A REGIONAL DYNAMIC GENERAL-EQUILIBRIUM MODELOF ALTERNATIVE CLIMATE-CHANGE STRATEGIES

BY

WILLIAM D. NORDHAUSAND

ZILI YANG

COWLES FOUNDATION PAPER NO. 930

rat

COWLES FOUNDATION FOR RESEARCH IN ECONOMICSAT YALE UNIVERSITY

Box 208281New Haven, Connecticut 06520-8281

1996

MONOGRAPHS

The monographs of the Cowles Commission and Cowles foundation which are currently in print are

listed below :No. 12 SOCIAL CHOICE AND INDIVIDUAL VALUES, by Kenneth J . Arrow, 1951 . Methods of

symbolic logic are applied to the question whether a social valuation of alternatives can be consistently de-rived from given, partly conflicting, individual valuations .

No. 13 ACTIVITY ANALYSIS OF PRODUCTION AND ALLOCATION, Proceedings of a Confer-ence, edited by Tjalling C . Koopmans, 1951 . Contributions from economists and mathematicians on the theoryand techniques of efficient allocations of resources and programming of activities .

No . 16 . PORTFOLIO SELECTION : Efficient Diversification of Investments, by Harry M . Markowitz,1959 . Presents methods of translating anticipations about future yields of securities, and about their interrela-tions, into investment decisions that give minimum expected risk for given expected return .

No . 17 . THEORY OF VALUE, AN AXIOMATIC ANALYSIS OF ECONOMIC EQUILIBRIUM, byGerard Debreu, 1959 . A rigorous presentation of the theories of producers' behavior, consumers' behavior,Walrasian equilibrium, Paretian optimum, and of their extensions to uncertainty .

No. 22. ECONOMIC THEORY OF TEAMS, by Jacob Marschak and Roy Radner, 1972 . This mono-graph emphasizes the informational aspect of the problem of designing efficient organizations . After anintroduction of decision-making under uncertainty and to the economics of information, a wide variety ofmodels is treated within a unifying conceptual framework .

No. 24. THE COMPUTATION OF ECONOMIC EQUILIBRIA, by Herbert E . Scarf, 1973 . The firstgeneral method for the explicit numerical solution of the price system and economic equilibrium is presented .An important connection between computational methods and economic theory is made which promises to beof use as a practical tool for the evaluation of economic policy .

No. 26 . THE EFFICIENT USE OF ENERGY RESOURCES, by William D . Nordhaus, 1979 . A theo-retical and empirical investigation of the efficient use of energy resources . It examines the conditions underwhich exhaustible resources are allocated over time in competitive markets and then sets out a linear-program-ming model of the energy sector - based on econometric estimates of energy demand functions and energyresources and extraction costs. Concluding chapters calculate the time path of the efficient use of energy ; theimpact of OPEC on energy markets ; the costs and benefits of new energy technologies ; and the effects ofcarbon-dioxide control programs in the energy sector.

No . 27 . DISEQUILIBRIUM DYNAMICS ; A Theoretical Analysis of Inflation and Unemployment, byKatsuhito Iwai, 1981 . A dynamic macroeconomic theory is built on non Walrasian microeconomic founda-tions . Interdependent firms are in monopolistic competition in product markets and labor markets ; their pricesand wage offers are decisions they must make with uncertainty about demands and supplies . Expectationscannot be rational . The system as a whole cannot be described as a moving equilibrium or as movementtowards a steady state independent of its history . The theory provides new interpretations of, and rigoroussupport for, Wicksellian and Keynesian propositions about inflation and unemployment .

Volume 86Number 4September 1996

A Regional Dynamic General-Equilibrium Modelof Alternative Climate-Change Strategies

By WILLIAM D. NORDHAUS AND ZILI YANG

Reprinted from

THE AMERICAN ECONOMIC REVIEW

© The American Economic Association

A Regional Dynamic General-Equilibrium Modelof Alternative Climate-Change Strategies

By WILLIAM D. NORDHAUS AND ZILI YANG*

Most analyses treat global warming as a single-agent problem . The present studypresents the Regional Integrated model of Climate and the Economy (RICE)model. By disaggregating into countries, the model analyzes different nationalstrategies in climate-change policy : pure market solutions, efficient cooperativeoutcomes, and noncooperative equilibria. This study finds that cooperative pol-icies show much higher levels of emissions reductions than do noncooperativestrategies ; that there are substantial differences in the levels of controls in boththe cooperative and the noncooperative policies among different countries; andthat high-income countries may be the major losers from cooperation . (JEL H41,Q4, Q2, Q20)

Although the issue of greenhouse warmingwas first seriously studied a century ago, ithas over the last decade emerged as the centralinternational environmental question. Most na-tions have adopted the Framework Conventionon Climate Change negotiated at the 1992 RioEarth Summit. Under the Convention, nationsagreed to take steps to limit carbon dioxide(C02) and other greenhouse gas (GHG) emis-sions before they reach "dangerous" levels .Having increased its CO2 emissions at an av-erage growth rate of almost 2 percent annuallyfor about a century, the United States has com-mitted itself to capping its emissions at 1990levels, and many other high-income countrieshave made similar or even more ambitiousproposals (for a review of commitments, seeDaniel M. Bodansky [1995] or InternationalEnergy Agency (IEA) [19941) .

The climate-change issue is so controversialprimarily because the stakes are so high . If un-

* Nordhaus: Department of Economics, Yale Univer-sity, 28 Hillhouse Ave ., New Haven, CT 06511 ; Yang :Center for Energy and Environmental Policy Research,MIT, Cambridge, MA 02137 . This research was supportedby the National Science Foundation and the U .S . Environ-mental Protection Agency . This research has benefitedfrom discussions and comments of Richard Eckaus,William Hogan, Alan Manne, Richard Richels, HerbertScarf, and two referees . All views and errors of omissionor commission are the sole responsibility of the authors .Correspondence can be directed to W. D. Nordhaus .

741

checked, recent surveys indicate that over thenext century the globally averaged surface tem-perature will rise around 3°C (degrees Celsius),which would produce climates that are unprec-edented during the entire span of human civili-zation . While warming may seem benign, it hasmajor and unpredictable impacts on weatherpatterns, ocean currents, sea-level rise, river run-offs, storm and monsoonal tracks, desertifica-tion, and other geophysical phenomena . Manyscientists and ecologists view these changes anduncertainties with alarm.

The other half of the calculus is the cost ofslowing climate change . Even the most dra-conian policies (such as a virtual phaseout offossil fuels) would only slow and not stop cli-mate change, and significant steps to slow therate of increase of climate change would costhundreds of billions of dollars annually usingtoday's energy technologies . Given the manyeconomic issues facing humanity, it would re-quire an unusually dire risk and uncommonlystatesmanlike behavior for nations to divert 1or 2 percent of their national incomes today toreduce conjectural risks that will not occur un-til well into the next millennium .

In addition to the grave risks and huge costs,the issue of greenhouse warming is difficultbecause the problem is so complex. It involvesa series of poorly understood systems, includ-ing the carbon cycle, climate reactions, geo-physical, ecological, and biological impacts of

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SEPTEMBER 1996

climate changes, economic impacts, alongwith potential adaptations and new technolo-gies, with all of these stretching over a periodof a century or more. Social and natural sci-entists have made impressive advances in un-derstanding each of these systems over the lastquarter century, and numerous efforts are un-derway today to link together the differentcomponents into an integrated assessment ofclimate change policies . One of the earliest in-tegrated models was the DICE model, whichis a globally aggregated model integrating ageneral-equilibrium model of the global econ-omy with a climate system including emissions,concentrations, climate change, impacts, andoptimal policy (see Nordhaus, 1992, 1994) .Other recent integrated models of climatechange include Alan S . Manne and RichardRichels (1992), Stephen C . Peck and ThomasJ. Teisberg (1992), and Zili Yang (1993) .

Globally aggregated models have the short-coming of losing many of the interesting andimportant details of different regions . Perhapsthe central shortcoming, however, is thatglobal models ignore the fact that policy de-cisions to reduce GHG emissions are takenprimarily at the national level. It is singlenations, not the United Nations, that determineenergy and environmental policy, so any granddesign to slow global warming must be trans-lated into national measures . The purpose ofthe present study is to improve the realism ofintegrated assessments by lodging policy mak-ing at the more appropriate national level . Thisinvolves introducing a number of regions ofthe world and considering different degrees ofcooperation among nations .

The present paper reports on the results ofthe current version of the RICE model .' It out-lines briefly the philosophy, sketches the mod-eling structure, and describes the major results .

'An experimental version of the RICE model with il-lustrative data was presented at the MIT Conference onthe Environment (see Nordhaus, 1990) . The current ver-sion (called RICE-6 .3 .2 for purposes of documentation)incorporates a number of changes, primarily a revision ofthe treatment of non-CO2 greenhouse gases and improvedestimates of the economic and emissions data . A majorcause of the long gestation period of this research has beenthe difficulty in finding a satisfactory algorithm for solvingthe intertemporal general equilibrium (see below) .

I. Description of the RICE Model

A. Overview

This section begins with a succinct descrip-tion of the RICE model ; the equations of themodel are provided in Appendix A . 2 The RICEmodel, or Regional Integrated model of Cli-mate and the Economy, is a regional, dynamic,general-equilibrium model of the economywhich integrates economic activity withthe sources, emissions, and consequences ofgreenhouse-gas emissions and climate change .Most existing models of global climate changetake the vantage point of the Global Com-moner engaged in determining how nationsshould design sensible strategies to cope withfuture climate change . The RICE model takesa positive point of view by asking how nationswould in practice choose climate-change pol-icies in light of economic trade-offs and na-tional self-interests. Put differently, globaloptimization models ask how nations wouldchoose the optimal (or Pareto-efficient) pathfor reductions of GHGs. The RICE modelallows us to calculate not only the efficientpath (which we designate the cooperative ap-proach)' but also to compare that path withnoncooperative approaches .

