title: Value of the future: Discounting in random environments.
abstract: We analyze how to value future costs and benefits when they must be discounted relative to the present. We introduce the subject for the nonspecialist and take into account the randomness of the economic evolution by studying the discount function of three widely used processes for the dynamics of interest rates: Ornstein-Uhlenbeck, Feller, and log-normal. Besides obtaining exact expressions for the discount function and simple asymptotic approximations, we show that historical average interest rates overestimate long-run discount rates and that this effect can be large. In other words, long-run discount rates should be substantially less than the average rate observed in the past, otherwise any cost-benefit calculation would be biased in favor of the present and against interventions that may protect the future.
authors.affiliation: Institute for New Economic Thinking at the Oxford Martin School and Mathematical Institute, University of Oxford, Eagle House, Walton Well Rd. Oxford OX2 6ED, United Kingdom.|Santa Fe Institute, Santa Fe, New Mexico.
authors.forename: J Doyne
authors.initials: JD
authors.lastname: Farmer
authors.affiliation: Santa Fe Institute, Santa Fe, New Mexico.|Department of Economics, Yale University, New Haven, Connecticut, USA.
authors.forename: John
authors.initials: J
authors.lastname: Geanakoplos
authors.affiliation: Departament de Física Fonamental, Universitat de Barcelona, Diagonal, 645 08025 Barcelona, Spain.
authors.forename: Jaume
authors.initials: J
authors.lastname: Masoliver
authors.affiliation: Departament de Física Fonamental, Universitat de Barcelona, Diagonal, 645 08025 Barcelona, Spain.
authors.forename: Miquel
authors.initials: M
authors.lastname: Montero
authors.affiliation: Departament de Física Fonamental, Universitat de Barcelona, Diagonal, 645 08025 Barcelona, Spain.
authors.forename: Josep
authors.initials: J
authors.lastname: Perelló