Measuring the Welfare Cost of Climate Change Policies: A Comparative Assessment Based on the Computable General Equilibrium Model GEMINI-E3

Environmental Modeling and Assessment 8: 199–217, 2003. 2003 Kluwer Academic Publishers. Printed in the Netherlands.

Measuring the welfare cost of climate change policies:A comparative assessment based on the computable general

equilibrium model GEMINI-E3

Alain L. Bernard a and Marc Vielle b

a Conseil Général des Ponts et Chaussées, Ministère de l’Equipement, des Transports et du Logement, Tour Pascal B,92055 Paris La Défense Cedex 04, France

E-mail: [email protected] CEA - IDEI - LEERNA, Université des Sciences Sociales, Place Anatole France, 31042 Toulouse, France

E-mail: [email protected]

Measuring the welfare cost of climate change policies is a real challenge, raising difficult issues of micro- and macro-economics: cost-benefit analysis on the one hand, foreign trade and international specialization on the second hand. At the domestic level the possibleexistence of distortions, in particular in the fiscal system, may either increase or alleviate the welfare cost of a climate change policy, asillustrated by the debate on “double dividend”. Effects on the prices in international markets and distorted competition between countriescommitted to abate (Annex B) and uncommitted countries affect both the sharing of the burden, in particular through the change in the termsof trade, and the allocation of activities with the frequently waved threat of “delocalization”. Based on a companion theoretical analysis, thepresent paper aims at putting order in the welfare analysis of climate change policy and to present and compare various estimations, issuingfrom macro- or computable general equilibrium models. Beside the global welfare cost, the paper focuses on the marginal abatement costand its relation to the carbon price.

Most present conceptual and applied analysis is based on the case of a single domestic household-consumer. Taking into account severalconsumers raises new challenges, concerning equity but even more fundamentally the mere definition of fiscal distortion, which have notyet been really addressed.

Keywords: Kyoto Protocol, carbon tax, tradable permit, marginal abatement cost, terms of trade, deadweight loss of taxation, welfare cost

1. Introduction

Measuring the welfare cost of climate change policies isa real challenge, as evidenced by the very large range ofresults obtained in the literature for comparable scenarios,such as, for instance, the implementation of the Kyoto Pro-tocol. Even the sign of the welfare change is a topic fordebate as the “double-dividend” theory aims at pointing thatthe cost may be negative, yielding a welfare gain in additionto the environmental benefit.

The cost of these policies, which is basically linked todistortions created in the economy – coming, in some cir-cumstances, on top of already existing distortions – is wellknown in the economic literature as the “Deadweight Loss ofTaxation”. But in actual situations its measurement may bevery difficult to perform with a good precision. The analysisis moreover complicated by the spill-over effects channeledthrough international markets and yielding, according to thecases and to the countries, a gain or a loss from “terms oftrade”. Finally, not only the total welfare cost is at stake – anindicator of the lower limit of the environmental gain whichjustifies to implement the contemplated policy – but also themarginal cost, which is relevant for a country in determiningwhether to purchase or to sell, and in which amount, in aneventual market of tradable permits. This marginal cost isnot necessarily – and is not generally – equal to the carbonprice (though often in the literature, and in particular in the

presentation of results obtained with numerical models, thetwo are undistinguished).

The present paper, which is based on classical economicconcepts and theoretical developments presented in the lit-erature and in other papers by the authors, aims at show-ing how they can be implemented in an actual and compre-hensive representation of the world economy. ComputableGeneral Equilibrium models are obvious candidates for thistask. The model GEMINI-E3, which has been specificallydesigned in this perspective, and benefits now of a contin-uous eight years experience, has been selected for this pre-sentation and for comparison with results of other models orstudies, but it is to be viewed mainly in its pedagogical as-pect. Numerical results depend on assumptions which wouldbe too long to present in detail and argue. Qualitative results– in particular the structure of costs and the relative impor-tance of their components – is the important lesson whichmay hopefully be expected.

The paper has five sections. Section 2 briefly points tothe specific characteristics of the greenhouse effect external-ity (sometimes labeled as a “pollution” though it is not in-trinsically a pollution) compared to other externalities (pol-lutions), which explain why a micro-economic measurement– or an assessment through a partial equilibrium model – isirrelevant in the general case and misses to capture all com-ponents of the welfare cost. Specific macro-economic costs,

200 A.L. Bernard, M. Vielle / Measuring the welfare cost of climate change policies

resulting from distortions1 in the economy and from foreigntrade spill-over effects, are to be taken into account.

Section 3 recalls the theoretical concepts and tools of wel-fare analysis that are relevant for assessing global policiessuch as climate change, and in particular the definition ofcosts – total and marginal – and their measurement in actualsituations. A simple algebraic presentation is given in thecase of a closed economy, illustrating the concept of Dead-weight Loss of Taxation and the effect of initial distortions.Interactions between domestic and imported costs are thendealt with.

Section 4 presents the main characteristics of the modelGEMINI-E3, and section 5 the results of standard climatechange policy scenarios, with a comparison to results fromother – either of the CGE type or sectoral – models andspecific studies, in particular an important appraisal of theKyoto Protocol performed by the US Department of En-ergy.

Section 6 recapitulates the main teachings of the paperand lists some further desirable developments, in particularthe issues raised by redistributive effects of climate changepolicies and equity considerations.

2. The main characteristics of the greenhouse effect

As an externality, the greenhouse effect has several char-acteristics which set it apart from other externalities, andin particular the main usual pollutions. Consequently, cost-benefit analysis in this area raises specific problems, whichwill be presented and thoroughly developed in the next sec-tion.

The first and obvious characteristic of greenhouse effectis the global, and not local, scope of the associated “pol-lution”. Where the emission takes place is unimportant, atleast in a first approximation, with respect to global warm-ing and even the distribution of climate changes all over theEarth. A closely linked aspect, not encountered in any otherform of pollution, is the observation that effects and notablyeconomic damages (eventually benefits) vary from one re-gion to the other, and thus from one country to the other.One can speak, as does Nordhaus [19], of a “global publicgood”. A collective response to the challenge, and in par-ticular some form of coordination of domestic policies, areobviously essential considering the risks usually experiencedin the provision of public goods: insufficient coverage of de-mand due to the “free rider” phenomenon, inefficiencies inthe production and distribution of the good, inequitable shar-ing of the costs.

A second characteristic is the very long delay betweenemissions and effects on climate, due in particular to therole played by oceans in the retention of gases, notably thedioxide of carbon. Any present action, for instance a steadycurbing down of emissions, has no significant effect beforethe middle of the present century. Closely linked to these

1 This term has to be clarified, and will be in later developments.

characteristics is uncertainty, in particular concerning tech-nical progress: on the one hand global productivity in theworld economy, which affects the average growth of produc-tion and of demand for energy; on the other hand, technicalprogress and new technology in the use and in the productionof energy, in particular renewable energy.

