Testing the Dismal Theorem

Abstract

Weitzman’s “dismal theorem” has that the expected net present value of a stock problem with a stochastic growth rate with unknown variance is unbounded. Cost-benefit analysis can therefore not be applied to greenhouse gas emission control. We use the generalized central limit theorem to show that the dismal theorem can be tested, in a finite sample, by estimating the tail index. We apply this test to social cost of carbon estimates from three commonly used integrated assessment models and to previously published estimates. Two of the three models do not support the dismal theorem, but the third one does for low discount rates and most estimators. The meta-analysis does offer qualified support for the dismal theorem.