In the RICE model, the world is dividedinto a number of regions . Each is endowedwith an initial capital stock, population, andtechnology. Population and technology growexogenously, while capital accumulation is de-termined by optimizing the flow of consump-tion over time . Output is produced by aCobb-Douglas production function in capital,labor, and technology . In the long run, capitalis fully mobile so that the real return on capital

2 The structural equations of the RICE model are gen-erally the same as those of the aggregated DICE model .For a detailed discussion of the derivation of the equations,see Nordhaus (1994). The GAMS program for the RICEmodel is available from the authors upon request.

' This study identifies the cooperative solution as theone that generates an efficient level and distribution ofemissions . The solutions that might emerge from in-ternational negotiations are a further issue that is notaddressed in this study . Issues concerning possible bar-gaining outcomes are discussed below in Section lI .C,"Welfare Effects by Region ."

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743

is equalized across regions . The preferencefunction of each region is a utility functionwhich is the sum of discounted utilities of percapita consumption times population, wherethe pure rate of social time preference (the dis-count rate on utility) is 3 percent per year ineach region. The utility function is logarithmicin per capita consumption .

The major contribution of the integrated ap-proaches like the RICE model is to integratethe climate-related sectors with the economicmodel. This part of the model contains a num-ber of geophysical relationships that link to-gether the different forces affecting climatechange, generate the greenhouse-gas emis-sions, and measure the impacts of climatechange. RICE includes region-specific emis-sions equations, a global concentrations equa-tion, a global climate-change equation, andregional climate-damage relationships . En-dogenous emissions are limited to CO 2 , whileother greenhouse gases are treated as exoge-nous. Uncontrolled emissions are a slowlydeclining fraction of gross output-a relation-ship which is consistent with the observed"decarbonization" in most countries over thiscentury that is also predicted by more detailedenergy models. CO2 emissions can be con-trolled by increasing the prices of factors oroutputs that are CO2 intensive, and we repre-sent the C02-reduction cost schedule paramet-rically by drawing upon a number of studiesof the cost of CO2 reductions . Climate changeis represented by the realized global mean sur-face temperature, which uses relations basedon current climate models . The economic im-pacts of climate change are assumed to be in-creasing along with the realized temperatureincrease . The impacts of climate change areestimated from a number of different studies,but it must be recognized that this is the mostuncertain part of the model .The major economic choices faced by

nations (or the concert of nations) in this ap-proach are (a) to consume goods and services,(b) to invest in productive capital, and (c) toslow climate change through reducing CO 2emissions. The new element introduced in theRICE model and not present in other modelsof global warming is the possibility of differ-ent strategies undertaken by nations . We dis-tinguish three distinct approaches :

•

Market policies. The market approach isone in which there are no controls on theemissions of greenhouse gases . This hasbeen the approach followed by virtually allnations up to now.

•

Cooperative policies . The second approachis the ideal one in which global environ-mental concerns are treated cooperativelythrough the efficient actions of all nations .In this approach, nations agree to reduceCO2 emissions in a globally efficient way .This solution is efficient but requires an un-realistically high degree of cooperation .

•

Noncooperative policies. In the third ap-proach, individual nations undertake poli-cies that are in their national self-interestsand ignore the spillovers of their actions onother nations. In the noncooperative ap-proach, to the extent that nations are smalland the externality is truly global, efforts toreduce CO 2 emissions will be much smallerthan in the global cooperative solution . Thissolution is inefficient but realistic .

B . Basic Structure

We outline here the major features and in-novations of the RICE model; the equations ofthe model are contained in Appendix A .

The RICE model divides the global econ-omy into 10 different regions . The first five are1) the United States, 2) Japan, 3) China, 4 )the European Union, 5) and the former SovietUnion (FSU) . Each is treated as a single de-cision maker. The last five regions have dif-ferent numbers of countries, and each istreated as multiple decision makers . These fiveregions are 6) India, 7) Brazil and Indonesia,8) 11 large countries, 9) 38 medium-sizedcountries, and 10) 137 small countries . (Basicdata on the major regions are contained in Ap-pendix B .) To reduce the severe computationalcomplexity of the solution, we sometimes ag-gregate regions 6 through 10 into one regionas the "rest of the world" or "ROW ."

The goal in creating the different regions isto structure the problem so that the noncoop-erative equilibrium is equivalent to the full butenormous game with about 200 countries . Thisis done by allocating the smaller countries togroups so that within each group the nationalbenefits from slowing climate change are

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roughly equal. We then mimic the free-ridingtemptations of global public goods by dividingthe benefit function for each region by thenumber of countries (that is, decision-makingunits) within that region .

An example will clarify the way regions areused. Region 9 contains 38 countries-includ-ing Bulgaria and Hungary, which are countrieswith roughly similar populations and econo-mies. We assume that all the countries in re-gion 9 are similar in terms of their sizes,mitigation cost functions, and damage func-tions . Hence, for region 9 the (slightly simpli-fied) net benefit function to be maximized inthe noncooperative case isN(E9 ) = B(E9)/38 -C(E9 ), where N(E9) is the net benefits ofemissions for region 9, E9 is emissions in re-gion 9, B(E9 ) is the benefit of emissions, 38is the number of equal-sized decision makersin region 9, and C(E9 ) is the cost function .Therefore, when the representative country inregion 9 maximizes its net economic welfarein the noncooperative case, not only will it ig-nore the benefits accruing outside region 9, butit will also internalize only '/38 of the benefitsof the region. This procedure includes in acomputationally feasible manner all the dif-ferent countries while ensuring that the incen-tives for free-riding are maintained .

A major difficulty in constructing the RICEmodel has been to estimate the regional pa-rameters of the different functions .' Gross do-mestic products, populations, CO 2 emissions,and capital stocks are taken from a variety ofinternational sources. Future population growthestimates are taken from the United Nationsprojections. The major uncertainty in the eco-nomic projections is long-run levels of percapita output in the different regions . Theseprojections are based on the assumption ofpartial convergence of per capita incomes .That is, we assume that the relative differencesin regions' per capita incomes decline overtime but do not disappear . The extent of con-vergence is a controversial issue, but to theextent that differences in per capita incomesare primarily based on differences in the extentof adoption of available technologies, produc-

° A detailed list of sources and data are available fromthe authors.

SEPTEMBER 1996

TABLE 1-FUTURE LEVELS OF INCOMES,DIFFERENT REGIONS

Note : These values are the values of per capita GDP gen-erated by the market solution for the RICE model . TheGDPs are calculated using market exchange rates .

tivity differences should largely disappearover the long, run .

The assumed ratios of long-run levels of percapita GDPs to that of the United States aregiven in Table 1, showing the observed valuesfor 1990 along with projections for 2100 and2200. While highly conjectural, these esti-mates are consistent with recent trends incountry GDP growth. One interesting featureof this approach is that it gives considerablyhigher estimates of output and emissions thando the conventional global models, such asthose used by governments in the Intergovern-mental Panel on Climate Change (IPCC) . Forthe modeling, each region's income growth isgenerated through Hicks-neutral technologicalchange, which starts at approximately the ob-served rates for 1960-1990. After 1990,growth rates are assumed to decline exponen-tially in a manner leading to the asymptoticproductivity ratios shown in Table 1 .CO2 emissions are separated into industrial

emissions (largely from fossil fuels) and thosefrom land-use changes and are calibrated to1990 levels. The ratio of CO2 emissions to out-put is assumed initially to decline at differentrates, with each region's decline rate decreas-ing along with the overall rate of technologicalchange by region. Here again, asymptoticCO 2-output ratios are assumed to convergeconsiderably but not completely in the future .

The costs of reducing emissions by regionare estimated separately on the basis of the ex-isting studies of the cost of reduction of CO 2

Ratio of region's per capitaincome to that of the

United States (US 19w = 1)

Region 1990 2100 2200

1) United States 1 .00 3 .11 4.692) Japan 1 .09 4 .07 4.833) China 0.02 0 .47 1 .554) European Union 0 .85 2 .89 4 .275) Former Soviet Union 0 .14 0.87 2 .026) Rest of the world 0 .07 0.84 1 .69

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745

emissions . Most studies are based on theUnited States and Europe, and estimates forother regions have low levels of reliability . Wehave parametrized the cost function using thefunctional form from earlier studies but haveestimated the intercepts of the cost functionson the basis of the international comparisonsundertaken by the OECD and by Energy Mod-eling Forum 13 . 5

Estimates of the economic impacts or dam-ages from climate change are sparse at thisstage . There are numerous studies of the esti-mated impact of climate change on the mar-keted sectors for the United States, but fewreliable studies for the nonmarket sectors orfor developing countries. To estimate the im-pacts in different regions, we assume that thedamage function from climate change is iden-tical for each industry across different regions,and that the cost functions have the same pa-rameters as those estimated for the UnitedStates. Impacts in different regions are cal-culated by taking the estimated shares of dif-ferent sectors (agriculture, coastal activities,and so on) in national output and then ag-gregating those up to obtain overall nationalestimates. (This approach is described inNordhaus [1994].) The results in the aggre-gate do not differ markedly from the othermajor estimates (see particularly SamuelFankhauser [1993 ] and the survey of expertsin Nordhaus [19941), but it must be empha-sized that the distribution of climate impactsacross countries is at this stage highly con-jectural . Table 2 shows the major inputs as-sumptions for the different regions .

