تجزیه و تحلیل هزینه و منفعت تحت عدم قطعیت - تذکر بر قضیه نرخ پایین ویتزمن

Weitzman's (2009) famous dismal theorem argues that “fat tails” in the distribution of warming may pose problems for cost–benefit analysis as it may imply that society might be willing to exchange today's consumption for future consumption at an infinite rate. His analysis is based on the stochastic discount factor. We show that in situations in which the stochastic discount factor is applicable, it is optimal for society to devote only a finite amount of resources to protect against climate change. For general assumptions on the investment returns, cost–benefit analysis must consider the joint distribution of the marginal utility of future consumption and marginal returns to investment in the different future states of nature. We explore the range of situations under which challenges for applying cost–benefit analysis under uncertainty remain.

Weitzman (2009) laid out a dismal theorem which shows a potential problem for applying cost–benefit analysis in the realm of large structural uncertainty. Using the example of climate change, he shows that the rate at which society would be willing to exchange today's consumption for future consumption might very well be infinite. The implication is that climate change may be a situation in which society should be willing to devote all of its resources to protect against future climate change. The conclusions from the dismal theorem have received an intense discussion (e.g., Karp, 2009, Nordhaus, 2009 and Nordhaus, 2011). In this note, we argue that Weitzman's derivation is missing a crucial term. This term represents the technological and policy options available for addressing climate change, an essential element of models for cost–benefit analysis. Since both future income and the future returns to investment may be subject to the same underlying uncertainties, any decision criterion must be based on their joint distribution. Thus, cost–benefit analysis cannot generally be based on the stochastic discount factor which Weitzman takes as the basis for his arguments. We reformulate the model to explicitly account for investment options and find that it rarely implies that society should “invest everything”. We show that the infinity result can still occur, although under narrower conditions than Weitzman originally claimed.1

Weitzman (2009) laid out a dismal theorem which shows a potential problem for applying cost–benefit analysis in the realm of large structural uncertainty. Using the example of climate change, he shows that the rate at which society would be willing to exchange today's consumption for future consumption might very well be infinite. The implication is that climate change may be a situation in which society should be willing to devote all of its resources to protect against future climate change. The conclusions from the dismal theorem have received an intense discussion (e.g., Karp, 2009, Nordhaus, 2009 and Nordhaus, 2011). In this note, we argue that Weitzman's derivation is missing a crucial term. This term represents the technological and policy options available for addressing climate change, an essential element of models for cost–benefit analysis. Since both future income and the future returns to investment may be subject to the same underlying uncertainties, any decision criterion must be based on their joint distribution. Thus, cost–benefit analysis cannot generally be based on the stochastic discount factor which Weitzman takes as the basis for his arguments. We reformulate the model to explicitly account for investment options and find that it rarely implies that society should “invest everything”. We show that the infinity result can still occur, although under narrower conditions than Weitzman originally claimed.1