The Stern Review on the Economics of Climate Change

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Journal of Economic Literature Vol. XLV (September 2007), pp. 703–724

A Review of The Stern Review on the Economics of Climate Change

∗ MARTIN L. WEITZMAN

The Stern Review calls for immediate decisive action to stabilize greenhouse gases because “the benefits of strong, early action on climate change outweighs the costs.” The economic analysis supporting this conclusion consists mostly of two basic strands. The first strand is a formal aggregative model that relies for its conclusions primarily upon imposing a very low discount rate. Concerning this discount-rate aspect, I am skeptical of the Review’s formal analysis, but this essay points out that we are actually a lot less sure about what interest rate should be used for discounting climate change than is commonly acknowledged. The Review’s second basic strand is a more intuitive argument that it might be very important to avoid possibly large uncertainties that are difficult to quantify. Concerning this uncertainty aspect, I argue that it might be recast into sound analytical reasoning that might justify some of the Review’s conclusions. The basic issue here is that spending money to slow global warming should perhaps not be conceptualized primarily as being about consumption smoothing as much as being about how much insurance to buy to offset the small change of a ruinous catastrophe that is difficult to compensate by ordinary savings.

1. Introduction on a vivid actuality to breathe new life into otherwise arcane matters of economic analy- he issue of global climate change and sis. Beyond the issue of whether it is right or what to do about it has put economics to T wrong in its conclusions, the Stern Review on a severe test in which economists have been the Economics of Climate Change is an challenged to think afresh about how to opportunity for economists to take stock of model (or at least how to conceptualize) such what we know about this subject, how we fundamental notions as risk, uncertainty, and know it, what we don’t know, and why we discounting. There is nothing like being don’t know it. asked for a specific policy recommendation The Stern Review is a full-fledged economic analysis of climate change that was ∗ Weitzman: Harvard University. For helpful detailed officially commissioned by the British gov- comments on earlier drafts of this paper, but without ernment and, for reasons both economic and implicating them for its remaining defects, I am grateful to Scott Barrett, Roland Benabou, Olivier Blanchard, political, is an unusual—and unusually Richard Cooper, Stephen DeCanio, Howard important—document. Sir Nicholas Stern is Gruenspecht, Cameron Hepburn, Chris Hope, Donald a professional economist of high standing Ludwig, Robert Mendelsohn, Larry Samuelson, Robert Solow, Nicholas Stern, Lawrence Summers, and Hal and a distinguished public servant. Weighing Varian. in at close to 700 pages, the Stern Review is

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comprehensive in its scope and ambitious in strong and early action far outweigh the eco- its aims, with an attractive multicolored visu- nomic costs of not acting” (p. xv) and calls for al design that makes topics like cost–benefit stabilizing greenhouse gas atmospheric con- analysis of dynamic externalities look almost centrations at ≈ 550 parts per million (ppm)

glamorous. Anyone wanting to get a good of CO2-equivalent (CO2e). (The current ≈ feel for the basic issues of global climate level is 430 ppm CO2e, compared with ≈ change could profitably browse through this 280 ppm CO2e before the Industrial report, which covers well its multiple facets Revolution.) This would make temperatures in a reader-friendly format. The Review con- a hundred years from now be at E[ΔT] ≈ 2˚C tains much of value and interest aside from and would (hopefully) stabilize future tem- its cost–benefit analysis of mitigation poli- peratures permanently thereafter at cies, although that is naturally the part which Δ ≈ 3˚C. By contrast, along the more grad-

most grabs the attention of economists. A ual majoritarian optimal trajectories CO2e detailed Review of the Review is out of place concentrations a century from now are > 600 here—it would be too long, and besides the ppm and E[ΔT] ≈ 2.5˚C—with temperatures Stern Review reads well and is available expected to continue rising to well above online. Instead, I concentrate here on trying E[ΔT] ≈ 3˚C after year 2105. To accomplish to distill the Review down to what I think is the Review’s ambitious goal, greenhouse gas its analytical essence as a piece of applied emissions would need to be progressively cut cost–benefit analysis, because there can be by ≈ 3 percent each year, beginning more or difficulty seeing the forest for the trees when less immediately. Which brings us to a cen- there are so many trees. tral question. Why is there such a big differ- To make a long story short, the Stern ence between what Stern is recommending Review comes down very strongly on the side and what most other serious analysts favor? of undertaking decisive—and expensive— This paper makes five basic points about

measures starting now to reduce CO2 and the economics of climate change: (1) the dis- other greenhouse gas emissions because count rate we choose is all important and (and this quote captures well the tone of Stern’s results come from choosing a very low urgency about moving quickly to avoid cata- discount rate; (2) we are a lot less sure about strophic possibilities that is evident through- core elements of discounting for climate out the report): “Our actions over the change than we commonly acknowledge coming few decades could create risks of because critical puzzles, projections, and major disruption to economic and social ambiguities are yet unresolved; (3) standard activity, later in this century and in the next, approaches to climate change (even those that on a scale similar to those associated with the purport to treat uncertainty) fail to account great wars and economic depression of the fully for the implications of large conse- first half of the 20th century” (p. xv). Such a quences with small probabilities; (4) structur- strong call to immediate decisive action is at al parameter uncertainty that manifests itself odds with what most other economic analy- in the thick tails of reduced-form probability ses of climate change have concluded. The distributions—not risk—is what likely matters majority view of most other economic ana- most; (5) gathering information about thick- lysts finds it optimal to pursue a more grad- tailed uncertainties representing rare climate ualist course by starting with greenhouse gas disasters (and developing a realistic emer- emissions reductions at far lower levels than gency plan were they to materialize) should what the Stern Review advocates for the be a priority of research. To anticipate my near future, but which after that ramp up main finding, spending money now to slow considerably over time. The Review analysis, global warming should not be conceptualized on the other hand, finds that “the benefits of primarily as being about optimal consumption sep07_Article4 8/17/07 4:31 PM Page 705

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smoothing so much as an issue about how time profile by imposing discounting at a much insurance to buy to offset the small bare-minimum rate of interest. chance of a ruinous catastrophe that is diffi- Global climate change unfolds over a time cult to compensate by ordinary savings. While scale of centuries and, through the power of I am (along with most other economist- compound interest, what to do now is hugely critics) skeptical of Stern’s formal analysis, I sensitive to the discount rate that is postulat- believe that the Review’s informal emphasis ed. In fact, it is not an exaggeration to say that on climate-change uncertainty can be recast the biggest uncertainty of all in the econom- into sound analytical arguments that might ics of climate change is the uncertainty about justify some of its conclusions. which interest rate to use for discounting. In one form or another, this little secret is 2. Interest Rates and Long-Term known to insiders in the economics of climate Discounting change, but it needs to be more widely appre- ciated by economists at large. The insight that Overall, I believe it is fair to say that the the strong conclusions of the Review are driv- Stern Review consistently leans toward (and en mainly by the low assumed discount rate consistently phrases issues in terms of) has been picked up and commented upon assumptions and formulations that empha- already by several insider critics.1 Here I size optimistically low expected costs of mit- want to paraphrase this important debate for igation and pessimistically high expected outsider economists and in the process bring damages from greenhouse warming—rela- some new ingredients to the mix. tive to most other studies of the economics An Integrated Assessment Model—here- of climate change. But far more crucially, after IAM—is insider lingo for a multiple- the key assumption that drives its strong equation computer-simulated model that conclusions is the mundane fact that a very combines dynamic economics with geophys- low interest rate is postulated, with which ical climate dynamics for the purposes of distant-future benefits and costs are then analyzing the economic effects of global cli- discounted. The upward-sloping “climate mate change.2 An IAM is essentially a model policy ramp” of ever-tighter emissions of economic growth with a controllable reductions in the majority of other models externality of endogenous greenhouse warm- (but not beginning just yet, please) is a ing. The Review uses an IAM called PAGE, familiar consumption-smoothing conse- on which some numbers have been crunched quence of discounting: the higher the inter- and some conclusions have been based, but est rate the stronger the desire to move the exact connection between PAGE and toward getting more pleasure now at the Stern’s conclusions is elusive, frustrating, and expense of postponing more pain until later. ultimately unsatisfactory for a professional An efficient trajectory has a cost minimizing economist who honestly wants to understand substructure similar to a Hotelling extrac- where the strong policy recommendations tion problem: consumption flows are are coming from.3 The analytical core of the smoothed over time by maximizing present discounted utility subject to a stock con- 1 Variants of this argument are made in Partha straint on accumulated CO2e, which results Dasgupta (2007), Robert O. Mendelsohn (2007), William in an “as if” CO e shadow tax that grows over D. Nordhaus (2007), and Richard S. J. Tol and Gary W. 2 Yohe (2006). time at (approximately) the rate of interest. 2 A survey of integrated asssessment models for climate The Stern Review simultaneously raises change control is provided in David L. Kelly and Charles overall greenhouse gas reductions and flat- D. Kolstad (1999). 3 A nice description of how the Stern Review uses (and tens the “climate policy ramp” in its misuses) PAGE is contained in David Maddison (2006). Hotelling-analogous consumption smoothing PAGE itself is described in Chris Hope (2006). sep07_Article4 8/17/07 4:31 PM Page 706