'See Andrew Dean and Peter Hoeller (1992) andDarius W. Gaskins and John P. Weyant (1993) . The func-tional form of the mitigation-cost function in the DICEmodel was estimated from studies of the cost of CO 2 re-duction in nine families of models primarily based on theUnited States and takes the form Ci (t) = b,,,µi(t)b2Y(t),where i is region i, C,(t) = the cost of reducing CO2 emis-sions, b,,, and b2 are parameters, µi (t) is the emission-control rate or fractional reduction in emissions from themarket path, Y(t) is region i's gross regional product, andt is the time period . The RICE model assumes that theexponents (b 2) are the same across countries and calibratesthe intercepts (b,, i ) to estimates of the cost functions fromthe different countries or regional models mentionedabove .

The climate-change policies are character-ized by "control rates" and "carbon taxes ."Control rates are simply the percentage reduc-tions in CO2 emissions relative to a baselineor uncontrolled path . Carbon taxes representthe marginal cost of reducing CO2 emissions .A carbon tax would equal the price of acarbon-emissions permit if there were tradablepermits, and the prices of such permits in dif-ferent countries would obviously be equalized(at market exchange rates) if permits werefreely tradable . In the market solution, carbontaxes are zero . In the cooperative solution,emissions are curtailed in a cost-effectivemanner. The model does not deal explicitlywith mechanisms by which winners mightcompensate losers, although we discuss someof the issues below .

C. Algorithm to CalculateGeneral Equilibrium

The RICE model presents a radically differ-ent philosophy for estimating strategies tocope with global warming from global-optimization models used in many integratedassessments. The baseline calculation is cali-brated to a market equilibrium of the worldeconomy with all the differences in popula-tions, technologies, and incomes-the worldis taken as it is for the purpose of the baselinecalibration. We then calculate different strat-egies for global warming conditional on theexisting distribution of capital, labor, and tech-nology. The strategies include doing nothing(the market solution), finding an efficientsolution given the existing distribution of in-come (the cooperative solution), and findingthe solution in which nations select policies tomaximize national preferences alone (the non-cooperative or nationalistic equilibrium) . Thispublic-choice approach is in sharp contrast tomany of the debates on climate change today ;in these, the distributional issues of who shallpay to slow climate change rise to the top ofthe agenda.

We now describe the algorithm for findingthe cooperative solution in the RICE model .The technique we employ originates withT. Negishi (1960), was discussed briefly inNordhaus (1990) in the context of globalwarming, and has been used in similar models

by Manne and Thomas Rutherford (see, par-ticularly, 1994) . The theoretical basis for thealgorithm is a theorem of Negishi which relieson the second theorem of welfare economics .Negishi suggested and proved that under cer-tain conditions a competitive equilibrium canbe found by maximizing a social welfare func-tion of N agents in which the welfare weightof each of the agents is adjusted to satisfy theagent's budget constraint . We will call thisequilibrium the Negishi solution .

What are the appropriate welfare weights?In our calibration, we adopt the realistic ap-proach by taking the welfare weights that re-flect the actual economic outcome acrossregions. We do this not as a brief for the ex-isting international distribution of resourcesand income but because it is the starting pointfor analyzing potential improvements in eco-nomic welfare that would arise from policiesthat are imposed on the actual world economy .Hence, the weights are ones such that the ex-cess demands in all markets are zero at thegiven welfare weights and prices .' More pre-cisely, the algorithmic procedure is the follow-ing. We first solve the RICE model by

' A brief but illuminating discussion of the Negishi ap-proach is in contained in Andreu Mas-Colell et al. (1995pp . 630-31).

The intercept of cost function equals the fraction of annual output required to reduce net CO 2 emissions to 0.'The intercept of climate-damage function equals the reduction in annual net output from an increase of 2 .5°C in

global mean temperature.° Emissions are measured in billions of tons carbon per year . Land-use emissions are primarily from deforestation .Emissions are measured in billions of tons carbon per year . Industrial uses primarily from burning fossil fuels .

'Population is in billions of people.fGross domestic product (GDP) is measured at 1990 market exchange rates in thousands of 1990 U.S . dollars .9 The ratio is of industrial CO2 emissions to GDP (tons of carbon per $1000 of output in 1990 U.S . dollars).

optimizing a global social welfare function ofthe form :

N

(1)

W =

O'U'[c`(1), c`(2), . . . ,

c`(t), . . . , c`(T)l

where W is the value of the global social wel-fare function and 0' are the welfare or Negishiweights for country i, i = 1, . . . , N . The U' arethe preference functions for the different coun-tries, and the c' ( t) are the consumption bun-dles of the countries .

The relevant excess demand is found in theintertemporal budget constraint of each region .To find the competitive equilibrium, we add aconstraint to the problem that requires each re-gion to satisfy its intertemporal budget con-straint, which is represented by terminal netforeign assets, NFA' (T) , T being the lastperiod :

(2) NFA'(T) = 0,

i = 1, . . . , N .

Next, define qf' (T) as the dual variable ofNFA'(T), which in economic terms is themarginal utility of consumption or income inthe last period . Given condition (2), qi'(T) isa function of the welfare weights and we canwrite these functions as qi `( T) = G' ((P ' , ¢ 2 ,

. . . , O N), i = 1, . . . , N . Without condition (2),

746 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1996

TABLE 2-MAJOR INPUT PARAMETERS FOR THE RICE MODEL

Climate CO2 emissions, 1990 Per capitaCost damage Population output CO2 ratio,

Region intercepts intercept' Land-use' Industrial° 2100° (2100) f 21009

United States 0.07 0 .01102 0.010 1 .360 0.294 68 .8 0.1190Japan 0.05 0.01174 0.000 0.292 0.125 89 .1 0.0630China 0.15 0.01523 0.136 0.669 1 .656 9 .9 0.5120European Union 0.05 0.01174 0.100 0.872 0.427 63 .0 0.0740Former Soviet Union 0.15 0 .00857 0.000 1 .066 0.366 18 .9 0.3220Rest of world 0 .10 0.02093 1 .730 1 .700 6.738 18.1 1 .1850

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an arbitrary set of social welfare weightswould generate a set of nonzero NFA' (T) ,which implies that at least one region does notlive within its budget. However, when the dualvariables are equalized across all countries, thewelfare-weighted marginal utilities of incomeare equal and the intertemporal budget con-straints is therefore satisfied.

Hence, the algorithm works by searching forthe welfare weights, as a function of the dualvariables ql '(T) , so that the marginal utilitiesof consumption are equalized:

(3) 4,'(T) = G(¢', ¢2 , . . . , 01) = q*,

for alli= 1, . ..,N .

Combining (1), (2), and (3), we know thateach of the country budget constraints is sat-isfied and that no region can gain from achange in the resulting allocation. Hence, bythe Negishi theorem, we know that this op-timized outcome using the welfare weightsgenerated in (3) represents a competitiveequi-librium consistent with the initial en-dowments, technology, and preferences . Theequilibrium thus found is the "pure Negishisolution ."

Unsatisfactory aspects of the solution ledto the following refinements of the pureNegishi solution . The major problem with thepure Negishi solution was that it generated ex-tremely large capital flows among regions(this is a common feature in intertemporallyoptimized models) .' Because these are un-realistic, we took one further step which wasto impose certain flow and stock constraintson debt and current accounts to ensure that netforeign investment does not exceed certainlimits . These limitations limited the export-GDP ratio to 1, limited the ratio of net foreignassets to output to 0.1, and limited the currentaccount deficit to GDP ratio to 0 .1 (see Ap-pendix A for details) . These constraints werebased on observed limitations, but they made

'The difficulty raised by unrealistically high capitalflows is not related to the use of the Negishi technique ;the same issue would occur if fixed-point methods wereemployed.

virtually no difference for the results of theanalysis below .

Given these constraints on internationalcapital flows, our algorithm will not producethe necessary complete price equalization forcarbon-trading permits, which are assumed tobe fully tradable and reach price . To ensureprice equalization for carbon-emission rights,we adjust the Negishi weights across regionsfor every period . We call this new algorithmthe time-dependent Negishi solution . It differsfrom the pure Negishi solution because it in-corporates the constraints on capital flows sothat the regional budget constraints are bindingfor every period. As a result, carbon-emissionspermits have equal prices in all regions in eachtime period (at market exchange rates) . Underthis revised algorithm, we seek the time-dependent Negishi weights, 0'(t) . To findthese, we first solve the model with an arbi-trary set of welfare weights while continuingto impose (2) . Following the Negishi theorem,we then reset the welfare weights for all coun-tries and time periods according to the follow-ing formula:

1

(4) qY(t) =n~ (t)

i

'(t)

This equation sets the welfare weights equalto the inverse of the marginal utilities of con-sumption. The search algorithm based on (4)very quickly converges to a solution that sat-isfies (2) and (3) . We have conducted anumber of experiments and have found no in-dication of multiple equilibria.

What is the underlying economic rationalefor this algorithm? The solution represents acompetitive equilibrium under the assumptionthat the preferences or technological con-straints limit the international flows of capital .For example, there may be strong home-country preferences in portfolios because oflimitations of the marketability of human cap-ital. The limitation of this approach is thatto the extent that the constraints on capitalflows have nonmarket-clearing elements dueto rationing, the excess demands will not bezero and we may depart from the market

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equilibrium (which would in any case be dif-ficult to compute) .

