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Pricing the Planet's FutureThe Economics of Discounting in an Uncertain World$
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Christian Gollier

Print publication date: 2012

Print ISBN-13: 9780691148762

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691148762.001.0001

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Random Walk and Mean-Reversion

Random Walk and Mean-Reversion

Chapter:
(p.62) 4 Random Walk and Mean-Reversion
Source:
Pricing the Planet's Future
Author(s):

Christian Gollier

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691148762.003.0004

This chapter illustrates that the shape of the term structure of discount rates is determined by the way the wealth effect and the precautionary effects evolve with the time horizon. When the growth rate of consumption is constant, then consumption increases exponentially, and the intertemporal rate of substitution, which is the discount factor, decreases exponentially. This requires that the discount rate is constant. The simplest extension of this to uncertainty is to assume that the growth rate of the economy follows a random walk. In that case, the variance of log consumption increases linearly, which yields an exponentially increasing precautionary effect for the discount factor. This justifies a constant precautionary effect on the discount rate, yielding a crucial result for the theory of efficient discount rates.

Keywords:   term structure, random walk, mean-reversion, consumption, substitution, precautionary effect, efficient discount rates

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