A Review of The Stern Review on the Economics of Climate ... · known to insiders in the economics of climate change, but it needs to be more widely appre-ciated by economists at

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

A Review of The Stern Review on theEconomics of Climate Change

MARTIN L. WEITZMAN∗

703

1. Introduction

The issue of global climate change andwhat to do about it has put economics to

a severe test in which economists have beenchallenged to think afresh about how tomodel (or at least how to conceptualize) suchfundamental notions as risk, uncertainty, anddiscounting. There is nothing like beingasked for a specific policy recommendation

on a vivid actuality to breathe new life intootherwise arcane matters of economic analy-sis. Beyond the issue of whether it is right orwrong in its conclusions, the Stern Review onthe Economics of Climate Change is anopportunity for economists to take stock ofwhat we know about this subject, how weknow it, what we don’t know, and why wedon’t know it.

The Stern Review is a full-fledged eco-nomic analysis of climate change that wasofficially commissioned by the British gov-ernment and, for reasons both economic andpolitical, is an unusual—and unusuallyimportant—document. Sir Nicholas Stern isa professional economist of high standingand a distinguished public servant. Weighingin at close to 700 pages, the Stern Review is

∗ Weitzman: Harvard University. For helpful detailedcomments on earlier drafts of this paper, but withoutimplicating them for its remaining defects, I am gratefulto Scott Barrett, Roland Benabou, Olivier Blanchard,Richard Cooper, Stephen DeCanio, HowardGruenspecht, Cameron Hepburn, Chris Hope, DonaldLudwig, Robert Mendelsohn, Larry Samuelson, RobertSolow, Nicholas Stern, Lawrence Summers, and HalVarian.

The Stern Review calls for immediate decisive action to stabilize greenhouse gasesbecause “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 primari-ly upon imposing a very low discount rate. Concerning this discount-rate aspect, I amskeptical of the Review’s formal analysis, but this essay points out that we are actual-ly a lot less sure about what interest rate should be used for discounting climatechange than is commonly acknowledged. The Review’s second basic strand is a moreintuitive argument that it might be very important to avoid possibly large uncertain-ties that are difficult to quantify. Concerning this uncertainty aspect, I argue that itmight be recast into sound analytical reasoning that might justify some of theReview’s conclusions. The basic issue here is that spending money to slow globalwarming should perhaps not be conceptualized primarily as being about consump-tion smoothing as much as being about how much insurance to buy to offset the smallchange of a ruinous catastrophe that is difficult to compensate by ordinary savings.

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comprehensive in its scope and ambitious inits aims, with an attractive multicolored visu-al design that makes topics like cost–benefitanalysis of dynamic externalities look almostglamorous. Anyone wanting to get a goodfeel for the basic issues of global climatechange could profitably browse through thisreport, which covers well its multiple facetsin a reader-friendly format. The Review con-tains much of value and interest aside fromits cost–benefit analysis of mitigation poli-cies, although that is naturally the part whichmost grabs the attention of economists. Adetailed Review of the Review is out of placehere—it would be too long, and besides theStern Review reads well and is availableonline. Instead, I concentrate here on tryingto distill the Review down to what I think isits analytical essence as a piece of appliedcost–benefit analysis, because there can bedifficulty seeing the forest for the trees whenthere are so many trees.

To make a long story short, the SternReview comes down very strongly on the sideof undertaking decisive—and expensive—measures starting now to reduce CO2 andother greenhouse gas emissions because(and this quote captures well the tone ofurgency about moving quickly to avoid cata-strophic possibilities that is evident through-out the report): “Our actions over thecoming few decades could create risks ofmajor disruption to economic and socialactivity, later in this century and in the next,on a scale similar to those associated with thegreat wars and economic depression of thefirst half of the 20th century” (p. xv). Such astrong call to immediate decisive action is atodds with what most other economic analy-ses of climate change have concluded. Themajority view of most other economic ana-lysts finds it optimal to pursue a more grad-ualist course by starting with greenhouse gasemissions reductions at far lower levels thanwhat the Stern Review advocates for thenear future, but which after that ramp upconsiderably over time. The Review analysis,on the other hand, finds that “the benefits of

strong and early action far outweigh the eco-nomic costs of not acting” (p. xv) and calls forstabilizing greenhouse gas atmospheric con-centrations at ≈ 550 parts per million (ppm)of CO2-equivalent (CO2e). (The currentlevel is ≈ 430 ppm CO2e, compared with≈ 280 ppm CO2e before the IndustrialRevolution.) This would make temperaturesa hundred years from now be at E[ΔT] ≈ 2˚Cand would (hopefully) stabilize future tem-peratures permanently thereafter atΔ� ≈ 3˚C. By contrast, along the more grad-ual majoritarian optimal trajectories CO2econcentrations a century from now are > 600ppm and E[ΔT] ≈ 2.5˚C—with temperaturesexpected to continue rising to well aboveE[ΔT] ≈ 3˚C after year 2105. To accomplishthe Review’s ambitious goal, greenhouse gasemissions would need to be progressively cutby ≈ 3 percent each year, beginning more orless immediately. Which brings us to a cen-tral question. Why is there such a big differ-ence between what Stern is recommendingand what most other serious analysts favor?

This paper makes five basic points aboutthe economics of climate change: (1) the dis-count rate we choose is all important andStern’s results come from choosing a very lowdiscount rate; (2) we are a lot less sure aboutcore elements of discounting for climatechange than we commonly acknowledgebecause critical puzzles, projections, andambiguities are yet unresolved; (3) standardapproaches to climate change (even those thatpurport to treat uncertainty) fail to accountfully for the implications of large conse-quences with small probabilities; (4) structur-al parameter uncertainty that manifests itselfin the thick tails of reduced-form probabilitydistributions—not risk—is what likely mattersmost; (5) gathering information about thick-tailed uncertainties representing rare climatedisasters (and developing a realistic emer-gency plan were they to materialize) shouldbe a priority of research. To anticipate mymain finding, spending money now to slowglobal warming should not be conceptualizedprimarily as being about optimal consumption

704 Journal of Economic Literature, Vol. XLV (September 2007)


1 Variants of this argument are made in ParthaDasgupta (2007), Robert O. Mendelsohn (2007), WilliamD. Nordhaus (2007), and Richard S. J. Tol and Gary W.Yohe (2006).

2 A survey of integrated asssessment models for climatechange control is provided in David L. Kelly and CharlesD. Kolstad (1999).

3 A nice description of how the Stern Review uses (andmisuses) PAGE is contained in David Maddison (2006).PAGE itself is described in Chris Hope (2006).

smoothing so much as an issue about howmuch insurance to buy to offset the smallchance of a ruinous catastrophe that is diffi-cult to compensate by ordinary savings. WhileI am (along with most other economist-critics) skeptical of Stern’s formal analysis, Ibelieve that the Review’s informal emphasison climate-change uncertainty can be recastinto sound analytical arguments that mightjustify some of its conclusions.

2. Interest Rates and Long-TermDiscounting

Overall, I believe it is fair to say that theStern Review consistently leans toward (andconsistently phrases issues in terms of)assumptions and formulations that empha-size optimistically low expected costs of mit-igation and pessimistically high expecteddamages from greenhouse warming—rela-tive to most other studies of the economicsof climate change. But far more crucially,the key assumption that drives its strongconclusions is the mundane fact that a verylow interest rate is postulated, with whichdistant-future benefits and costs are thendiscounted. The upward-sloping “climatepolicy ramp” of ever-tighter emissionsreductions in the majority of other models(but not beginning just yet, please) is afamiliar consumption-smoothing conse-quence of discounting: the higher the inter-est rate the stronger the desire to movetoward getting more pleasure now at theexpense of postponing more pain until later.An efficient trajectory has a cost minimizingsubstructure similar to a Hotelling extrac-tion problem: consumption flows aresmoothed over time by maximizing presentdiscounted utility subject to a stock con-straint on accumulated CO2e, which resultsin an “as if” CO2e shadow tax that grows overtime at (approximately) the rate of interest.The Stern Review simultaneously raisesoverall greenhouse gas reductions and flat-tens the “climate policy ramp” in itsHotelling-analogous consumption smoothing

time profile by imposing discounting at abare-minimum rate of interest.

Global climate change unfolds over a timescale of centuries and, through the power ofcompound interest, what to do now is hugelysensitive to the discount rate that is postulat-ed. In fact, it is not an exaggeration to say thatthe biggest uncertainty of all in the econom-ics of climate change is the uncertainty aboutwhich interest rate to use for discounting. Inone form or another, this little secret isknown to insiders in the economics of climatechange, but it needs to be more widely appre-ciated by economists at large. The insight thatthe strong conclusions of the Review are driv-en mainly by the low assumed discount ratehas been picked up and commented uponalready by several insider critics.1 Here Iwant to paraphrase this important debate foroutsider economists and in the process bringsome new ingredients to the mix.

