Holcomb and Nelson, 1992). The most striking effect is an “immediacy effect”
(Prelec and Loewenstein 1991): discounting is dramatic when one delays con-
sumption that would otherwise be immediate.
Declining discount rates have also been observed in experimental studies involv-
ing real money outcomes. Horowitz (1992) tested the constancy of discounting by
auctioning “bonds” in a Vickrey (highest-rejected-bid) auction. The amount bid for
a bond represented how much a subject was willing to give up at the time of the auc-
tion for certain future payoffs. Discount rates again decreased as the horizon grew
longer. Pender (1996) conducted a study in which Indian farmers made several
choices between amounts of rice that would be delivered either sooner or later. Fix-
ing the earlier rice ration and varying the amount of rice delivered later gives an
estimate of the discount rate. To avoid immediacy effects, none of the choices was
delivered immediately. Per-period discount rates decline with the increasing hori-
zon: the mean estimated discount rate was .46 for 7 months and .33 for 5 years.
Hyperbolic time discounting implies that people will make relatively farsighted
decisions when planning in advance—when all costs and benefits will occur in
the future—but will make relatively shortsighted decisions when some costs or
benefits are immediate. The systematic changes in decisions produced by hyper-
bolic time discounting create a time-inconsistency in intertemporal choice not
present in the exponential model. An agent who discounts utilities exponentially
would, if faced with the same choice and the same information, make the same
decision prospectively as he would when the time for a decision actually arrived.
In contrast, somebody with time-inconsistent hyperbolic discounting will wish
prospectively that in the future he would take farsighted actions; but when the fu-
ture arrives he will behave against his earlier wishes, pursuing immediate gratifi-
cation rather than long-run well-being.
Strotz (1955) first recognized the planning problem for economic agents who
would like to behave in an intertemporally consistent fashion, and discussed the
important ramifications of hyperbolic time discounting for intertemporal choice.
Most big decisions—regarding, e.g., savings, educational investments, labor sup-
ply, health and diet, crime and drug use—have costs and benefits that occur at dif-
ferent points in time. Many authors such as Thaler (1981), Thaler and Shefrin
(1981), and Schelling (1978) discussed the issues of self-control and stressed their
importance for economics. Laibson (1997) accelerated the incorporation of these
issues into economics by adopting a “quasi-hyperbolic” time discounting function
(first proposed by Phelps and Pollak [1968] to model intergenerational utility). The
quasi-hyperbolic form approximates the hyperbolic function with two parameters,
b
and
d
, in which the weight on current utility is 1 and the weight on period-
t
instantaneous utility is
bd
t
for
t
.
0. The parameter
b
measures the immediacy ef-
fect: if
b
5
1 the model reduces to standard exponential discounting. When de-
layed rewards are being compared, the immediacy premium
b
divides out so that
the ratio of discounted utilities is solely determined by
d
t
(consistent with the ob-
servations of Benzion, Rapoport, and Yagil 1989).
Thus, quasi-hyperbolic time discounting is basically standard exponential time
discounting plus an immediacy effect; a person discounts delays in gratification
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