Uncertainty also affects the scientific knowledge itself onthe greenhouse effect phenomenon, the actual role played byhuman activities as well as the nature and the importance ofthe damages caused by climate warming. Existence of irre-versible effects – either resulting from an increased concen-tration of GHG in the atmosphere in the case of a “laissez-faire” policy or on the contrary in the form of sunk-costs inthe case of an active abatement policy – still complicates thepicture.

A third specific – and probably the most important – char-acter of the greenhouse effect is that there does not exist, atleast up to now, an “end-of-pipe” device giving a direct con-trol on emissions which would be at the magnitude of theproblem: existing sinks are of limited importance, and har-nessing techniques are not likely to be operational and eco-nomically profitable before long. Mitigation of the green-house effect rests mainly on indirect actions and in particu-lar on curbing down of demand for fossil fuels. This is tobe obtained through various substitutions in the economy:(i) between fossil fuels, in favor of the fuels that have theleast carbon content relatively to the heat capacity (naturalgas in particular); (ii) between factors of production, notablybetween energy and capital; and (iii) between commoditiesin final consumption, in favor of the goods which have asmaller carbon content. A uniform carbon tax or a marketof emission permits, without compensation or rebate for in-stance in the form of “grand-fathering”, appears to be thesimplest and most efficient way of giving the incentives –in the short run – and the signal – in the long run – for thedesirable substitutions2.

As a consequence of this limited availability of mitiga-tion policies, there does not exist a direct or micro-economicmeasure of the cost of emission abatement. The tax is notin itself a cost or an economic loss because it is redistrib-uted, in one way or another, in the economy. There is never-theless a cost because taxation (or any equivalent tool) gen-erates distortions in the economy, or increases (eventuallyalleviates) them when distortions are pre-existing. The wel-fare cost of the mitigation policy then results from the globalmechanisms at work in the economy, involving the decisionsof all agents and the re-balancing of markets, and eventually

2 Any mechanism aiming at compensating firms of the increased cost ofproduction resulting from the tax (free allowance of permits through“grandfathering” or “output-based allocation”) is not fully efficient be-cause, if it may give the adequate incentive to abate for concerned firms,it has no incentive effects downstream on users of the goods produced bythese firms. It is desirable not only to refrain emissions from pollutingindustries, but also to refrain consumption of goods which have a highpollution content (compared to goods which have a low pollution con-tent). However, in some specific situations and in particular in the case ofunregulated industries, it may be desirable to provide for a compensationmechanism for regulated industries (see in particular [5]).

A.L. Bernard, M. Vielle / Measuring the welfare cost of climate change policies 201

depending on the way environmental levies are redistributedto agents.

A classical result is that, if there is no distortion in theeconomy, which means in particular that the tax system isneutral or “optimized” and that there is no rigidity nor ra-tioning in any market, then the marginal abatement cost isexactly equal to the tax (and remains equal to the environ-mental tax when abatement increases, if the tax system re-mains neutral or “optimized”). Total cost is then the integralof the marginal cost along the demand curve.

In the economic reality there are distortions, of differenttype, and one can expect that the marginal cost deviates fromthe tax, sometimes significantly. Then the previous simplerule does not apply and the measure of costs – global andthe marginal – becomes a more complex exercise.

3. Welfare analysis for climate change policies

A very abundant and diverse literature has grown-up inthe past fifteen years on the welfare analysis applicable toclimate change policies. A primer in the tradition of first-best analysis is from Nordhaus [16–18].

Goulder [15] was probably the first to evoke the conse-quences on the measurement of welfare cost of pre-existingdistortions in the economy, through the interactions withother taxes. This has lead to the burgeoning so-called“double-dividend” literature, which stresses that in somecases the negative effects of pre-existing distortions canbe alleviated when implementing a climate change policythrough environmental levies, under the condition that ac-cruing receipts are adequately redistributed. Possibility of adouble-dividend is obvious, but in some way naïve or evena truism. Consider the case of a country subsidizing energyfor customers, either firms or households – it is not a purelyhypothetical assumption, as it was the case of Soviet Unionand other Eastern Europe countries before 1990, and appearsto be still the case at least in Russia and Ukraine. Such a pol-icy, which deviates from the conditions of Pareto efficiency,a priori entails a welfare loss. Taxing now energy (witha new label, such as GHG tax or environmental levy) can-cels partly or totally the pre-existing subsidization and thenbrings the economy closer to the Pareto optimum. There isthen a welfare gain, in addition to the environmental gain ofabating emissions.

But the true question is why the subsidy? It may resultfrom unavoidable constraints (their removing being costlierthan their welfare consequences), or for specific policy tar-gets such as equity considerations. For instance, it is wellknown that, in developed countries, the share of energy itemsis higher for low-income than for high-income households.Subsidizing energy is then desirable for equity considera-tions, but of course it must be channeled through the relevantfiscal tools.

Underlying the consideration of possible distortions (andnotably tax-distortions) in the economy is the unavoid-able reference to optimal taxation and second-best analysis.

Starting from Boiteux [8] and later Diamond and Mirrlees[10], there is now a robust theoretical corpus to which well-known economists have brought additions and/or generaliza-tions (in particular [13]). Concerning the inclusion of exter-nalities or pollutions, the primer is from Sandmo [20], but ina limited framework of restrictive assumptions.

What appears obvious – and at the same time important– is that in a second best3 framework a double-dividend ef-fect is not likely to appear: adding new constraints on theeconomy may only entail a welfare loss (independently ofthe eventual environmental gain). It is then in such a frame-work, as general as possible and in particular taking into ac-count foreign trade, that the welfare analysis of global en-vironmental policies can be coped with. Let us note that aComputable General Equilibrium model is an implicit rep-resentation of such a second-best framework: not an explicitone because it has not been checked if the initial situationis effectively an optimum, and in particular with respect towhich Social Welfare Function (for each country or for theworld economy)? We will come back later on the “implicit”CGE approach, and consider theory first.

3.1. General results of second-best theory

How does the consideration of externalities affect opti-mal taxation? The issue is in fact twofold. The first as-pect is purely domestic and is the topic of Sandmo’s paper:how (indirect) taxation, aimed at financing public outlays, ischanged when the final consumption by households of somecommodities generates externalities or pollution?

The second aspect is the generalization to the case of aworld externality, as is the GHG effect, in the framework ofa world market of tradable permits in which countries maypurchase or sell emissions rights. The problem is the exis-tence and the properties of an economic equilibrium betweencountries, each implementing a second-best fiscal policy in-cluding the possibility of trading pollution rights in the in-ternational market. In both cases, which are closely interre-lated, it is consistent with observation and in fact clearer toconsider emissions both by firms and by households. Thenthe carbon price is the tax set to firms, and the issue of opti-mal commodity taxation is how this carbon price is incorpo-rated in the prices of final goods.