An Integrated Assessment Model—here-after IAM—is insider lingo for a multiple-equation computer-simulated model thatcombines dynamic economics with geophys-ical climate dynamics for the purposes ofanalyzing the economic effects of global cli-mate change.2 An IAM is essentially a modelof economic growth with a controllableexternality of endogenous greenhouse warm-ing. The Review uses an IAM called PAGE,on which some numbers have been crunchedand some conclusions have been based, butthe exact connection between PAGE andStern’s conclusions is elusive, frustrating, andultimately unsatisfactory for a professionaleconomist who honestly wants to understandwhere the strong policy recommendationsare coming from.3 The analytical core of the

705Weitzman: A Review of the Stern Review


Review is chapter 6 (“Economic Modelling ofClimate-Change Impacts”), which is looselytied to PAGE. However, the rest of the bookcontains lots of stories and examples suggest-ing that difficult-to-quantify uncertaintyabout really bad climate extremes may actu-ally be an important informal part of Stern’soverall case. Economists are justifiably suspi-cious when someone refuses to aggregatevarious probability-weighted scenarios intoan overall cost–benefit assessment, which atleast can serve as a conversation starter. (Howelse are we to evaluate overall policy advice,such as what Stern recommends to us, exceptin the context of some overall model whereassumptions and specifications are spelledout clearly?) As economic analysis, the SternReview dwells in a nonscientific state oflimbo where it uses an IAM but simultane-ously refuses to commit to it or to any otherconsistent overarching framework withinwhich its radical recommendations might bedeconstructed and judged by others. Instead,the Review dances around the significance ofthe aggregative analysis of chapter 6 by argu-ing that conclusions from IAMs are sugges-tively useful but not crucial to the basic storyline that anything above ultimate stabilizationat ≈ 550 ppm of CO2e and Δ� ≈ 3˚C is self-evidently just too risky for the planet to bear.In trying to make some overall sense ofStern’s mixed methodology (called “multidi-mensional” in the Review), I propose here tolay out the core issues of how risk, uncertain-ty, and discounting interact with the econom-ics of climate change in terms of the simplestgeneral-equilibrium model I can think of.Then I will try to clothe some parts of Stern’sintuitions about climate-change uncertaintyin formal garb.

Irving Fisher taught us that an interestrate, like any other price, is the outcome of adynamic general-equilibrium interaction oftastes with technology. The modern incarna-tion of Fisher’s idea in a deterministic settingis the famous Frank Ramsey equation

(1) r = δ + ηg,

where r is the interest rate (more on theinterest rate later), δ is the rate of pure timepreference, g is the per capita growth rate ofconsumption, and η is the elasticity of mar-ginal utility, or, equivalently, the coefficient ofrelative risk aversion. In the shorthand nota-tion of (1), the parameters δ and η capturetwo critical aspects of “tastes” (or “prefer-ences”) while the reduced-form representa-tion of “technology” is the growth rate ofconsumption g. The important distinctionbetween δ and r is that δ is a more primitiverate of pure time preference that discountsutility, while r is the much more familiarinterest rate used to discount consumption,which is derived from all of the more primi-tive underlying parameters of tastes andtechnology via (1). The other taste parameterη represents the relative curvature of theutility function and is simultaneously a meas-ure of aversion to interpersonal inequalityand a measure of personal risk aversion. Onthe technology side, formula (1) holdswhether g is endogenous or exogenous. InRamsey’s time, g was conceptualized as com-ing from capital accumulation, and thereforein long run equilibrium with diminishingreturns to capital g → 0 and r → δ. We nowknow from modern post-Solow growth theory(but Ramsey and Fisher didn’t) that, in bal-anced growth steady-state equilibrium, g isessentially the underlying growth rate of labor-augmenting technological progress that,behind the scene, is pushing the entire econo-my forward (at least in a world without agreenhouse-warming externality). What I pro-pose to do here is use the Ramsey equation asa transparency-based springboard for recast-ing the economics of climate change in termsof the four critical variables that appear in (1):δ, η, g, and r. I will ultimately argue that, in agreenhouse gas world, g needs to be seen as arandom variable whose probability distribu-tion has a climate-change-thickened left tailthat carries most of the weight of expectedmarginal utility in cost–benefit analysis.

To cut sharply to the essence of the corediscounting issue behind the Review’s strong



conclusions, pretend there are just two periods—the present and the future—wherethe “future” is about one hundred years fromnow. For the purposes at hand, I am about toconduct a gigantic macroeconomic cost–benefit exercise trading off less present con-sumption from greenhouse gas abatementfor more future consumption from mitigat-ing the bad effects a century hence of globalwarming. Technically speaking, the possibili-ty of extreme left-tail values of g occurringwith small positive probability is outside thismarginalist framework and requires us to goback to the fundamentals of expected utilitytheory that lie behind cost–benefit analysisunder uncertainty, but I will cross that bridgewhen I come to it later and the take-awaymessage will turn out to be similar anyway.

Of course such an incredible oversimplifi-cation of the economics of climate changeignores or distorts truly monumental chunksof reality. As just one example among many,a very important part of the global warmingstory concerns the huge stock–flow lags andenormous built-in inertias from having sucha long pipeline between greenhouse gasemissions and ultimate temperaturechanges. This built-in inertia causes ΔT tocontinue to rise to levels above E[ΔT] ≈ 3˚Cafter a century from now (and also causesthe tail probabilities of very high tempera-tures ΔT > 6˚C to be relatively much biggertwo centuries from now than one centuryfrom now) along any trajectory that does notstabilize atmospheric greenhouse gases at≈ 550 ppm CO2e—including the majority-opinion gradualist climate-policy-ramp tra-jectory. The ultimate high-temperatureconsequences of the huge inertial lag of ΔTto greenhouse gases already in the pipelineanimate the Stern Review passion for severecurtailment of greenhouse gas emissions tobegin soon, because at current flow rates wewill attain a stock of 550 ppm of CO2e with-in about a half-century and move (essential-ly irreversibly) thereafter beyond any hopeto stabilize ultimate E[ΔT] at ≈ 3°C.However, the point here is to put aside

temporarily such details as the optimalconsumption-smoothing profile of measuresto slow greenhouse warming (and their iner-tial consequences) in favor of immediatetransparency by focusing on the highly aggre-gated macroeconomic big picture of what ismost essential in driving the Stern Reviewresults, for which purpose focusing on a cen-tury hence is a good enough approximation.

Going right to the target here, my ownrough point-guesstimate of what most econo-mists might think are decent parameter val-ues would be something like a “trio of twos”:δ = 2 percent, g = 2 percent (both on anannual basis), and η = 2 percent. For thesake of moving along, I am not going to try todefend the “trio of twos values” with a bunchof citations but instead I pretend for thetime being that every critic of Stern thinksthey are about right, so we can temporarilyshelve this issue. Plugging these primitivesinto (1) makes “the” annual interest rate ber = 6 percent. Other reasonable—in myview—parameter combinations, say δ = 1percent, g = 2 percent, η = 2.5 (or evenδ = 0 percent, g = 2 percent, η = 3) alsogive r = 6 percent.

Concerning the rate of pure time prefer-ence, Stern follows a decidedly minoritypaternalistic view (which, however, includesa handful of distinguished economists) thatfor social discounting selects the lowest con-ceivable value δ ≈ 0 according to the a prioriphilosophical principle of treating all gener-ations equally—irrespective of preferencesfor present over future utility that peopleseem to exhibit in their everyday savings andinvestment behavior. In a similar spirit ofchoosing extreme taste parameters, Sternselects as its base-case coefficient of relativerisk aversion the value η = 1 that is the low-est lower bound of just about any economist’sbest-guess range. Some other taste-parametervalues are considered in a halfhearted sensi-tivity analysis postscript to the original ver-sion of the Review, which is reported as ifindicating robustness but I would interpretas more nearly the opposite because, no



matter what spin is put on it, there is noescaping the impact of higher interest rateson undoing the Review’s extreme policy con-clusions. With its preferred base-case param-eter values δ = 0.1 percent p.a., g = 1.3percent p.a., η = 1, Stern’s discount ratefrom (1) is r = 1.4 percent. The present dis-counted value of a given global-warming lossfrom a century hence at the non-Stern annu-al interest rate of r = 6 percent is one hun-dreth of the present discounted value of thesame loss at Stern’s annual interest rate ofr = 1.4 percent. The disagreement over whatinterest rate to use for discounting is equiva-lent here in its impact to a disagreementabout the estimated damage costs of globalwarming a hundred years hence of two ordersof magnitude. Bingo!

If D is aggregate damages from global cli-mate change and Y is GDP, then values ofthe ratio D

Y− a century from now (if nothing orvery little is done to halt greenhouse gasemissions) are commonly taken to be some-where in the range of about 0 percent to 3percent. The Stern Review effectively usesDY− ≈ 5 percent as its base case. This highvalue is consistent with what an uncharitablecritic might see as a philosophy of focusingon the gloomier outcomes in a heuristic-intuitive attempt to include extreme dam-ages, because in Stern’s language “when wetry to take due account of the upside risksand uncertainties, the probability-weightedcosts look very large.” Actually, the Reviewgoes well beyond 5 percent in its multi-dimensional approach by making numerousliterary and numerical allusions to the darkpossibilities lurking in the tails of the distri-bution of possible outcomes (and then, as itwere, rubbing salt in the wound of numeri-cal calibration by noting how centrist it isactually being by not choosing much higherprobability-weighted distant-future dam-ages, which could be as big as D

Y− ≈ 20 percent–35 percent when one considerscatastrophes that might materialize after2105). Stern also estimates the annual costsof its ambitious abatement strategy as being

equivalent to about 1 percent of GDP(which seems rather on the low side bymaybe a factor of two or more, but that is notso relevant here).