Once we have obtained a competitive equi-librium, we then perturb various elements,such as the climate parameters or the costfunctions, and resolve the maximization in(1) . We do this holding the welfare weightsconstant across runs . This resolves the indexnumber problem of changing prices by calcu-lating the welfare changes at the market wel-fare weights .'

D . Finding the Noncooperative Equilibrium

The algorithm just described provides thesolutions for both the market and the cooper-ative equilibrium . A different approach is nec-essary to find the noncooperative equilibrium .The noncooperative or nationalistic equilib-rium exists as the equilibrium of the strategiesof the different countries . We hence need anassumption about strategies and a method offinding the equilibrium .

As for strategies, we assume that each na-tion determines its policies by maximizing itsdomestic intertemporal utility function assum-ing that other nations' strategies are unaffectedby its policies . The noncooperative strategiesare hence dynamic, full-information, Nashstrategies, and we are seeking the Nash equi-librium. Technically, our solution is a Nashequilibrium in a finite game with perfect in-formation, and it is therefore time consistent .Such games have pure strategy Nash equilibriawhich can be calculated through backward in-duction, which is essentially what our algo-rithm does (for a discussion, see Mas-Colellet al . [1995 Chapter 91) .

More precisely, we assume that each nationsets its own control rate over time [1i ={µ`(1), µ'(2), µ`(3), . . . , µ`(t), . . . , lc`(T)} ;i = 1, . . . , N] so as to maximize its nationalobjective function taking the control rates ofthe other regions { IA', . . . , µ -' , µ +' , . . .µ"' } as given . Beginning with an initial set ofcontrol rates, we iterate through the different

'The RICE model runs on the GAMS software (seeAnthony Brooke et al ., 1988) . The full model includingsearching for welfare weights takes approximately 6 hourson a 486-66 processor .

regions by optimizing for each region holdingthe control rates and resulting emissions, con-centrations, and impacts in other regions fromthe previous iteration fixed. We continue tocycle through this sequence until the set ofcontrol rates are unchanged given the set ofnoncooperative strategies of other countries,which is then the Nash equilibrium . The out-come matches well the theoretical predictionsand is in our simulations invariant to initialconditions, which suggests that the Nash equi-librium is unique .

How reasonable is this solution concept?While the pure Nash equilibrium is a sensi-ble assumption for small countries like Chad,whose global warming policies will hardlymake the front pages, it may lack realism forlarge or influential countries. Large coun-tries like China and influential countries likethe United States would probably want totake into account the effect of their policieson other countries' policies . The ambivalentpolicy on global warming by the UnitedStates over the last decade has undoubtedlystrengthened the hand of those in other coun-tries who want to do little. An alternativeapproach would be for countries to positconjectural variations or reactions of othercountries to their policies . For example, theUnited States might assume that Japan or Eu-rope would be a follower in terms of carbon-tax policies or tradable emissions policies .Another possibility would be to model coa-litions of different countries . We have notexplored these alternative solution strategiesin the present paper. Once we admit nonzeroconjectural variations, we are in a deepthicket and the possibilities become unlim-ited. Future research will examine the pos-sibility of coalitions of countries .

E . The Economic and Environmental Impactof Alternative Strategies

Using the algorithms just described, we willanalyze the three different strategies as de-scribed in Table 3 : market, cooperative, andnoncooperative . In addition, for reference wesometimes compare the results of the RICEmodel to those of its parent, the DICE model,which is essentially a one-region efficient orcooperative solution .

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TABLE 3-ALTERNATIVE SOLUTION CONCEPTS FOR THE

regional outputs are shown in Figure 1 ; theseindicate that the projected relative sizes ofthe Chinese and ROW economies growsharply over the next century . The outputgrowth in the RICE model is significantlylarger than that in many projections preparedby international study groups, most of whichenvision a stability of current relative in-come differentials rather than the projectedpartial convergence in the RICE model . Noteas well that we use market exchange ratesbecause we will want to find the equilibriumin which the prices of internationally-tradedcarbon-emissions permits are equalized .

Emissions are also considerably higher inRICE than in the many other projections. Forexample, CO2 emissions in the RICE modelreach 38 billion tons of carbon by the year2100 in the market or uncontrolled run . Thiscompares with an estimated 21 billion tons inthe DICE model and a range of 5 to 35 billiontons in the IPCC projections (see T . M. L .Wigley [19941 for a description) . CO2 emis-sions grow substantially faster in the RICEmodel partially because of the projected rapidgrowth in output and partially because of therising output share of regions with highemission-output ratios .

Figure 2 shows the resulting CO2 emissionsunder the different solution concepts and alsocompares estimates from this study with theearlier DICE model. Model estimates (notshown) indicate that the share of CO 2 emis-sions will rise sharply in China, region S 1(India), region S3 (middle-sized developingcountries like Thailand), and region S4 (smallerdeveloping countries) . These four regions ac-counted for about one third of CO 2 emissionsin 1990 but are projected in the market runs ofthe RICE model to comprise three quarters ofemissions by 2100 .CO2 concentrations are shown in Figure 3 .

Given the higher emissions rates in the RICEmodel, its concentrations rise more rapidly thanin the DICE model. It is useful to examine thedate of doubling of CO2 concentrations relative

RICE MODEL

1. Market RICE: This strategy assumes that thereis no correction for the climate-changeexternality and that there is therefore noabatement of CO2 emissions .

2. Cooperative RICE: In this strategy, countriesundertake policies that reduce greenhouse-gasemissions efficiently . The reduction of CO2emissions is efficient across countries andacross time .

3 . Noncooperative RICE: This strategic conceptassumes that each country sets its CO 2emissions controls to maximize its owneconomic welfare assuming that othercountries' control strategies are invariant to acountry's policies .

II . Results

We now report the results of the policies andstrategies described above . As in all modelingefforts of this kind, they should be interpretedwith caution as this study is the first empiricalapplication of noncooperative game theory toglobal environmental policy . On the otherhand, the major results concerning the level ofstringency of climate-change policies havebeen relatively stable over a wide variety ofmodels and alternative specifications of theRICE model, so we have considerable con-fidence in these estimates (conditional, ofcourse, on the assumptions underlying the ma-jor components, such as those concerning thelong-run growth projections, the costs anddamages, and the discount rate) .

A. Output, Emissions, and Climate Change

The projections for the major economicand environmental variables are shown asFigures 1 through 4 . One important outcomeof this study is that the RICE model has sub-stantially higher projected world output andemissions by the end of the next century thando many other integrated assessments, suchas the earlier DICE model .' Projections for

emmental Panel on Climate Change (IPCC) (1990), the re-sults in Nordhaus (1994), and preliminary results of the sur-

v This statement is based on a comparison of the results

vey of models by the Energy Modeling Forum 14 directedin the RICE model with the projections of the Intergov-

by John Weyant, Energy Modeling Forum (EMF) (1995).

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to preindustrial concentrations ; that benchmarkis taken to be 1,200 billion tons of atmosphericCO2 concentrations (or 565 parts per million ofC02 ) . The doubling date is 2100 in the (coop-erative) DICE model, 2070 in the cooperativeRICE model, and 2065 in both the market andthe noncooperative model . The doubling timefor the CO2 equivalent of all greenhouse gasesis slightly earlier than those for CO 2 alone.

The projected increase in global mean tem-perature over the 1990-2100 period is shownin Figure 4. 1° The estimated temperature in-crease from the mid-nineteenth century to 2100is estimated to be 3 .06 °C in the market run . Thecooperative strategy lowers global temperatureby 0.22°C in 2100, whereas the noncooperative

10 The climate model used in the RICE model is a cal-ibrated version of the two-equation Schneider-Thompsonmodel with an equilibrium temperature sensitivity coefficientof 3°C for a doubling of CO 2 concentrations. The derivationof the climate model is discussed in Nordhaus (1994) .

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strategies reduce warming by considerably less(a reduction of 0 .086°C in 2100), both com-pared to the market strategy . One reason thatthe difference in the temperature increase be-tween the cooperative and the market runs is sosmall is because of the long time lag betweenchanges in emissions and temperature increases(the difference between the runs grows overtime as the lags in the emissions-concentrations-temperature relationship plays out) ." Addi-tionally, the difference is small because of thenonlinear relationship between CO 2 concen-trations and temperature . 12 But the major rea-

" The projected temperature difference between the coop-erative and market runs is 0 .41°C in 2200 whereas that betweenthe noncooperative and market tuns is only 0.12°C in 2200.

12 More recent estimates of global warming show con-siderably less near-term warming than earlier estimates(compare the current RICE with the 1992 DICE model) .Recent evidence suggests that the cooling effects of sul-fates derived primarily from fossil-fuel emissions willlower global mean temperature increases until the end ofthe next century .

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son for the small decrease in temperaturebetween the market and cooperative runs isthat the high cost of control means that theeconomically efficient strategy is for only asmall reduction in CO2 emissions .

B . Policy Variables

We next examine the policy variables forthe different degrees of cooperation amongnations (market, noncooperative, and cooper-ative) . The results are shown in terms of boththe control rates for CO 2 emissions and thecarbon taxes . Carbon taxes should be inter-preted as the marginal cost of control of CO 2whether these are efficiently implementedthrough taxes, regulations, or tradable permits .