The problem in its generality has been examined in [3],considering two paradigms of optimal taxation. In the Dia-

3 Second-best theory – in opposition to the first-best or Paretian framework– aims at taking into account constraints which are not solely “physical”(those resulting from production and utility functions, initial resourcesand the balance of demands and supplies in every market). Non-physicalconstraints are mainly budgetary, and involve the budget surplus or deficitof government or public utilities, but may also be of other types (for in-stance, what R. Guesnerie labels “deviant behavior” by some agents).The first appearance of the term “second-best” is in the famous Lipsey–Lancaster article of 1956, but the first rigorous treatment is from Boiteux(also in 1956) concerning budgetary balance of public utilities with in-creasing returns. Transposition to optimal fiscal policy – which is themain field of application of second-best theory – is due to Diamond &Mirrlees. Generalizations have been implemented by R. Guesnerie.


mond and Mirrlees paradigm, the results are very close tofirst best (except of course commodity taxation). This isrelated to a fundamental property of this model which isproduction efficiency. In particular the marginal abatementcost is equal to the pollution (or carbon) tax, and a compet-itive equilibrium between second-best economies is Paretoefficient (with a definition of Pareto efficiency taking intoaccount second-best constraints applying to each country).Consequently, each country purchases or sells permits ac-cording to its domestic pollution tax – which is also the mar-ginal abatement cost. Carbon prices – and marginal abate-ment costs – are then equalized across countries, and we canspeak of a world carbon price and a world abatement cost,the two being equal.

Another consequence is that there is no counter-indicationfor allowing firms, eventually households, to buy or sell per-mits in the international market (if, of course, their rightsare precisely defined). The only purely domestic decisionis commodity taxation, which incorporates domestic con-straints on taxation and domestic targets, in particular eq-uity considerations. Comparison between two similar coun-tries will for instance probably show, in the specific case ofclimate change, that energy taxation for households will belower in a country aiming at far-reaching income or welfareredistribution than in a country aiming at moderate or no re-distribution.

Specific – and nice – properties of the D&M paradigm arelinked to the assumption that there is no constraint on taxa-tion, and in particular that profits can be totally taxed. Dis-carding this assumption complicates considerably the pic-ture, and only consideration of a single final consumer maybe contemplated in order to get manageable results. This iswhat is referred to in [3] as the “Boiteux paradigm”, sincethe model then closely parallels the seminal paper of 1956which set the foundations of second-best methodology.

In such a framework, the carbon price and the marginalabatement cost usually differ, though numerical simulationsshow that the difference is fairly small. The rational behaviorby each country is to trade permits according to its marginalabatement cost. Then, in a competitive equilibrium betweensecond-best economies, marginal abatement costs – and notpollution (or carbon) taxes – are equalized across countries.Consequently allowing firms or households to trade directlyin the international market of permits is not desirable be-cause it would lead to the equalization of pollution taxes,not of marginal abatement costs4. This would in particularlead to the “paradoxical” situation for some countries of ex-periencing a welfare loss from trading permits, a worse-offsituation after than before trading, which is easy to under-stand because a country then sells permits at a price inferiorto its cost, or purchases at a price higher than the cost [1].

That the rational behavior by each country is to equal-ize its marginal abatement cost to the international price ofpermits is non-debatable leaves open the question of Pareto

4 Unless a specific domestic tax compensating the difference between thecarbon price and the marginal abatement cost is implemented in eachcountry, see [7].

efficiency (as above, taking into account the constraints andthe domestic targets of taxation). The result demonstratedin [3] is that Pareto efficiency holds only if the global pro-duction function in each country is homothetically separablewith respect to the vector of output. However, if this prop-erty is not verified and as shown by numerical simulations,the Pareto inefficiency is not likely to be important enough tojustify a centralized coordination of domestic climate changepolicies.

3.2. An illustrative presentation with a two-commoditymodel

Assessing climate change policies is now and to a verygreat extent performed through models, and in particularthrough CGE models which present the great advantage oftaking into account all the effects – direct and indirect, do-mestic and international – of an exogenous change in the(world) economy and then giving the opportunity to performall desirable welfare calculations. From micro-economicdata yielded by scenario simulations – mainly changes inprices and quantities of all goods and factors, demands andsupplies by all economic agents – all aggregations and wel-fare calculations can be performed, but it is necessary fora clear understanding of the results to give some sense andstructure to these aggregates, and if possible compare them.

In the results of most CGE models presented in the lit-erature, welfare cost is usually represented either by thechange in GDP at constant prices or by the change in House-holds’ Final Consumption at constant prices. For micro-economists, and in particular welfare economists, the rel-evant measure is surplus, at it was originally defined byDupuit, and is expressed in the modern welfare literature bythe Compensating5 Variation of Income (CVI).

That the two first indicators do not provide a relevantmeasure of the economic cost can be easily understood. One– even the major – effect of the considered policy is tochange the relative prices, precisely in order to favor the de-sirable, and least costly, substitutions. Any measure by anaggregate quantity at constant prices, in line with the rulesof national accounting, cannot capture the very part of thewelfare loss (eventually gain) resulting from this change inrelative prices.

Households’ surplus provides a reliable measure by rep-resenting the effect of change in relative prices by an equiva-lent income loss. In particular, the sign of surplus is the sameas the sign of utility change, positive if utility increases andnegative if utility decreases. However, households’ surplusis a partial indicator as it does not take into account changesin other elements of aggregate demand, notably investmentand government consumption. The latter is generally con-sidered as constant, i.e., the same in the policy and in thereference scenarios. In order to cope with the problem raisedby investment, two possibilities are available:

5 Eventually, “Equivalent” Variation of Income (EVI). When the change inthe economic equilibrium is not too important, the two figures are veryclose one to the other.


– consider only the discounted surplus over a long term pe-riod. Changes in productive investment then materializein changes in aggregate production of subsequent periodsand consequently of households’ consumption and this isconsistent with the approach of optimal growth theory;

– constrain global investment (but evidently not its alloca-tion among sectors) to remain unchanged. This is themethod favored in GEMINI-E3 as it will be detailed later,in order to get significant annual welfare costs. Effec-tively, as it will be shown below, this is essential for reck-oning marginal costs. Imports and exports are not to bespecifically constrained for this calculation because CGEmodels, and it is the case of GEMINI-E3, usually incor-porate a global constraint of foreign trade balance (zeroor exogenous deficit) for each country6.

3.2.1. The case of a closed economy7

The starting point of welfare analysis is the indirect utilityfunction

V (p1, p2, . . . , pn, R)

and the expression of the Compensative Variation of Income(CVI). For a given change in the consumer prices:

p0i ⇒ p1

i .

CVI is such that:

V(p0

i , R0) = V

(p1

i , R0 + CVI

),

i.e., is the change in income that would leave utility un-changed.

Surplus is then defined by:

S = R1 − R0 − CVI,

i.e., the difference between “effective” and “compensative”variations of income.