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Review is chapter 6 (“Economic Modelling of where r is the interest rate (more on the Climate-Change Impacts”), which is loosely interest rate later), δ is the rate of pure time tied to PAGE. However, the rest of the book preference, g is the per capita growth rate of contains lots of stories and examples suggest- consumption, and η is the elasticity of mar- ing that difficult-to-quantify uncertainty ginal utility, or, equivalently, the coefficient of about really bad climate extremes may actu- relative risk aversion. In the shorthand nota- ally be an important informal part of Stern’s tion of (1), the parameters δ and η capture overall case. Economists are justifiably suspi- two critical aspects of “tastes” (or “prefer- cious when someone refuses to aggregate ences”) while the reduced-form representa- various probability-weighted scenarios into tion of “technology” is the growth rate of an overall cost–benefit assessment, which at consumption g. The important distinction least can serve as a conversation starter. (How between δ and r is that δ is a more primitive else are we to evaluate overall policy advice, rate of pure time preference that discounts such as what Stern recommends to us, except utility, while r is the much more familiar in the context of some overall model where interest rate used to discount consumption, assumptions and specifications are spelled which is derived from all of the more primi- out clearly?) As economic analysis, the Stern tive underlying parameters of tastes and Review dwells in a nonscientific state of technology via (1). The other taste parameter limbo where it uses an IAM but simultane- η represents the relative curvature of the ously refuses to commit to it or to any other utility function and is simultaneously a meas- consistent overarching framework within ure of aversion to interpersonal inequality which its radical recommendations might be and a measure of personal risk aversion. On deconstructed and judged by others. Instead, the technology side, formula (1) holds the Review dances around the significance of whether g is endogenous or exogenous. In the aggregative analysis of chapter 6 by argu- Ramsey’s time, g was conceptualized as coming that conclusions from IAMs are sugges- ing from capital accumulation, and therefore tively useful but not crucial to the basic story in long run equilibrium with diminishing line that anything above ultimate stabilization returns to capital g → 0 and r → δ. We now ≈ Δ ≈ at 550 ppm of CO2e and 3˚C is self- know from modern post-Solow growth theory evidently just too risky for the planet to bear. (but Ramsey and Fisher didn’t) that, in bal- In trying to make some overall sense of anced growth steady-state equilibrium, g is Stern’s mixed methodology (called “multidi- essentially the underlying growth rate of labor- mensional” in the Review), I propose here to augmenting technological progress that, lay out the core issues of how risk, uncertain- behind the scene, is pushing the entire econo- ty, and discounting interact with the econom- my forward (at least in a world without a ics of climate change in terms of the simplest greenhouse-warming externality). What I pro- general-equilibrium model I can think of. pose to do here is use the Ramsey equation as Then I will try to clothe some parts of Stern’s a transparency-based springboard for recast- intuitions about climate-change uncertainty ing the economics of climate change in terms in formal garb. of the four critical variables that appear in (1): Irving Fisher taught us that an interest δ, η, g, and r. I will ultimately argue that, in a rate, like any other price, is the outcome of a greenhouse gas world, g needs to be seen as a dynamic general-equilibrium interaction of random variable whose probability distribu- tastes with technology. The modern incarna- tion has a climate-change-thickened left tail tion of Fisher’s idea in a deterministic setting that carries most of the weight of expected is the famous Frank Ramsey equation marginal utility in cost–benefit analysis. To cut sharply to the essence of the core (1) r = δ + ηg, discounting issue behind the Review’s strong sep07_Article4 8/17/07 4:31 PM Page 707

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conclusions, pretend there are just two temporarily such details as the optimal periods—the present and the future—where consumption-smoothing profile of measures the “future” is about one hundred years from to slow greenhouse warming (and their iner- now. For the purposes at hand, I am about to tial consequences) in favor of immediate conduct a gigantic macroeconomic cost– transparency by focusing on the highly aggre- benefit exercise trading off less present con- gated macroeconomic big picture of what is sumption from greenhouse gas abatement most essential in driving the Stern Review for more future consumption from mitigat- results, for which purpose focusing on a cen- ing the bad effects a century hence of global tury hence is a good enough approximation. warming. Technically speaking, the possibili- Going right to the target here, my own ty of extreme left-tail values of g occurring rough point-guesstimate of what most econo- with small positive probability is outside this mists might think are decent parameter val- marginalist framework and requires us to go ues would be something like a “trio of twos”: back to the fundamentals of expected utility δ = 2 percent, g = 2 percent (both on an theory that lie behind cost–benefit analysis annual basis), and η = 2 percent. For the under uncertainty, but I will cross that bridge sake of moving along, I am not going to try to when I come to it later and the take-away defend the “trio of twos values” with a bunch message will turn out to be similar anyway. of citations but instead I pretend for the Of course such an incredible oversimplifi- time being that every critic of Stern thinks cation of the economics of climate change they are about right, so we can temporarily ignores or distorts truly monumental chunks shelve this issue. Plugging these primitives of reality. As just one example among many, into (1) makes “the” annual interest rate be a very important part of the global warming r = 6 percent. Other reasonable—in my story concerns the huge stock–flow lags and view—parameter combinations, say δ = 1 enormous built-in inertias from having such percent, g = 2 percent, η = 2.5 (or even a long pipeline between greenhouse gas δ = 0 percent, g = 2 percent, η = 3) also emissions and ultimate temperature give r = 6 percent. changes. This built-in inertia causes ΔT to Concerning the rate of pure time prefer- continue to rise to levels above E[ΔT] ≈ 3˚C ence, Stern follows a decidedly minority after a century from now (and also causes paternalistic view (which, however, includes the tail probabilities of very high tempera- a handful of distinguished economists) that tures ΔT > 6˚C to be relatively much bigger for social discounting selects the lowest con- two centuries from now than one century ceivable value δ ≈ 0 according to the a priori from now) along any trajectory that does not philosophical principle of treating all gener- stabilize atmospheric greenhouse gases at ations equally—irrespective of preferences ≈ 550 ppm CO2e—including the majority- for present over future utility that people opinion gradualist climate-policy-ramp tra- seem to exhibit in their everyday savings and jectory. The ultimate high-temperature investment behavior. In a similar spirit of consequences of the huge inertial lag of ΔT choosing extreme taste parameters, Stern to greenhouse gases already in the pipeline selects as its base-case coefficient of relative animate the Stern Review passion for severe risk aversion the value η = 1 that is the low- curtailment of greenhouse gas emissions to est lower bound of just about any economist’s begin soon, because at current flow rates we best-guess range. Some other taste-parameter

will attain a stock of 550 ppm of CO2e with- values are considered in a halfhearted sensi- in about a half-century and move (essential- tivity analysis postscript to the original ver- ly irreversibly) thereafter beyond any hope sion of the Review, which is reported as if to stabilize ultimate E[ΔT] at ≈ 3°C. indicating robustness but I would interpret However, the point here is to put aside as more nearly the opposite because, no sep07_Article4 8/17/07 4:31 PM Page 708

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matter what spin is put on it, there is no equivalent to about 1 percent of GDP escaping the impact of higher interest rates (which seems rather on the low side by on undoing the Review’s extreme policy con- maybe a factor of two or more, but that is not clusions. With its preferred base-case param- so relevant here). eter values δ = 0.1 percent p.a., g = 1.3 The question for the Stern Review analy- percent p.a., η = 1, Stern’s discount rate sis then effectively becomes: is it worthwhile from (1) is r = 1.4 percent. The present dis- to sacrifice costs C ≈ 1 percent of GDP now counted value of a given global-warming loss to remove damages D ≈ 5 percent of GDP a from a century hence at the non-Stern annu- century from now? With g and r being al interest rate of r = 6 percent is one hun- expressed on an annual basis, the benefit- dreth of the present discounted value of the over-cost ratio of such an investment would B−= − − = same loss at Stern’s annual interest rate of be C 5 exp(100(g r)). From (1), r g r = 1.4 percent. The disagreement over what (η − 1)g + δ, so that by picking the extreme interest rate to use for discounting is equiva- values η = 1, δ = 0.1 percent, Stern guaran- lent here in its impact to a disagreement tees that the difference r − g is always the about the estimated damage costs of global miniscule amount δ = 0.1 percent, no matter warming a hundred years hence of two orders what value of g is chosen, which is really of magnitude. Bingo! stacking the deck in favor of approving such If D is aggregate damages from global cli- kind of fractional GDP swaps across time. mate change and Y is GDP, then values of (The Review could have made life easier D− the ratio Y a century from now (if nothing or here by just rounding down a mere tenth of very little is done to halt greenhouse gas a percent by assuming δ = 0, which along emissions) are commonly taken to be some- with η = 1 would make cost–benefit analysis where in the range of about 0 percent to 3 really simple because a fixed fraction of percent. The Stern Review effectively uses GDP would then always be worth the same D−≈ Y 5 percent as its base case. This high fixed fraction of GDP at any future time.) value is consistent with what an uncharitable With Stern’s preferred parameter values, the −=B critic might see as a philosophy of focusing benefit–cost ratio is C 4.5 (close to the −=B on the gloomier outcomes in a heuristic- upper bound of C 5 from assuming a zero intuitive attempt to include extreme dam- rate of pure time preference)—a clear slam- ages, because in Stern’s language “when we dunk accept. The alternative non-Stern val- try to take due account of the upside risks ues g = 2 percent, r = 6 percent make −=B −1 and uncertainties, the probability-weighted C 10 —a clear reject. This simple kind of costs look very large.” Actually, the Review exercise is what drives the Stern Review goes well beyond 5 percent in its multi- results and, in a nutshell, is what accounts for dimensional approach by making numerous the difference with the more conventional literary and numerical allusions to the dark analyses of its critics. The no-frills stripped- possibilities lurking in the tails of the distri- down variant of the Ramsey model I am bution of possible outcomes (and then, as it using here is liable to a thousand and one were, rubbing salt in the wound of numeri- legitimate questions and criticisms about its cal calibration by noting how centrist it is oversimplifications but, at the end of the day, actually being by not choosing much higher I believe this exercise is highlighting fairly probability-weighted distant-future dam- what really counts in the economics of cli- D−≈ ages, which could be as big as Y 20 mate change—the hidden discounting percent–35 percent when one considers assumptions whose role tends to be more catastrophes that might materialize after obscured than informed by the big IAMs. 2105). Stern also estimates the annual costs For most economists, a major problem of its ambitious abatement strategy as being with Stern’s numbers is that people are not sep07_Article4 8/17/07 4:31 PM Page 709