The question for the Stern Review analy-sis then effectively becomes: is it worthwhileto sacrifice costs C ≈ 1 percent of GDP nowto remove damages D ≈ 5 percent of GDP acentury from now? With g and r beingexpressed on an annual basis, the benefit-over-cost ratio of such an investment wouldbe B

C− = 5 exp(100(g − r)). From (1), r − g =(η − 1)g + δ, so that by picking the extremevalues η = 1, δ = 0.1 percent, Stern guaran-tees that the difference r − g is always theminiscule amount δ = 0.1 percent, no matterwhat value of g is chosen, which is reallystacking the deck in favor of approving suchkind of fractional GDP swaps across time.(The Review could have made life easierhere by just rounding down a mere tenth ofa percent by assuming δ = 0, which alongwith η = 1 would make cost–benefit analysisreally simple because a fixed fraction ofGDP would then always be worth the samefixed fraction of GDP at any future time.)With Stern’s preferred parameter values, thebenefit–cost ratio is B

C− = 4.5 (close to theupper bound of B

C− = 5 from assuming a zerorate of pure time preference)—a clear slam-dunk accept. The alternative non-Stern val-ues g = 2 percent, r = 6 percent makeBC− = 1

10−—a clear reject. This simple kind ofexercise is what drives the Stern Reviewresults and, in a nutshell, is what accounts forthe difference with the more conventionalanalyses of its critics. The no-frills stripped-down variant of the Ramsey model I amusing here is liable to a thousand and onelegitimate questions and criticisms about itsoversimplifications but, at the end of the day,I believe this exercise is highlighting fairlywhat really counts in the economics of cli-mate change—the hidden discountingassumptions whose role tends to be moreobscured than informed by the big IAMs.

For most economists, a major problemwith Stern’s numbers is that people are not



observed to behave as if they are operatingwith δ ≈ 0 and η ≈ 1. To gauge the magni-tude of the headache this presents for Stern’staste-parameter values, consider the follow-ing thought experiment expressed in terms ofthe permanent income hypothesis in a deter-ministic setting. Suppose that on the marginan individual representing a long-liveddynasty faces a constant interest rate, r, andhas a level of wealth, W, representing thecapitalized value of future earnings plus ini-tial holdings. Then permanent income is rWand an optimal consumption trajectory savesa constant amount s of permanent income.Plugging the implied balanced growth rateg = sr into (1) and rearranging gives

r − δ(2) s = ⎯⎯⎯ .ηr

With Stern’s preferred values δ ≈ 0, η ≈ 1,equation (2) implies s ≈ 100 percent irre-spective of r—a reductio ad absurdum. Inthe economics of uncertainty, plausible valuesof the coefficient of relative risk aversion ηare commonly taken to be somewherebetween 1 and 4 (I use the geometric-averagepoint estimate η = 2). A reader can plugfavorite parameter values into (2) and backout implied values of δ. For me (and I sus-pect most economists), sensible savings ratesin this and other variants of market-behavior-based thought experiments requires the rateof pure time preference to be significantlygreater than zero (or at least if δ is chosen tobe relatively small then η should be chosento be relatively big). Stern’s worldview tendsto blow off market-based observations andbehavioral inferences as being (for a varietyof reasons including market incompleteness)largely irrelevant to long-run discounting,which should instead be based primarilyupon the “ethical” value δ ≈ 0 that Sternimposes on a priori grounds. Readers willhave to make up their own minds about “eth-ical” values of preference parameters. Whilethere may be something to Stern’s positionabout the limited relevance of market-based

inferences for putting welfare weights on theutilities of one’s great-grandchildren, andthere might be some sporadic support forStern’s preferred taste parameters scatteredthroughout the literature, I ultimately findsuch an extreme stance on the primacy ofδ ≈ 0, η ≈ 1 unconvincing when super-strongpolicy advice is so dependent upon noncon-ventional assumptions that go so stronglyagainst mainstream economics.

3. Puzzles and Ambiguities of UncertainDiscounting

The most worrisome omission from anyanalysis based on the Ramsey approach (1) isuncertainty. As a first-pass informal cut atuncertainty, suppose we admit that we don’treally know for sure whether Stern or Stern’scritics are right about the interest rate to usefor discounting costs and benefits a hundredyears or so from now. An important featureof interest rates under uncertainty is thatthey don’t aggregate arithmetically into asimple certainty-equivalent interest rate. A 12−chance of r = 6 percent and a 1

2− chance ofr = 1.4 percent are not at all the same thingas splitting the difference by selecting theaverage r = 3.7 percent. It is not discountrates that need to be averaged but discountfactors. A 1

2− chance of a discount factor of e−6 a century hence and a 1

2− chance of a dis-count factor of e−1.4 a century hence make anexpected discount factor of 0.5e−6 + 0.5e−1.4 acentury hence, which, when you do themath, is equivalent to an effective interestrate of r = 2 percent. According to this logic,the interest rate we should be using to dis-count a dollar of costs or benefits a centuryfrom now is in between the Stern value ofr = 1.4 percent and the more conventionalvalue of r = 6 percent, but with the abovenumbers it is a lot closer to the Stern valueand is not anywhere near the arithmeticaverage of r = 3.7 percent. More generallyhere, if there is a subjective probability pi

that discount rate ri is the correct rate to use,then the effective discount rate for time t is



ln∑pie−rit

(3) r(t) = − ⎯⎯⎯⎯ ,t

which declines monotonically over timefrom the expected interest rate r(0) = ∑piri

to an asymptotic limit of r(�) = miin{ri}. The

moral of this story is that the Stern value mayend up being more right than wrong when fullaccounting is made for the uncertainty of thediscount rate itself, which arguably is the mostimportant uncertainty of all in the economicsof climate change. The very same force ofcompound interest that makes costs and ben-efits a century from now seem relativelyinsignificant, and that additionally creates the“majority tilt” of a pain-postponing climatepolicy ramp of emissions reductions startingfrom a low gradual base, also forces us to rec-ognize the logic that over such long periodswe should be using interest rates at the lowerend of the spectrum of possible values.

In the certain world of the Ramsey deter-ministic formula (1), there is no distinctionamong rates of return on various assets and ris just the economywide rate of return oncapital or, more succinctly, the interest rate.In nondeterministic reality, there are manyrates of return out there and they differ con-siderably. The point has already been estab-lished that it makes a tremendous differencefor long time periods of a century or morewhat interest rate is used for discounting. Tounderstand better which discount rate to use,we need to enrich the Ramsey model by for-mally introducing uncertainty, which allowsus at least to distinguish between rates ofreturn on capital from two fundamentally dif-ferent sorts of investments: a risky economy-wide rate of return applicable to investmentsthat have payoff characteristics parallel to theeconomy itself and a risk free rate of returnapplicable to investments whose payoffs areorthogonal to the economy as a whole. Afterthat, we need to decide which of these tworates is more appropriate for discountingcosts and benefits of mitigating climatechange. Then we need to plug in numbersand see what happens. The simplest formal

way to begin this process is by making thegrowth rate be a random variable.

Continuing here in the spirit of being sim-ple, suppose that the growth rate g in anygiven year is i.i.d. normal with known mean� and known variance � 2. (The fact that �and � 2 are known will later become signifi-cant when we inquire what happens undergreenhouse warming when � and � 2 aremodeled as not known.) With g ∼ N(�,� 2),the Ramsey formula (1) becomes

1(4) r f = δ + η� − − η 2� 2,2

where r f in equation (4) denotes the risk freeinterest rate. The introduction of uncertaintyalso allows consideration of a risky asset witha different rate of return. Following theasset-pricing expository literature, supposewe model comprehensive or representativeequity at a high level of abstraction as being aclaim on the consumption dividend pro-duced by the macroeconomy itself. Supposethis abstract macroeconomy is representedby a dynamic stochastic general equilibriumin the Lucas–Mehra–Prescott fruit-treemodel. Let the random variable Re be thegross arithmetic return on equity whiler e = lnRe is the more familiar geometric rateof return on equity. When g is i.i.d. N(�,� 2)in this fruit-tree economy, the equity riskpremium over the safe rate then reduces tothe well-known expression

(5) −r e − r f = �� 2,

where −r e is defined by the oblique-lookingexpected-value formula −r e ≡ lnE[Re], whichis close enough to E[r e] to make them inter-changeable for my purposes here.4Combining (5) with (4) gives the averagereturn on equity as

1(6) −r e = δ + η� − − η 2� 2 + η� 2.2


4 The formulas (4) and (5) are explained in mostgraduate-level textbooks covering asset pricing.


Extending the previous “trio of twos” param-eter values to a not-implausible knee-jerk“quartet of twos” δ = 2 percent, η = 2,E[g] = 2 percent, �[g] = 2 percent (on anannual basis, for long time series) makesvery little difference on the risk free ratebecause now r f = 5.9 percent in (4) instead ofthe previous value for “the” interest rate ofr = 6 percent in (1). The correspondingequity premium from (5) is −r e − r f = 0.1 per-cent and the average return on equity from(6) is −r e = 6 percent. The actual empiricalnumbers are closer to r f ≈ 1 percent, −r e −r f ≈ 6 percent, −r e ≈ 7 percent. (The calibra-tion r f ≈ 1 percent refers to short-termtreasury bills, while −r e ≈ 7 percent refers tooverall returns on comprehensive indexes ofpublicly traded shares of common stocks, butI don’t think the numbers would be funda-mentally different for other empirical meas-ures of returns from investments for theeconomy as a whole.) So with the not-implausible “quartet of twos” parameter val-ues the theory does a decent job ofpredicting the average return on equity butfails miserably on the risk free rate and theequity premium—thereby giving rise to thenotorious “risk free rate puzzle” and the evenmore notorious “equity premium puzzle.”

