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Weitzman, Martin

This paper in applied theory argues that there is a loose chain of reasoning connecting the following three basic links in the economics of climate change: 1) additive disutility damages may be appropriate for analyzing some impacts of global warming; 2) an uncertain feedback-forcing coefficient, which might be near one with infinitesimal probability, can cause the distribution of the future time trajectory of global temperatures to have fat tails and a high variance; 3) when high-variance additive damages are discounted at an uncertain rate of pure time preference, which might be near zero with infinitesimal probability, it can make expected present discounted disutility very large. Some possible implications for welfare analysis and climate-change policy are briefly noted.

Should governments use a discount rate that declines over time when evaluating the future benefits and costs of public projects? The argument for using a declining discount rate (DDR) is simple: if the discount rates that will be applied in the future are uncertain but positively correlated, and if the analyst can assign probabilities to these discount rates, then the result will be a declining schedule of certainty-equivalent discount rates. There is a growing empirical literature that estimates models of long-term interest rates and uses them to forecast the DDR schedule. However, this literature has been criticized because it lacks a connection to the theory of project evaluation. In benefit-cost analysis, the net benefits of a project in year t (in consumption units) are discounted to the present at the rate at which society would trade consumption in year t for consumption in the present. With simplifying assumptions, this leads to the Ramsey discounting formula, which results in a declining certainty-equivalent discount rate if the rate of growth in consumption is uncertain and if shocks to consumption are correlated over time. We conclude that the arguments in favor of a DDR are compelling and thus merit serious consideration by regulatory agencies in the United States.

At high enough greenhouse gas concentrations, climate change might conceivably cause catastrophic damages with small but non-negligible probabilities. If the bad tail of climate damages is sufficiently fat, and if the coefficient of relative risk aversion is greater than one, the catastrophe-reducing insurance aspect of mitigation investments could in theory have a strong influence on raising the social cost of carbon. In this paper I exposit the influence of fat tails on climate change economics in a simple stark formulation focused on the social cost of carbon. I then attempt to place the basic underlying issues within a balanced perspective.

It is difficult to resolve the global warming free-rider externality problem by negotiating n different quantity targets. By contrast, negotiating a single internationally binding minimum carbon price (the proceeds from which are domestically retained) counters self-interest by incentivizing agents to internalize the externality. The model of this article indicates an exact sense in which each agent’s extra cost from a higher emissions price is counterbalanced by that agent’s extra benefit from inducing all other agents to simultaneously lower their emissions in response to the higher price. Some implications are discussed. While the study is centered on a formal model, the tone of the policy discussion resembles more an exploratory think piece.

Suppose that there is a probability density function for how bad things might get, but that the overall rate at which this probability density function slims down to approach zero in the tail is uncertain. The paper shows how a basic precautionary principle of tail fattening could then apply. The worse is the contemplated damage, the more should a decision maker consider the bad tail to be among the relatively fatter-tailed possibilities. A rough numerical example is applied to the uncertain tail distribution of climate sensitivity.

In economic project analysis, the rate at which future benefits and costs are discounted relative to current values often determines whether a project passes the benefit-cost test. This is especially true of projects with long time horizons, such as those to reduce greenhouse gas (GHG) emissions. Whether the benefits of climate policies, which can last for centuries, outweigh the costs, many of which are borne today, is especially sensitive to the rate at which future benefits are discounted. This is also true of other policies, e.g., affecting nuclear waste disposal or the construction of long-lived infrastructure.

The choice of an overall discount rate for climate change investments depends critically on how different components of investment payoffs are discounted at differing rates reflecting their underlying risk characteristics. Such underlying rates can vary enormously, from ≈1 percent for idiosyncratic diversifiable risk to ≈7 percent for systematic nondiversifiable risk. Which risk-adjusted rate is chosen can have a huge impact on cost-benefit analysis. In this expository paper, I attempt to set forth in accessible language with a simple linear model what I think are some of the basic issues involved in discounting climate risks. The paper introduces a new concept that may be relevant for climate-change discounting: the degree to which an investment hedges against the bad tail of catastrophic damages by insuring positive expected payoffs even under the worst circumstances. The prototype application is calculating the social cost of carbon.

In this article, I revisit some basic issues concerning structural uncertainty and catastrophic climate change. My target audience here are general economists, so this article could also be viewed as a somewhat less technical exposition that supplements my previous work. Using empirical examples, I argue that it is implausible that low-probability, high-negative impact events would not much influence an economic analysis of climate change. I then try to integrate the empirical examples and the theory together into a unified package with a unified message that the possibility of catastrophic climate change needs to be taken seriously.

The so-called “Weitzman–Gollier puzzle” is the fact that two seemingly symmetric and equally plausible ways of dealing with uncertain future discount rates appear to give diametrically opposed results. The puzzle is resolved when agents optimize their consumption plans. The long run discount rate declines over time toward its lowest possible value.