The major results are shown in Figures 5through 9. The central finding of this study isthat the noncooperative policies produce sig-nificantly lower control rates and carbon taxesthan does global cooperation . The reason is

FIGURE 2. CO2 EMISSIONS: DIFFERENT APPROACHES

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straightforward : when countries free-ride onthe climate-change policies of other countries,then they cut back their own efforts substan-tially. Begin with the emissions control rates,shown in Figure 5 . The global average rate ofcontrol of CO 2 is around 10 percent in the co-operative solution . This varies by region, withrelatively high controls in China and the formerSoviet Union; for these regions, we estimate themarginal costs of control to be relatively low .For the efficient case, the lowest control ratesare in Japan and the European Union, whichare already relatively energy efficient andwhere the marginal costs of controls are con-sequently relatively high . According to the dataused in the RICE model, the efficient controlrates for 2000 range from 17 percent in Chinato about 7 percent in Japan . The United Statesis in the middle of the pack, with an efficientcontrol rate of slightly below 9 percent . Thecontrol rates rise over time as the marginaldamages from CO2 emissions rise. (Note that

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these relative control rates would be roughlyproportional to those shown here if the overalllevel of controls were raised or lowered .)

One immediate conclusion that comes fromthis result is that current approaches to com-bating global warming make no sense from thepoint of view of pure economic efficiency . Thecurrent Framework Convention calls for majoremissions reductions in the OECD region withno immediate reductions in the developingcountries-this being exactly the opposite ofthe efficient solution . The only potential ration-ale for the Framework Convention is that it putsa very high weight on equity (by relieving poorcountries of obligations to reduce emissions)and rules out the possibility of side payments(say through allocation of emissions permits) .

The control rates in the noncooperative solu-tion are markedly lower (not shown but avail-able from the authors) . There are two majorfindings here. First, the aggregate global emis-sions control rate for the noncooperative equi-librium is in 2000 only 2.3 percent as compared

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with the average of 9 .7 percent in the cooper-ative case . The reason for the lower control rateis completely intuitive : it results from the free-riding wherein each nation ignores the impactsof its CO 2 emissions on the welfare of othernations (as well, of course, as assuming thatother nations' efforts are unaffected by its ownself-interested behavior) . The size of the free-riding effect is the major new result here .

The second interesting conclusion in thenoncooperative approach is the distribution ofcontrol rates . This model predicts that the larg-est (albeit small) efforts will be taken by thelargest regions-particularly by the UnitedStates and the European Union. This predic-tion seems quite on the mark . It also correctlysuggests that developing countries, particu-larly small and poor countries such as Beninand Kyrgyzstan, will not be in the forefront ofglobal-warming politics .

Figures 6 through 7 show the results for es-timated carbon taxes. Looking first at Figure6, we can compare the aggregate carbon taxes

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under different strategies. Note that the coop-erative RICE model looks quite similar tothe older DICE model (which also foundthe global optimum) . The carbon tax startsslightly higher and grows more rapidly be-cause of the steeper trajectory for emissions .The first-period carbon tax in the cooperativecase is $6.19 per ton carbon in 2000 versus$5.94 in the DICE model. (Here and through-out, all dollar figures refer to prices in 1990U.S. dollars at 1990 market exchange rates .)

The cooperative tax rates are significantlyhigher than the noncooperative or nationalisticpolicies for all regions and periods . Theweighted average carbon tax for the nonco-operative policy is 24 cents per ton carbon forthe noncooperation equilibrium in 2000. Thedistribution of carbon taxes for the noncoop-erative policy is shown in Figure 7 . For thenoncooperative strategies, large countries tend

FIGURE 4 . TEMPERATURE CHANGE

to have significantly more (but not very) strin-gent controls as compared to small countries .The noncooperative carbon taxes are highestin the European Union ($0.86 per ton in 2000)and the United States ($0.65 per ton in 2000) .The difference reflects the slightly larger out-put in the European Union . For smaller coun-tries, the tax rates are much smaller: 10 centsper ton in India, and only 1 cent per ton in theS4 group of countries .

It seems appropriate to conclude that outsidethe United States, Europe, and Japan, the ra-tional noncooperative strategy would be sim-ply to ignore global warming at the presenttime . Even by the end of the 21st century, nocountry acting in a noncooperative frameworkwould have carbon taxes above $2 per ton C .If we define the "cooperation ratio" as theratio of the noncooperative carbon tax to thecooperative carbon tax, we can calculate that

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this ratio ranges from essentially zero in thesmallest countries to between 10 and 15 per-cent for the United States and Europe .

What happens to the cooperation ratio overtime? According to our calculations, the de-gree of cooperation is expected to fall in thenoncooperative solution. Cooperation in theNash equilibrium decreases as the extent ofinequality of country income falls. Hence, theextent of cooperation is calculated to declineslightly over the next four decades as the shareof the United States, Japan, and Europe declinesand the distribution of economic sizes of nationsbecomes more equal . Greater equality leads tosmaller incentives to be a good global citizen .

For small countries (with GDPs of under$20 billion) the noncooperative optimal con-trol rates and carbon taxes are minuscule,$0.01 per ton carbon versus $5 .98 in the globalcooperative case . While the taxes in the non-cooperative strategies are significantly lower

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FIGURE 5 . CO2 CONTROL RATES :COOPERATIVE SCENARIO

than those in the global cooperative strategies,some have expressed surprise that they arenot even lower . The reason is that there are afew countries or regions (notably the UnitedStates, China, Japan, and Europe) which arelarge enough so that it is their own self interestto reduce CO2 emissions even ignoring thebenefits to other countries . Were China tobreak up, were Europe to make decisions on anational level, or were the Republican Revo-lution in the United States to devolve environ-mental decisions to the states, the predicteddegree of cooperation would be even lower .

There are a few other intriguing details ofthe runs worth noting. China is definitely a keyplayer and exhibits a different pattern . Figure5 shows that China has the highest cooperativecontrol rates of all the regions-this reflectingthe relatively high CO2 emissions per unit out-put (see Table 2) . But countries which arehardly players today (India, China, and the

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smaller developing countries) dominate CO2emissions by the middle of the next centuryand will have to behave cooperatively if thegains from cooperation are to be realized .

C. Welfare Effects by Region

What are the overall economic effects byregion? The gain to cooperation is calcu-lated as the present value of the change inconsumption valued using the region-specificdiscount rates on consumption (not to be con-fused with the pure rates of social time pref-erence, or discount rates on utility, which areequal across regions) . The discount ratesin this calculation are region and time spe-cific, and they average about 4 I/z percent peryear (in real terms) over the next century . Inthese runs, there are no international transfers,which essentially means that each country

FIGURE 6 . AVERAGE CARBON TAXES

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is assigned its optimal policy without anyside payments from other countries . This isequivalent to each country receiving in the co-operative equilibrium a quota of tradable emis-sions permits equal to the quantity of its ownemissions .

The resulting impacts upon economic wel-fare are shown in Table 4 . Note first that theoverall results from the cooperative RICE so-lution are quite close to those of the originalDICE model. The former is about one quarterhigher because of the higher growth rates inthe RICE model. By contrast, the noncooper-ative, six-region RICE model shows extremelyslim net benefits-only $43 billion in dis-counted benefits as opposed to $344 billion forthe cooperative RICE or $271 for the coop-erative DICE model .

Figure 8 shows the gains to different regionsfor the cooperative and noncooperative cases .

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Table 4 and Figure 8 present a number of sur-prises in the regional results. The noncooper-ative solution produces positive net benefitsrelative to the market solution for all regions .This result is expected because the noncoop-erative policies improve welfare while the ex-ternal interactions among countries are onesthat are beneficial relative to the market case .The net benefits in the noncooperative case arerelatively uniform across the different regions,with most of the positive effects coming fromthe reductions in damage from climate change .

The major surprise in these results is the lop-sided benefits from the cooperative strategy .The United States actually loses in the coop-erative solution relative to the noncooperativeequilibrium . The reason is that, with its rela-tively large emissions, the United States wouldbe slated to incur major costs today, while itsbenefits would be relatively small given its de-clining share of the world economy. Similarly,the former Soviet Union has quite modest net

FIGURE 7. NONCOOPERATIVE CARBON TAXES

benefits in the cooperative strategy because itis required to undertake significant mitigationefforts and has few benefits because of itsnortherly location . By contrast, the ROW re-gion reaps major net benefits from the coop-erative solution because the mitigation effortsare undertaken primarily in the high-incomecountries early in time while the major benefitsin terms of damages avoided accrue to the de-veloping countries in several decades .

These results indicate that the cooperativesolution-one in which nations are allocatedemissions equals to their efficient emissions-might well not emerge as the outcome of abargaining process in which nations will onlysign on to an agreement that improves theireconomic welfare . Of course, the pattern of netgains can in principle be altered through dif-ferent schemes for allocating emissions rightsto countries (that is, by adding side paymentsto the program analyzed here) ; the gains andlosses could be made much more equal over

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TABLE 4-NET BENEFITS OF DIFFERENT STRATEGIES BY REGION RELATIVE TO THE MARKET EQUILIBRIUM(BILLIONS OF 1990 U .S. DOLLARS, DISCOUNTED TO 1990)

Note: Each entry indicates the net benefits for a region relative to the market or uncontrolled s trategy. NA

is not available

.'From the aggregate DICE model in Nordhaus (1994) .

space and time through different allocations orside payments . Determining possible bargain-ing outcomes is, however, a difficult empiricalissue that is outside the scope of the presentpaper and is the subject of current research bythe authors. What this study examines is theset of national emissions that is consistent withan efficient allocations of emissions over spaceand time. The interesting new result of thispaper is that a scheme with no side paymentswill reduce the standards of living of all majorregions for at least half a century and will re-duce the discounted net welfare of the UnitedStates when all time periods are considered .Moreover, it is interesting to note that all theemission-rights allocations proposals that arecurrently under consideration are even moreunfavorable to the United States than the oneunderlying the cooperative equilibrium andare therefore even less likely to be acceptableto high-income countries than the program ex-amined here .