What does all of this have to do with theeconomics of climate change? Well, a lotactually. But before getting into the relation-ship between the asset-return puzzles andthe economics of climate change, we need toput the puzzling numerical mismatches tem-porarily aside in favor of first asking a funda-mental prenumerical question: in principle(leaving aside their correct numerical val-ues) should we be using the risk free rate orthe risky economywide rate of return for dis-counting costs and benefits of climatechange?

The issue of which rate of return tochoose (as between r f and −r e) for discount-ing a project comes down to the extent towhich the payoffs from the project are pro-portional to or independent from returns toinvestments for the economy as a whole. In

the oversimplified two-period formulationhere, a project to mitigate the effects ofglobal warming incurs consumption costs inthe present period by curtailing CO2e emis-sions, investing in costly new technologies,and so forth, but consumption in the futureperiod is increased by having reduced thedetrimental impacts at that time fromgreenhouse warming. The payoff is the extraconsumption available in the distant-futureperiod. Suppose that the correlation coeffi-cient between the increased output of theproject and returns to the economy as awhole is β. An investment beta is intendedto represent a correlation coefficient thatapplies to discount factors as contrastedwith discount rates (i.e., here β is the corre-lation between the investment payoff andRe, not r e). It then follows from essentiallythe same considerations as went into deriv-ing formula (3) that the relevant interestrate for discounting costs and benefits attime t here is

ln[βexp(− −r et) + (1 − β)exp(− r ft)](7) r (t) = − ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ ,t

which declines monotonically over timefrom r (0) = β−r e + (1 − β)r f to an asymptoticlimit of r (�) = r f. So the question herebecomes: what is the right β for the kinds ofprojects that the Stern Review has in mindfor mitigating global warming?

Overall damages from climate change aremodeled in most IAMs, including thePAGE model that crunches some numbersfor the Review, as a pure production exter-nality equivalent to losing output via a par-ticular subaggregator equation of themultiplicative form

(8) D(t) = Y∗(t) − Y(t) = f(ΔT(t))Y∗(t),

where t is time, D is the total damages ofgreenhouse warming, ΔT is atmospherictemperature relative to the base period, Y∗ ispotential GDP (or NDP, no distinction beingmade here) in the absence of any green-house warming, and Y is actual GDP with



greenhouse warming. The standard func-tional form actually chosen in most IAMs isf(ΔT) = k(ΔT)γ for some coefficients γ and k,where typically γ = 2 (quadratic loss in tem-perature change). The parameter k is usual-ly calibrated so as to make DY− a century henceunder mild or no abatement (withΔT ≈ 2.5˚C) be somewhere between approx-imately 0 percent and approximately 5 per-cent (depending on who is doing thecalibrating). There is no question here aboutthe value of beta implicit in the multiplica-tive formulation (8): it is one! Therefore, bythe very logic of the IAM used by the SternReview itself, the interest rate for discount-ing costs and benefits should be the returnsto the economy as a whole, −r e. This stillleaves open the question of which rate to usefor −r e—the empirical returns on a broadindex of publicly traded shares of stocks ofabout 7 percent (representing economy-wide average returns and used, e.g., by theCongressional Budget Office for evaluatingU.S. government projects) or the value of6 percent predicted by formula (5) frommy non-Stern “quartet of twos” parametervalues—but the discrepancy between 6 per-cent and 7 percent is insignificant for pur-poses here. Whatever number is used for −r e,if it in any reasonable way represents thereturns to the economy as a whole then it willcompletely undo the Review conclusionsabout drastic consumption smoothing andbring the results back to the much more mod-erate take-it-more-slowly climate-policy-ramptime profile of emissions reductions advocatedby most mainstream critics of Stern.

This important dispute about what interestrate to use for discounting costs and benefitsof mitigating greenhouse warming duplicatesthe same debate about the same subject morethan a decade ago between William R. Clineand Nordhaus, two early pioneers of model-ing the economic effects of climate change.5

Like Stern, the essentially identical earlierformulation of Cline used parameter valuesthat made the Ramsey formula (5) deliver alow interest rate—in Cline’s case the assumedparameter values were δ = 0 percent, η = 1.5,g = 1 percent, which combined to make theinterest rate be r = 1.5 percent per year. Alsolike Stern, the strong activist conclusions ofCline’s analysis fifteen years earlier tracedback to the very low discount rate beingused. Furthermore, Cline and Stern are soul-mates in their cri de coeur justifying δ ≈ 0 byrelying mostly on a priori philosopher-kingethical judgements about the immorality oftreating future generations differently fromthe current generation—instead of trying toback out what possibly more representativemembers of society than either Cline orStern might be revealing from their behavioris their implicit rate of pure time preference.An enormously important part of the “disci-pline” of economics is supposed to be thateconomists understand the differencebetween their own personal preferences forapples over oranges and the preferences ofothers for apples over oranges. Inferringsociety’s revealed preference value of δ is notan easy task in any event (here for purposesof long-term discounting, no less), but atleast a good-faith effort at such an inferencemight have gone some way towards convinc-ing the public that the economists doing thestudies are not drawing conclusions primari-ly from imposing their own value judge-ments on the rest of the world.

In part because Cline’s results, and wherethey were coming from, were more trans-parent (largely from not being buried withina big mysterious IAM, which was not yetreadily available around 1990), his studyattempted to seize the analytical highground by emphasizing that an assumedannual interest rate of r = 1.5 percent is calibration-consistent with the real return onrelatively safe U.S. Treasury bills historicallybeing about 1 percent or so per annum.Missing from Cline’s reasoning was a seriousdiscussion of the implications of risk and of


5 Cline (1992), Nordhaus (1994). See also the laterstudies and reflections on discounting for climate changecontained in Paul R. Portney and John P. Weyant (1999).


payoff correlations for the choice of a dis-count rate that might justify using r = r f.Nordhaus, whose careful pragmatic model-ing throughout his DICE series of IAMs haslong set a standard in this arena, arguedforcefully over a decade ago that the risk freeinterest rate should not be used for dis-counting costs and benefits of climatechange. In this argument, Nordhaus was fol-lowing Robert Lind who, in a comprehen-sive summary of an influential book heedited in 1984 entitled Discounting for Timeand Risk in Energy Policy, concluded that“unless there is substantial evidence to thecontrary, the returns associated with publicprojects should be assumed to be highly cor-related with returns to the economy as awhole” (p. 77).

All of this having been said, there wasnever any deep economic rationale in thefirst place for damages from greenhouse gaswarming being modeled as entering utilityfunctions through the particular reduced-form route of being a pure production exter-nality that substitutes perfectly with outputaccording to the multiplicative subaggrega-tor function (8). It was more due to an his-torical accident of stumbling upon a simpleunderstandable analytical form whoseparameters could be conveniently adjustedto match various scenarios than the result ofserious thought about whether damagesfrom global warming are better specified asmultiplicative or additive with GDP, or evenentering the utility function as a direct argu-ment (rather than substituting one-for-onewith economic output)—all of which wouldhave been seen as a secondary issue. So, withthe benefit of hindsight, let us now ask: Isthere any economic rationale by which green-house-warming damages are as much uncor-related as they are correlated with aggregateeconomic activity? The answer, when youthink about it, is yes. No one has ever tried toargue that the effects of global warming willbe evenly spread among regions of the worldor sectors of the economy. The parts of aneconomy likely to be most impacted by

global warming involve its “outdoor” aspects(broadly defined) like agriculture, coastalrecreational areas, and natural landscapes(including the existence value of ecosystems,species, and so forth). Climate-affected “out-door” activities may be differently impactedby greenhouse warming than “indoor” eco-nomic activities constituting the bulk of theeconomy, which are largely going to be dom-inated by the unknown future growth rate oflabor-augmenting technological progress.Instances of changes in “outdoor” activitiesunder global warming include what happensto tropical agriculture, losing significant partsof Bangladesh (or Florida) to rising sea lev-els, the “consumption” of an altered naturalworld that is a direct argument in the utilityfunction, and so forth. These kinds ofchanges, which include the existence value ofnatural environments, are presumably nothighly correlated with technological progressin computing power, furniture making, orbetter pharmaceuticals a century from now.The relevant share of the “outdoor” subset ofthe economy in investment-beta calculationsmight be disproportionately large because it isdisproportionately largely impacted by green-house warming. Furthermore, it might plausi-bly be argued that the high income elasticityof environmental awareness will make for ahigh existence value of unaltered natural habi-tats when per capita incomes have increasedten-fold over the course of a century or more.

