The value of the distant future: Discounting in random environments

We analyze how future costs must be balanced against present costs. This is traditionally done using an exponential function with a constant discount rate. The choice of discount rate can dramatically effect the question on what is the value of the future. This is specially critical for environmental problems such as global warming, and it has generated a controversy as to the urgency for immediate action (Stern, 2006; Nordhaus, 2007a,b). We briefly review the issue 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: OrnsteinUhlenbeck, Feller and log-normal. We also outline our previous empirical survey on 14 countries over time spans ranging up to more than 300 years We estimate the parameters of one of the models studied (the Ornstein-Uhlenbeck process) and obtain the long-run discount rate for all these countries. The long-run discount obtained for stable countries (countries that have not suffered periods of destabilizing inflation) supports the low discounting rate proposed by Stern (2006) over higher rates that have been advocated by others (Nordhaus, 2007a,b)