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observed to behave as if they are operating inferences for putting welfare weights on the with δ ≈ 0 and η ≈ 1. To gauge the magni- utilities of one’s great-grandchildren, and tude of the headache this presents for Stern’s there might be some sporadic support for taste-parameter values, consider the follow- Stern’s preferred taste parameters scattered ing thought experiment expressed in terms of throughout the literature, I ultimately find the permanent income hypothesis in a deter- such an extreme stance on the primacy of ministic setting. Suppose that on the margin δ ≈ 0, η ≈ 1 unconvincing when super-strong an individual representing a long-lived policy advice is so dependent upon noncon- dynasty faces a constant interest rate, r, and ventional assumptions that go so strongly has a level of wealth, W, representing the against mainstream economics. capitalized value of future earnings plus ini- tial holdings. Then permanent income is rW 3. Puzzles and Ambiguities of Uncertain and an optimal consumption trajectory saves Discounting a constant amount s of permanent income. Plugging the implied balanced growth rate The most worrisome omission from any g = sr into (1) and rearranging gives analysis based on the Ramsey approach (1) is uncertainty. As a first-pass informal cut at − δ uncertainty, suppose we admit that we don’t (2) s =⎯⎯r ⎯ . ηr really know for sure whether Stern or Stern’s critics are right about the interest rate to use With Stern’s preferred values δ ≈ 0, η ≈ 1, for discounting costs and benefits a hundred equation (2) implies s ≈ 100 percent irre- years or so from now. An important feature spective of r—a reductio ad absurdum. In of interest rates under uncertainty is that the economics of uncertainty, plausible values they don’t aggregate arithmetically into a η −1 of the coefficient of relative risk aversion simple certainty-equivalent interest rate. A 2 = −1 are commonly taken to be somewhere chance of r 6 percent and a 2 chance of between 1 and 4 (I use the geometric-average r = 1.4 percent are not at all the same thing point estimate η = 2). A reader can plug as splitting the difference by selecting the favorite parameter values into (2) and back average r = 3.7 percent. It is not discount out implied values of δ. For me (and I sus- rates that need to be averaged but discount −1 pect most economists), sensible savings rates factors. A 2 chance of a discount factor of −6 −1 in this and other variants of market-behavior- e a century hence and a 2 chance of a dis- based thought experiments requires the rate count factor of e−1.4 a century hence make an of pure time preference to be significantly expected discount factor of 0.5e−6 + 0.5e−1.4 a greater than zero (or at least if δ is chosen to century hence, which, when you do the be relatively small then η should be chosen math, is equivalent to an effective interest to be relatively big). Stern’s worldview tends rate of r = 2 percent. According to this logic, to blow off market-based observations and the interest rate we should be using to dis- behavioral inferences as being (for a variety count a dollar of costs or benefits a century of reasons including market incompleteness) from now is in between the Stern value of largely irrelevant to long-run discounting, r = 1.4 percent and the more conventional which should instead be based primarily value of r = 6 percent, but with the above upon the “ethical” value δ ≈ 0 that Stern numbers it is a lot closer to the Stern value imposes on a priori grounds. Readers will and is not anywhere near the arithmetic have to make up their own minds about “eth- average of r = 3.7 percent. More generally

ical” values of preference parameters. While here, if there is a subjective probability pi there may be something to Stern’s position that discount rate ri is the correct rate to use, about the limited relevance of market-based then the effective discount rate for time t is sep07_Article4 8/17/07 4:31 PM Page 710

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− ∑ rit = − ⎯⎯⎯⎯ln pie way to begin this process is by making the (3) r(t) t , growth rate be a random variable. Continuing here in the spirit of being sim- which declines monotonically over time ple, suppose that the growth rate g in any = from the expected interest rate r(0) ∑piri given year is i.i.d. normal with known mean to an asymptotic limit of r() = min{r }. The and known variance 2. (The fact that i i moral of this story is that the Stern value may and 2 are known will later become signifi- end up being more right than wrong when full cant when we inquire what happens under accounting is made for the uncertainty of the greenhouse warming when and 2 are discount rate itself, which arguably is the most modeled as not known.) With g ∼ N(, 2), important uncertainty of all in the economics the Ramsey formula (1) becomes of climate change. The very same force of compound interest that makes costs and ben- (4) r f = δ + η −−1 η 2 2, efits a century from now seem relatively 2 insignificant, and that additionally creates the “majority tilt” of a pain-postponing climate where r f in equation (4) denotes the risk free policy ramp of emissions reductions starting interest rate. The introduction of uncertainty from a low gradual base, also forces us to rec- also allows consideration of a risky asset with ognize the logic that over such long periods a different rate of return. Following the we should be using interest rates at the lower asset-pricing expository literature, suppose end of the spectrum of possible values. we model comprehensive or representative In the certain world of the Ramsey deter- equity at a high level of abstraction as being a ministic formula (1), there is no distinction claim on the consumption dividend pro- among rates of return on various assets and r duced by the macroeconomy itself. Suppose is just the economywide rate of return on this abstract macroeconomy is represented capital or, more succinctly, the interest rate. by a dynamic stochastic general equilibrium In nondeterministic reality, there are many in the Lucas–Mehra–Prescott fruit-tree rates of return out there and they differ con- model. Let the random variable Re be the siderably. The point has already been estab- gross arithmetic return on equity while lished that it makes a tremendous difference r e = lnRe is the more familiar geometric rate for long time periods of a century or more of return on equity. When g is i.i.d. N(, 2) what interest rate is used for discounting. To in this fruit-tree economy, the equity risk understand better which discount rate to use, premium over the safe rate then reduces to we need to enrich the Ramsey model by for- the well-known expression mally introducing uncertainty, which allows −e − f = 2 us at least to distinguish between rates of (5) r r , return on capital from two fundamentally dif- − where r e is defined by the oblique-looking ferent sorts of investments: a risky economy- − expected-value formula r e ≡ lnE[Re], which wide rate of return applicable to investments is close enough to E[r e] to make them inter- that have payoff characteristics parallel to the changeable for my purposes here.4 economy itself and a risk free rate of return Combining (5) with (4) gives the average applicable to investments whose payoffs are return on equity as orthogonal to the economy as a whole. After that, we need to decide which of these two − (6) r e = δ + η −−1 η 2 2 + η 2. rates is more appropriate for discounting 2 costs and benefits of mitigating climate change. Then we need to plug in numbers 4 The formulas (4) and (5) are explained in most and see what happens. The simplest formal graduate-level textbooks covering asset pricing. sep07_Article4 8/17/07 4:31 PM Page 711