If CVI can be measured locally, the change in house-holds’ income R1 − R0 results from the global working ofthe economy and requires that the model be “closed”, i.e.,describe the change in the general equilibrium through there-balancing of markets and the re-allocation of income.

In a two-commodity economy, consisting of a numéraireand a current good, the second order approximation of theCVI is given by the classical formula:

CVI = x�p + 1

2s(�p)2

with s: (compensated) derivative of demand.

6 It is of course possible to implement a two-steps procedure: first workout scenarios without any constraint on investment, either total amount orits sectoral allocation; then perform new runs taking into account, year byyear and country by country, the constraint on total investment. Obviouslythis procedure is heavy and costly, for a very limited expected gain.

7 The following developments are drawn from [2] and [6].

The graphical representation below shows that CVI isrepresented by the integral under the demand curve, consis-tently with Dupuit’s definition of surplus.

Algebraically, the calculations can be performed as fol-lows. The variation of income is equal to:

�R = �[(p − π)x

]with π , production price; and three cases of increasing gen-erality can be considered.

In the first case, two simplifying assumptions are made:π constant (infinite price elasticity of supply),p = π (no price distortion in the initial situation).

Then

�R = x�p + �x�p,

= x�p + s(�p)2

and

S = 1

2s(�p)2,

which yields the classical formula of the Deadweight Loss ofTaxation (DWL). It can be expressed in terms of the changein demand:

S = 1

2s(�x)2

or alternately by the formula known as the Harberger’s tri-angle:

S = 1

2�p�x.

In a second case, the assumption related to the price-elasticity of supply is relaxed:

π variable (finite price elasticity of supply, equal to t),p = π (no price distortion in the initial situation).The relation between the changes in the production and

the consumption prices, deriving from the condition ofequality in the changes in demand and supply, is:

t�π = s�p.

There is now a producer’s surplus, equal to the change inprofit:

Sp = −1

2t (�π)2


and the total surplus becomes:

S = 1

2

(1

s− 1

t

)(�x)2.

In the general two-commodity case, when relaxing all re-strictive assumptions, i.e., considering a finite price elasticityof supply and a possible price distortion in the initial situa-tion (p �= π), the calculations and the results are as follows:variation of income

�R = x�p + �x�p + (p − π)�x,

total surplus

S = (p − π)�x + 1

2

(1

s− 1

t

)(�x)2,

formula which exhibits in the expression of the DeadweightLoss of Taxation two terms, one representing the effect ofinitial distortions and the other the “pure cost of carbon tax-ation”.

In particular, it results from the existence of initial dis-tortions in the economy (i.e., the fact, in the limited frame-work of this two-commodity model, that the current good isinitially taxed or subsidized) that the marginal cost of abate-ment is not equal to zero and then that the curves of MarginalAbatement Cost and of Carbon Price differ.

In the general case with more than two commodities, theapproximation formulas become much more complex butCVI and effective variation of income can nevertheless becomputed from the results of a global model such as a Com-putable General Equilibrium model.

3.2.2. The case of an open economyTheoretical aspects have been presented in the previous

sub-section, and here it will be considered the practical as-pects of implementation with a CGE model. There are twoissues, the spill-over effects through foreign trade and thetrade of pollution permits.

Concerning the first, the issue is how domestic costs asdescribed above combine with imported costs, representedby Gains (or Losses) from Terms of Trade (GTT). This isdetailed in table 1 presenting the algebra of the welfare costin an open economy.

Total welfare can be computed through the indirect utilityfunction as in the formula which has been given previouslyin the case of a closed economy. Gains from terms of trade

can be reckoned from the change in the prices – or the quan-tities – of foreign trade, according to one or the other of thetwo equivalent formulas of the table above. Difference be-tween the two terms then determine the Deadweight Loss ofTaxation, i.e., the domestic component of the welfare cost.

Concerning the second issue, the basis on which the emis-sion permits are to be traded between countries, it has beenlengthily analyzed previously and rests on the observationthat each country has to compare the cost of abating domes-tic emissions to the cost of buying (or the gain from selling)permits. What appears is:

– first that only the marginal DWL of taxation is at stake(the country has no direct effect on international prices);

– second, that the financing of imported permits is oper-ated through fiscal receipts, then incorporating the costof recovering taxes (marginal cost of public funds).

At the margin:

cost of imported permits = MCPF · νwith:

– MCPF, marginal cost of public funds,

– ν, price of permits in the international market

and

welfare gain = ∂DWL

∂A.

Then

ν = 1

MCPF

∂DWL

∂A,

formula which is rigorously demonstrated in [3].It is convenient to label the second member of the relation

“marginal abatement cost” as it gives the rule for setting thenet demand for permits.

Implementation of this formula in a CGE model first re-quires one to determine the marginal cost of public funds, foreach country and each period. This is performed through anincremental scenario in which public consumption in eachcountry (and each period) is incremented of a small percent-age (0.5% in GEMINI-E3). The MCPF is then per monetaryunit of incremented public consumption the welfare loss netof the associated gains or losses from terms of trade.

As for the marginal DWL of taxation, it results from thesame type of incremental scenario in which domestic abate-ment in each country and each period is increased of a small

Table 1Measurement and components of Welfare Cost.

S = �R − CVI

(Total Welfare Gain) (Variation of Income) (Compensative Variation of Income)

= −DWL + G

(Deadweight Loss of Taxation) (Gains from Terms of Trade)

G = ∑EXP�PEXP − ∑

IMP�PIMP

∼= ∑PIMP�IMP − ∑

PEXP�EXP


Table 2Identification card of GEMINI-E3.

Full name: General Equilibrium Model of International–National-Interaction for Economy-Energy-Environment/General Equilibrium Model for assess-ment of World Tradable Permits

7 Zones: France, Other European countries (EU11), USA, Japan, Former Soviet Union (FSU), Energy Exporting Countries (EEC), Rest of the World(ROW)

3 Institutional Sectors (IS): Households (incl. Private Administrations), Firms, Government

12 sectors/commodities for France and EU11; 8 for USA, Japan, FSU, EEC and ROW (5 of which for Energy: Coal, Gas, Electricity, Crude oil, Refinedoil products)

Starting year: 1990

Terminal year: 2040 (with yearly steps)

Production functions: Nested CES with Fix Factors for fossil fuel sectors

Households’ demand functions: Linear Expenditure System (Stone-Geary model)

Functions of imports: Nested with domestic production (consistent with Armington assumption)

Indirect taxation and social contributions: 13 categories with rates differentiated:

– by commodity (taxes on production, on imports)– by sector (social contributions, subsidies)– by sector × commodity (intermediate consumption)– by commodity × institutional sector (final demand)– by commodity × sector × IS (investment)

Linkage of periods: with endogenous real rates of interest (determined by equilibrium between savings and investment)

Linkage of national/regional models: with endogenous real exchange rates (resulting from constraints on foreign trade deficits or surpluses)

Outputs: by country, annually:– carbon taxes, marginal abatement costs and price of tradable permits when relevant– effective abatement of CO2 emissions, net sales of tradable permits (when relevant)– total net welfare loss, disaggregated in: net loss from terms of trade, pure deadweight loss of taxation, net purchases of tradable permits (when relevant)– macro-economic aggregates: production, imports and final demand (change in volume and change in price); real exchange rates and real interest rates– sectoral data: production and factors of production (change in volume and change in price or remuneration)

percentage. Change in welfare is netted from the importedterms of trade component, in order to obtain a pure domesticcost. Results, concerning MCPF and MAC will be presentedin section 4, following a rapid presentation of the modelGEMINI-E3 and its main characteristics.

