Estimating Time Preferences from Convex Budgets

Abstract

Experimentally elicited discount rates are frequently higher than what one would infer from market interest rates and seem unreasonable for economic decision-making. Such high rates have often been attributed to present bias and hyperbolic discounting. A commonly recognized bias of standard elicitation techniques is the use of linear preferences for identification. When attempts are made to correct this bias with additional experimental measures, researchers find exceptional degrees of utility function curvature. We present a new methodology for identifying time preferences, both discounting and utility function curvature, from simple allocation decisions. We estimate annual discount rates substantially lower than normally obtained, dynamically consistent discounting, and limited though significant utility function curvature.

How Soon Is Now? Evidence of Present Bias from Convex Time Budget Experiments

“…We follow several recent studies (cf. Andersen, Harrison, Lau, and Rutström 2008, Andreoni and Sprenger 2012a, Giné, Goldberg, Silverman, and Yang 2017, Carvalho, Meier, and Wang 2016 in equalizing the financial and cognitive transaction costs associated with immediate and delayed payments. For example, we adopt Andreoni and Sprenger's (2012a) approach of dividing the show-up fee into two equal, dated payments; and we use a payment technology (M-Pesa) with which subjects are extremely familiar.…”

“…Complete instructions and screenshots of the computer interface are included in the Online Appendix. 13 We follow Andreoni and Sprenger (2012a) in ensuring that all payment dates occur on the same day of the week to eliminate any end-of-week confounds. As discussed below, we also made sure that payment dates did not fall on holidays or the last day of the month.…”

“…23 Making payments at the end of the day mimics the approach used in Andreoni and Sprenger (2012a). Andersen, Harrison, Lau, and Rutström (2008), Giné, Goldberg, Silverman, and Yang (2017) and Carvalho, Meier, and Wang (2016) introduce longer delays (of at least 1 day) before the earliest possible payments can be accessed.…”

“…For example, Frederick, Loewenstein, and O'Donoghue (2002) point out that most experimental studies documenting present bias among humans ask subjects to choose between smaller, immediate cash payments -which are typically given out at the end of the experimental session -and larger, delayed payments. If subjects are not sure that they will actually receive the later payments, or if collecting delayed payments involves larger transaction costs (because, for example, subjects would need to return to the lab to pick up a check), they may appear present-biased when in fact they are not (Halevy 2008, Andreoni and Sprenger 2012b, Gabaix and Laibson 2017. Another concern is that many experiments assume that utility is linear in money; such an assumption will lead to over-estimates of the degree of present bias if subjects are risk averse -because the utility difference between larger future payments and smaller immediate payments is not as large as the dollar difference between the payment amounts (Andersen, Harrison, Lau, and Rutström 2008).…”

“…For example, as discussed above, Andreoni and Sprenger (2012a) make "immediate" payments by placing a personal check in each subject's mailbox before the close of the business day. 4 Thus, "immediate" payments may not always be accessible immediately.…”