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Extending the previous “trio of twos” param- the oversimplified two-period formulation eter values to a not-implausible knee-jerk here, a project to mitigate the effects of “quartet of twos” δ = 2 percent, η = 2, global warming incurs consumption costs in = = E[g] 2 percent, [g] 2 percent (on an the present period by curtailing CO2e emis- annual basis, for long time series) makes sions, investing in costly new technologies, very little difference on the risk free rate and so forth, but consumption in the future because now r f = 5.9 percent in (4) instead of period is increased by having reduced the the previous value for “the” interest rate of detrimental impacts at that time from r = 6 percent in (1). The corresponding greenhouse warming. The payoff is the extra − equity premium from (5) is r e − r f = 0.1 per- consumption available in the distant-future cent and the average return on equity from period. Suppose that the correlation coeffi- − (6) is r e = 6 percent. The actual empirical cient between the increased output of the − numbers are closer to r f ≈ 1 percent, r e − project and returns to the economy as a − r f ≈ 6 percent, r e ≈ 7 percent. (The calibra- whole is β. An investment beta is intended tion r f ≈ 1 percent refers to short-term to represent a correlation coefficient that − treasury bills, while r e ≈ 7 percent refers to applies to discount factors as contrasted overall returns on comprehensive indexes of with discount rates (i.e., here β is the corre- publicly traded shares of common stocks, but lation between the investment payoff and I don’t think the numbers would be funda- Re, not r e). It then follows from essentially mentally different for other empirical meas- the same considerations as went into deriv- ures of returns from investments for the ing formula (3) that the relevant interest economy as a whole.) So with the not- rate for discounting costs and benefits at implausible “quartet of twos” parameter val- time t here is ues the theory does a decent job of − ln[βexp(− r et) +(1 − β)exp(− r ft)] predicting the average return on equity but = − ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ (7) r(t) t , fails miserably on the risk free rate and the equity premium—thereby giving rise to the which declines monotonically over time − notorious “risk free rate puzzle” and the even from r(0) = β r e + (1 − β)r f to an asymptotic more notorious “equity premium puzzle.” limit of r() = r f. So the question here What does all of this have to do with the becomes: what is the right β for the kinds of economics of climate change? Well, a lot projects that the Stern Review has in mind actually. But before getting into the relation- for mitigating global warming? ship between the asset-return puzzles and Overall damages from climate change are the economics of climate change, we need to modeled in most IAMs, including the put the puzzling numerical mismatches tem- PAGE model that crunches some numbers porarily aside in favor of first asking a funda- for the Review, as a pure production exter- mental prenumerical question: in principle nality equivalent to losing output via a par- (leaving aside their correct numerical val- ticular subaggregator equation of the ues) should we be using the risk free rate or multiplicative form the risky economywide rate of return for discounting costs and benefits of climate (8) D(t) = Y∗(t) − Y(t) = f(ΔT(t))Y∗(t), change? The issue of which rate of return to where t is time, D is the total damages of − choose (as between r f and r e) for discount- greenhouse warming, ΔT is atmospheric ing a project comes down to the extent to temperature relative to the base period, Y∗ is which the payoffs from the project are pro- potential GDP (or NDP, no distinction being portional to or independent from returns to made here) in the absence of any green- investments for the economy as a whole. In house warming, and Y is actual GDP with sep07_Article4 8/17/07 4:31 PM Page 712

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greenhouse warming. The standard func- Like Stern, the essentially identical earlier tional form actually chosen in most IAMs is formulation of Cline used parameter values f(ΔT) = k(ΔT)γ for some coefficients γ and k, that made the Ramsey formula (5) deliver a where typically γ = 2 (quadratic loss in tem- low interest rate—in Cline’s case the assumed perature change). The parameter k is usual- parameter values were δ = 0 percent, η = 1.5, −D = ly calibrated so as to make Y a century hence g 1 percent, which combined to make the under mild or no abatement (with interest rate be r = 1.5 percent per year. Also ΔT ≈ 2.5˚C) be somewhere between approx- like Stern, the strong activist conclusions of imately 0 percent and approximately 5 per- Cline’s analysis fifteen years earlier traced cent (depending on who is doing the back to the very low discount rate being calibrating). There is no question here about used. Furthermore, Cline and Stern are soul- the value of beta implicit in the multiplica- mates in their cri de coeur justifying δ ≈ 0 by tive formulation (8): it is one! Therefore, by relying mostly on a priori philosopher-king the very logic of the IAM used by the Stern ethical judgements about the immorality of Review itself, the interest rate for discount- treating future generations differently from ing costs and benefits should be the returns the current generation—instead of trying to − to the economy as a whole, r e. This still back out what possibly more representative leaves open the question of which rate to use members of society than either Cline or − for r e—the empirical returns on a broad Stern might be revealing from their behavior index of publicly traded shares of stocks of is their implicit rate of pure time preference. about 7 percent (representing economy- An enormously important part of the “disci- wide average returns and used, e.g., by the pline” of economics is supposed to be that Congressional Budget Office for evaluating economists understand the difference U.S. government projects) or the value of between their own personal preferences for 6 percent predicted by formula (5) from apples over oranges and the preferences of my non-Stern “quartet of twos” parameter others for apples over oranges. Inferring values—but the discrepancy between 6 per- society’s revealed preference value of δ is not cent and 7 percent is insignificant for pur- an easy task in any event (here for purposes − poses here. Whatever number is used for r e, of long-term discounting, no less), but at if it in any reasonable way represents the least a good-faith effort at such an inference returns to the economy as a whole then it will might have gone some way towards convinc- completely undo the Review conclusions ing the public that the economists doing the about drastic consumption smoothing and studies are not drawing conclusions primari- bring the results back to the much more mod- ly from imposing their own value judge- erate take-it-more-slowly climate-policy-ramp ments on the rest of the world. time profile of emissions reductions advocated In part because Cline’s results, and where by most mainstream critics of Stern. they were coming from, were more trans- This important dispute about what interest parent (largely from not being buried within rate to use for discounting costs and benefits a big mysterious IAM, which was not yet of mitigating greenhouse warming duplicates readily available around 1990), his study the same debate about the same subject more attempted to seize the analytical high than a decade ago between William R. Cline ground by emphasizing that an assumed and Nordhaus, two early pioneers of model- annual interest rate of r = 1.5 percent is ing the economic effects of climate change.5 calibration-consistent with the real return on relatively safe U.S. Treasury bills historically being about 1 percent or so per annum. 5 Cline (1992), Nordhaus (1994). See also the later studies and reflections on discounting for climate change Missing from Cline’s reasoning was a serious contained in Paul R. Portney and John P. Weyant (1999). discussion of the implications of risk and of sep07_Article4 8/17/07 4:31 PM Page 713

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payoff correlations for the choice of a dis- global warming involve its “outdoor” aspects count rate that might justify using r = r f. (broadly defined) like agriculture, coastal Nordhaus, whose careful pragmatic model- recreational areas, and natural landscapes ing throughout his DICE series of IAMs has (including the existence value of ecosystems, long set a standard in this arena, argued species, and so forth). Climate-affected “out- forcefully over a decade ago that the risk free door” activities may be differently impacted interest rate should not be used for dis- by greenhouse warming than “indoor” eco- counting costs and benefits of climate nomic activities constituting the bulk of the change. In this argument, Nordhaus was fol- economy, which are largely going to be dom- lowing Robert Lind who, in a comprehen- inated by the unknown future growth rate of sive summary of an influential book he labor-augmenting technological progress. edited in 1984 entitled Discounting for Time Instances of changes in “outdoor” activities and Risk in Energy Policy, concluded that under global warming include what happens “unless there is substantial evidence to the to tropical agriculture, losing significant parts contrary, the returns associated with public of Bangladesh (or Florida) to rising sea lev- projects should be assumed to be highly cor- els, the “consumption” of an altered natural related with returns to the economy as a world that is a direct argument in the utility whole” (p. 77). function, and so forth. These kinds of All of this having been said, there was changes, which include the existence value of never any deep economic rationale in the natural environments, are presumably not first place for damages from greenhouse gas highly correlated with technological progress warming being modeled as entering utility in computing power, furniture making, or functions through the particular reduced- better pharmaceuticals a century from now. form route of being a pure production exter- The relevant share of the “outdoor” subset of nality that substitutes perfectly with output the economy in investment-beta calculations according to the multiplicative subaggrega- might be disproportionately large because it is tor function (8). It was more due to an his- disproportionately largely impacted by green- torical accident of stumbling upon a simple house warming. Furthermore, it might plausi- understandable analytical form whose bly be argued that the high income elasticity parameters could be conveniently adjusted of environmental awareness will make for a to match various scenarios than the result of high existence value of unaltered natural habi- serious thought about whether damages tats when per capita incomes have increased from global warming are better specified as ten-fold over the course of a century or more. multiplicative or additive with GDP, or even What happens to the discount rate for cli- entering the utility function as a direct argu- mate-change investments naturally depends ment (rather than substituting one-for-one on the actual value of β that is assumed. If with economic output)—all of which would β = 0 in (7), then r(t) = r f = 1 percent. If − have been seen as a secondary issue. So, with β = 1 in (7), then r(t) = r e = 7 percent. The the benefit of hindsight, let us now ask: Is more interesting question concerns what there any economic rationale by which green- happens to r(t) for in-between values of β. house-warming damages are as much uncor- Suppose for the sake of argument we split related as they are correlated with aggregate the difference and imagine that the dispro- economic activity? The answer, when you portionate impact of climate change on think about it, is yes. No one has ever tried to generalized-land-usage “outdoor” activities argue that the effects of global warming will of the economy warrants an overall correla- be evenly spread among regions of the world tion coefficient of, say, β ≈ 0.5. With β ≈ 0.5 or sectors of the economy. The parts of an in (7), the relevant interest rate for a centu- economy likely to be most impacted by ry from now becomes r(100) = 1.7 pecent, sep07_Article4 8/17/07 4:31 PM Page 714