What is the time profile of benefits? Figure 9shows the time paths of discounted cumulativeconsumption in different regions . More pre-cisely, the numbers are the sum of the consump-tion differences between the cooperative strategyand the market strategy from the beginning ofthe period (1990) until the date shown on thehorizontal axis. For each region, the consump-tion figures are discounted back to 1990 and thediscount rate is the region-specific and variablediscount rate on consumption.

This figure shows the problem of globalwarming in a nutshell . It indicates how eachregion would experience the economic im-pacts of a cooperative strategy relative to the

market solution through different time periods .For example, it shows that the United Stateswould have a cumulative discounted con-sumption loss from cooperation relative to themarket of $12 billion through 2050. The cal-culation indicates that a cooperative global-warming accord would reduce the cumulativediscounted consumption of all countries ex-cept Japan through 2050. The ROW regionsuffers major losses, approaching a total of$100 billion by mid-century . Moreover, as canbe seen by adding the numbers for the differentregions together, there is still a negative effecton cumulative global consumption by the mid-dle of the next century .

On a longer time scale (not shown), theROW breaks even by the end of the next cen-tury and is the major beneficiary after thatpoint . The United States and the former SovietUnion experience a reduction in discountedcumulative consumption through the end ofthe next century . All the curves are heading upat the end of the period, and the discountedcumulative totals over the 250-year estimationperiod, shown in Table 4, are positive for allregions and quite large for the ROW region .

The estimates of the regional costs andbenefits in the RICE model are sensitive to pa-rameters of the mitigation-cost and climate-damage functions, but the major determinantof the patterns is initial emissions and growthof output, which are considerably more securethan the cost and damage estimates . The basicdilemma is clear: the long period betweenemissions reductions and reduced climate dam-age means that countries must be extraordi-narily farsighted . In addition, the pattern of

Strategy

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gains and losses, with the major long-run gainscoming to developing countries while the netbenefits to the United States and the formerSoviet Union are minimal, is a most surprisingand troubling finding .

D. Sensitivity Analysis

To understand the full range of outcomesand policy responses to the threat of globalwarming, we must assess the fact that many ofthe underlying processes are imperfectly un-derstood. Social scientists have developed avariety of tools to incorporate uncertainty intoquantitative modeling, and these can help putbounds on potential future outcomes.' Although

See M. Granger Morgan and Max Henrion (1990)for a recent survey of tools for the analysis of uncertaintyin quantitative risk and policy analysis .

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uncertainties are often critical to determiningpolicies, formal techniques for determiningthe uncertainty of future trajectories or of im-pacts have been rarely applied to major policyissues ."

A full-scale analysis of the uncertainties as-sociated with the RICE model-including un-certainty about model structure as well asabout individual parameters-is beyond thescope of the current article. Many of the cen-tral uncertainties have been examined in thecontext of the DICE model (see Nordhaus,

14 One notable and controversial example of the sys-tematic application of statistical techniques is the Ras-mussen report (Nuclear Regulatory Commission, 1975),which estimated the risk of accidents of different levels ofseverity in commercial nuclear power plants . An exem-plary study used probabilistic assessments for ozone de-pletion (National Academy of Sciences, 1979) .

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1994 Chapters 6-8), and those results applyequally well to the RICE model . To under-stand the extent of sensitivity of the model wepresent here a limited sensitivity analysis withrespect to the important parameters of themodel. For each of the important parametersof the model (see the description in AppendixA), we have varied the parameter by changingit from the subjective 50th percentile to thesubjective 90th percentile ." The exact deri-vation of the uncertainty range was developed

'S Symbolically, we can represent the RICE model as amapping, Y, = F(X,_,- ; 1'), where Y, is the vector of en-dogenous and policy variables, X, _ r is a vector of currentand lagged exogenous variables, and r is the set of un-certain parameters . The base run estimates outcomes forthe "best-guess" parameters (r 90, which represents the50th percentile of the distribution of the parameters) . In

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in Nordhaus (1994 Table 6 .1) , and the readeris referred to that reference for a full discussion .

Figure 10 shows the results of the sensitivityanalysis . That figure shows the sensitivity ofthree important variables in the cooperativeequilibrium : the carbon tax in 2000, the effi-cient reduction of CO 2 emissions in 2000, andthe change in global mean temperature in

the sensitivity analyses, we estimate the (subjective) 90thpercentile of the distribution, T 90 . Figure 10 shows theratio of different outcomes for the 90th percentile of avariables to the 50th percentile of that variable ; that is,Di = F(X,_ t ; F90)/F(Xr_, ; F 50) where Ai is the ratio ofoutcomes for variables of interest when varying the ithparameter, F 50 is the vector of I' with all variables set attheir 50th percentile while F9° is the vector of parameterswith all variables but the ith set at the 50th percentile whilethe ith parameter is set at its 90th percentile .

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Figure 10 indicates that the results are ex-tremely sensitive to the pure rate of social timepreference. The low rate of time preference(equal to 1 rather than 3 percent per year) in-creases the carbon tax by a factor of 4 and thecontrol rate by a factor of almost 2 . In addition,the damage intercept (which is the fraction ofoutput lost from a doubling of atmosphericC02 ) leads to a marked increase in both thecarbon tax and the control rate . The other

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FIGURE 10. SENSITIVITY TESTS FOR PARAMETERS

Note : The variables on the horizontal axis are parameters of the RICE model as defined in Appendix A . The markersindicate the ratio of the outcome variable in the sensitivity case to the outcome for the base case . The sensitivity casesset the values of the variables at the subjective 90th percentile . The outcome variables are the optimal cooperative carbontax in 2000, the optimal cooperative reduction rate for CO, emissions in 2000, and global mean temperature in 2100 .

variables are relatively unimportant for theresults . t6

In analyzing model sensitivity, it is easy tobecome lost in the details. For policy purposes,however, the single most critical question ishow an uncertainty affects current policy,which is best seen in the effect on the carbontax. By this standard, the two crucial parame-ters are the discount rate (which indicates the

16 These results parallel closely the findings of otherstudies on the sensitivity of policy to uncertainties aboutmajor variables .

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relative importance of the future compared tothe present) and the damages from climatechange (which measure the willingness topay to prevent or slow climate change) . It isinteresting to note that both major uncer-tainties involve human preferences ratherthan pure questions of `fact" about the nat-ural sciences.

III. Conclusions

To summarize, this paper has presented theRICE model, which is a new dynamic, multi-region, general-equilibrium model of climateand the economy . It differs from earlier work,which focussed on a globally aggregated ap-proach, by introducing production, consump-tion, emissions, and damages for differentregions. This approach compares three differ-ent strategies for the control of global warm-ing : a market approach in which no climatechange policies are taken, a global coopera-tive approach in which all countries chooseclimate-change policies to maximize global in-comes, and a noncooperative or nationalisticapproach in which each country takes policiesto maximize its own national income . Theseresults are tentative and subject to revision .Further work will be necessary to test their ro-bustness against alternative assumptions, toappraise the results for different coalitions, andto compare the results against other models .Subject to these reservations, the following arethe major conclusions .

First, the model produces results for thebaseline (market or uncontrolled) which dif-fer significantly from other projections ."Output and emissions in the RICE model areestimated to grow much more rapidly thanin the DICE model or than in many inter-national projections (such as that of the In-tergovernmental Panel on Climate Change) .The more rapid growth comes largely froma view of the growth process in which thereis considerable but incomplete convergenceof per capita incomes of countries . Thehigher projected growth of output, emis-

sions, and CO2 concentrations as comparedwith the earlier DICE model is largely offsetby revisions in estimated effects of othergreenhouse gases. As a result the estimatedextent of global warming in the market caseby the year 2100-approximately 3°C-differs little between the RICE model andother estimates .

Second, the efficient or cooperative policiesin the regional model confirm estimates madein globally aggregated models, such as theDICE model. The best summary variable forefficient controls is the carbon tax, which iscalculated to be about $6 per ton carbon in2000, a number that is virtually identical toestimates for the efficient policy in the DICEmodel. '$ The estimated degree of control in theRICE model is, however, estimated to growsomewhat more rapidly than in the DICE andother models, with estimated efficient carbontaxes at the end of the next century near $27per ton carbon.

Third, the RICE model provides estimatesof the efficient control rates in differentregions as well. In the efficient solution, car-bon taxes are identical in all regions . The con-trol rates will differ, however, because ofdifferent costs of reducing CO2 emissions. Theestimates presented here indicate that the ef-ficient emissions control rates will be highestin China and the former Soviet Union and low-est in Japan and Europe, with the differencesbeing at least a factor of two . These resultsindicate that there will be substantial ineffi-ciencies in any policy (such as that currentlyin force under the Framework Convention)that equalizes emissions control rates acrosscountries or does not allow trading of emis-sions permits .

Fourth, a major contribution of this studyis to estimate the difference between the ef-ficient policy and the noncooperative policy .The noncooperative or nationalistic policyis one in which countries maximize theireconomic welfare taking policies of othercountries as given . This implies that smallcountries, whose climate-change policieshave little effect on their own economic

"In the discussion that follows, the results for theDICE model refer to DICE-123 as presented in Nordhaus

$ All dollar figures refer to prices in 1990 U .S . dollars(1994) .

at 1990 market exchange rates .

