Stochastic Sustainability in the Presence of Unknown Parameters

Abstract

“Clearly, global warming is rife with uncertainty — about future emissions paths, GHGs (Green House Gases)-climate linkage, about the timing of the climate change, about the impacts of climate upon flora and fauna (and human economic activity), about the costs of slowing climate change and even about the speed with which we can reduce the uncertainties. How should we proceed in the face of uncertainty?” (Nordhaus, 1991, p. 58).¹ Most of the times a certain functional form is assumed and the “certainty equivalence” analysis is applied simply ignoring uncertainty. Even conceding that the assumed functional form is the correct one, uncertainty about the unknown parameters remains. As is well known “when the point estimator… (has) a probability density function, the probability (that the estimate is equal to) the parameter being estimated (is) 0” (Mood et al., 1974, p. 372). For this reason “the potential consumer of the applied… model must be reasonably convinced of the reliability… of the model and its parameters before he can have any degree of confidence in its results” (Lau, 1984, p. 135). Hence the need to consider both the parameter estimates and the measures of their reliability.

The author would like to thank A Vercelli for his steadfast encouragement and suggestions, during the various stages of the research, and G. Heal for reading and carefully commenting on an earlier draft of this work. The usual disclaimers apply.