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which is close to Stern’s r = 1.4 percent or The relevant discounting rate r(t) from (7) Cline’s earlier r = 1.5 percent. In this case then lies between 5.9 percent and 6 percent investments for mitigating global climate independent of the assumed value of β. change become attractive as an insurance When 5.9 percent ≤ r(t) ≤ 6 percent, the policy that secures food supplies, preserves Review conclusions are again undone and coastal areas, and maintains natural environ- the more orthodox mainstream policies of ments in a world where future aggregate moderate greenhouse gas slowing in the growth rates are uncertain. I am not trying to near future come back. The practical ques- defend this particular formulation or the tion of what interest rate to use for discount- particular value β = 0.5. Rather, the moral of ing costs and benefits of climate change thus this story is that the nature of the impacts of becomes intertwined with the interpretation climate change determine whether we should of the equity premium and risk free rate end up closer to using the risk-free rate or the puzzles. It is a measure of how deep and economywide return on capital—and there serious these puzzles are that even after are plenty of stories suggesting that the rele- thousands of articles there is still no agreed- vant investment beta here is significantly less upon resolution of them. If we use numbers than one. When the overall discount factor is that resolve the puzzles in the descriptive a combination of more primitive discount direction, then r is sensitive to β and r ≈ 1.7 factors (as is the case here when the correla- percent for β = 0.5. If we use numbers that tion coefficient β is some midrange value resolve the asset-return puzzles in the pre- between zero and one), the risk free interest scriptive direction, then r ≈ 6 percent inde- rate, which is close to the Stern interest rate, pendent of β. And, to whip a horse long then may well end up being more right than dead, it makes a huge difference to the eco- wrong. Over a time horizon of a century or nomics of climate change whether r ≈ 1.7 so, this “midrange β effect,” which is not percent or r ≈ 6 percent. implausible when one considers the highly- Critics of the Stern Review are fond of uneven impacts of greenhouse warming on pointing out that δ ≈ 0, η ≈ 1 is inconsistent the different regions and sectors of the world with observed economic behavior, especial- economy, can be a strong factor in lowering ly savings behavior. While this is true, and discounting rates significantly—from the it is a genuine problem for Stern, it is just same underlying analytical source as the the tip of an iceberg that threatens all such force of compound interest and the logic of formulations—not just Stern’s. The biggest the climate-policy ramp. Remarkably, the and most troubling disconnect between the big IAMs with their casually built-in specifi- prescriptive numbers that theory says we cation of β≈1 obscure rather than clarify should be using for discounting and the the critical role in climate-change analysis of descriptive discount-rate numbers that are assumptions about investment betas. actually out there concerns the asset-return Next, suppose we try to repeat the above puzzles. These puzzles very strongly suggest numerical exercise but in place of the empir- that something fundamental is amiss in the − ical values r f = 1 percent, r e = 7 percent, we paradigm framework for pricing assets and use the values predicted by the theoretical deriving the rates of return that we are rely- formulas via assuming the quartet of twos ing upon to produce discount rates for eval- parameter values, which then implies r f = 5.9 uating new investment opportunities. For − percent from (4) and r e = 6 percent from (6). example, perhaps the taste parameters δ and Because the equity premium predicted η that we are commonly using (here δ = 2 from (5) is a miniscule 0.1 percent, there is percent p.a. and η = 2 ) are wrong. If we essentially no difference in this case treat (4) and (5) as two equations in two − between r f = 5.9 percent and r e = 6 percent. unknowns (δ and η), we can then invert the sep07_Article4 8/17/07 4:31 PM Page 715

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two equations to back out the hypothetical climate-change-affected events a century or values δˆ and ηˆ that would “explain” the so from now. stylized-fact empirical observation that r f ≈ 1 −e − f ≈ percent and r r 6 percent. When this is 4. Uncertainty Tends to Matter Much More = = done (for 2 percent, 2 percent), it than Risk produces the mega-puzzle that the estimated rate of pure time preference is δˆ ≈ 151 If the conclusion from the last section—that percent per year and the coefficient of rela- what to do about global warming depends tive risk aversion is ηˆ ≈ 150. One does not overwhelmingly on the imposed interest know whether to laugh or to cry at the rate—is seen as disappointing, then a second prospect of what the Stern Review IAM conclusion is likely to seem downright might end up recommending as its preferred unnerving. As noted, the choice of appropri- policy for climate change in its number- ate discount rate is itself extraordinarily sen- crunching simulations if the parameter val- sitive to seemingly arcane modeling details ues δˆ ≈ 151 percent, ηˆ ≈ 150 were fed into like the value of the climate-change invest- PAGE. So much for the fantasy that values of ment beta and how the asset-return puzzles the taste parameters δ and η should be chosen are resolved. One interpretation of the asset- to be consistent with the revealed-preference return puzzles, which could also have some observed stylized facts of economic behavior! relevance for the economics of climate At the end of the day, where do these change, is the idea that investors are dispro- dizzying and disconcerting numerical exercis- portionately afraid of rare disasters. These es leave us with respect to the economics of rare disasters are not fully reflected in the climate change? One inescapably strong con- available data samples that, being limited, clusion is that the emissions reductions that are naturally deficient in coverage. Besides, go along with optimal growth under endoge- even if we had an infinite time series of past nous climate change are extraordinarily sensi- observations, they are of restricted relevance tive to the interest rate that has implicitly in an evolving world whose features are been built into whatever model is being used always changing and whose past never fully for the analysis. The present discounted value repeats itself. With this interpretation of the of a future cost (or benefit) is the product of puzzles, people are willing to pay high pre- an imposed discount factor times the project- miums for relatively safe stores of value that ed future cost (or benefit). Trying to forecast might represent “catastrophe insurance” costs and benefits of climate change scenarios against out-of-sample or newly evolved rare a hundred years or so from now is more the disasters.6 Such an ongoing catastrophe- art of inspired guesstimating by analogy than insurance effect could readily explain why a science (imagine forecasting today’s world a observed r f is so low relative to the observed century ago). But in my opinion the unsure past average of realized r e. prediction of future costs and benefits of cli- There is little doubt that the worst-case mate change a century or two hence is over- scenarios of global-warming catastrophes are shadowed by the unsure interest rate to use genuinely frightening. The Stern Review in the discount factor, which makes the dis- goes over several of these highly unlikely, count factor more uncertain than predicted poorly understood threshold-crossing disas- costs (or benefits) of climate change by about ters associated with abrupt large-scale irre- an order of magnitude. Of the two multipli- versible changes in the climate system: cands in the product of a discount factor times an expected cost (or benefit), empiri- 6 The theme of catastrophe insurance and the underlying motivation for the treatment of structural uncertainty cally it is the discount-factor uncertainty that as tail thickening of posterior-predictive distributions is looms much larger in practice for analyzing developed in Martin L. Weitzman (forthcoming). sep07_Article4 8/17/07 4:31 PM Page 716

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sudden collapse of the Greenland and West unavoidable that the reduced-form probabil- Antarctica ice sheets, weakening or even ity of ΔT > 6˚C increases substantially above reversal of thermohaline circulations that 3 percent after the next century just from might radically affect such things as the the enormous inertial lags for what by then Gulf Stream and European climate, run- will be in the climate-change pipeline. away climate-sensitivity amplification of Societies and ecosystems whose average global warming due to positive-reinforcing temperature has changed in the course of a multiplier feedbacks (including, but not lim- century or so by ΔT > 6˚C (for U.S. readers: ited to, loss of polar albedo, weakened car- Δ6˚C ≈Δ11˚F) are located in the terra incog- bon sinks, and rapid releases of methane nita of what any honest economic modeler from the thawing of arctic permafrost). would have to admit is a planet Earth recon- More gradual but still very serious examples figured as science fiction, since such high of uncertain climate-change effects are: sea- temperatures have not existed for some tens level dynamics, drowned coastlines of of millions of years. unknown magnitude, very different and pos- The idea behind analyzing climate- sibly extreme weather patterns including change projects by converting future costs droughts and floods, ecosystem destruction, and benefits into present discounted values mass species extinctions, big changes in is that society has alternative investment worldwide precipitation patterns and distri- opportunities, whose proxy rate of return is bution of fresh water, tropical-crop failures, the discount rate, representing alternative large-scale migrations of human populations, capital-accumulation opportunities through- humidity-nourished contagious diseases—and out the rest of the economy that would the list goes on and on. compensate us for the economic losses suf- Translated into the language of the simple fered from climate change. Human-capital model used here, such rare disasters are far investments in education or public health out in the right tail of very high ΔT, which have consistently been found to have high corresponds to being far out in the left tail of rates of return, arguably far greater than 10 the consumption-growth random variable g. percent for less-developed countries and The probability distribution of long-run ΔT regions. More mundane examples of alter-

is disturbingly spread apart, largely because natives to CO2e mitigation from middle-of- of structural-parameter uncertainty about the-probability-distribution mild warming the unknown “climate sensitivity” multiplier might include accumulating air conditioners that amplifies greenhouse gas concentra- to counter high temperatures or erecting tions into ultimate steady-state greenhouse sea walls to keep the rising ocean out of warming. The recently released Fourth coastal cities. Such alterative investments Assessment Report of the IPCC (2007) pre- compensate mostly for potential loss of dicts for one hundred years from now a “indoor” consumption and they tend to be a mean temperature change of further plane- lot less expensive than wholesale abatement tary warming (from averaging six “equally of greenhouse gases. The real problem is in sound” marker scenarios) of E[ΔT] = 2.8˚C the tails and it mostly concerns “outdoor” with a thick-tailed upper-end standard devi- consumption. If the definition of consump- ation ≈ 1.6˚C (table SPM-3). This means the tion is broadened (as it should be) to probability that ΔT > 4.5˚C is approximately include nonmarket enjoyment of the natural 15 percent and the probability of ΔT > 6˚C is environment—like habitats, ecosystems, very roughly about 3 percent. IPCC does not and species—then it is difficult to imagine extend its projections beyond 2105 on the what the compensating investments are for basis that predictions into the twenty-second which we should now be saving more as an century are too uncertain, but it seems alternative that might substitute for holding sep07_Article4 8/17/07 4:31 PM Page 717

