Discounting the Distant Future

J. Farmer, John Geanakoplos (), Jaume Masoliver, Miquel Montero () and Josep Perello
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John Geanakoplos: Cowles Foundation, Yale University, https://economics.yale.edu/people/faculty/john-geanakoplos
Jaume Masoliver: Departament de Fisica Fonamental, Universitat de Barcelona
Josep Perello: Departament de Fisica Fonamental, Universitat de Barcelona

No 1951, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: If the historical average annual real interest rate is m > 0, and if the world is stationary, should consumption in the distant future be discounted at the rate of m per year" Suppose the annual real interest rate r(t) reverts to m according to the Ornstein Uhlenbeck (OU) continuous time process dr(t) = alpha[m - r(t)]dt + kdw(t), where w is a standard Wiener process. Then we prove that the long run rate of interest is r_infinity = m-k^2/2alpha^2. This confirms the Weitzman-Gollier principle that the volatility and the persistence of interest rates lower long run discounting. We fit the OU model to historical data across 14 countries covering 87 to 318 years and estimate the average short rate m and the long run rate r_infinity for each country. The data corroborate that, when doing cost benefit analysis, the long run rate of discount should be taken to be substantially less than the average short run rate observed over a very long history.

Keywords: Discounting; Environment; Interest rates; Inflation; Ornstein-Uhlenbeck process (search for similar items in EconPapers)
JEL-codes: C1 G12 Q5 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2014-07
New Economics Papers: this item is included in nep-his
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Citations: View citations in EconPapers (4)

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