Uncertain outcomes and climate change policy

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Abstract

I incorporate distributions for temperature change and its economic impact in an analysis of climate change policy. As a measure of willingness to pay (WTP), I estimate the fraction of consumption w(τ) that society would be willing to sacrifice to ensure that any increase in temperature at a future point is limited to τ. Using information on distributions for temperature change and economic impact from recent studies assembled by the IPCC and others, I fit displaced gamma distributions for these variables. These fitted distributions, which roughly reflect the “state of knowledge” regarding warming and its impact, generally yield values of w(τ) below 2%, even for small values of τ, consistent with moderate abatement policies. I also calculate WTP for shifts in the mean and standard deviation of the temperature distribution, and show how WTP, and thus the demand for abatement, are driven more by outcome uncertainty than expected outcomes.

Introduction

Economic analyses of climate change policies often focus on “likely”scenarios – those within a roughly 66–90% confidence interval – for emissions, temperature, economic impacts, and abatement costs. It is hard to justify the immediate adoption of a stringent abatement policy given these scenarios and consensus estimates of discount rates and other relevant parameters.1 I ask (1) whether a stringent policy might be justified by a cost–benefit analysis that accounts for a full distribution of possible outcomes; and (2) whether the demand for abatement depends more on expected outcomes or on outcome uncertainty.

Recent climate science and economic impact studies allow one to at least roughly estimate the distributions for temperature change and its economic impact.2 I show how these distributions can be incorporated in and affect conclusions from analyses of climate change policy. As a framework for policy analysis, I estimate a simple measure of “willingness to pay” (WTP): the fraction of consumption w(τ) that society would be willing to sacrifice, now and throughout the future, to ensure that any increase in temperature at a specific horizon H is limited to τ. Whether the reduction in consumption corresponding to a particular w(τ) is sufficient to limit warming to τ is a separate question which I do not address. In effect, I focus only on the “demand side” of climate policy.

I treat the studies upon which I draw as the current “state of knowledge” of global warming and its impact. Using information on the distributions for temperature change from scientific studies assembled by the IPCC [16], [17], [18] and information about economic impacts from recent “integrated assessment models” (IAMs), I fit gamma distributions for these variables. Unlike most IAMs, however, I model economic impact as a relationship between temperature change and the growth rate of GDP as opposed to its level. This distinction is justified on theoretical and empirical grounds, and implies that warming can have a permanent impact on future GDP. I then examine whether reasonable values for the remaining parameters (e.g., the starting growth rate and the index of risk aversion) can yield values of w(τ) above 2% or 3% for small values of τ, which might support stringent abatement. I also show how w(τ) depends on the mean versus standard deviation of future temperature, and I calculate “iso-WTP” curves—combinations of means and standard deviations for which WTP is constant. This provides additional insight into how uncertainty drives WTP.

To explore the case for stringent abatement, I use a counterfactual and pessimistic scenario for temperature change: under “business as usual” (BAU), the atmospheric GHG concentration immediately increases to twice its pre-industrial level, which leads to an (uncertain) increase in temperature at the horizon H, and then (from feedback effects or further emissions) a gradual further doubling of that temperature increase.

This paper builds on work by Weitzman [43], but takes a very different approach. Suppose there is some underlying probability distribution for temperature change, but its variance is unknown and is estimated through ongoing Bayesian learning. Weitzman shows that this “structural uncertainty” implies that the posterior-predictive distribution of temperature is “fat-tailed,” i.e., approaches zero at a less than exponential rate.3 If welfare is given by a power utility function, this means that the expected loss of future welfare from warming is infinite, so that society should be willing to sacrifice all current consumption to avoid future warming. This result, however, does not translate into a policy prescription, e.g., what percentage of consumption society should sacrifice to avoid warming.

I utilize a (thin-tailed) displaced gamma distribution for temperature change, which I calibrate using estimates of its mean and confidence intervals inferred from the studies surveyed by the IPCC. Besides its simplicity and reasonable fit to the IPCC studies, this approach avoids infinite welfare losses (or the need to arbitrarily bound the utility function to avoid infinite losses). Also, the variance or mean of the distribution can be altered while holding other moments fixed, providing additional insight into effects of uncertainty.

To model economic impact, I relate temperature change to the growth rate of GDP and consumption, and calibrate the relationship using damage functions from several IAMs. Although these damage functions are based on levels of GDP, I can calibrate a growth rate function by matching estimates of GDP/temperature change pairs (along with 66% confidence intervals) at a specific horizon. I then use the distribution for GDP reductions to fit a gamma distribution for the growth rate impact.