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down ΔT directly. With roughly 3 percent a cost–benefit calculation of what to do IPCC-4 probability, we will “consume” a about it is the greatest exercise in Bayesian terra incognita biosphere within a hundred decision theory that we economists have ever years whose mass species extinctions, radical performed. Formally, of course, cost–benefit alterations of natural environments, and analysis can deal with uncertainty—by taking other extreme outdoor consequences of a expected values, relying on expected-utility different planet will have been triggered by theory, accounting for risk aversion, and a geologically-instantaneous temperature using all of the other, by now familiar, para- change that is significantly larger than what phernalia of the modern theory of the eco- separates us now from past ice ages. nomics of uncertainty. In principle, it does In the rest of this paper, marginal analysis not matter whether the probabilities that is set aside and g stands for the unknown show up in our cost–benefit calculations are growth rate of a comprehensive future “con- objective or subjective because the mathe- sumption” that includes the consumption of matical formulas are the same for either natural environments, ecosystems, species, case. But in lumping together objective and and the like. The cost of low-g disasters from subjective uncertainties and thereby obscur- high-ΔT scenarios more properly constitutes ing their distinction—to the extent that a uncertainty in the sense of Knight or Keynes graduate student today hardly knows, or than risk, because the scale and probability even cares, what kinds of probabilities are of these disasters are both unknown. Not legitimate to plug into a rational expectations only is it very difficult to estimate tail proba- equilibrium and what kinds of probabilities bilities of high-ΔT outcomes—due, ultimate- are illegitimate for such purposes—I think ly, to the underlying sampling-theory that contemporary macroeconomics goes too principle that the rarer is an event the more far and leads to a mindset that too easily unsure is our estimate of its probability—but identifies probability (and “economic sci- translating this into g-equivalent economic- ence”) with exercises in calibration to sample damage units introduces enormous further frequencies from past data. fuzziness, especially when g includes exis- I do not propose to rehash here the ages- tence values of natural habitats. With an evo- old, never-resolved foundational controversy lutionary stochastic process like global about whether probabilities are better con- climate change, the world is not standing still ceptualized on the most fundamental level as long enough for us to accumulate the rele- objective frequencies or subjective beliefs. vant information to accurately assess tail Personally, I do not think there exists a pure probabilities. The net result is thicker left case of either extreme pole, but rather there tails for the distribution of g under dynami- is a continuum of situations with some being cally evolving global climate change than we closer for practical modeling purposes to the are accustomed to dealing with in our much objective pole and others being closer for more familiar dynamic stochastic general practical modeling purposes to the subjec- equilibrium macro models, which in practice tive pole. Here I just want to point out that if are based upon the stationary thin-tailed sto- something like radioactive decay is close to chastic processes that we use to model a being a pure case of objective frequencies, rational expectations equilibrium whose then climate change, and especially the eco- structure is (supposedly) fully known and nomics of climate change, is as close to being understood. a pure case of modeling probabilities by sub- Every cost–benefit analysis is an exercise jective judgements as we economists are in subjective uncertainty. If, as the Stern ever likely to encounter in practice. To para- Review puts it, “climate change is the great- phrase the language of the Stern Review yet est externality the world has ever seen,” then again, the economics of climate change is the sep07_Article4 8/17/07 4:31 PM Page 718

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greatest application of subjective uncertainty but, far more importantly in this context, it theory the world has ever seen. thins the left tail of the distribution as well. To the extent that it makes any sense at all The thickened tails of the reduced form to think in terms of some approximately bell- of the distribution of g that are an inevitable shaped meta-distribution of growth rates g consequence of taking expectations of that is out there, the part of the probability expectations can have surprisingly strong distribution that corresponds most closely to effects on cost–benefit calculations by low- objective-frequency risk is in its body around ering significantly expected utility and rais- the middle because, from previous experi- ing significantly expected marginal utility. ence, past observations, plausible extrapola- To get a sense of just how strong the effect tions, and maybe even the law of large can be of tails thickened by having structur- numbers, we have at least some modicum of al parameters that we do not know but confidence in being able to construct a rea- whose values must be inferred indirectly sonable approximation of the central regions from limited experience—and therefore a of the probability distribution. As we move sense of how much we could be missing in toward probabilities in the tails of the g dis- our economic analysis by ignoring the terra tribution, however, we are increasingly mov- incognita of the greenhouse-warming ing into the unknown territory of subjective extremes—consider this prosaic example. uncertainty where our probability estimates Suppose that in the good old days before we of the probability distributions themselves understood human-induced climate change becomes increasingly diffuse because the we were sure that g ∼ N(, 2), where we frequencies of rare events in the tails cannot somehow knew that = 2 percent and = 2 be pinned down by previous experiences, percent. Normalize current marginal utility past observations, or computer simulations. to be unity. Then from using the familiar for- The upshot of this uncertainty about uncer- mula for the expectation of a lognormally tainties is that the reduced-form probability distributed random variable, the expected distribution of g (after integrating out the marginal utility of an extra sure unit of con- probabilities of probabilities)—which is a sumption in the pre-climate-change era reduced form for the economics of climate would have been EMU = E[exp(− ηg)] = − η + −1 η 2 2 change in the sense that g here is the growth exp( 2 ). (It is precisely this kind of rate of comprehensive consumption that calculation that lies behind the risk free rate includes the natural environment—has a and equity-premium formulas (4) and (5).) thick left tail. The exact thickness of this left Imagine next that the possibility of green- tail of g depends not only upon how bad an house warming has now made us unsure environmental catastrophe global warming about and . Let us preliminarily model might induce and with what probabilities, this greenhouse-warming-induced uncertain but also upon how imprecise are our prob- situation, where we don’t know the true val- ability estimates of the probabilities of ues of and because of limited experience those bad catastrophes. Uneasiness about with climate change, as if we are limited projecting uncertain uncertainties prevents because we only have data from some finite IPCC and most economic analyses from number n of past observations (or finite sim- taking a stand on the increasing—and ulation outcomes from the data generating increasingly diffuse—probabilities of extreme process of some model) and we run a regres- temperatures after the year 2105, which sion to estimate and . For simplicity, sup- hardly eliminates the underlying problem. pose further that the point estimates ˆ = 2 Mitigating the future consequences of percent and ˆ = 2 percent from this regres- greenhouse warming does not just shift the sion just so happen to be the very same num- center of the distribution of g to the right bers as the presumed-known population sep07_Article4 8/17/07 4:31 PM Page 719

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parameters for the normal distribution There is a general point here and a partic- before climate change was understood to be ular application to the economics of climate a possibility. Then the reduced-form situa- change. The general point is that from expe- tion is as if g is distributed as a Student-t dis- rience alone one cannot acquire sufficiently tribution with n − 1 degrees of freedom. The accurate information about the probabilities Student-t here has the same mean as the of tail disasters to prevent the expected mar- normal and for large n has almost the same ginal utility of an extra sure unit of consump- standard deviation, but if you look closely tion from becoming unbounded for any with a magnifying glass its tails are naturally utility function having everywhere-positive thickened due to the “true” values of the relative risk aversion, thereby effortlessly structural parameters and being uncer- driving cost-benefit applications of expected tain. This kind of structural uncertainty utility theory. The degree to which this kind about the parameters of the probability dis- of “generalized precautionary principle” is tribution spreads apart the reduced-form relevant in a particular application must be (“predictive posterior” in Bayesian jargon) decided on a case-by-case basis that distribution of g, an effect that is especially depends upon the extent to which a priori pronounced in the thickened tails because knowledge in a particular case limits the they are especially difficult to learn about. If extent of posterior-predictive tail thickening. we now calculate the expected marginal util- In the particular application to the econom- ity of an extra sure unit of consumption using ics of climate change, where there is so obvi- this Student-t distribution (which is a natural ously limited data and limited information manifestation of limited experience or limit- about the global catastrophic reach of cli- ed information), then EMU = E[exp(− mate extremes for the case ΔT > 6˚C, to ηg)] =+, which is mathematically equiva- ignore or suppress the significance of rare lent to the fact that the moment generating tail disasters is to ignore or suppress what function of a Student-t distribution is infi- economic theory is telling us loudly and nite. The bombshell fact that EMU =+ (as clearly is potentially the most important part soon as we admit that we don’t know the of the analysis. While it is always fair game to underlying stochastic structure, and there- challenge the assumptions of a model, when fore parameters must be estimated) changes economic theory provides a generic result the rules of the game. Such a mechanism, (like “free trade is Pareto optimal”) the bur- for example, explains the asset-return puz- den of proof is commonly taken as resting on zles for reasonable values of δ and η as being whomever wants to overturn the theorem in due to a fear of relatively rare tail disasters a particular application. The take-away mes- that is theoretically difficult or impossible to sage here is that the burden of proof in the eliminate when the underlying tail-structure economics of climate change is presumptive- remains uncertain. The fact that under ly upon whomever wants to model optimal- structural uncertainty EMU =+ represents expected-utility growth under endogenous a mathematically generic result not limited greenhouse warming without having structur- to isoelastic utility or the normal parent dis- al uncertainty tending to matter much more tribution and Student-t child distribution of than risk. Such a middle-of-the-distribution the example. I claim this general result has modeler needs to explain why the significant economic repercussions which inescapably thickened tails of the posterior- are not easily brushed aside, not least of all predictive distribution, for which the thick for cost–benefit analysis of climate change left tail of g represents rare disasters under because such an effect in principle over- uncertain structure, is not the primary focus shadows the discounting of far-future of attention and does not play the decisive events. role in the analysis. sep07_Article4 8/17/07 4:31 PM Page 720

