Discounting the Distant Future

32 Pages Posted: 16 Jul 2014

See all articles by J. Doyne Farmer

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School; Santa Fe Institute

John Geanakoplos

Yale University - Cowles Foundation

Jaume Masoliver

University of Barcelona - Department of Physics

Miquel Montero

University of Barcelona - Departament de Física de la Matèria Condensada

Josep Perelló

University of Barcelona - Department of Physics

Date Written: July 14, 2014

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

JEL Classification: C1, G12, Q5

Suggested Citation

Farmer, J. Doyne and Geanakoplos, John D and Masoliver, Jaume and Montero, Miquel and Perello, Josep, Discounting the Distant Future (July 14, 2014). Cowles Foundation Discussion Paper No. 1951. Available at SSRN: https://ssrn.com/abstract=2465953 or http://dx.doi.org/10.2139/ssrn.2465953

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

HOME PAGE: http://www.inet.ox.ac.uk/people/view/4

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States
505-984-8800 (Phone)
505-982-0565 (Fax)

HOME PAGE: http://www.santafe.edu/~jdf/

John D Geanakoplos (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3397 (Phone)
203-432-6167 (Fax)

HOME PAGE: http://cowles.econ.yale.edu/P/au/d_gean.htm

Jaume Masoliver

University of Barcelona - Department of Physics ( email )

Barcelona, E-08028
Spain
00 34 3 402 11 59 (Phone)
00 34 3 402 11 49 (Fax)

Miquel Montero

University of Barcelona - Departament de Física de la Matèria Condensada ( email )

Martí i Franquès, 1
Barcelona, Catalonia 08028
Spain
+34 93 403 92 53 (Phone)
+34 93 402 11 55 (Fax)

Josep Perello

University of Barcelona - Department of Physics ( email )

Diagonal, 647
Barcelona, E-08028
Spain
+34 9 34021150 (Phone)
+34 34021149 (Fax)

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