Vol. XLV (September 2007), pp. 703 - PDF document

Vol. XLV (September 2007), pp. 703Ð724ARTINfundamental notions as risk, uncertainty, andknow it, what we donÕt know, and why wedonÕt know it.and a distinguished public servant. WeighingWeitzman: Harvard University. For helpful detailedcomments on earlier drafts of this paper, but withoutRichard Cooper, Stephen DeCanio, HowardSolow, Nicholas Stern, Lawrence Summers, and HalVarian. Õs formal analysis, but this essay points out that we are actual-Õs second basic strand is a moreties that are difficult to quantify. Concerning this uncertainty aspect, I argue that itÕs conclusions. The basic issue here is that spending money to slow global sep07_Article4 PM 703 in a reader-friendly format. The To make a long story short, the activity, later in this century and in the next, Revolution.) This would make temperaturesRevolution.) This would make temperaturesT]2ûCand would (hopefully) stabilize future tem-peratures permanently thereafter at3ûC. By ualmajoritarian optimal trajectories COmajoritarian optimal trajectories COT]2.5ûCÑwith temperaturesexpected to continue rising to well aboveE[T]3ûC afteryear 2105. To accomplishÕs ambitious goal, greenhouse gasless immediately. Which brings us to a cen-Õs results come from choosing a very lowbe a priority of research. To anticipate myJournal of Economic Literature, Vol. XLV (September 2007) sep07_Article4 PM 704 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).misuses) PAGE is contained in David Maddison (2006).PAGE itself is described in Chris Hope (2006). Õs formal analysis, IÕs informal emphasisInterest Rates and Long-Termof climate change. But far more crucially,policy rampÓ of ever-tighter emissionsexpense of postponing more pain until later.Stern Review one form or another, this little secret isequation computer-simulated model thatuses an IAM called PAGE,the exact connection between PAGE andÕs conclusions is elusive, frustrating, andThe analyticalcore of theWeitzman: A Review of the sep07_Article4 PM 705 tied to PAGE. However, the rest of the bookleast can serve as a conversation starter. (Howout clearly?) As economic analysis, the evidently just too risky for the planet to bear.Õs mixed methodology (called Òmultidi-ty, and discounting interact with the econom-tastes with technology. The modern incarna-tion of FisherÕs idea in a deterministic setting(1) ginal utility, or, equivalently, the coefficient ofRamseyÕs time, .We now(but Ramsey and Fisher didnÕt) that, in bal-essentially the underlying growth rate of labor-To cut sharply to the essence of the coreÕs strongJournal of Economic Literature, Vol. XLV (September 2007) sep07_Article4 PM 706 periodsÑthe present and the futureÑwherenow. For the purposes at hand, I am about towarming. Technically speaking, the possibili-under uncertainty, but I will cross that bridgemessage will turn out to be similar anyway.of reality. As just one example among many,,T]3ûCafter a century from now (and also causesthe tail probabilities of veryhigh tempera-tures T�6ûC to be relatively much biggertwo centuries from now than one centuryfrom now) along any trajectory that does notstabilize atmospheric greenhouse gases at550 ppm CO2eÑincluding the majority-opinion gradualist climate-policy-ramp tra-jectory. The ultimate high-temperature. The ultimate high-temperatureT] at 3¡C.However, the point here is to put aside2 percent (both on an2percent. For thepaternalistic view (which, however, includesinvestment behavior. In a similar spirit of1that is the low-est lower bound of just about any economistÕsWeitzman: A Review of the sep07_Article4 PM 707 matterwhat spin Õs extreme policy con-clusions. With its preferred base-case param-Õs discount rateÕs annual interest rate ofis GDP, then values ofÕs language Òwhen wecosts look very large.