4. The model GEMINI-E3 and its main characteristics

GEMINI-E3 is the name of the first General Equilib-rium Model developed in collaboration between FrenchMinistry of Equipment, Transportation and Housing andCEA (French Atomic Energy Agency). It is now the nameof a family of models, including GEMINI-E3/GemWTraP,which is a world dynamic semi-aggregate model, andGEMINI-E3/XL France, which is a static detailed one-country model (France, 88 sectors).

GEMINI-E3/GemWTraP (GEMINI-E3 for short in therest of the paper) is a multi-country, multi-sector, dynamicGeneral Equilibrium Model incorporating a highly detailedrepresentation of indirect taxation. For some purposes,namely assessment of energy policies directly involving theelectric sector and in particular investment in nuclear plants,the model can incorporate a technological sub-model ofpower generation better suited for comparing different typesof generators. The model has been especially designed toestimate marginal abatement costs (MAC), i.e., the welfareloss of a unit increase of pollution abatement, and then to

simulate tradable permits markets based either on carbontaxes or on marginal abatement costs. The present versionof the model is the third one.

4.1. The overall structure of the model

Table 2 gives an overall description and the main charac-teristics of the model. Beside a comprehensive descriptionof indirect taxation (mainly for France), the specificity of themodel is to simulate all relevant markets: markets for com-modities (through relative prices), for labor (through wages),for domestic and international savings (through rates of in-terest and exchange rates). Terms of trade, i.e., transfers ofreal income between countries resulting from variations ofrelative prices of imports and exports, and then “real” ex-change rates are endogenous variables8.

4.2. The specification of production and utility functions

Figure 1 represents the nesting of factors in productionfunctions, for all sectors and all countries or regions excepteventually power generation in France, which in some ver-

8 The real exchange rate between two countries is the relative price of thenuméraires chosen in each country (and usually based on a basket ofgoods representative of GDP). It is not identical to the monetary exchangerate: in particular, the real exchange rate can change with time betweencountries belonging to a same monetary union.


Figure 1. Nesting of factors in the production function (example of France).

sions of the model resorts to an engineering-based specifica-tion.

Concerning households’ demand the specification whichwas selected is as in most CGE models the Linear Expen-diture Model (also known as Stone–Geary model). Thoughthis model is not fully flexible, it is considered by most mod-eling teams as convenient considering the limited informa-tion – and consequently possibility of econometric adjust-ment – on households’ consumption. Calculation of the CVIfrom this demand system is straightforward, and directly in-corporated in the model.

Important parameters are the various elasticities of substi-tution, between imports and domestic production, betweenaggregate domestic factors (capital, labor, energy, other in-puts), and for the two last nests, between individual fuelsand between commodities. By incorporating more or lessflexibility between factors, the choice of these parameters af-fects directly the numerical results of scenarios: abatementof CO2 emissions (with a given carbon-tax), and then cost ofabatement; substitution of domestic factors to imports andthen terms of trade, and so on.

The values of elasticity of substitution selected in themodel were determined according to various sources andin particular econometric estimations presented in the litera-ture.

4.3. The baseline scenario

The main assumptions or exogenous data for designing abaseline (or Business as Usual) scenario in a CGE model are

the rate of growth of the economy and the rate of growth ofenergy demand, the difference representing the autonomousindex of energy efficiency (A.I.E.E.). World prices of en-ergy, oil in particular, are also important exogenous data.

The baseline scenario of GEMINI-E3 has been calibrated,for the period 2000 to 2020, on the long term forecasts set upby the US Department of Energy (Energy Information Ad-ministration) and published in the 1999 International EnergyOutlook. For the subsequent period, 2020 to 2040, trendsof economic growth and energy intensity were extrapolated.Concerning world oil price, considerations of relative ex-haustion of resources lead to the assumption of a yearly priceincrease of 2% in constant dollars.

Table 3 recapitulates the rates of growth of GDP, energyconsumption, and CO2 emissions for each country/region.

Table 3Baseline scenario annual average growth 1995–2040.

Countries/regions GDP Energy consumption Carbon emissions

France 2.1 1.1 1.0EU11 2.2 1.0 0.7USA 2.1 1.0 0.9Japan 1.9 0.8 0.6Former Soviet Union 2.4 1.3 1.1Energy Exporting Countries 4.2 2.8 2.7Rest of the World 4.0 2.6 2.4

World 2.9 1.9 1.8


Table 4CO2 emissions abatement in energy consumption consistent with the Kyoto Protocol.

Kyoto Protocol committed Required abatement of energy Effective abatement in 2010abatement of total GHG CO2 emissions accounting for (relatively to BaU)

emissions (relatively to 1990) abatement of other greenhousegases (relatively to 1990)

France 0% +1.5% −16%European Union (except France) −8% −6% −26%USA −7% −3% −29%Japan −6% −6% −22%Former Soviet Union 0% 0% +44%

4.4. Energy related emissions consistent with the KyotoProtocol

Commitments of emissions abatement set in the KyotoProtocol concern all kinds of GHG and all sources. Ac-counting of emissions and sinks from activities related toagriculture, land use and forestry, and expected reductionsfrom other GHG determine, by difference, the targets forCO2 emissions related to fossil fuels.

The resulting rates of abatement are given in table 4. Sim-ulation beyond 2010 rests on the assumption, taken by mostother modeling teams, of the so-called Kyoto forever as-sumption, meaning the stability of emissions from then onin Annex B countries and no constraint or commitment fornon-Annex B countries. An important aspect in building sce-narios is the assumption concerning the allocation of fiscalreceipts accruing from the carbon tax or the sale of permits.In all our simulations we supposed that they are redistributedin the form of tax rebates, on Value Added Tax in Europeancountries where this tax applies, on production taxes in allother countries/regions. From the viewpoint of efficiency, arebate on indirect taxation is preferable to lump sum trans-fers because it allows to minimize fiscal distortions. Thiswas verified with GEMINI-E3, for each OECD country orregion described in the model [7].

5. Welfare cost of climate change policies:an assessment through GEMINI-E3

A first issue, in the line of the conceptual developmentsof section 2, is the comparison between the different indi-cators of welfare change appearing in the literature, classi-cal surplus, change in GDP at constant prices and change inHouseholds’ Final Consumption (HFC) at constant prices.In other terms, considering that the relevant measure is sur-plus, how biased are the two macro-economic aggregates asindicators of welfare cost?