What happens to the discount rate for cli-mate-change investments naturally dependson the actual value of β that is assumed. Ifβ = 0 in (7), then r(t) = r f = 1 percent. Ifβ = 1 in (7), then r(t) = −r e = 7 percent. Themore interesting question concerns whathappens to r(t) for in-between values of β.Suppose for the sake of argument we splitthe difference and imagine that the dispro-portionate impact of climate change ongeneralized-land-usage “outdoor” activitiesof the economy warrants an overall correla-tion coefficient of, say, β ≈ 0.5. With β ≈ 0.5in (7), the relevant interest rate for a centu-ry from now becomes r(100) = 1.7 pecent,



which is close to Stern’s r = 1.4 percent orCline’s earlier r = 1.5 percent. In this caseinvestments for mitigating global climatechange become attractive as an insurancepolicy that secures food supplies, preservescoastal areas, and maintains natural environ-ments in a world where future aggregategrowth rates are uncertain. I am not trying todefend this particular formulation or theparticular value β = 0.5. Rather, the moral ofthis story is that the nature of the impacts ofclimate change determine whether we shouldend up closer to using the risk-free rate or theeconomywide return on capital—and thereare plenty of stories suggesting that the rele-vant investment beta here is significantly lessthan one. When the overall discount factor isa combination of more primitive discountfactors (as is the case here when the correla-tion coefficient β is some midrange valuebetween zero and one), the risk free interestrate, which is close to the Stern interest rate,then may well end up being more right thanwrong. Over a time horizon of a century orso, this “midrange β effect,” which is notimplausible when one considers the highly-uneven impacts of greenhouse warming onthe different regions and sectors of the worldeconomy, can be a strong factor in loweringdiscounting rates significantly—from thesame underlying analytical source as theforce of compound interest and the logic ofthe climate-policy ramp. Remarkably, thebig IAMs with their casually built-in specifi-cation of β ≈ 1 obscure rather than clarifythe critical role in climate-change analysis ofassumptions about investment betas.

Next, suppose we try to repeat the abovenumerical exercise but in place of the empir-ical values r f = 1 percent, −r e = 7 percent, weuse the values predicted by the theoreticalformulas via assuming the quartet of twosparameter values, which then implies r f = 5.9percent from (4) and −r e = 6 percent from (6).Because the equity premium predictedfrom (5) is a miniscule 0.1 percent, there isessentially no difference in this casebetween r f = 5.9 percent and −r e = 6 percent.

The relevant discounting rate r(t) from (7)then lies between 5.9 percent and 6 percentindependent of the assumed value of β.When 5.9 percent ≤ r(t) ≤ 6 percent, theReview conclusions are again undone andthe more orthodox mainstream policies ofmoderate greenhouse gas slowing in thenear future come back. The practical ques-tion of what interest rate to use for discount-ing costs and benefits of climate change thusbecomes intertwined with the interpretationof the equity premium and risk free ratepuzzles. It is a measure of how deep andserious these puzzles are that even afterthousands of articles there is still no agreed-upon resolution of them. If we use numbersthat resolve the puzzles in the descriptivedirection, then r is sensitive to β and r ≈ 1.7percent for β = 0.5. If we use numbers thatresolve the asset-return puzzles in the pre-scriptive direction, then r ≈ 6 percent inde-pendent of β. And, to whip a horse longdead, it makes a huge difference to the eco-nomics of climate change whether r ≈ 1.7percent or r ≈ 6 percent.

Critics of the Stern Review are fond ofpointing out that δ ≈ 0, η ≈ 1 is inconsistentwith observed economic behavior, especial-ly savings behavior. While this is true, andit is a genuine problem for Stern, it is justthe tip of an iceberg that threatens all suchformulations—not just Stern’s. The biggestand most troubling disconnect between theprescriptive numbers that theory says weshould be using for discounting and thedescriptive discount-rate numbers that areactually out there concerns the asset-returnpuzzles. These puzzles very strongly suggestthat something fundamental is amiss in theparadigm framework for pricing assets andderiving the rates of return that we are rely-ing upon to produce discount rates for eval-uating new investment opportunities. Forexample, perhaps the taste parameters δ andη that we are commonly using (here δ = 2percent p.a. and η = 2 ) are wrong. If wetreat (4) and (5) as two equations in twounknowns (δ and η), we can then invert the



two equations to back out the hypotheticalvalues δ̂ and η̂ that would “explain” the stylized-fact empirical observation that r f ≈ 1percent and −r e − r f ≈ 6 percent. When this isdone (for � = 2 percent, � = 2 percent), itproduces the mega-puzzle that the estimat-ed rate of pure time preference is δ̂ ≈ 151percent per year and the coefficient of rela-tive risk aversion is η̂ ≈ 150. One does notknow whether to laugh or to cry at theprospect of what the Stern Review IAMmight end up recommending as its preferredpolicy for climate change in its number-crunching simulations if the parameter val-ues δ̂ ≈ 151 percent, η̂ ≈ 150 were fed intoPAGE. So much for the fantasy that values ofthe taste parameters δ and η should be chosento be consistent with the revealed-preferenceobserved stylized facts of economic behavior!

At the end of the day, where do thesedizzying and disconcerting numerical exercis-es leave us with respect to the economics ofclimate change? One inescapably strong con-clusion is that the emissions reductions thatgo along with optimal growth under endoge-nous climate change are extraordinarily sensi-tive to the interest rate that has implicitlybeen built into whatever model is being usedfor the analysis. The present discounted valueof a future cost (or benefit) is the product ofan imposed discount factor times the project-ed future cost (or benefit). Trying to forecastcosts and benefits of climate change scenariosa hundred years or so from now is more theart of inspired guesstimating by analogy thana science (imagine forecasting today’s world acentury ago). But in my opinion the unsureprediction of future costs and benefits of cli-mate change a century or two hence is over-shadowed by the unsure interest rate to usein the discount factor, which makes the dis-count factor more uncertain than predictedcosts (or benefits) of climate change by aboutan order of magnitude. Of the two multipli-cands in the product of a discount factortimes an expected cost (or benefit), empiri-cally it is the discount-factor uncertainty thatlooms much larger in practice for analyzing

climate-change-affected events a century orso from now.

4. Uncertainty Tends to Matter Much Morethan Risk

If the conclusion from the last section—thatwhat to do about global warming dependsoverwhelmingly on the imposed interestrate—is seen as disappointing, then a secondconclusion is likely to seem downrightunnerving. As noted, the choice of appropri-ate discount rate is itself extraordinarily sen-sitive to seemingly arcane modeling detailslike the value of the climate-change invest-ment beta and how the asset-return puzzlesare resolved. One interpretation of the asset-return puzzles, which could also have somerelevance for the economics of climatechange, is the idea that investors are dispro-portionately afraid of rare disasters. Theserare disasters are not fully reflected in theavailable data samples that, being limited,are naturally deficient in coverage. Besides,even if we had an infinite time series of pastobservations, they are of restricted relevancein an evolving world whose features arealways changing and whose past never fullyrepeats itself. With this interpretation of thepuzzles, people are willing to pay high pre-miums for relatively safe stores of value thatmight represent “catastrophe insurance”against out-of-sample or newly evolved raredisasters.6 Such an ongoing catastrophe-insurance effect could readily explain whyobserved r f is so low relative to the observedpast average of realized r e.

There is little doubt that the worst-casescenarios of global-warming catastrophes aregenuinely frightening. The Stern Reviewgoes over several of these highly unlikely,poorly understood threshold-crossing disas-ters associated with abrupt large-scale irre-versible changes in the climate system:


6 The theme of catastrophe insurance and the underly-ing motivation for the treatment of structural uncertaintyas tail thickening of posterior-predictive distributions isdeveloped in Martin L. Weitzman (forthcoming).


sudden collapse of the Greenland and WestAntarctica ice sheets, weakening or evenreversal of thermohaline circulations thatmight radically affect such things as theGulf Stream and European climate, run-away climate-sensitivity amplification ofglobal warming due to positive-reinforcingmultiplier feedbacks (including, but not lim-ited to, loss of polar albedo, weakened car-bon sinks, and rapid releases of methanefrom the thawing of arctic permafrost).More gradual but still very serious examplesof uncertain climate-change effects are: sea-level dynamics, drowned coastlines ofunknown magnitude, very different and pos-sibly extreme weather patterns includingdroughts and floods, ecosystem destruction,mass species extinctions, big changes inworldwide precipitation patterns and distri-bution of fresh water, tropical-crop failures,large-scale migrations of human populations,humidity-nourished contagious diseases—andthe list goes on and on.

Translated into the language of the simplemodel used here, such rare disasters are farout in the right tail of very high ΔT, whichcorresponds to being far out in the left tail ofthe consumption-growth random variable g.The probability distribution of long-run ΔTis disturbingly spread apart, largely becauseof structural-parameter uncertainty aboutthe unknown “climate sensitivity” multiplierthat amplifies greenhouse gas concentra-tions into ultimate steady-state greenhousewarming. The recently released FourthAssessment Report of the IPCC (2007) pre-dicts for one hundred years from now amean temperature change of further plane-tary warming (from averaging six “equallysound” marker scenarios) of E[ΔT] = 2.8˚Cwith a thick-tailed upper-end standard devi-ation ≈ 1.6˚C (table SPM-3). This means theprobability that ΔT > 4.5˚C is approximately15 percent and the probability of ΔT > 6˚C isvery roughly about 3 percent. IPCC does notextend its projections beyond 2105 on thebasis that predictions into the twenty-secondcentury are too uncertain, but it seems

unavoidable that the reduced-form probabil-ity of ΔT > 6˚C increases substantially above3 percent after the next century just fromthe enormous inertial lags for what by thenwill be in the climate-change pipeline.Societies and ecosystems whose averagetemperature has changed in the course of acentury or so by ΔT > 6˚C (for U.S. readers:Δ6˚C ≈ Δ11˚F) are located in the terra incog-nita of what any honest economic modelerwould have to admit is a planet Earth recon-figured as science fiction, since such hightemperatures have not existed for some tensof millions of years.

