Hyperbolic Discounting Is Rational: Valuing the Far Future with
Uncertain Discount Rates

Conventional economics supposes that agents value the present vs.
the future using an exponential discounting function. In contrast,
experiments with animals and humans suggest that agents are better described
as hyperbolic discounters, whose discount function decays much more slowly
at large times, as a power law. This is generally regarded as being time
inconsistent or irrational. We show that when agents cannot be sure of their
own future one-period discount rates, then hyperbolic discounting can become
rational and exponential discounting irrational. This has important
implications for environmental economics, as it implies a much larger weight
for the far future.