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: OrnsteinUhlenbeck, 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.

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

“…The existing economics literature on valuing investments in climate change abatement has developed a variety of models with vastly different theoretical implications for discounting cash flows from these investments. Some of this literature has argued for a downward-sloping term structure of discount rates (DDR) for investments in climate change abatement, where benefits that occur in later periods are discounted at a lower per-period discount rate (Arrow et al, 2013b;Cropper et al, 2014;Farmer et al, 2015;Traeger, 2014b). 32 As discussed in the introduction, these arguments have motivated policy changes in France and the U.K., which have adopted a downward-sloping term structure of discount rates for evaluating long-run investments.…”

“…Our framework also helps to determine which models generate term structures, for risky or hedging assets, that are compatible with equilibrium outcomes and with the new empirical evidence presented in this paper. In particular, declining discount rate (DDR) functions have become increasingly common in environmental economics (Arrow et al, 2013b;Cropper et al, 2014;Farmer et al, 2015;Traeger, 2014b) and, in some cases, have been adopted by governmental institutions for the conduct of cost-benefit analyses. 4 While superficially our results are consistent with a DDR schedule, we find that the mechanisms that generate the downward slope differ dramatically across papers in the climate change literature, and are in many cases at odds with or orthogonal to our empirical findings.…”

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

“…The existing economics literature on valuing investments in climate change abatement has developed a variety of models with vastly different theoretical implications for discounting cash flows from these investments. Some of this literature has argued for a downward-sloping term structure of discount rates (DDR) for investments in climate change abatement, where benefits that occur in later periods are discounted at a lower per-period discount rate (Arrow et al, 2013b;Cropper et al, 2014;Farmer et al, 2015;Traeger, 2014b). 32 As discussed in the introduction, these arguments have motivated policy changes in France and the U.K., which have adopted a downward-sloping term structure of discount rates for evaluating long-run investments.…”

“…Our framework also helps to determine which models generate term structures, for risky or hedging assets, that are compatible with equilibrium outcomes and with the new empirical evidence presented in this paper. In particular, declining discount rate (DDR) functions have become increasingly common in environmental economics (Arrow et al, 2013b;Cropper et al, 2014;Farmer et al, 2015;Traeger, 2014b) and, in some cases, have been adopted by governmental institutions for the conduct of cost-benefit analyses. 4 While superficially our results are consistent with a DDR schedule, we find that the mechanisms that generate the downward slope differ dramatically across papers in the climate change literature, and are in many cases at odds with or orthogonal to our empirical findings.…”

Jump-Diffusion Models for Valuing the Future: Discounting Under Extreme Situations

“…We have recently analyzed these issues by considering three of the most popular stochastic models for the dynamics of interest rates [2]: Ornstein-Uhlenbeck [26], Feller [27], and lognormal [28] processes, which are also very relevant in statistical physics. However, we are interested in real rates (recall, nominal rates corrected by inflation) 1 which can be negative even during prolonged periods of time [1,4].…”