Thinking and Deciding

DISCOUNTING 483
The high subjective discount rate (and resulting neglect of the future) is illustrated
in the effect of mandatory pension plans (provided by employers) on voluntary
saving. If people really looked out for their future, in this case, then those without
mandatory pension plans would start their own voluntarily. Other things being equal,
people without mandatory pension plans should save more (on their own) than those
that have them, yet (before the introduction of government incentives in the form of
tax breaks), this was not the case.
Another study reviewed by Thaler and Shefrin examined purchases of home air
conditioners. Air conditioners differ, of course, in initial cost and operating expense
(including the cost of electricity). The researchers found that people paid most attention
to the initial cost. If one calculates the subjective discount rate from such
purchase decisions, it is over 25%, well over any interest rate available at the time.
(If one wanted to maximize income, one ought to buy the more expensive but more
economical model — if necessary, borrowing money to buy it.) 7
As people get older, it appears that their discount rate gets lower. They give
greater weight to the future, even though there is less of it (Green, Fry, and Myerson,
1994).
Dynamic inconsistency
It is difficult to draw conclusions about the personal discount rate because this rate
is not constant (Chapman, 1998; Kirby, 1997; Loewenstein and Prelec, 1993). Discount
rates are higher for shorter delays. This leads to dynamic inconsistency.
Figure 19.2 shows a different function relating the utility of a reward to time.
Again, it contrasts a smaller, sooner reward and a larger, later reward. The first reward
is available at T1, and the second at T2. In this case, the discount rate increases
sharply as the time of the reward approaches, so sharply that it cannot be shown on
the graph. As a result, the choice between the two rewards will depend on when the
choice is made. If it is made far away from both, at the left side of the graph, then it
will favor the larger later reward. If it is made soon before the smaller shorter reward
is available, it will favor that one. This is like the candy example described earlier.
A person with these discount functions would be dynamically inconsistent.
This inconsistency is a clear example of the difference between decision utility
and experienced utility, discussed in Chapter 13. We can describe the decision as
determined by some sort of hypothetical quantity — decision utility — that is somewhat
unrelated to the true utility of interest, the extent to which goals are achieved.
In Figure 19.2, decision utility is proportional to the reciprocal of the time between
the decision and the reward. The function is a hyperbola. This function cannot be
exactly right, because it would imply that the reward has infinite utility when it is
finally available. But this function comes amazingly close to describing the behavior
7 The conclusions of Thaler and Shefrin have been questioned by Modigliani (1986), who has found
that many economic data can be accounted for by assuming that people treat all periods of their lives
equally. Few of these data, however, directly concern the temporal myopia that Thaler and Shefrin have
suggested.