The second issue is the relative importance of the compo-nents – domestic and imported – of the welfare cost. Re-sults presented below from simulations with GEMINI-E3are based on a standard “No Trade” (i.e., without trade ofpermits) scenario of the Kyoto Protocol (Kyoto Forever) onthe 2010 to 2040 period and assuming participation of theUS in the Protocol.

Figure 2. Comparison of indicators of aggregate cost (in billions of 1990US$).

5.1. Aggregate welfare cost and components

5.1.1. Comparison of indicatorsResults presented in the graphs below, corresponding to

the extreme years 2010 and 2040, show that in the case ofAnnex B countries (except FSU, which owing to its Hot Airis not required to abate), welfare loss measured by house-holds’ surplus is nearly always higher than the change inHFC at constant prices, and smaller than the change in GDPat constant prices. However, differences between change inGDP and households’ surplus are relatively small, particu-larly in the case of the US.

As for non-Annex B countries, households’ surplus andchange in HFC are very close and this result was easy toexpect because relative consumption prices remain approxi-mately constant. The two measures differ significantly fromthe change in GDP at constant prices, which is much smaller,


even close to zero for Energy Exporting Countries. Theseconsiderations have to be kept in mind when comparing theresults of different models, some (in fact most of them) pro-viding measures of aggregate cost in terms of GDP or HFCat constant prices, others (in fact very few) in terms of house-holds’ surplus.

5.1.2. The components of welfare costIn the present case of climate change policies, aiming at

curbing demand for fossil fuels from Annex B countries andentailing a decrease of energy prices in world energy mar-kets, it can easily be expected that changes in terms of tradewill benefit to net importers of energy, to the detriment ofnet exporters. Results from the model confirm this analysis,as shown in figure 3.

It is important to note that gains or losses from termsof the trade are predominant in the initial stages of carbonabatement compared to the domestic cost, but become oflimited relative importance for higher levels of abatement,i.e., in the long run. This is because terms of trade follow, infirst approximation, a linear law with respect to abatement(they are proportional to price changes, themselves approx-imately proportional to total world abatement). On the con-trary, the DWL of taxation follows a quadratic law, and thenoutweighs in the long run the imported cost.

5.2. Marginal abatement cost and comparison to carbonprice

A series of simulations corresponding to various levelsof emissions abatement have been performed to determine,according to the methodology described in section 2, thecurves of carbon price and marginal abatement cost9.

5.2.1. Marginal Cost of Public FundsThe first item is the Marginal Cost of Public Funds.

Results are given in table 5, which shows a hierarchy ofcosts, with the lowest (and very close to unity) values forthe US, Japan, Energy Exporting Countries and Rest of theWorld, intermediate values for European countries includ-ing France, and the highest value for FSU. They appear tobe representative of the relative importance of public out-lays in GDP, and the associated constraints on Governmentand other public administration budgets.

5.2.2. Curves of carbon price and marginal abatement costResults obtained with GEMINI-E3 for Annex B coun-

tries/regions individualized in the model except FSU aregiven in figure 410 for years 2010 and 2020.

The major result is that, for all four countries/regions,the curve of marginal cost is systematically above the curveof carbon price at a distance relatively more important forFrance and Japan than for other European countries and the

9 See [7].10 Abatement in millions t of C in x axis.

Table 5Marginal Cost of Public Funds.

2010 2015 2020 2030 2040

France 1.12 1.13 1.13 1.14 1.14UE11 1.13 1.14 1.14 1.16 1.17USA 1.02 1.02 1.02 1.02 1.02Japan 1.03 1.03 1.03 1.03 1.03FSU 1.23 1.23 1.23 1.23 1.23EEC 1.03 1.04 1.04 1.03 1.03ROW 1.01 1.01 1.00 1.03 1.03

United States11. A second observation is that, for high levelsof abatement, the relative gap between the two curves tendsto decrease.

It may happen that the curve of marginal cost is situ-ated below the curve of carbon price, which means in par-ticular that the marginal abatement cost is negative (at leastin the first stages of carbon abatement) then exhibiting a“double-dividend” phenomenon. The circumstances leadingto a double-dividend are several, and there is in the literaturea real competition for producing new cases. Two appear themost important and plausible: energy subsidization; distor-tions in markets and “rationing” due to price rigidity.

Energy subsidization is clearly the situation prevailing inFSU, and results obtained with the model effectively showthat, contrary to other Annex B countries, the curve of MACis below the curve of carbon price. But as it appears in Fig-ure 5, the gap is fairly small, and this may be explained bythe low reliability of the statistical system, particularly con-cerning fiscal data.

Concerning the other possible source of double-dividend,i.e., distortions and rationing in markets, the most likely caseis the labor market and it is often claimed that a wise use ofenvironmental levies may reduce unemployment. It wouldthen result in an important welfare gain, as the additionalGDP in the economy outweighs the pure distorting effectof indirect taxation. Such a scenario has been checked withGEMINI-E3, assuming that indexation of wages on the Con-sumer Price Index would be responsible of “classical” unem-ployment in each Annex B country (except FSU).

Detailed results are presented in [21]. In the case of Euro-pean countries, the use of environmental levies for rebatingthe Value Added Tax (and reducing proportionally its rate)effectively allows to slow the rise of nominal wage and thusto fill the gap between the actual and the “full employment”

11 Some models exhibit very large, and then not very realistic, differencesbetween carbon tax and marginal abatement cost. It is in particular thecase of PRIMES, a model developed under supervision of the EuropeanCommission, which yields for a scenario of Kyoto Protocol without tradeof permits the following estimations, issued in two separate publications:

– carbon price: Great Britain: 123 US$95/tC; Germany: 88 US$95;France: 144 US$95; Italy: 173 US$95.

– marginal abatement cost: Great Britain: 42 ECUs 99/tC; Germany: 42ECUs 99; France: 5 ECUs 99; Italy: 126 ECUs 99.

Contrary to all other estimations quoted in the paper, marginal abatementcost is systematically smaller than the carbon price, and the gap appearsparticularly incredible in the case of France.


Figure 3. Respective shares of the welfare cost components (in percentage of households’ final consumption).

Source: GEMINI-E3.

Figure 4. Curves of carbon price and marginal abatement cost (in ECUs 1990 per t of C).


prices of labor. Of course, this mechanism plays for lim-ited levels of carbon abatement and carbon price. With highlevels of abatement and carbon price, the deadweight of tax-ation becomes predominant compared to the welfare gainof reduced unemployment, and the global balance becomesnegative in terms of welfare.

This mechanism does not play in the same manner fornon-European countries, Japan and US, which are not en-dowed with a neutral indirect tax of the VAT type. Whathappens is that abating indirect taxation does not concentratetax rebates on households and final consumption, but scatters

Source: GEMINI-E3.

