The article which Robin pointed to is available in PDF format for a $5
charge. In order to make it more accessible, I have taken the liberty
of manually typing in section 2.2, where they make their main case for
time inconsistency, and I offer it here for future criticism.
Keep in mind that this article is offered as an argument for government
intervention into the decisions of private individuals. Individuals
consistently regret their past actions, according to this argument, and
a wise and enlightened government will therefore intervene to coerce or
persuade them into taking a more far-sighted view. Those who object to
such paternalistic actions may wish to consider the argument especially
carefully.
A couple of notes: having typed it in by hand, typographic errors are
my fault. I have not included the bibliographic references, but I can
supply those on request.
Also, the authors do refer to one equation from earlier in the paper,
"delta = 1/beta". The idea here is that delta is the discount rate into
the future, so if it were 0.95 per year that would mean that pleasures
a year from now are worth 5% less than pleasures I can experience today.
Beta is the discount rate into the past, so if it were also 0.95 per year
that would mean a pleasure a year ago was worth 5% less than that same
pleasure experienced today. To be time-consistent and avoid regreat,
delta = 1/beta must be true; i.e if delta is 0.95 then beta must be
about 1.05, and pleasures a year ago must be 5% MORE valuable than if
they were experienced today.
With that introduction, here is section 2.2, excerpted from
http://papers.nber.org/papers/W7983
The Social Discount Rate
Andrew Caplin, John Leahy
NBER Working Paper No. W7983 Issued in October 2000
================================================
2.2 The Argument for Discounting: Future and Past
Ever since Bohm-Bawerk [1959] first proposed discounting as one of the
prime reasons for positive interest rates, there has been near
unanimity among economists that individuals discount future felicity
relative to present felicity.[Note 3] The main argument in favor of
discounting is empirical. It appears to be the revealed preference of
individuals that current pleasure is preferred to future pleasure, and
future pain to current pain. Introspection supports this view, as do
market interest rates in excess of the growth rate of population and
productivity, and so does the available experimental evidence from
economics and psychology.[Note 4]
Given that individuals discount the future, invariance requires that
agents weight the past more heavily than they do the present. In
other words, it requires that a thirty year old cares more about an
apple that was consumed at age three than about an apple to be
consumed today. moreover, the importance of that apple at age three
relative to an apple today must grow at an exponential rate as the
consumer ages.
This implication of invariance is difficult to accept. Rather than
viewing past consumption as progressively more important as the
consumer ages, it is more plausible that agents discount past
consumption. When asked most people would prefer having completed an
onerous task last week over having to perform one this evening; they
would prefer a pleasurable meal this evening to one ten years ago; and
they would prefer to be leaving on vacation to returning to work when
their vacation is over.[Notes 5,6] Whenever one thinks, "I'm glad it
is finally three o'clock and that lecture is over," it reflects
discounting of the past. The disagreeable experience is less painful
when it is in the past than when it is being experienced in the
present.[Note 7]
Beyond revealed preference, the strongest theoretical argument in
favor of discounting, involves what Bohm-Bawerk referred to as the
"brevity and uncertainty of human life." According to this view,
people discount future felicity because they may not be around to
enjoy it. An individual weighs pleasures at date t by the conditional
probability of living until date t.
There is a parallel between mortality and forgetfulness. The past
dies when we forget.[Note 8] Do we value today meals eaten ten years
ago, if we cannot even remember what we ate? How is our current
utility reduced by past pains that we cannot even remember? Imperfect
memory justifies discounting the past in much the same way that
mortality justifies discounting the future, and just as mortality
suggests that we discount the far off future more than the near
future, imperfect memory suggests that we discount the far off past
more than the recent past.
Finally, heterogeneity in discount rates across individuals undermines
the case for retrospective consistency. If, as is commonly believed,
the rich and educated are more forward looking, do they place
relatively _less_ weight on the past as invariance would require? To
the extent that individual discount rates are endogenous, as argued by
Becker and Mulligan [1997], does the weight on the past adjust to
maintain delta = 1/beta? Or is the weight on the past also
endogenous? After all, we spend considerable resources keeping the
past alive, through stories, photographs, souvenirs, and diaries. If
the weight on the past is endogenous, wouldn't it be a remarkable
quirk of fate of [sic] this weight were exactly equal to the inverse
of the discount factor?
We conclude that in almost any reasonable formulation, future selves
weight current consumption less heavily than does the current self.
The implication is that tastes change over time. We now consider the
welfare implications of this observation.
====
Note 3. For a rare statement of dissent see Becker and Stigler
[1977].
Note 4. Although supportive of discounting, the experimental evidence
does not necessarily support exponential discounting. See Ainslie
[1992].
Note 5. This last statement assumes that the vacation is a
pleasurable experience. For some families this may not be true. In
this case the inequality is reversed, but the point is the same.
Note 6. There will, of course, be exceptions. There may be that
particularly pleasurable occurrence which yields memories for years to
come, memories so precious that one is glad that the experience was in
the past so that the memories could be enjoyed over an extended period
of time. Similar exceptions, however, apply to discounting the
future. One may, for example, want to delay a particularly
pleasurable event in order to savor the feelings of anticipation that
it engenders (Loewenstein [1987]). The existence of a few exceptions,
however, does not alter the general rule.
Note 7. Some suggestive evidence comes from DeGenova [1992] who found
that when people looked back on their lives they most regretted not
spending time on education. Education, being an activity with current
costs and future rewards, is a prime candidate for retrospective time
inconsistency.
Note 8. The experimental evidence in psychology indicates that
exponential decay of recall probabilities fits the data rather well,
although a power function may perform better (See Crovits and
Schiffman [1974]).
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