The value of the distant future: The process of discount in random environments

Abstract

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 e_ect 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 briey 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: Ornstein-Uhlenbeck, Feller and log-normal.We also outline our previous empirical survey on 9 stable countries (countries that have not su_ered periods of destabilizing ination) over time spans ranging up to more than 300 years (Farmer et. al. 2014). 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 supports the low discounting rate proposed by Stern (2006) over higher rates that have been advocated by others (Nordhaus, 2007a,b).