762

welfare, will have little incentive to reduceemissions while the largest countries willhave greatly attenuated incentives to engagein costly reductions in CO 2 emissions. Thecalculations here indicate that the controls inthe noncooperative case (as measured by theaverage rate of carbon tax) will be only '/ 25 ofthe level of the cooperative case. That is, whilethe average carbon tax in 2000 is estimatedto be about $6 per ton carbon in the coop-erative case, it is calculated to be about $0 .24per ton in the noncooperative case . More-over, the divergence between the coopera-tive and the noncooperative policies iscalculated to increase over time as the in-equality of county sizes decreases, and thisdivergence would increase further if largecountries like China, India, Russia, Canadaor the United States splinter into smallercountries or decision-making units .

Fifth, these results indicate that the stakes incontrolling global warming are modest in thecontext of overall economic activity over thenext century. If our estimates are accurate,they indicate that the losses from global warm-ing will be in the range of 1 to 2 percent ofglobal income over the next century . The netcosts (that is, climate-change damages lessmitigation costs) can be reduced by perhaps'/3 percent of income by a judicious choiceof climate-change policies-although, to besure, the impact is much greater on our de-scendants than on ourselves. According toRICE, successful cooperation would lead tonet gains, but the failure to cooperate is un-likely to lead to economic disaster over thenext century .

Sixth, the pattern of gains and lossesfrom different strategies is quite surprising.All countries gain from the noncooperativeapproach, although the amount of gain isrelatively small . The net gains from coop-eration without international transfers arequite unevenly distributed, with the majorgains accruing to developing countries withlow and rapidly growing emissions . High-income countries have but modest gains tocooperation, but the United States actuallyloses from cooperating relative to a nonco-operative strategy. In addition, the time pathof gains and losses indicates that even inthe cooperative scenario, all regions except

THE AMERICAN ECONOMIC REVIEW

SEPTEMBER 1996

Japan show reductions in cumulative dis-counted consumption until after the middleof the next century .

Seventh, the results indicate that there aremajor gains to taking an efficient cooperativeapproach to coping with global warming asopposed to the noncooperative approach. Weestimate that the net economic gain from anefficient policy has a discounted value of $344billion relative to the market scenario, whilethe noncooperative policy has a gain of only$43 billion . Hence, there are clear gains to at-taining a cooperative policy (assuming, ofcourse, that the policy is itself efficient) . Thegains from cooperation would be even largerif climate change proved to have catastrophicconsequences that are very unevenly felt acrossnations .

In sum, the results of this new integratedmodel of climate and the economy empha-sizes the implications of the fact that whileclimate change is a global externality, thedecision makers are national and relativelysmall. These inherent difficulties involved inplanning over a horizon of a century or moreabout so uncertain and complex a phenom-enon are compounded by the dispersed na-ture of the decisions and the strong tendencyfor free-riding by nonparticipants in anyglobal agreement . Countries may thereforebe triply persuaded not to undertake costlyefforts today-first because the benefits areso conjectural, secondly because they occurso far in the future, and third because no in-dividual country can have a significant im-pact upon the pace of global warming. Thepresent study indicates that the third of these,the dispersed nature of the decision makingand the consequent diluted incentives to act,is a powerful hindrance to setting efficientclimate-change policies .

APPENDIX A: EQUATIONS OF THE RICE MODEL

This appendix gives the details of the RICE model . Wefirst list and define the variables and then provide the com-plete equation listing .

1 . Variables

The variables are as follows. In the listing, t alwaysrefers to time (t = 1990, 2000, . . .) while i refers to theregion (i = 1, . . . , n = USA, Japan, Europe, . . .) . Theregional definition is given in Appendix B .

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NORDHAUS AND YANG: CLIMATE-CHANGE STRATEGIES

763

Exogenous Variables . 2. Equations

A; (t) = level of technologyPi (t) = population at time t, also proportional to labor (Al) max W= (piU[ei(t),Pi(t)]

inputs ,;co

r-0 i=1 1+(

P)0(t) = forcings of exogenous greenhouse gases

4iPi(t)[ci(t)' - - 1]

oi= (1 - a)(1 + p)'Parameters.

a = elasticity of marginal utility of consumptionb,, i , b2 = parameters of emissions-reduction cost function,6 = marginal atmospheric retention ratio of CO 2

emissionsy = elasticity of output with respect to capital6, = rate of depreciation of the capital stock

subject to

(A2)

Qi(t)=Ai(t)K(t)''Pi(t)'-r

(A3)

Y,(t)=0i(t)Qi(t)

(A4)

Ci (t) = Y(t) - Ii(t) + I IMi .i(t)6M = rate of transfer of CO 2 from atmosphere to other

reservoirs1. = feedback parameter in climate model (inverse to

temperature-sensitivity coefficient)p = pure rate of social time preferenceQ t (t) = CO 2 emissions/output ratio

-

EXi.i(t)i*i

G, (t)r,, T 2 , T 3 , r 4 = parameters of climate equation (T, is a (A5) ei(t) = I, (t)

function of the heat capacity of the atmosphere and up-per ocean while r 2 depends upon the turnover time be- (A6) Ki(t)=(1-6K)Ki(t-1)+1(t)tween the upper ocean and the deep ocean)

0 , i , 0 2 = parameters of climate damage function (A7) Ei(t) _ [I - pi (t) I u i (t) Qi (t),

0 G

Endogenous Variables .(A8) M(t) = /3 Ei (t) + (1 - 6M)M(t - 1)Ci (t) = total consumption

ci (t) = per capita consumption'CAi (t) = current account balance (A9) T(t) = T(t - 1)

Di (t) = damage from greenhouse warmingEi (t) = CO2 emissions +r,[F(t)-XT(t- 1)] -T2[T(t- 1)-T*(t- 1)]EX i ,i (t) = exports from region i to region j T3F(t) = radiative forcing from all greenhouse gas

concentrations (A10)T(t - 1)-T*(t- 1)

T*(t) = T*(t - 1) +Sl i (t) = output scaling factor due to emissions controls T4and to damages from climate change

Ki(t) = capital stocklMi , (t) = imports from region i to region jM(t) = increase in mass of CO 2 in atmosphere from pre-

industrial level

(All)

(A12)

4 .1 log[ M(t)/M(0) ] 0(t)F(t) =

+log (2)

1 - b, .iµi (t) °S2 ; (t) =

i = 1,'

, 2, . . . , n .NFAi (t) = net foreign assets of country i¢ i = welfare weight on country iQ i (t) = gross domestic or regional productR(t) = net rate of return on capitalT(t) = atmospheric temperature relative to preindustrial (A13)

+ B,,i T(t) e2

E YQi(t)`

8KR(t) = >

-level

T*(t) = deep ocean temperature relative to preindustriallevel (A14)

E Ki (t)i=i

NFA i (t)=NFAi (t-1)+CAi(t-1)ui (t) = u i [ci (t)] = utility of per capita consumptionW = social welfare function determined by country con- (A15) CA i (t) = R(t)NFAi (t)

sumption levelsY,, (t) = gross national or regional product (net of climate

damage and mitigation costs)

(A16)

+ I, IMi,i(t) - ± EXi.i(t)iii

i'i

-CAi(t) < 0.1Qi (t)

(A17) -NFA i (t) s 0 .1Q i (t)Policy Variables .

Ii (t) = gross investment (A18) EXi.i(t) :~ Qi(t) .p i (t) = rate of emissions reduction i*i

Less than 50,000 tons per year .

REFERENCES

Bodansky, Daniel M. "Emerging Climate ChangeRegime." Annual Review of Energy and theEnvironment, 1995, 20, forthcoming.

Brooke, Anthony; Kendrick, David and Meeraus,Alexander. GAMS: A user's guide . Red-wood City, CA : The Scientific Press,1988 .

Dean, Andrew and Hoeller, Peter . Costs of re-ducing CO2 emissions : Evidence from sixglobal models, OCDE/GD(92)140, Orga-

nization for Economic Cooperation and De-velopment, Paris, processed 1992 .

EMT, Energy Modeling Forum 14 . "BackgroundPapers" and "Tabulations of Model Runs ."Unpublished, 1995 .

Fankhauser, Samuel. "The Economic Costsof Global Warming : Some Monetary Esti-mates," in Y . Kaya, N. Nakicenovic, W. D .Nordhaus, and F. L . Toth, Costs, impacts, andbenefits of CO2 mitigation . Laxenburg, Aus-tria: International Institute for Systems Anal-ysis, Laxenburg, Austria, CP-93-2, 1993 .

1) United States2) Japan3) Former Soviet Union4) China5) Europe6) Huge7) Large8) Midsized9) Small10) Tiny

TotalBottom 5 groups (ROW)

1

5,464,7961

2,932,0551

855,2071

370,0241

6,828,0421

295,7602

586,07211

2,155,91038

1,272,414137

318,464

21,078,7464,628,621

250,372123,537289,324

1,133,683366,497849,515327,274442,370876,027607,503

5,266,1023,102,689

1,370 .0291 .5

1,065.7805 .5872 .3215 .4593 .0789 .7

1,212 .0623 .9

7,839 .13,434 .0

Selected countries in groups 6 through 10 :

Code CountryGross domestic product(millions of 1990 US $)

Population, 1990(thousands)

CO 2 emissions, 1990(millions of tons C)

S 1 India 295,760 849,515 215.4S2 Brazil 479,214 149,042 317.1

Indonesia 106,859 178,232 275.9S3 Canada 566,694 26,522 127.6

Australia 296,053 17,045 72 .1Mexico 244,046 81,724 144 .1Argentina 141,353 32,322 33 .1Turkey 108,447 56,098 35 .3South Africa 101,963 37,959 78 .0

S4 Venezuela 48,599 19,325 43 .0Romania 37,625 23,200 59 .4Nigeria 35,460 96,203 95 .9Egypt 35,400 52,426 22 .3Slovenia 17,331 2,000 4 .8

S5 Kenya 8,675 24,160 5 .0Iceland 6,024 255 0 .5Honduras 2,944 5,105 12 .0Maldives 174 214 0.01Anguilla 23 7 0.01Tuvalu 5 9 0.01

764 THE AMERICAN ECONOMIC REVIEW

APPENDIX B : REGIONAL GROUPING IN THE RICE MODEL

SEPTEMBER 1996

Number of

Gross domestic product

Population, 1990 CO 2 emissions, 1990Country or group countries

(millions of 1990 US $)

(thousands) (millions of tons C)

VOL. 86 NO . 4

NORDHAUS AND YANG : CLIMATE-CHANGE STRATEGIES

Gaskins, Darius W. and Weyant, John P. "EMF-12 :Modeling Comparisons of the Costs of Re-ducing CO 2 Emissions." American EconomicReview, May 1993, 83(2), pp. 318-23 .

