# Measuring Discounting without Measuring Utility

By Arthur E. Attema, Han Bleichrodt, Yu Gao, Zhenxing Huang and Peter P. Wakker - May 7, 2016

This paper introduces a new method to measure intertemporal discounting, which is much easier than existing methods. Samuelson’s discounted utility evaluates an income stream X0,…,X52 (getting €X0 now, , …, €X52 after 52 weeks) by d0U(X0)+…+d52U(X52) Here, U describes the utility of money and dj is the subjective discount weight of week j, usually less than 1 (impatience). How can discounting and utility be measured from revealed preferences? The difficulty is that there are two unknowns, which may interact. For a long time, researchers did not know and simply assumed linear utility. If (€98,0,…,0)~(0,€100,0,…,0) then they just took d1=0.98, ignoring utility curvature. But any self-respecting economist should allow for utility curvature. It was a challenge to the field.

Andersen et al. (2008 Econometrica) proposed deriving utility from choices under risk, where classical methods are available, and then using this utility to measure discounting. This approach has two problems. First, behavioral studies showed violations of those classical methods. Second, many economists believe that risk and intertemporal utility cannot be simply equated. Some recent studies suggest that they are different. Andreoni & Sprenger (2012, American Economic Review), alternatively, used complex data fittings requiring restrictive parametric commitments to measure discounting.

This paper introduces a simple solution: if receiving €10 during, say, weeks 11-20 is equivalent to receiving €10 during weeks 42-52, then weeks 11-20 have the same total discounted weight as weeks 42-52. Such equations allow measurement of the entire discount function without the need to know utility. Utility can be anything because it drops from the equations anyhow. The paper gives a theoretical justification and shows that our method works well empirically. It is considerably simpler and less time-consuming than existing methods while giving the same results.

#### Arthur E. Attema (EUR), Han Bleichrodt, Yu Gao, Zhenxing Huang and Peter P. Wakker (EUR), Measuring Discounting Without Measuring Utility, American Economic Review, June 2016, Vol. 106(1), 1476-1494. Read the article in the American Economic Review.

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