Ó Actually, the century from now? With over-cost ratio of such an investment would5exp(100(With Õs preferredparameter values, theoversimplifications but, at the end of the day,Õs numbers is that people are notJournal of Economic Literature, Vol. XLV (September 2007) sep07_Article4 PM 708 1. To gauge the magni-(2) =With Õs preferredvalues of the coefficient of relative risk aversion . For me (and I sus-in this and other variants of market-behavior-basedthought experiments requires the rateÕs worldview tendsÕs positionutilities of oneÕs great-grandchildren, andÕs preferred taste parameters scattered1 unconvincing when super-stronguncertainty. As a first-pass informal cut atuncertainty, suppose we admit that we donÕtyears or so from now. An important featurethey donÕt aggregate arithmetically into aWeitzman: A Review of the sep07_Article4 PM 709 (3) =Š}. Theamong rates of capital or, more succinctly, In nondeterministic reality, there are manysiderably. The point has already been estab-what interest rate is used for discounting. Tomally introducing uncertainty, which allows known.) With (4) of return on equity. When in this fruit-tree economy, the equity risk(5) (5) Re], whichis close enough to E[re] to make them inter-changeable for my purposes here.4Combining (5) with (4) gives the averagereturn on equity as1(6) Journal of Economic Literature, Vol. XLV (September 2007) sep07_Article4 PM 710 g]=2 percent, [g]=2 percent (on anannual basis, for long time series) makesvery little difference on the risk free ratebecause now rf=5.9 percent in (4) instead ofthe previous value for ÒtheÓ interest rate ofr=6 percent in (1). The correspondingequity premium from (5) is ŠreŠrf=0.1 per-cent and the average return on equity from(6) is Šre=6 percent. The actual empiricalnumbers are closer to rf1 percent, ŠreŠrf6 percent, Šre7 percent. (The calibra-tion rf1 percent refers to short-termtreasury bills, while Šre7percent refers toI donÕt think the numbers would be funda-economics of climate change? Well, a lotactually. But before getting into the relation-. But before getting into the relation-exp(ŠŠret)+(1Š)exp(Šrft)](7) r(t)=Š. So the question herePAGE model that crunches some numbers(8) potential GDP (or NDP, no distinction beingWeitzman: A Review of the sep07_Article4 PM 711 tive formulation (8): it is one! Therefore, bythan a decade ago between William R. Cline low interest rateÑin ClineÕs case the assumed1percent, which combined to make 1.5percent per year. AlsoClineÕs analysis fifteen years earlier traced0 byrelying mostly on a priori philosopher-kingsocietyÕs revealed preference value of In part because ClineÕs results, and whererelatively safe U.S. Treasury bills historicallyMissing from ClineÕs reasoning was a seriousJournal of Economic Literature, Vol. XLV (September 2007)contained in Paul R. Portney and John P. Weyant (1999). sep07_Article4 PM 712 Discounting for Timeand Risk in Energy Policy,contrary, the returns associated with publicmultiplicative or additive with GDP, or evenment (rather than substituting one-for-oneeconomic activity? The answer, when youor sectors of the economy. The parts of anglobal economy, which are largely going to be dom-labor-augmenting in computing power, furniture making, orbetter pharmaceuticals a century from now.tion coefficient of, say, 0.5. With (100)=1.7 pecent,Weitzman: A Review of the sep07_Article4 PM 713 which is close to SternÕs ClineÕs earlier Rather, the moral ofeconomy, can be a strong factor in loweringdiscounting rates significantlyÑfromthethe climate-policy ramp. Remarkably, the6percent from (6). 1 is inconsistentwith observed economic behavior, especial-ly savings behavior. While this is true, andÕs. The biggestJournal of Economic Literature, Vol. XLV (September 2007) sep07_Article4 PM 714 policy for climate change in its number-PAGE. So much for the fantasy that values ofAt the end of the day, where do theseed future cost (or benefit). Trying to forecasta science (imagine forecasting todayÕs world ain the discount factor, which makes the dis-so from now.Uncertainty Tends to Matter Much Morerepeats itself. With this interpretation of thegoes over several of these highly unlikely,Weitzman: A Review of the as tail thickening of posterior-predictive distributions isdeveloped in Martin L. Weitzman (forthcoming). sep07_Article4 PM 715 sudden collapse of the Greenland and Westbution of fresh water, tropical-crop failures,Translated into the language of the simpleranslated into the language of the simpleT]=2.8ûCwith a thick-tailed upper-end standard devi-1.6ûC (table SPM-3). This means the the discountrate, the-probability-distributionmild Journal of Economic Literature, Vol. XLV (September 2007) sep07_Article4 PM 716 directly. With roughly 3 percentIPCC-4 probability, we will ÒconsumeÓ aIn the rest of this paper, marginal analysisly, to the underlying sampling-theorytence values of natural habitats. With an evo-in subjective uncertainty. If, as the performed. Formally, of course, costÐbenefitanalysis