On the economics of global warming with threshold effects

I develop a simplified model designed to study optimal emission policies in the face of a discontinuous and irreversible jump in economic costs caused by an abrupt shift in climatic conditions. I examine the infinite-horizon discounted dynamic programming problem where the choice variable is greenhouse gas (GHG) emissions. Emissions are necessary for economic welfare, but lead to an accumulation of atmospheric GHG. If atmospheric GHG surpasses a threshold, the costs of global warming jump discontinuously. The value function and stationary optimal policy are characterized. It is shown that the optimal policy and path are non-monotone, with reduced emissions as the level of GHG approaches the threshold and an increase in emissions just before the threshold is reached. The value function and optimal policy are comprised of segments, with each segment corresponding to a finite number of periods in which it is optimal to reach the threshold. The optimal emission is discontinuous in the initial state.; I calibrate the model to a particular global warming threshold, that of a potential collapse in the North Atlantic thermohaline circulation process. Because the results of long-horizon cost benefit studies are almost entirely driven by the choice of discount factor, I study the interaction of discount factor uncertainty and this particular long-horizon threshold. Accounting for discount factor uncertainty facilitates recognition of an associated real option value. The option value arises because ex ante preference uncertainty and irreversibility create a potential value to delaying the time at which a central planner would optimally choose to surpass the irreversible threshold. I use the calibrated threshold model to compute one measure of the magnitude of this option value. I show that for distributions calibrated from the empirical literature, the impact of discount factor uncertainty is significantly larger than the impact of catastrophic cost uncertainty. With any given discount factor, the present value of uncertainty in the catastrophic costs is virtually negligible. With any given catastrophic cost, the present value of uncertainty in the discount factor is quite significant.