons of parameter magnitudes across treatment (without necessitating an unduly large number of digits), we report weekly discount factors throughout the analysis.

  22. These levels of impatience are higher than those observed in studies in Western populations; e.g., Andreoni and Sprenger (2012a) report yearly discounting between 30 and 38%. This difference is in line with recent evidence showing higher levels of impatience in Sub-Saharan Africa compared to North America and Europe (Falk et al. 2018).

  23. Though we take an entirely different approach to preference elicitation, our results are similar to estimates of risk aversion in broadly comparable field populations (cf. Harrison et al. 2010; Jakiela and Ozier 2016).

  24. We are unable to estimate individual parameters for 17 of our 494 subjects. 6 subjects always allocated their entire endowment to the earlier payment date, and 9 always allocated their entire endowment to the later payment date. Estimation does not converge for 2 of the remaining subjects.

  25. Like other recent studies of individual preferences (cf.  Choi et al. 2007b; Fisman et al. 2007, 2017; Andersen et al. 2008), we observe tremendous individual heterogeneity in preferences, much of which is not explained by demographic and socioeconomic characteristics. The 5th percentile of \(\hat{\beta }_i\) is 0.164, and the 95th percentile is 1.598. The 5th percentile of \(\hat{\delta }_i\) is 0.473, and the 95th percentile is 1.388. The 5th percentile of \(\hat{\rho }_i\) is 0.243, and the 95th percentile is 17.878.

  26. We cannot reject the hypothesis that the proportion of subjects with estimated \(\hat{\beta }_i\) parameters below 1 is equal in the immediate and end-of-day payment treatments (p value 0.211).

  27. We can reject the hypothesis that the average individual-level \(\hat{\beta }_i\) parameter in the immediate payment treatment (i.e. the constant in the OLS regression reported in Column 1 of Table 3) is equal to 1 (p value \(<0.001\)). We cannot reject the hypothesis that the average individual-level \(\hat{\beta }_i\) parameter in the end-of-day payment treatment is equal to 1 (p value 0.389).

  28. See, for example, Andreoni and Sprenger (2012a, b), Augenblick et al. (2015), Dean and Sautmann (2016), Halevy (2015), Epper (2015), Carvalho et al. (2016), Giné et al. (2017), Janssens et al. (2017).

  29. Across all subjects, only 1.8% always allocate their entire endowment to the later payment date, and only 8.9% always do so at the higher interest rates.

  30. Interestingly, our results differ from those of Andreoni and Sprenger (2012a) in this regard: 70% of the CTB decisions observed in their experiment are corner solutions, suggesting that arbitrage may be a more reasonable explanation of behavior in that context. In our experiment, subjects who are not liquidity-constrained choose corner solutions 46.5% of the time; those who are potentially liquidity-constrained choose corner solutions 38.5% of the time.

  31. This finding is in line with earlier work by Meier and Sprenger (2010): in a sample of low-income tax-filers in the U.S., they find that “time preference measures are generally uncorrelated with credit constraints, future liquidity, or credit experience. This indicates that differential credit access, liquidity, and experience are unlikely to be drivers of experimental responses, and cannot explain the observed heterogeneity of present bias” (Meier and Sprenger 2010, pp. 202–203).

  32. Ambrus et al. (2015) is an excellent example of work in this vein.

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Acknowledgements

We are grateful to Chaning Jang, James Vancel, and the staff of the Busara Center for Behavioral Economics for excellent research assistance, and to Ned Augenblick, Stefano DellaVigna, Pascaline Dupas, Ray Fisman, Jess Goldberg, Anett John, Shachar Kariv, Supreet Kaur, Maggie McConnell, Owen Ozier, Charles Sprenger, Dmitry Taubinsky, several anonymous referees, and numerous conference and seminar participants for helpful comments. This research was supported by Cogito Foundation Grant R-116/10 and NIH Grant R01AG039297 to Johannes Haushofer.

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  1. IMPAQ International, Washington, DC, USA

    Uttara Balakrishnan

  2. Princeton University, Princeton, USA

    Johannes Haushofer

  3. Busara Center for Behavioral Economics, Nairobi, Kenya

    Johannes Haushofer

  4. Center for Global Development, Washington, DC, USA

    Pamela Jakiela

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  1. Uttara Balakrishnan
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Balakrishnan, U., Haushofer, J. & Jakiela, P. How soon is now? Evidence of present bias from convex time budget experiments. Exp Econ 23, 294–321 (2020). https://doi.org/10.1007/s10683-019-09617-y

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