Intergovernmental Panel on Climate Change(IPCC). Climate change: The IPCC scien-tific assessment, J. T. Houghton, G. J.Jenkins, and J . J . Ephraums, eds . New York:Cambridge University Press, 1990 .

International Energy Agency (IEA) . Climatechange policy initiatives : 1994 update, Vol.1 . Paris : Organization of Economic Coop-eration and Development, 1994 .

Manne, Alan S. and Richels, Richard . Buyinggreenhouse insurance : The economic costsof CO2 emission limits . Cambridge, MA :MIT Press, 1992 .

Manne, Alan S. and Rutherford, Thomas F. "In-ternational Trade, Capital Flows and Sec-toral Analysis: Formulation and Solutionof Intertemporal Equilibrium Models," inW. W. Cooper and A . B. Whinston, eds .,New directions in computational econom-ics . Dordrecht, Netherlands : Kluwer, 1994,pp. 191-205 .

Mas-Colell, Andreu; Whinston, Michael D. andGreen, Jerry R . Microeconomic theory . NewYork: Oxford University Press, 1995 .

Morgan, M . Granger and Henrion, Max . Uncer-tainty: A guide to dealing with uncertaintyin quantitative risk and policy analysis .New York: Cambridge University Press,1990 .

National Academy of Sciences . Stratosphericozone depletion by halocarbons : Chemistryand transport . Report of a committee of theNational Research Council, National Re-search Council, Washington, DC, 1979 .

765

Negishi, T. "Welfare Economics and the Ex-istence of an Equilibrium for a CompetitiveEconomy." Metroeconomica, 1960,12, pp .92-97 .

Nordhaus, William D . "An IntertemporalGeneral-Equilibrium Model of EconomicGrowth and Climate Change," in Wood,David, ed ., Proceedings of a Conference atMIT, October 1990 .. "To Slow or Not to Slow : The Eco-

nomics of the Greenhouse Effect ." Eco-nomic Journal, July 1991, 101(407), pp .920-37 .. "An Optimal Transition Path for

Slowing Climate Change." Science, No-vember 20, 1992, pp . 1315-19 .. Managing the global commons : The

economics of the greenhouse effect . Cam-bridge, MA : MIT Press, 1994 .

Nuclear Regulatory Commission . Reactor safetystudy: An assessment of accident risks inU.S. Commercial nuclear power plants,NUREG-75/014 WASH-1400. Washing-ton, DC: 1975 .

Peck, Stephen C. and Teisberg, Thomas J ."CETA: A Model for Carbon EmissionsTrajectory Assessment." Energy Journal,1992,13(l), pp. 55-77 .

Wigley, T. M. L. "The Contribution from Emis-sions of Different Gases to the EnhancedGreenhouse Effect," in Ted Hanisch, ed .,Climate change and the agenda for re-search . Boulder, CO: Westview Press,1994, pp. 193-222.

Yang, Zili. "Essays on the International As-pects of Resource and EnvironmentalEconomics." Ph.D. dissertation, Yale Uni-versity, 1993 .

COWLES FOUNDATION PAPERS

This series includes selected articles published by members of the Cowles Foundation staff or byothers working in close association with the Foundation .

Papers not out of print are available from the Cowles Foundation on request . A list of recent papers isgiven below . For a complete list of papers apply to the Foundation .

No . 901 . PRADEEP DUBEY AND JOHN GEANAKOPLOS, "The Value of Money in a Finite-Horizon Economy : ARole for Banks," ECONOMIC ANALYSIS OF MARKETS AND GAMES, edited by Partha Dasgupta, Dou-glas Gale, Oliver Hart and Eric Maskin, 1992 .No. 902. DONALD W .K. ANDREWS, "Nonparametric Kernel Estimation for Semiparametric Models," Econo-metric Theory, 11, 1995 .No. 903 . PETER C .B . PHILLIPS AND Mtco LORETAN, "On the Theory of Testing Covariance Stationarity UnderMoment Condition Failure," ADVANCES IN ECONOMETRICS AND QUANTITATIVE ECONOMICS,edited by G .S . Maddala, Peter C.B . Phillips and T.N . Srinivasan, 1995 .No. 904 . ALVIN K . KLEVOtrtcK, "The Economic Theory of Crime and the Problems of a Society in Transition,"International Journal of the Economics of Business, Vol . 2, No . 2, 1995 .No. 905 . PETER C .B . PHILLIPS, "Fully Modified Least Squares and Vector Autoregression," Eco nometrica,Vol . 63, No. 5, 1995 .No. 906 . WILLIAM COOK, THOMAS RUTHERFORD, HERBERT E . SCARF AND DAVID SHALLCROSS, "An Imple-

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No. 911 . PETER C .B . PHILLIPS, "Bayesian Model Selection and Prediction with Empirical Applications,"Journal of Econometrics, 69, 1995 .No. 912 . PETER C .B . PHILLIPS, "Robust Nonstationary Regression," Econometric Theory, 11, 1995 .No. 913. YUICHI KITAMURA AND PETER C .B . PHILLIPS, "Efficient IV Estimation in Nonstationary Regres-sion," Econometric Theory, 11, 1995 .No. 914 . PETER C .B. PHILLIPS, "Trending Multiple Time Series," Econometric Theory, 11, 1995 .No. 915 . OLIVER LINTON, "Second Order Approximation in the Partially Linear Regression Model,"Econometrica, Vol . 63, No . 5, 1995 .No. 916. DONALD W .K. ANDREWS AND WERNER PLOBERGER, "Admissibility of the Likelihood Ratio TestWhen a Nuisance Parameter is Present Only Under the Alternative," TheAnnals of Statistics, Vol . 23, No .5,1995 .No. 917 . PETER C .B . PHILLIPS AND WERNER PLOBERGER, "An Asymptotic Theory of Bayesian Inference forTime Series," Econometrica, Vol . 64, No.2, 1996 .No. 918 . OLIVER LINTON AND JENS PERCH NIELSEN, "A Kernel Method of Estimating Structured Nonpara-metric Regression Based on Marginal Integration," Biometrika, 82, 1995 .

No. 919. YOOSOON CHANG AND PETER C.B. PHILLIPS, "Time Series Regression with Mixtures of IntegratedProcesses," Econometric Theory, 11, 1995 .

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No. 920 . WILLIAM D . NORDHAUS, "Locational Competition and the Environment : Should Countries Harmo-

nizeTheir Environmental Policies," LOCATIONAL COMPETITION IN THE WORLD ECONOMY : SYM-

POSIUM 1994, edited by Horst Siebert, 1995 .

No. 921. PETER C .B . PHILLIPS, JAMES W . McFARLAND AND PATRICK C . McMAHON, "Robust Tests of ForwardExchange Market Efficiency with Empirical Evidence from the 1920s," Journal of Applied Econometrics,

Vol . 11, 1996 .No. 922. ROBERT J . SHILLER, FuMIKO KON-YA AND YOSHIRO TsuTsul, "Why Did the Nikkei Crash? Expand-ing the Scope of Expectations Data Collection," The Review of Economics and Statistics, Vol . 78, No . 1,1996 .No. 923. DONALD W .K. ANDREWS . "Admissibility of the Likelihood Ratio Test When the Parameter Space isRestricted Under the Alternative," Econometrica, Vol . 64, No . 3, 1996 .

No. 924. VASSILIS HAJIVASSILIOU, DANIEL MCFADDEN AND PAUL RUUD, "Simulation of Multivariate NormalRectangle Probabilities and Their Derivatives : Theoretical and Computational Results," Journal of Econo-

metrics, 72, 1996.No. 925. DONALD W .K. ANDREWS, INPYO LEE AND WERNER PLOBERGER, "Optimal Changepoint Tests forNormal Linear Regression," Journal of Econometrics, 70, 1996 .No. 926 . PETER C.B . PHILLIPS, "Econometric Model Determination," Econometrica, Vol . 64, No . 4, 1996 .

No. 927 . RAY C . FAIR, "Econometrics and Presidential Elections," Journal of Economic Perspectives, Vol .

10, No . 3, 1996 .No. 928. ADAM BRANDENBURGER AND BEN POLAK, "When Managers Cover Their Posteriors : Making theDecision the Market Wants to See," Rand Journal of Economics, Vol . 27, No. 3, 1996.

No. 929. MARTIN SHUBIK, "Why Equilibrium? A Note on the Noncooperative Equilibria of Some MatrixGames," Journal of Economic Behavior and Organization, 29, 1996 .No. 930. WILLIAM D. NORDHAUS AND ZILI YANG, "A Regional Dynamic General-Equilibrium Model ofAlternative Climate-Change Strategies," American Economic Review, Vol . 86, No . 4, 1996 .

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