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5. Climate Uncertainty and the Value of the “ethical judgements on the distribution Information of income” is Stern-speak for picking η ≈ 1. Such “ethical judgements” could appear to Because the Stern Review is imbued with an uncharitable critic as if designed to justi- the laudable moral imperative of not expos- fy the activist conclusions that are consid- ing future generations to the tribulations of ered necessary to avoid the climate-change global warming, it does not shy away from horror scenarios. In the context of its self- emphasizing (at least discursively in its “mul- imposed “multidimensional” methodology, tidimensional” text) the possibilities of rare by choosing η ≈ 1 the Review appears to be high-ΔT, low-g catastrophes from climate playing both sides of the street against the change. Indeed, reading between the lines middle. On the one hand, it wants η to be as of the report, one has the feeling that the high as possible to reflect its tremendous immorality of relegating future generations humanitarian concern with distributional to live under the shadow of the open-ended inequities across space, which would allow it possibilities of uncertain large-scale changes to argue (informally, if passionately, in scat- in the climate system, when for a mere tered prose and numerical examples) that the annuity cost of a percent or two (or at most disproportionate negative impact of climate three) of GDP each year we might have pur- change on the world’s poor (whose marginal chased an insurance policy on their behalf utility is high because η in this story is that avoided this scary uncertainty (or at implicitly large) calls for urgent action now least greatly reduced it), is a major underly- to avoid future massive spatial redistribution ing leitmotif of the Review. This feeling of of relative income from the poor to the rich. guilt has no place to go analytically (under Simultaneously, the Stern Review wants to the conventional analytical confines adopted further exacerbate distributional inequities by the IAMs, including PAGE), so to speak, by redistributing income across time from except to be subliminally channelled into the relatively poor present to the much- choosing such low values of δ ≈ 0 and of richer future a century or two from now η ≈ 1 (and, secondarily, such high values of (when standards of living are likely to be ten −≈D −≈C Y 5 percent and low values of Y 1 per- times higher) via—an uncharitable critic cent) as will operate through the back door might suspect—choosing the lowest imagi- of conventional economic analysis to weight nable value η ≈ 1 that might be used (along present-discounted future damages high with δ ≈ 0) to reverse-engineer the really low enough relative to present mitigation costs r needed to prop up its technical case for to make the IAM want to reduce substan- immediate urgent action. The same contra- tially the disastrous possibilities. The Review diction about values of η shows itself in puts it directly: “Averaging across possibili- Stern’s heuristic justification for big values of −D ties conceals risks. The risks of outcomes probability-weighted Y as being due, in much worse than expected are very real and effect, to a risk-averse high-curvature high-η they could be catastrophic. Policy on climate utility function interacting with highly change is in large measure about reducing uncertain damages. these risks. They cannot be fully eliminated, I think that rather than trying to go but they can be substantially reduced. Such though the back door with unreasonably low a modeling framework has to take account of values of δ and η (or, secondarily, “averaging ethical judgements on the distribution of across possibilities” by heuristically making −≥D income and how to treat future generations.” business-as-usual Y 5 percent instead of The “ethical judgements” in the above some smaller more plausible point estimate), quote about “how to treat future genera- it is much better to go directly through the tions” is Stern-speak for picking δ ≈ 0, while front door with the legitimate concern that sep07_Article4 8/17/07 4:31 PM Page 721

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there is a chance, whose subjective probabil- embrace the currently politically incorrect ity is small but diffuse (thereby resulting in a idea, which is a third rail few policymakers dangerously thickened left tail of compre- dare to touch and Stern doesn’t even men- hensive consumption growth rates), that tion, that in the extremely unlikely event of a global warming may eventually cause disas- truly extraordinary unfolding disaster it trous temperatures and environmental might be a good emergency-backup plan to catastrophes. If one accepts that global cli- purposely geoengineer spaceship Earth to mate change is as likely an arena as any for a reverse previous inadvertent geoengineering valid application of the general principle that from burning too much fossil fuel? Or, per- thickened tails from uncertain structural haps more to the point here, can anyone parameters must dominate expected dis- imagine how the public would not embrace counted utility calculations, then many hard such an idea and demand that we should do questions need to be asked. What are early all in our power to avert a climate-change- warning signs of impending runaway envi- induced catastrophe at some hypothetical ronmental disasters like melting ice sheets, future time when environmental disaster thermohaline inversions, or just plain know- seems imminent? And how does the tail thick- ing beforehand that we are on a trajectory ness of climate-change disasters compare toward ΔT > 6˚C? How much would it cost to with the tail thickness of aerosol geoengi- put in place the very best system of sensors neering, or the tail thickness inherent in that money can buy for detecting early-warn- widespread nuclear power possibly going ing signals of impending climate catastro- awry, or the tail thickness of massive sudden-

phes? How early might the warning from release mishaps from buried-CO2 sequestra- monitoring systems be before the full effects tion because some remote “hypothetical” are felt? What could we do as an emergency materialized? response if we received such early-warning I trust that a few readers may be able to signals? Would last-ditch emergency geo- think of more such questions about the real engineering measures to ward off disaster by option value of waiting to gather information reversing the worst consequences of global (and the empirical issue of what to do about warming be available in time to help? (Such it), some of which might hopefully be more emergency measures are likely to be so grounded in reality than my highly specula- extreme as to be defensible only for an even tive examples. Whether or not my particular more extreme environmental catastrophe in hypothetical stories are realistic, these kinds the making—perhaps they might include of questions become relevant once the focus painting all human-made structures on the of the economics of climate change shifts planet reflective white and creating a from the middle range of the distribution of “Pinatubo effect” by seeding the upper what might happen with ΔT at a IPCC-4 atmosphere with metallic dust or aerosols.7) mean of ≈ 2.8˚C a hundred years hence to Could such last-ditch measures be made thinking more about what might be in the reversible by building in decay mechanisms, tails with ΔT > 6˚C, which is just two IPCC- as with sulfate aerosols, while we then used 4 standard deviations out for a century from the new information to really undertake dra- now, meaning a probability ≈ 3 percent (and conian measures to cut greenhouse gas emis- presumably a yet higher probability after sions drastically? Are there other aerosol 2105). This thick tail is where most of the precursors than sulfates with possibly better cost–benefit action may well be even if—or environmental properties? Can the public perhaps precisely because—our estimates of the probabilities involved are themselves 7 On the feasible use of sulfate aerosol precursors to so highly uncertain. Anything is possible in reverse global warming, see T. M. L. Wigley (2006). the tails of a nondogmatic distribution. sep07_Article4 8/17/07 4:31 PM Page 722

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(“Nondogmatic” in Bayesian parlance just early detection is impossible, or it is too means that no event is ruled out a priori by expensive, or it comes too late (this is Stern’s having been assigned zero probability in the line, and it might, or might not, happen to be prior distribution.) A responsible policy true), or because nothing practical can be approach neither dismisses the horror sto- done about reversing greenhouse warming ries just because they are two standard devi- anyway—so we should stop stalling and start ations away from what is likely nor gets making serious down payments on catastro-