The idea behind analyzing climate-change projects by converting future costsand benefits into present discounted valuesis that society has alternative investmentopportunities, whose proxy rate of return isthe discount rate, representing alternativecapital-accumulation opportunities through-out the rest of the economy that wouldcompensate us for the economic losses suf-fered from climate change. Human-capitalinvestments in education or public healthhave consistently been found to have highrates of return, arguably far greater than 10percent for less-developed countries andregions. More mundane examples of alter-natives to CO2e mitigation from middle-of-the-probability-distribution mild warmingmight include accumulating air conditionersto counter high temperatures or erectingsea walls to keep the rising ocean out ofcoastal cities. Such alterative investmentscompensate mostly for potential loss of“indoor” consumption and they tend to be alot less expensive than wholesale abatementof greenhouse gases. The real problem is inthe tails and it mostly concerns “outdoor”consumption. If the definition of consump-tion is broadened (as it should be) toinclude nonmarket enjoyment of the naturalenvironment—like habitats, ecosystems,and species—then it is difficult to imaginewhat the compensating investments are forwhich we should now be saving more as analternative that might substitute for holding



down ΔT directly. With roughly 3 percentIPCC-4 probability, we will “consume” aterra incognita biosphere within a hundredyears whose mass species extinctions, radicalalterations of natural environments, andother extreme outdoor consequences of adifferent planet will have been triggered bya geologically-instantaneous temperaturechange that is significantly larger than whatseparates us now from past ice ages.

In the rest of this paper, marginal analysisis set aside and g stands for the unknowngrowth rate of a comprehensive future “con-sumption” that includes the consumption ofnatural environments, ecosystems, species,and the like. The cost of low-g disasters fromhigh-ΔT scenarios more properly constitutesuncertainty in the sense of Knight or Keynesthan risk, because the scale and probabilityof these disasters are both unknown. Notonly is it very difficult to estimate tail proba-bilities of high-ΔT outcomes—due, ultimate-ly, to the underlying sampling-theoryprinciple that the rarer is an event the moreunsure is our estimate of its probability—buttranslating this into g-equivalent economic-damage units introduces enormous furtherfuzziness, especially when g includes exis-tence values of natural habitats. With an evo-lutionary stochastic process like globalclimate change, the world is not standing stilllong enough for us to accumulate the rele-vant information to accurately assess tailprobabilities. The net result is thicker lefttails for the distribution of g under dynami-cally evolving global climate change than weare accustomed to dealing with in our muchmore familiar dynamic stochastic generalequilibrium macro models, which in practiceare based upon the stationary thin-tailed sto-chastic processes that we use to model arational expectations equilibrium whosestructure is (supposedly) fully known andunderstood.

Every cost–benefit analysis is an exercisein subjective uncertainty. If, as the SternReview puts it, “climate change is the great-est externality the world has ever seen,” then

a cost–benefit calculation of what to doabout it is the greatest exercise in Bayesiandecision theory that we economists have everperformed. Formally, of course, cost–benefitanalysis can deal with uncertainty—by takingexpected values, relying on expected-utilitytheory, accounting for risk aversion, andusing all of the other, by now familiar, para-phernalia of the modern theory of the eco-nomics of uncertainty. In principle, it doesnot matter whether the probabilities thatshow up in our cost–benefit calculations areobjective or subjective because the mathe-matical formulas are the same for eithercase. But in lumping together objective andsubjective uncertainties and thereby obscur-ing their distinction—to the extent that agraduate student today hardly knows, oreven cares, what kinds of probabilities arelegitimate to plug into a rational expectationsequilibrium and what kinds of probabilitiesare illegitimate for such purposes—I thinkthat contemporary macroeconomics goes toofar and leads to a mindset that too easilyidentifies probability (and “economic sci-ence”) with exercises in calibration to samplefrequencies from past data.

I do not propose to rehash here the ages-old, never-resolved foundational controversyabout whether probabilities are better con-ceptualized on the most fundamental level asobjective frequencies or subjective beliefs.Personally, I do not think there exists a purecase of either extreme pole, but rather thereis a continuum of situations with some beingcloser for practical modeling purposes to theobjective pole and others being closer forpractical modeling purposes to the subjec-tive pole. Here I just want to point out that ifsomething like radioactive decay is close tobeing a pure case of objective frequencies,then climate change, and especially the eco-nomics of climate change, is as close to beinga pure case of modeling probabilities by sub-jective judgements as we economists areever likely to encounter in practice. To para-phrase the language of the Stern Review yetagain, the economics of climate change is the



greatest application of subjective uncertaintytheory the world has ever seen.

To the extent that it makes any sense at allto think in terms of some approximately bell-shaped meta-distribution of growth rates gthat is out there, the part of the probabilitydistribution that corresponds most closely toobjective-frequency risk is in its body aroundthe middle because, from previous experi-ence, past observations, plausible extrapola-tions, and maybe even the law of largenumbers, we have at least some modicum ofconfidence in being able to construct a rea-sonable approximation of the central regionsof the probability distribution. As we movetoward probabilities in the tails of the g dis-tribution, however, we are increasingly mov-ing into the unknown territory of subjectiveuncertainty where our probability estimatesof the probability distributions themselvesbecomes increasingly diffuse because thefrequencies of rare events in the tails cannotbe pinned down by previous experiences,past observations, or computer simulations.The upshot of this uncertainty about uncer-tainties is that the reduced-form probabilitydistribution of g (after integrating out theprobabilities of probabilities)—which is areduced form for the economics of climatechange in the sense that g here is the growthrate of comprehensive consumption thatincludes the natural environment—has athick left tail. The exact thickness of this lefttail of g depends not only upon how bad anenvironmental catastrophe global warmingmight induce and with what probabilities,but also upon how imprecise are our prob-ability estimates of the probabilities ofthose bad catastrophes. Uneasiness aboutprojecting uncertain uncertainties preventsIPCC and most economic analyses fromtaking a stand on the increasing—andincreasingly diffuse—probabilities of extremetemperatures after the year 2105, whichhardly eliminates the underlying problem.Mitigating the future consequences ofgreenhouse warming does not just shift thecenter of the distribution of g to the right

but, far more importantly in this context, itthins the left tail of the distribution as well.

The thickened tails of the reduced formof the distribution of g that are an inevitableconsequence of taking expectations ofexpectations can have surprisingly strongeffects on cost–benefit calculations by low-ering significantly expected utility and rais-ing significantly expected marginal utility.To get a sense of just how strong the effectcan be of tails thickened by having structur-al parameters that we do not know butwhose values must be inferred indirectlyfrom limited experience—and therefore asense of how much we could be missing inour economic analysis by ignoring the terraincognita of the greenhouse-warmingextremes—consider this prosaic example.Suppose that in the good old days before weunderstood human-induced climate changewe were sure that g ∼ N(�,� 2), where wesomehow knew that � = 2 percent and � = 2percent. Normalize current marginal utilityto be unity. Then from using the familiar for-mula for the expectation of a lognormallydistributed random variable, the expectedmarginal utility of an extra sure unit of con-sumption in the pre-climate-change erawould have been EMU = E[exp(− ηg)] =exp(− η� + 1

2−η 2� 2). (It is precisely this kind ofcalculation that lies behind the risk free rateand equity-premium formulas (4) and (5).)

Imagine next that the possibility of green-house warming has now made us unsureabout � and �. Let us preliminarily modelthis greenhouse-warming-induced uncertainsituation, where we don’t know the true val-ues of � and � because of limited experiencewith climate change, as if we are limitedbecause we only have data from some finitenumber n of past observations (or finite sim-ulation outcomes from the data generatingprocess of some model) and we run a regres-sion to estimate � and �. For simplicity, sup-pose further that the point estimates �̂ = 2percent and �̂ = 2 percent from this regres-sion just so happen to be the very same num-bers as the presumed-known population



parameters for the normal distributionbefore climate change was understood to bea possibility. Then the reduced-form situa-tion is as if g is distributed as a Student-t dis-tribution with n − 1 degrees of freedom. TheStudent-t here has the same mean as thenormal and for large n has almost the samestandard deviation, but if you look closelywith a magnifying glass its tails are naturallythickened due to the “true” values of thestructural parameters � and � being uncer-tain. This kind of structural uncertaintyabout the parameters of the probability dis-tribution spreads apart the reduced-form(“predictive posterior” in Bayesian jargon)distribution of g, an effect that is especiallypronounced in the thickened tails becausethey are especially difficult to learn about. Ifwe now calculate the expected marginal util-ity of an extra sure unit of consumption usingthis Student-t distribution (which is a naturalmanifestation of limited experience or limit-ed information), then EMU = E[exp(−ηg)] = + �, which is mathematically equiva-lent to the fact that the moment generatingfunction of a Student-t distribution is infi-nite. The bombshell fact that EMU = + � (assoon as we admit that we don’t know theunderlying stochastic structure, and there-fore parameters must be estimated) changesthe rules of the game. Such a mechanism,for example, explains the asset-return puz-zles for reasonable values of δ and η as beingdue to a fear of relatively rare tail disastersthat is theoretically difficult or impossible toeliminate when the underlying tail-structureremains uncertain. The fact that understructural uncertainty EMU = + � representsa mathematically generic result not limitedto isoelastic utility or the normal parent dis-tribution and Student-t child distribution ofthe example. I claim this general result hassignificant economic repercussions whichare not easily brushed aside, not least of allfor cost–benefit analysis of climate changebecause such an effect in principle over-shadows the discounting of far-futureevents.