I calculate WTP using a constant relative risk aversion (CRRA) utility function. In addition to the initial growth rate and index of risk aversion, WTP is affected by the rate of time preference (the rate at which future utility is discounted). I set this rate to zero, the “reasonable” (if controversial) value that gives the highest WTP.4

My estimates of w(τ) are generally below 2%, even for τ around 2 or 3 °C. This is because there is limited weight in the tails of the calibrated distributions for temperature and growth rate impact. Larger estimates of WTP result for certain parameter values (e.g., an index of risk aversion close to 1 and a low initial GDP growth rate), or if I assume a much larger expected temperature increase. But overall, given the current “state of knowledge” of warming and its impact, my results are consistent with moderate abatement. Of course the “state of knowledge” is evolving and new studies might lead to changes in the distributions. The framework developed here could then be used to evaluate the policy implications of such changes. This framework can also be used to examine the relative importance of expected outcomes versus outcome uncertainty, which I do by varying the mean and standard deviation of the temperature distribution and calculating the resulting WTPs.

This paper ignores the implications of the opposing irreversibilities inherent in climate change policy and the value of waiting for more information. Immediate action reduces the largely irreversible build-up of GHGs in the atmosphere, but waiting avoids an irreversible investment in abatement capital that might turn out to be at least partly unnecessary, and the net effect of these irreversibilities is unclear. I focus instead on the nature of the uncertainty and its application to a relatively simple dynamic cost–benefit analysis.5

The next section explains the methodology used in this paper and its relationship to other studies of climate change policy. Section 3 discusses the probability distribution for temperature change and Section 4 discusses the economic impact function and corresponding probability distribution. Section 5 shows estimates of willingness to pay, and its dependence on free parameters and on the expectation versus standard deviation of temperature change. Section 6 discusses some fundamental modeling issues and concludes.

Section snippets

Background and methodology

Most economic analyses of climate change policy have five elements: (1) projections of future emissions of a CO2 equivalent (CO2e) composite (or individual GHGs) under a “business as usual” (BAU) and one or more abatement scenarios, and resulting future atmospheric CO2e concentrations. (2) Projections of the average or regional temperature change likely to result from higher CO2e concentrations. (3) Projections of lost GDP and consumption resulting from higher temperatures. (This is probably

Temperature change

The IPCC [16] surveyed 22 studies of climate sensitivity, the temperature increase that would result from an anthropomorphic doubling of the atmospheric CO2e concentration. Given that a doubling (relative to the pre-industrial level) by 2050–2060 is the IPCC's consensus prediction, I treat climate sensitivity as a rough proxy for T a century from now. Each study surveyed provided both a point estimate and information about the uncertainty around that estimate, such as confidence intervals

Economic impact

What would be the economic impact (broadly construed) of a temperature increase of 7 °C or more? One might answer, as Stern [36], [37] does, that we simply do not (and cannot) know, because we have had no experience with this much warming, and existing models tell us little about the impact on production, migration, health, etc. Of course we could say the same thing about the probabilities of temperature increases of 7 °C or more, which are also outside the range of the climate science models

Willingness to pay

I assume that by giving up a fraction w(τ) of consumption now and throughout the future, society can ensure that at time H, TH will not exceed τ. Specifically, the distribution for T is cut off at τ and rescaled to integrate to 1.18 Using the CRRA utility function of Eq. (6) and the growth rate of consumption given by Eq. (2), w(τ) is the maximum fraction of consumption society would sacrifice to keep THτ. As explained in Section 2

Concluding remarks

I have examined the “demand side” of climate policy by calculating a simple WTP measure: the fraction of consumption w(τ) that society would sacrifice to ensure that any increase in temperature at a future point is limited to τ. This avoids having to make projections of GHG emissions and atmospheric concentrations, or estimate abatement costs. Instead I could focus directly on uncertainties over temperature change and over the economic impact of higher temperatures. For “conservative”

Acknowledgments

My thanks to Stacie Cho and Andrew Yoon for their excellent research assistance, and to Paul Fackler, Larry Goulder, Michael Greenstone, Geoff Heal, Paul Klemperer, Charles Kolstad, Raj Mehra, Steve Newbold, Steve Salant, V. Kerry Smith, Martin Weitzman, two anonymous referees, and seminar participants at the IMF, Resources for the Future, NBER, Arizona State University, Columbia, Harvard, M.I.T. and UC Berkeley for helpful comments and suggestions.

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