stampeded into overemphasizing false phe insurance by cutting CO2e emissions dichotomies as if we must make costly all-or- drastically. But these are conclusions we nothing investment decisions right now to need to reach empirically, rather than pre- avoid theoretically possible horrible outcomes judging them initially. Instead of declaring in the distant future. immediate all-out war on greenhouse gas In my opinion, public policy on greenhouse emissions as advocated by Stern, maybe we warming needs desperately to steer a middle would do better by steadily but surely ramp- course, which is not yet there, for dealing ing up greenhouse gas cuts over the next with possible climate-change disasters. This decade or two while simultaneously investi- middle course combines the gradualist gating seriously the nature of the runaway- climate-policy ramp of ever-tighter green- climate disasters in the thick tails and what house gas reductions that comes from main- might be done realistically about them should stream mid-probability-distribution analysis they start to materialize. We can always come (under reasonable parameter values) with the back in ten or twenty years time and declare option value of waiting for better information all-out war on global-warming emissions about the thick-tailed disasters. It takes seri- then—if we then think it is the best option ously whether or not possibilities exist for among a better-studied reasonably consid- finding out beforehand that we are on a run- ered portfolio of possible options. away-climate trajectory and—without “leav- Until we start seriously posing and trying ing it all up to geoengineering”—confronts to answer tough questions about rare global- honestly the possible options of undertaking warming catastrophes, we will not make real currently politically incorrect emergency progress in dealing constructively with the measures if a worst-case nightmare trajecto- nightmare scenarios and we will continue to ry happens to materialize. The overarching cope with them inadequately by trying to concern of such a middle course is to be con- shoehorn disaster policy into an either-or structive by having some semblance of a response category where it won’t fit. The game plan for dealing realistically with what Stern Review has its heart in the right might conceivably be coming down the road. place—it is not nice for us to play the role of The point is to supplement mainstream eco- nature’s grim reaper by bequeathing the nomic analysis of climate change (and main- enormously unsettling uncertainty of a very stream ramped-up mitigation policies for small, but essentially unknown (and perhaps dealing with it) by putting serious research unknowable), probability of a planet Earth dollars into early detection of rare disasters that in hindsight we allowed to get wrecked and by beginning a major public dialogue on our watch. However, Stern does not fol- about contingency planning for worst-case low through formally on this really unsettling scenarios perhaps akin to the way Americans part of the global warming equation (which a (at their best) might debate the pros and generous interpretation of its not-convincing cons of an anti-ICBM early warning system. economic analysis might say is the underly- It may well turn out that the option value of ing motivation for its overall alarmist tone) waiting for better information about cata- except indirectly, by choosing δ ≈ 0, η ≈ 1, −≈D −≈C strophic tail events is negligible because Y 5 percent, Y 1 percent (which an sep07_Article4 8/17/07 4:31 PM Page 723

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ungenerous interpretation might say is Review puts it, “the pricing of carbon, imple- reverse-engineering the drastic slowing mented through tax, trading, or regulation,” measures that the Review wants to impose is “required for an effective global response” on greenhouse gas emissions to neutralize (p. xvii). One can only wish that U.S. political the nightmare scenarios). I don’t mean to leaders might have the wisdom to understand imply that there is some off-the-shelf and the courage to act upon the breathtak- turnkey consensus model of the economics ingly simple vision that steady pressure from of uncertain catastrophes that the Stern the predictable presence of a high carbon Review was negligent in not using or that price reflecting social costs (whether such a model would (or should) provide imposed directly through taxes or indirectly ammunition for an excuse not to undertake via tradable permits) would do more to serious action soon to slow greenhouse emis- unleash the decentralized power of capitalis- sions. We just don’t yet know and we need tic American inventive genius on the problem badly to find out. The overarching problem of researching, developing, and finally invest- is that we lack a commonly accepted usable ing in economically efficient carbon-avoiding economic framework for dealing with these alternative technologies than all of the piece- kinds of thick-tailed extreme disasters, meal command-and-control standards and whose probability distributions are inherent- patchwork subsidies making the rounds in ly difficult to estimate (which is why the tails Washington these days. must be thick in the first place). But I think As we have seen, on the economic-analysis progress begins by recognizing that the hid- side the Stern Review predetermines the den core meaning of Stern vs. Critics may be outcome in favor of strong immediate action about tails vs. middle and about catastrophe to curtail greenhouse gas emissions by creat- insurance vs. consumption smoothing. ing a very low value of r ≈ 1.4 percent via the indirect route of picking point-estimate δ ≈ η ≈ 6. Getting it Right for the Wrong Reasons? parameter values 0 and 1 that are more like theoretically reasoned extreme The Stern Review is a political document— lower bounds than empirically plausible esti- in Keynes’s phrase an essay in persuasion—at mates of representative tastes. But we have least as much as it is an economic analysis also seen that a fair recognition of the truth and, in fairness, it needs ultimately to be that we are genuinely uncertain about what judged by both standards. To its great credit, interest rate should be used to discount costs the Review supports very strongly the politi- and benefits of climate changes a century cally unpalatable idea, which no democratic from now brings discounting rates down politician planning to remain in office any- from conventional values r ≈ 6 − 7 percent to where wants to hear, that (however it is pack- much lower values of perhaps r ≈ 2 − 4 per- aged and whatever spin is put on it) cent, which would create a more intermedi- substantial carbon taxes must be levied ate sense of urgency somewhere between because energy users need desperately to what the Stern Review is advocating and the start confronting the expensive reality that more modest measures to slow global warm- burning carbon has a significant externality ing advocated by many of its critics. The cost that ought to be taken into account by important remaining caveat is that such an being charged full freight for doing it. (This is intermediate position is still grounded in a the most central “inconvenient truth” of all, conventional consumption-smoothing ap- which was conveniently ignored in Al Gore’s proach to the economic analysis of climate award-winning film.) An entire chapter 22 in change that avoids formally confronting the Stern, entitled “Creating a Global Price for issue of what to do about catastrophe insur- Carbon,” is devoted to this theme. As the ance against the possibility of thick-tailed sep07_Article4 8/17/07 4:31 PM Page 724

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rare disasters, which from first principles of comprehensive measure of consumption economic–statistical reasoning presumptively that includes the natural environment. I drive expected discounted utility outcomes. have argued that this inherently thickened In conclusion, I think the Stern Review left tail of g is an important aspect of the deserves credit for effectively raising the economics of climate change that every ana- level of public discourse—by increasing gen- lyst—Stern and the critics of Stern—might eral awareness that climate change is a seri- do well to try to address more directly. ous issue which should be taken seriously, by History will judge whether the economic arguing cogently for what is effectively a analysis of the Stern Review ended up being global carbon tax as an essential component more wrong or more right and, if it was more of any reasonable solution, by openly dis- right, whether as pure economic reasoning it cussing adaptation to climate change (as well was right for the right reasons or it was right as mitigation), and by popularizing for a for the wrong reasons. wider audience than economists the idea REFERENCES that economic analysis of costs and benefits Cline, William R. 1992. The Economics of Global might be a useful legitimate method for Warming. Washington, D.C.: Institute for Inter- national Economics. evaluating policies to mitigate global warm- Dasgupta, Partha. 2007. “Commentary: The Stern ing. I think also that Stern deserves some Review’s Economics of Climate Change.” National measure of credit for elevating to promi- Institute Economic Review, 199: 4–7. Hope, Chris. 2006. “The Marginal Impact of CO2 from nence the problem of genuine uncertainty PAGE2002: An Integrated Assessment Model concerning rare but dangerous climate dis- Incorporating the IPCC’s Five Reasons for Concern.” asters, about which decisions must be made Integrated Assessment, 6(1): 19–56. Intergovernmental Panel on Climate Change. 2007. but whose scale and probability cannot be Climate Change 2007: The Physical Science Basis: known precisely. However, in my opinion, Summary for Policy Makers. http://www.ipcc.ch. Stern deserves a measure of discredit for Kelly, David L., and Charles D. Kolstad. 1999. “Integrated Assessment Models for Climate Change giving readers an authoritative-looking Control.” In The International Yearbook of impression that seemingly objective best- Environmental and Resource Economics: 1999/2000: available-practice professional economic A Survey of Current Issues, ed. H. Folmer and T. Tietenberg. Cheltenham, U.K. and Northampton, analysis robustly supports its conclusions, Mass.: Elgar, 171–97. instead of more openly disclosing the full Lind, Robert, ed. 1982. Discounting for Time and Risk extent to which the Review’s radical policy in Energy Policy. Washington, D.C.: Resources for the Future. recommendations depend upon controver- Maddison, David. 2006. “Further Comments on the sial extreme assumptions and unconvention- Stern Review.” http://www.economics.bham.ac.uk/ al discount rates that most mainstream maddison/Stern%20Comments.pdf. Mendelsohn, Robert O. 2007. “A Critique of the Stern economists would consider much too low. I Report.” Regulation, 29(4): 40–47. can’t help but feel after reading the Review Nordhaus, William D. 1994. Managing the Global that its urgent tone of morality and alarm Commons: The Economics of Climate Change. Cambridge, Mass. and London: MIT Press. comes not from the chapter 6 aggregative Nordhaus, William D. 2007. “A Review of the Stern economic modeling of climate-change Review on the Economics of Climate Change.” impacts, which deservedly has drawn strong Journal of Economic Literature, 45(3): 686–702. Portney, Paul R., and John P. Weyant, eds. 1999. criticism from economists, but more from a Discounting and Intergenerational Equity. Wash- not formally articulated fear of what might ington, D.C.: Resources for the Future. potentially be out there with greenhouse Tol, Richard S. J., and Gary W. Yohe. 2006. “A Review of the Stern Review.” World Economics, 7(4): 233–50. warming in (using my own ponderous termi- Weitzman, Martin L. Forthcoming. “Subjective nology here to make sure my expression is Expectations and Asset-Return Puzzles.” American exact) the inherently thickened left tail of Economic Review. Wigley, T. M. L. 2006. “A Combined Migration/ the reduced-form posterior-predictive prob- Geoengineering Approach to Climate Stabilization.” ability distribution of the growth rate of a Science, 314(5798): 452–54.