can deal with uncertaintyÑbytakingtheory, accounting for risk aversion, andusing all of the other, by now familiar, para-nomics of uncertainty. In principle, it doesold, never-resolved foundational controversyPersonally, I do not think there exists a pureever likely to encounter in practice. To para-Weitzman: A Review of the sep07_Article4 PM 717 To the extent that it makes any sense at alltribution, however, we are increasingly mov- ing significantly expected marginal utility.To get a sense of just how strong the effect), where we2percent and to be unity. Then from using the familiar for-. Then from using the familiar for-(Šg)]=exp(Š+12Š22). (It is precisely this kind ofsituation, where we donÕt know the true val-. For simplicity, sup-Journal of Economic Literature, Vol. XLV (September 2007) sep07_Article4 PM 718 a possibility. Then the reduced-form situa-as ifgg(Šg)]=+, which is mathematically equiva-lent to the fact that the moment generatingfunction of a Student-tdistribution is infi-nite. The bombshell fact that EMU=+(assoon as we admit that we donÕt know theshadows the discounting of far-futureutility theory. The degree to which this kindextent of posterior-predictive tail thickening.inescapably thickened tails of the posterior-Weitzman: A Review of the sep07_Article4 PM 719 Climate Uncertainty and the Value ofby the IAMs, including PAGE), so to speak,1 (and, secondarily, such high values of puts it directly: ÒAveraging across possibili- imposed ÒmultidimensionalÓ methodology,1 the to argue (informally, if passionately, in scat-change on the worldÕs poor (whose marginalSimultaneously, the richerfuture a Õs heuristic justification for big values of(or, secondarily, ÒaveragingJournal of Economic Literature, Vol. XLV (September 2007) sep07_Article4 PM 720 6ûC?How much would it cost tosignals? Would last-ditch emergency geo-warming be available in time to help? (Suchthe makingÑperhapsthey might includedoesnÕt even men-from burning too much fossil fuel? Or, per-awry, or the tail thickness of massive sudden-now, meaning a probability Weitzman: A Review of the reverse global warming, see T. M. L. Wigley (2006). sep07_Article4 PM 721 (ÒNondogmaticÓin dichotomies as if we must make costly all-or-Òleav-that the option value of drastically. But these are conclusions weneed to reach empirically, rather than pre-judging them initially. Instead of declaringtwo while simultaneously investi-they start to materialize. We can always comeif we thenamong a better-studied reasonably consid-shoehorn disaster policy into an either-orresponse category where it wonÕt fit. ThenatureÕs grim reaper by bequeathing theon our watch. However, except indirectly, by choosing Journal of Economic Literature, Vol. XLV (September 2007) sep07_Article4 PM 722 the nightmare scenarios). I donÕt mean tosions. We just donÕt yet know and we needGetting it Right for the Wrong Reasons?in KeynesÕs phrase an essay in persuasionÑatjudged by both standards. To its great credit,where wants to hear, that (however it is pack-which was conveniently ignored in Al GoreÕsaward-winning film.) An entire chapter 22 inWashington these days.indirect route of picking point-estimateWeitzman: A Review of the sep07_Article4 PM 723 ous issue which should be taken seriously, byknown precisely. However, in my opinion,Õs radical policyeconomists would consider much too low. IcanÕt help but feel after reading the the reduced-form posterior-predictive prob- do well to try to address more directly.Cline, William R. 1992. Warming. Washington, D.C.: Institute for Inter-Õs Economics of Climate Change.Ó ,199: 4Ð7.PAGE2002: An Integrated Assessment ModelIncorporating the IPCCÕs Five Reasons for Concern.Ó. http://www.ipcc.ch.Kelly, David L., and Charles D. Kolstad. 1999.The International Yearbook of, ed. H. Folmer and T.Tietenberg. Cheltenham, U.K. and Northampton,Mass.: Elgar, 171Ð97.Discounting for Time and Riskin Energy Policy.Washington, D.C.: Resources forStern Review.Ó http://www.economics.bham.ac.uk/Nordhaus, William D. 1994. Nordhaus, William D. 2007. ÒA Review of the Review on the Economics of Climate ChangePortney, Paul R., and John P. Weyant, eds. 1999.. Wash-Tol, Richard S. J., and Gary W. Yohe. 2006. ÒA Reviewof the World EconomicsWeitzman, Martin L. Forthcoming. ÒSubjectiveWigley, T. M. L. 2006. ÒA Combined Migration/Journal of Economic Literature, Vol. XLV (September 2007) sep07_Article4 PM 724