Adv Behav Econ pdf

172
F R E D E R I C K E T A L .
We care less about our further future . . . because we know that less of what we are
now—less, say, of our present hopes or plans, loves or ideals—will survive into the fur-
ther future . . . [if ] what matters holds to a lesser degree, it cannot be irrational to care
less. (Parfit 1971, p. 99)
Parfit’s claims are normative, not descriptive. He is not attempting to explain or
predict people’s intertemporal choices, but is arguing that conclusions about the
rationality of time preference must be grounded in a correct view of personal
identity. If this is the only compelling normative rationale for time discounting,
however, it would be instructive to test for a positive relation between observed
time discounting and changing identity. Frederick (1999) conducted the only
study of this type, and found no relation between monetary discount rates (as im-
puted from procedures such as “I would be indifferent between $100 tomorrow
and $——— in five years”) and self-perceived stability of identity (as defined by
the following similarity ratings: “Compared to now, how similar were you five
years ago [will you be five years from now]?”), nor did he find any relation be-
tween such monetary discount rates and the presumed correlates of identity sta-
bility (for example, the extent to which people agree with the statement “I am still
embarrassed by stupid things I did a long time ago”).
Discounted Utility Anomalies
Over the past two decades, empirical research on intertemporal choice has docu-
mented various inadequacies of the DU model as a descriptive model of behavior.
First, empirically observed discount rates are not constant over time, but appear to
decline—a pattern often referred to as hyperbolic discounting. Furthermore, even
for a given delay, discount rates vary across different types of intertemporal
choices: gains are discounted more than losses, small amounts more than large
amounts, and explicit sequences of multiple outcomes are discounted differently
than outcomes considered singly.
Hyperbolic Discounting
The best documented DU anomaly is hyperbolic discounting. The term 
hyper-
bolic discounting 
is often used to mean that a person has a declining rate of time
preference (in our notation, 
r
n
is declining in 
n
), and we adopt this meaning here.
Several results are usually interpreted as evidence for hyperbolic discounting.
First, when subjects are asked to compare a smaller-sooner reward to a larger-
later reward (to be discussed), the implicit discount rate over longer time horizons
is lower than the implicit discount rate over shorter time horizons. For example,
Thaler (1981) asked subjects to specify the amount of money they would require
one’s future welfare to a degree that exceeds the degree of psychological connectedness that obtains
between one’s current self and one’s future self.

---