Figure 5. Curves of carbon price and marginal abatement cost of FormerSoviet Union (in ECUs 1990 per t of C, millions t of carbon abated in x

axis).

them between all demands and all agents. Increased costsof energy for households outweigh tax rebates and widenrather than fill in the gap between the actual and the full em-ployment wage, then increasing instead of reducing unem-ployment. Of course, with policy measures focusing fiscalrebates on households and/or labor, such as for instance arebate on social security contributions, a positive effect onunemployment can be expected. Figure 6 presents, in termsof marginal abatement cost, the results of these scenarios.

5.3. Carbon price and marginal abatement cost: somecomparisons

The results obtained with GEMINI-E3 and presentedabove exhibit a positive gap – variable according to coun-tries/regions – between the carbon price and the marginalabatement cost. This is the sign of the existence of distor-tions in the concerned economies. For European countries,this can be related to the over-taxation of energy, in particu-lar fuels for households, but also, though at a lesser extent,power which is subject to specific taxation. But this resultcould merely be a “fallacy” of the model – CGE models ingeneral or specifically GEMINI-E3 – and it is enlighteningto compare to results obtained in other appraisals. It willbe considered successively the case of global or integratedapproaches and the case of sectoral approaches.

Source: GEMINI-E3.

Figure 6. Marginal abatement cost and carbon price with classical unemployment (in 1990 US$). Case of redistribution of environmental levies throughrebates in indirect taxation.


Source: DOE/EIA.

Figure 7. Effects on GDP of a climate change policy in the US.

Source: DOE/EIA, and calculations by the authors.

Figure 8. Curve of carbon tax and various estimations of the curve of marginal abatement cost in EIA study.

5.3.1. Comparing the results of global or integratedapproachesBeside CGE models, global or integrated approaches can

rely on the use of a sectoral energy model coupled to a clas-sical macroeconomic model. It is the methodology imple-mented by the Energy Information Administration of theU.S. Department of Energy, in its study on the “Impacts ofthe Kyoto Protocol on U.S. Energy Markets and EconomicActivity”, conducted in 1998 at the request of the US Senate.Models involved are the system of energy models NEMS,used by EIA mainly for long-term forecasts, and the macro-economic model DRI. The study does not aim at determin-ing – and does not directly determine – the marginal abate-ment cost associated to the various simulations performed,but gives aggregate results from which this cost can be cal-culated, more exactly approximated. It is of some intrinsicinterest to give some details on the study itself and on themethodology implemented by the authors to derive the asso-ciated curve of marginal abatement cost.

Various estimations of the welfare cost are presented inthe study, corresponding to different policy scenarios and/or

different measures of GDP: actual GDP or potential GDP(including a correction for under-utilization of productionfactors), taking into account or not gains from terms of trade(GTT), here only represented by the change in the price ofimported oil12.

The two investigated policy scenarios differ from eachother according to the accompanying fiscal rebates: eitheron the income tax or on the social security contributions.The following graphs yield, for years 2010 and 2020, andin function of the level of carbon abatement, the change inGDP.

Estimating a quadratic law of cost with respect to abate-ment allows to determine, by derivation, the curve of mar-ginal abatement cost to be compared to the curve of carbontax directly obtained in the simulations. Results are repre-sented in Figure 8.

They exhibit the great variety of estimated curves of mar-ginal abatement cost associated to the various policy scenar-ios and assumptions. They nevertheless confirm the result

12 As no information is given in the study on other import and export prices.


Table 6Carbon tax and emissions abatement in France according to the type of

model.

POLES GEMINI-E3

Emission abatement in millions t of C 17.5 19.2Emission abatement in percentage −14.40% −15.80%Carbon tax in FF 1990 1058 1033

obtained with GEMINI-E3: for the lower levels of abate-ment, both in 2010 and 2020, the marginal abatement cost ishigher than the carbon price, and the difference is very sig-nificant. For higher levels of abatement, the curve of MACmay go beneath the curve of carbon tax but this appears re-lated to pre-existing unbalances in the US economy. Theestimations which appear the most reliable – and directlycomparable to results from CGE models – are those basedon potential GDP and taking into account a correction forgains from terms of trade. They are selected for comparisonto the results of GEMINI-E3 and the results obtained withanother CGE model, which is the model EPPA of MIT.

Figure 9 represents, for years 2010 and 2020, the threecurves of carbon tax (left graphs) and the three curves ofmarginal abatement cost (right graphs). It must be noted,however, that the EPPA model does not determine explicitlythe marginal abatement cost, which is represented here bythe carbon price (the two terms being indifferently used bythe authors of the model to represent the same quantity).

The graphs show that if differences between models areimportant in 2010, they are relatively smaller in 2020, no-tably for the higher levels of abatement which are those as-sociated to the Kyoto Protocol in the “Kyoto Forever” speci-fication. This is particularly important because it shows thatif for small levels of abatement, because of possible fiscalor market distortions, the measure of the marginal cost israther imprecise, on the long term and for higher levels ofabatement, the uncertainty appears paradoxically smaller.As is was stressed in section 2, the relative weight of initialdistortions becomes less important when considering highlevels of abatement13.

5.3.2. Comparing the results of global to sectoralapproachesClimate change policies have been the topic of assess-

ment for two broad categories of economic models, sectoral(mainly energy) models and CGE models, both generally de-veloped for this purpose. Broad comparisons, in particularthe one performed in the EMF Working Group 16, have ex-hibited large differences in the results obtained for a samescenario between the two types of model, differences bigger

13 Other model comparisons have been performed in two working groupsof the Energy Modeling Forum. Results of WG 16 are published in theMay 1999 special issue of The Energy Journal [24]. Preliminary resultspresented by the various teams participating to WG 18 show a very largerange of estimations, from 40 to 400$ per ton of carbon in 2010 for the US,and from 30 to 440$ for Europe. But an important part of the differencescan be explained by differences in the reference scenarios designed by themodeling teams [22,23].

Table 7Comparative break down of the welfare cost of climate change policy for

France (in billions FF of 1990).

POLES GEMINI-E3

Pure cost of carbon taxation 8.6 7Distortion cost n.a. 7.3Gains from terms of trade n.a. 14

Total welfare cost n.a. −0.3

than within models of the same type which are already fairlylarge.

Factors explaining the differences can be precisely ana-lyzed, in particular from a comparison between GEMINI-E3and POLES14 – two models belonging each to one categorybut having in common to individualize France – performedat the request of the French Government (French PlanningBureau, which depends on the Office of the Prime Minister).It focuses on estimations of the carbon price and the totalwelfare cost [14].

The assessed scenario is the “No Trade” Kyoto Protocol.There are slight differences in the “Business as Usual” sce-narios of the two models, which yields slight differences inthe rates of emission abatement. As shown in table 6, theimportant result is that the estimated carbon tax is approxi-mately the same with the two models, a little over 1000 FFper t of C.

