198
F R E D E R I C K E T A L .
used in time-preference studies. The overwhelming evidence for reference-
dependent utility suggests, however, that this assumption may be invalid—that
people may not be integrating the stated amounts with their current and future
wealth, and therefore that curvature in the utility function may be substantial even
for these small amounts (see Bateman et al. 1997; Harless and Camerer 1994;
Kahneman and Tversky 1979; Rabin 2000; Rabin and Thaler 2001; Tversky and
Kahneman 1991).
Three techniques could be used to avoid this confound. First, one could request
direct utility judgments (for example, attractiveness ratings) of the same conse-
quence at two different times. Then, the ratio of the attractiveness rating of the
distant outcome to the proximate outcome would directly reveal the implicit dis-
count factor. Second, to the extent that utility is linear in probability, one can use
choices or judgment tasks involving different probabilities of the same conse-
quence at different times (Roth and Murnighan 1982). Evidence that probability
is weighted nonlinearly (see, for example, Starmer 2000) would, of course, cast
doubt on this approach. Third, one can separately elicit the utility function for the
good in question, and then use that function to transform outcome amounts into
utility amounts, from which utility discount rates could be computed. To our
knowledge, Chapman (1996) conducted the only study that attempted to do this.
She found that
utility
discount rates were substantially lower than the
dollar
dis-
count rates, because utility was strongly concave over the monetary amounts sub-
jects used in the intertemporal choice tasks.
29
UNCERTAINTY
In experimental studies, subjects are typically instructed to assume that delayed
rewards will be delivered with certainty. Whether subjects do (or can) accept this
assumption is unclear, because delay is ordinarily—and perhaps unavoidably—
associated with uncertainty. A similar problem arises for field studies, in which it
is typically assumed that subjects believe that future rewards, such as energy sav-
ings, will materialize. Due to this subjective (or
epistemic
) uncertainty associated
with delay, it is difficult to determine to what extent the magnitude of imputed
discount rates (or the shape of the discount function) is governed by time preference
per se, versus the diminution in subjective probability associated with delay.
30
Empirical evidence suggests that introducing objective (or
aleatory
) uncer-
tainty to both current and future rewards can dramatically affect estimated discount
rates. For instance, Keren and Roelofsma (1995) asked one group of respondents
29
Chapman also found that magnitude effects were much smaller after correcting for utility func-
tion curvature. This result supports Loewenstein and Prelec’s (1992) explanation of magnitude effects
as resulting from utility function curvature (see section on reference-point models herein).
30
There may be complicated interactions between risk and delay, because uncertainty about future
receipt complicates and impedes the planning of one’s future consumption stream (Spence and Zeck-
hauser 1972). For example, a 90% chance to win $10,000,000 in 15 years is worth much less than a
guarantee to receive $9,000,000 at that time, because, to the extent that one cannot insure against the
residual uncertainty, there is a limit to how much one can adjust one’s consumption level during those
15 years.
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