There is a general point here and a partic-ular application to the economics of climatechange. The general point is that from expe-rience alone one cannot acquire sufficientlyaccurate information about the probabilitiesof tail disasters to prevent the expected mar-ginal utility of an extra sure unit of consump-tion from becoming unbounded for anyutility function having everywhere-positiverelative risk aversion, thereby effortlesslydriving cost-benefit applications of expectedutility theory. The degree to which this kindof “generalized precautionary principle” isrelevant in a particular application must bedecided on a case-by-case basis thatdepends upon the extent to which a prioriknowledge in a particular case limits theextent of posterior-predictive tail thickening.In the particular application to the econom-ics of climate change, where there is so obvi-ously limited data and limited informationabout the global catastrophic reach of cli-mate extremes for the case ΔT > 6˚C, toignore or suppress the significance of raretail disasters is to ignore or suppress whateconomic theory is telling us loudly andclearly is potentially the most important partof the analysis. While it is always fair game tochallenge the assumptions of a model, wheneconomic theory provides a generic result(like “free trade is Pareto optimal”) the bur-den of proof is commonly taken as resting onwhomever wants to overturn the theorem ina particular application. The take-away mes-sage here is that the burden of proof in theeconomics of climate change is presumptive-ly upon whomever wants to model optimal-expected-utility growth under endogenousgreenhouse warming without having structur-al uncertainty tending to matter much morethan risk. Such a middle-of-the-distributionmodeler needs to explain why theinescapably thickened tails of the posterior-predictive distribution, for which the thickleft tail of g represents rare disasters underuncertain structure, is not the primary focusof attention and does not play the decisiverole in the analysis.



5. Climate Uncertainty and the Value ofInformation

Because the Stern Review is imbued withthe laudable moral imperative of not expos-ing future generations to the tribulations ofglobal warming, it does not shy away fromemphasizing (at least discursively in its “mul-tidimensional” text) the possibilities of rarehigh-ΔT, low-g catastrophes from climatechange. Indeed, reading between the linesof the report, one has the feeling that theimmorality of relegating future generationsto live under the shadow of the open-endedpossibilities of uncertain large-scale changesin the climate system, when for a mereannuity cost of a percent or two (or at mostthree) of GDP each year we might have pur-chased an insurance policy on their behalfthat avoided this scary uncertainty (or atleast greatly reduced it), is a major underly-ing leitmotif of the Review. This feeling ofguilt has no place to go analytically (underthe conventional analytical confines adoptedby the IAMs, including PAGE), so to speak,except to be subliminally channelled intochoosing such low values of δ ≈ 0 and ofη ≈ 1 (and, secondarily, such high values of DY− ≈ 5 percent and low values of C

Y− ≈ 1 per-cent) as will operate through the back doorof conventional economic analysis to weightpresent-discounted future damages highenough relative to present mitigation coststo make the IAM want to reduce substan-tially the disastrous possibilities. The Reviewputs it directly: “Averaging across possibili-ties conceals risks. The risks of outcomesmuch worse than expected are very real andthey could be catastrophic. Policy on climatechange is in large measure about reducingthese risks. They cannot be fully eliminated,but they can be substantially reduced. Sucha modeling framework has to take account ofethical judgements on the distribution ofincome and how to treat future generations.”

The “ethical judgements” in the abovequote about “how to treat future genera-tions” is Stern-speak for picking δ ≈ 0, while

the “ethical judgements on the distributionof income” is Stern-speak for picking η ≈ 1.Such “ethical judgements” could appear toan uncharitable critic as if designed to justi-fy the activist conclusions that are consid-ered necessary to avoid the climate-changehorror scenarios. In the context of its self-imposed “multidimensional” methodology,by choosing η ≈ 1 the Review appears to beplaying both sides of the street against themiddle. On the one hand, it wants η to be ashigh as possible to reflect its tremendoushumanitarian concern with distributionalinequities across space, which would allow itto argue (informally, if passionately, in scat-tered prose and numerical examples) that thedisproportionate negative impact of climatechange on the world’s poor (whose marginalutility is high because η in this story isimplicitly large) calls for urgent action nowto avoid future massive spatial redistributionof relative income from the poor to the rich.Simultaneously, the Stern Review wants tofurther exacerbate distributional inequitiesby redistributing income across time fromthe relatively poor present to the much-richer future a century or two from now(when standards of living are likely to be tentimes higher) via—an uncharitable criticmight suspect—choosing the lowest imagi-nable value η ≈ 1 that might be used (alongwith δ ≈ 0) to reverse-engineer the really lowr needed to prop up its technical case forimmediate urgent action. The same contra-diction about values of η shows itself inStern’s heuristic justification for big values ofprobability-weighted D

Y− as being due, ineffect, to a risk-averse high-curvature high-ηutility function interacting with highlyuncertain damages.

I think that rather than trying to gothough the back door with unreasonably lowvalues of δ and η (or, secondarily, “averagingacross possibilities” by heuristically makingbusiness-as-usual D

Y− ≥ 5 percent instead ofsome smaller more plausible point estimate),it is much better to go directly through thefront door with the legitimate concern that



there is a chance, whose subjective probabil-ity is small but diffuse (thereby resulting in adangerously thickened left tail of compre-hensive consumption growth rates), thatglobal warming may eventually cause disas-trous temperatures and environmentalcatastrophes. If one accepts that global cli-mate change is as likely an arena as any for avalid application of the general principle thatthickened tails from uncertain structuralparameters must dominate expected dis-counted utility calculations, then many hardquestions need to be asked. What are earlywarning signs of impending runaway envi-ronmental disasters like melting ice sheets,thermohaline inversions, or just plain know-ing beforehand that we are on a trajectorytoward ΔT > 6˚C? How much would it cost toput in place the very best system of sensorsthat money can buy for detecting early-warn-ing signals of impending climate catastro-phes? How early might the warning frommonitoring systems be before the full effectsare felt? What could we do as an emergencyresponse if we received such early-warningsignals? Would last-ditch emergency geo-engineering measures to ward off disaster byreversing the worst consequences of globalwarming be available in time to help? (Suchemergency measures are likely to be soextreme as to be defensible only for an evenmore extreme environmental catastrophe inthe making—perhaps they might includepainting all human-made structures on theplanet reflective white and creating a“Pinatubo effect” by seeding the upperatmosphere with metallic dust or aerosols.7)Could such last-ditch measures be madereversible by building in decay mechanisms,as with sulfate aerosols, while we then usedthe new information to really undertake dra-conian measures to cut greenhouse gas emis-sions drastically? Are there other aerosolprecursors than sulfates with possibly betterenvironmental properties? Can the public

embrace the currently politically incorrectidea, which is a third rail few policymakersdare to touch and Stern doesn’t even men-tion, that in the extremely unlikely event of atruly extraordinary unfolding disaster itmight be a good emergency-backup plan topurposely geoengineer spaceship Earth toreverse previous inadvertent geoengineeringfrom burning too much fossil fuel? Or, per-haps more to the point here, can anyoneimagine how the public would not embracesuch an idea and demand that we should doall in our power to avert a climate-change-induced catastrophe at some hypotheticalfuture time when environmental disasterseems imminent? And how does the tail thick-ness of climate-change disasters comparewith the tail thickness of aerosol geoengi-neering, or the tail thickness inherent inwidespread nuclear power possibly goingawry, or the tail thickness of massive sudden-release mishaps from buried-CO2 sequestra-tion because some remote “hypothetical”materialized?

I trust that a few readers may be able tothink of more such questions about the realoption value of waiting to gather information(and the empirical issue of what to do aboutit), some of which might hopefully be moregrounded in reality than my highly specula-tive examples. Whether or not my particularhypothetical stories are realistic, these kindsof questions become relevant once the focusof the economics of climate change shiftsfrom the middle range of the distribution ofwhat might happen with ΔT at a IPCC-4mean of ≈ 2.8˚C a hundred years hence tothinking more about what might be in thetails with ΔT > 6˚C, which is just two IPCC-4 standard deviations out for a century fromnow, meaning a probability ≈ 3 percent (andpresumably a yet higher probability after2105). This thick tail is where most of thecost–benefit action may well be even if—orperhaps precisely because—our estimates ofthe probabilities involved are themselvesso highly uncertain. Anything is possible inthe tails of a nondogmatic distribution.


7 On the feasible use of sulfate aerosol precursors toreverse global warming, see T. M. L. Wigley (2006).


(“Nondogmatic” in Bayesian parlance justmeans that no event is ruled out a priori byhaving been assigned zero probability in theprior distribution.) A responsible policyapproach neither dismisses the horror sto-ries just because they are two standard devi-ations away from what is likely nor getsstampeded into overemphasizing falsedichotomies as if we must make costly all-or-nothing investment decisions right now toavoid theoretically possible horrible outcomesin the distant future.

