Comment on “Risk Preferences Are Not Time Preferences”: On the Elicitation of Time Preference under Conditions of Risk

Abstract

Andreoni and Sprenger (2012a, b) report evidence that distinct utility functions govern choices under certainty and risk. I investigate the robustness of this result to the experimental design. I find that the effect disappears completely when a multiple price list instrument is used instead of a convex time budget design. Alternatively, the effect is reduced by half when sooner and later payment risks are realized using a single lottery instead of two independent lotteries. The result is thus at least partially driven by intertemporal diversification, supporting an explanation in terms of concavity of the intertemporal, and not only atemporal, utility function. (JEL C91, D81, D91)The past decade has seen rapid advances in the development of both experimental designs and estimation procedures to measure the utility and discount functions that govern individual choices over time. These advances are significant both because many important economic decisions entail consequences at different points in time, and because a substantial earlier literature found wide disparities in estimated discount rates-including many that seem extraordinarily large. 1 One important reason for these high discount rate estimates is the fact that estimates which assume a linear utility function will be upwardly biased when the utility function is, in fact, concave. This is because under concave utility, both diminishing marginal utility and discounting for time delay will tend to favor the choice of a smaller, sooner reward. Therefore, if the former is assumed away, then the effect of the latter will be overstated. The recent literature identifies at least three approaches to correcting for this bias. These are the joint estimation strategy 1 This early literature is thoroughly reviewed by Frederick, Loewenstein, and O'Donoghue (2002).

Measuring Time Preferences

“…For example, some authors have developed models with domain-specific discount functions (i.e., discounting health differently than discounting the consumption of material goods; e.g., Chapman 1996). 10 Relaxing the assumption that utility is the sum of discounted flow utilities-assumption A3 above-allows risk aversion to be separated from the intertemporal elasticity of substitution (see , Bommier 2006, Bommier and Rochet 2006, Cheung 2015, Abdellaoui et al 2017, and Andersen et al 2018). For instance, Andersen et al (2018) consider 10 Another literature examines systematic features of intertemporal choice that can operate on top of discounted utility or other models of time preference.…”

Comment on “Risk Preferences Are Not Time Preferences”: Balancing on a Budget Line

“…Concerning the baseline pair, average sooner consumption levels in the certain (1, 1)-condition are initially greater than in the risky (0.5, 0.5)-condition and drop more steeply with increasing interest rates r, as depicted in the left panel of Figure 1: AS's original graph shows a crossover of the (1, 1)-curve and the (0.5.0.5)-curve, a result that was recently replicated by Cheung (2015) and Miao and Zhong (2015). When both payments are guaranteed and the interest rate is zero, subjects allocate the greatest part of their budget to the sooner payment.…”

“…We surmise that subjects may have tried hedging across conditions, possibly because of difficulties of understanding the experimental instructions. See Cheung (2015), footnote 21 and his Appendix D. 14 See also the numerical calibrations in Table 2. 15 Refer, for example, to Figure 1 in Fehr-Duda and Epper (2012, p. C-1).…”

“…13 Cheung (2015) also studied behavior in CTBs under positively correlated payments. Contrary to Miao and Zhong (2015), where the average token allocation in the certain condition practically coincides with the allocation in the correlated condition, Cheung (2015) finds a crossover of the curves for the certain and the correlated-risk…”

“…This evidence of intertemporal diversification triggered successive experimental work by Cheung (2015) and Miao and Zhong (2015) who examine the robustness of the AS findings. The upshot of these investigations is that, by and large, subjects' behavior depends significantly on whether diversification opportunities are present or not.…”