In my opinion, public policy on greenhousewarming needs desperately to steer a middlecourse, which is not yet there, for dealingwith possible climate-change disasters. Thismiddle course combines the gradualist climate-policy ramp of ever-tighter green-house gas reductions that comes from main-stream mid-probability-distribution analysis(under reasonable parameter values) with theoption value of waiting for better informationabout the thick-tailed disasters. It takes seri-ously whether or not possibilities exist forfinding out beforehand that we are on a run-away-climate trajectory and—without “leav-ing it all up to geoengineering”—confrontshonestly the possible options of undertakingcurrently politically incorrect emergencymeasures if a worst-case nightmare trajecto-ry happens to materialize. The overarchingconcern of such a middle course is to be con-structive by having some semblance of agame plan for dealing realistically with whatmight conceivably be coming down the road.The point is to supplement mainstream eco-nomic analysis of climate change (and main-stream ramped-up mitigation policies fordealing with it) by putting serious researchdollars into early detection of rare disastersand by beginning a major public dialogueabout contingency planning for worst-casescenarios perhaps akin to the way Americans(at their best) might debate the pros andcons of an anti-ICBM early warning system.It may well turn out that the option value ofwaiting for better information about cata-strophic tail events is negligible because

early detection is impossible, or it is tooexpensive, or it comes too late (this is Stern’sline, and it might, or might not, happen to betrue), or because nothing practical can bedone about reversing greenhouse warminganyway—so we should stop stalling and startmaking serious down payments on catastro-phe insurance by cutting CO2e emissionsdrastically. But these are conclusions weneed to reach empirically, rather than pre-judging them initially. Instead of declaringimmediate all-out war on greenhouse gasemissions as advocated by Stern, maybe wewould do better by steadily but surely ramp-ing up greenhouse gas cuts over the nextdecade or two while simultaneously investi-gating seriously the nature of the runaway-climate disasters in the thick tails and whatmight be done realistically about them shouldthey start to materialize. We can always comeback in ten or twenty years time and declareall-out war on global-warming emissionsthen—if we then think it is the best optionamong a better-studied reasonably consid-ered portfolio of possible options.

Until we start seriously posing and tryingto answer tough questions about rare global-warming catastrophes, we will not make realprogress in dealing constructively with thenightmare scenarios and we will continue tocope with them inadequately by trying toshoehorn disaster policy into an either-orresponse category where it won’t fit. TheStern Review has its heart in the rightplace—it is not nice for us to play the role ofnature’s grim reaper by bequeathing theenormously unsettling uncertainty of a verysmall, but essentially unknown (and perhapsunknowable), probability of a planet Earththat in hindsight we allowed to get wreckedon our watch. However, Stern does not fol-low through formally on this really unsettlingpart of the global warming equation (which agenerous interpretation of its not-convincingeconomic analysis might say is the underly-ing motivation for its overall alarmist tone)except indirectly, by choosing δ ≈ 0, η ≈ 1, DY− ≈ 5 percent, C

Y− ≈ 1 percent (which an



ungenerous interpretation might say isreverse-engineering the drastic slowingmeasures that the Review wants to imposeon greenhouse gas emissions to neutralizethe nightmare scenarios). I don’t mean toimply that there is some off-the-shelfturnkey consensus model of the economicsof uncertain catastrophes that the SternReview was negligent in not using or thatsuch a model would (or should) provideammunition for an excuse not to undertakeserious action soon to slow greenhouse emis-sions. We just don’t yet know and we needbadly to find out. The overarching problemis that we lack a commonly accepted usableeconomic framework for dealing with thesekinds of thick-tailed extreme disasters,whose probability distributions are inherent-ly difficult to estimate (which is why the tailsmust be thick in the first place). But I thinkprogress begins by recognizing that the hid-den core meaning of Stern vs. Critics may beabout tails vs. middle and about catastropheinsurance vs. consumption smoothing.

6. Getting it Right for the Wrong Reasons?

The Stern Review is a political document—in Keynes’s phrase an essay in persuasion—atleast as much as it is an economic analysisand, in fairness, it needs ultimately to bejudged by both standards. To its great credit,the Review supports very strongly the politi-cally unpalatable idea, which no democraticpolitician planning to remain in office any-where wants to hear, that (however it is pack-aged and whatever spin is put on it)substantial carbon taxes must be leviedbecause energy users need desperately tostart confronting the expensive reality thatburning carbon has a significant externalitycost that ought to be taken into account bybeing charged full freight for doing it. (This isthe most central “inconvenient truth” of all,which was conveniently ignored in Al Gore’saward-winning film.) An entire chapter 22 inStern, entitled “Creating a Global Price forCarbon,” is devoted to this theme. As the

Review puts it, “the pricing of carbon, imple-mented through tax, trading, or regulation,”is “required for an effective global response”(p. xvii). One can only wish that U.S. politicalleaders might have the wisdom to understandand the courage to act upon the breathtak-ingly simple vision that steady pressure fromthe predictable presence of a high carbonprice reflecting social costs (whetherimposed directly through taxes or indirectlyvia tradable permits) would do more tounleash the decentralized power of capitalis-tic American inventive genius on the problemof researching, developing, and finally invest-ing in economically efficient carbon-avoidingalternative technologies than all of the piece-meal command-and-control standards andpatchwork subsidies making the rounds inWashington these days.

As we have seen, on the economic-analysisside the Stern Review predetermines theoutcome in favor of strong immediate actionto curtail greenhouse gas emissions by creat-ing a very low value of r ≈ 1.4 percent via theindirect route of picking point-estimateparameter values δ ≈ 0 and η ≈ 1 that aremore like theoretically reasoned extremelower bounds than empirically plausible esti-mates of representative tastes. But we havealso seen that a fair recognition of the truththat we are genuinely uncertain about whatinterest rate should be used to discount costsand benefits of climate changes a centuryfrom now brings discounting rates downfrom conventional values r ≈ 6 − 7 percent tomuch lower values of perhaps r ≈ 2 − 4 per-cent, which would create a more intermedi-ate sense of urgency somewhere betweenwhat the Stern Review is advocating and themore modest measures to slow global warm-ing advocated by many of its critics. Theimportant remaining caveat is that such anintermediate position is still grounded in aconventional consumption-smoothing ap-proach to the economic analysis of climatechange that avoids formally confronting theissue of what to do about catastrophe insur-ance against the possibility of thick-tailed



rare disasters, which from first principles ofeconomic–statistical reasoning presumptivelydrive expected discounted utility outcomes.

In conclusion, I think the Stern Reviewdeserves credit for effectively raising thelevel of public discourse—by increasing gen-eral awareness that climate change is a seri-ous issue which should be taken seriously, byarguing cogently for what is effectively aglobal carbon tax as an essential componentof any reasonable solution, by openly dis-cussing adaptation to climate change (as wellas mitigation), and by popularizing for awider audience than economists the ideathat economic analysis of costs and benefitsmight be a useful legitimate method forevaluating policies to mitigate global warm-ing. I think also that Stern deserves somemeasure of credit for elevating to promi-nence the problem of genuine uncertaintyconcerning rare but dangerous climate dis-asters, about which decisions must be madebut whose scale and probability cannot beknown precisely. However, in my opinion,Stern deserves a measure of discredit forgiving readers an authoritative-lookingimpression that seemingly objective best-available-practice professional economicanalysis robustly supports its conclusions,instead of more openly disclosing the fullextent to which the Review’s radical policyrecommendations depend upon controver-sial extreme assumptions and unconvention-al discount rates that most mainstreameconomists would consider much too low. Ican’t help but feel after reading the Reviewthat its urgent tone of morality and alarmcomes not from the chapter 6 aggregativeeconomic modeling of climate-changeimpacts, which deservedly has drawn strongcriticism from economists, but more from anot formally articulated fear of what mightpotentially be out there with greenhousewarming in (using my own ponderous termi-nology here to make sure my expression isexact) the inherently thickened left tail ofthe reduced-form posterior-predictive prob-ability distribution of the growth rate of a

comprehensive measure of consumptionthat includes the natural environment. Ihave argued that this inherently thickenedleft tail of g is an important aspect of theeconomics of climate change that every ana-lyst—Stern and the critics of Stern—mightdo well to try to address more directly.History will judge whether the economicanalysis of the Stern Review ended up beingmore wrong or more right and, if it was moreright, whether as pure economic reasoning itwas right for the right reasons or it was rightfor the wrong reasons.

REFERENCES

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Intergovernmental Panel on Climate Change. 2007.Climate Change 2007: The Physical Science Basis:Summary for Policy Makers. http://www.ipcc.ch.

Kelly, David L., and Charles D. Kolstad. 1999.“Integrated Assessment Models for Climate ChangeControl.” In The International Yearbook ofEnvironmental and Resource Economics: 1999/2000:A Survey of Current Issues, ed. H. Folmer and T.Tietenberg. Cheltenham, U.K. and Northampton,Mass.: Elgar, 171–97.

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Maddison, David. 2006. “Further Comments on theStern Review.” http://www.economics.bham.ac.uk/maddison/Stern%20Comments.pdf.

Mendelsohn, Robert O. 2007. “A Critique of the SternReport.” Regulation, 29(4): 40–47.

Nordhaus, William D. 1994. Managing the GlobalCommons: The Economics of Climate Change.Cambridge, Mass. and London: MIT Press.

Nordhaus, William D. 2007. “A Review of the SternReview on the Economics of Climate Change.”Journal of Economic Literature, 45(3): 686–702.

Portney, Paul R., and John P. Weyant, eds. 1999.Discounting and Intergenerational Equity. Wash-ington, D.C.: Resources for the Future.

Tol, Richard S. J., and Gary W. Yohe. 2006. “A Reviewof the Stern Review.” World Economics, 7(4): 233–50.

Weitzman, Martin L. Forthcoming. “SubjectiveExpectations and Asset-Return Puzzles.” AmericanEconomic Review.

Wigley, T. M. L. 2006. “A Combined Migration/Geoengineering Approach to Climate Stabilization.”Science, 314(5798): 452–54.



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A Review of The Stern Review on the Economics of Climate ... · known to insiders in the economics of climate change, but it needs to be more widely appre-ciated by economists at