As shown in section 2, welfare cost is the sum of an im-ported cost, reflecting the change in the terms of trade, anda domestic cost which can be broken down into two compo-nents. The first is a pure cost of carbon taxation, which isthe integral below the curve of carbon tax. It is the domesticcost that would emerge without initial distortion in the econ-omy. The second component is the additional cost (whetherpositive or negative) resulting from initial distortions in theeconomy. We can label it distortion cost, knowing that thesum of these two domestic costs is the deadweight loss oftaxation as above defined.

Sectoral models may only estimate the pure cost of car-bon taxation. Near-equality of the carbon tax in GEMINI-E3 and in POLES warrants that the two curves of carbontax are close to each other, and then so for the measure ofthe pure cost of carbon taxation. Taking into account theother cost components, the distortion cost and the importedcost, changes dramatically the picture. In the case of France,the total welfare cost in 2010 is close to zero, even nega-tive, owing to the very important gains from terms of trade.Comparative results are recapitulated in table 7.

5.4. The case of developing countries

A crucial question for setting a worldwide climate changepolicy is the compared costs of abatement in developingand developed countries. It is frequently claimed that thecost – for a same percentage of abatement – would bemuch smaller in developing that in developed countries, and

14 See [9].


Figure 9. Comparison of estimated curves of carbon price and marginal abatement cost.

Figure 10. Relation between emissions per dollar of GDP and average GDP per capita.

this would then highlight the very inefficiency of a mech-anism which exempts the former from any commitment inreducing emissions. Such a reasoning is based on com-parisons of emissions per dollar of GDP. Apart from thewell-known statistical difficulty of comparing GDP between

countries, in particular between developed and developing(at exchange rates, or at purchasing power parities) such aclaim does not acknowledge an evidence, that there are im-portant economies of scale in energy consumption (in par-ticular in the form of fixed costs). One would not otherwise


Figure 11. Average daily traffic on main roads in Democratic Republic of Congo.


Table 8Comparison of climate change policy scenarios: Welfare cost for Rest of the World (in 1990 US $).

2010 2020 2030 2040

Kyoto Protocol without trade of permits 12,808 24,963 44,296 64,381(in % of HFC) 0.18% 0.23% 0.27% 0.29%

Kyoto Protocol with trade of permits 4,688 11,182 20,894 32,928(in % of HFC) 0.06% 0.10% 0.13% 0.15%

Same rate of abatement in all countries 4,375 7,460 10,539 12,293(in % of HFC) 0.06% 0.07% 0.06% 0.06%

Permits allocation proportional to population with trade 36,334 53,523 67,918 97,144(in % of HFC) 0.50% 0.49% 0.42% 0.44%

understand why there is a long term decreasing trend in en-ergy intensity.

Figure 10 represents, for all countries for which statisticaldata are available (and for year 1995), except those whichhave both a low level of GDP per capita (under 5000 $) anda low level of emissions (0.5 t of C by dollar of GDP) andappear to be not comparable to others, the relation betweenthe two quantities. The curve is decreasing, which showsthat the poorer a country is the higher its level of emissionsper $ of GDP.

Concerning poorer countries, which have been excludedfrom the previous graph, nearly all of them are below thecurve linking the two quantities, which means that they havea still lower level of emissions per $ of GDP (that the oneresulting from the relation). It is then difficult to expect thatabating emissions would have only a small impact on theirstandard of living. This can be, for instance, illustrated bythe case of the Republic of Congo, which happens to haveexactly the same rate of emissions per $ of GDP than the US.An important part of fossil fuel consumed in this country isin the transportation sector. The map (figure 11) shows, forthe main roads, the traffic in vehicles per day in the middleof the 80s (there is no reason to think that the traffic has sincethen increased, just on the contrary!). How is it possible toexpect an energy efficiency of the same magnitude as in adeveloped country, in which the traffic on the main roads isaround several tens of thousands vehicles per day, makingit possible and economically profitable to build a modernnetwork of highways instead of earth roads.

The only reliable information on costs is the one deriv-ing from elasticity of demand for fossil fuels. This elasticitydoes not appear to differ significantly from the elasticity indeveloped countries, and this is how most CGE models arecalibrated. The curve of carbon price should then be compa-rable to developed countries. It, however, remains true that,remembering that the abatement cost follows a quadraticlaw, sharing the abatement between all countries is more effi-cient than concentrating on a small number. This is substan-tiated by scenarios performed with GEMINI-E3, comparingthe Kyoto Protocol to an hypothetic situation in which thesame total targeted world abatement is shared, through vari-ous mechanisms, between all countries.

With emission rights allocated proportionally to the pop-ulation, there appears a significant welfare gain for develop-

ing countries, which is approximately a half percent of theirstandard of living (as measured by Households’ Final Con-sumption). Symmetrically Annex B countries, which wouldapproximately break-even in the case of proportional abate-ment (losers would then be net energy exporters), would beara positive welfare cost but much smaller than within the Ky-oto Protocol framework (with tradable permits, and a fortioriwithout).

6. Concluding remarks and further developments

The aim of the paper was to demonstrate that the theoret-ical concepts and tools of welfare analysis can be success-fully applied to the economics of climate change, in spite ofits complexity and the existence of interactions at differentlevels: between sectors through the rebalancing of marketsand the closure of the economy; between periods; betweencountries. Implementation of these conceptual tools withina world General Equilibrium Model was shown to be possi-ble and consistent, yielding adequate measures of global andmarginal costs and their break-down between main compo-nents, and putting in light the factors underlying the deci-sions of economic agents and Governments.

Beside the spill-over effects channeled through interna-tional trade and contributing to alleviate or increase the bur-den of the different countries, the main difficulty arises fromthe possible existence in the initial situation of “distortions”,either market or fiscal distortions.

Market distortions is a relatively clear concept, easilycaptured in CGE models: there are market distortions ei-ther if (competitive) demand and (competitive) supply donot adjust each to other by the price mechanism, withoutrationing, or precisely if demand and/or supply are not com-petitive. Market distortions affect significantly the welfarecost of a climate change policy because they may eitheralleviate the rigidity of markets – then yielding a “double-dividend” – or on the contrary worsen the incidence of mar-ket rigidity. However, climate change policies are to be con-templated in the long – even very long – run, and short termmacro-economic unbalances may then be neglected in a firstapproximation. Computable General Equilibrium models,which are the relevant instruments for appraising climatechange policy on a time scale of 10 to 30 years (intervalduring which the main policy tools are taxation or emissions


Table 9Comparison of climate change policy scenarios: Welfare cost for Annex B countries (in 1990 US $).

2010 2020 2030 2040

Kyoto Protocol without trade of permits −61,518 −120,755 −176,841 −250,092(in % of HFC) −0.42% −0.66% −0.79% −0.91%

Kyoto Protocol with trade of permits −29,579 −65,687 −105,910 −163,286(in % of HFC) −0.20% −0.36% −0.47% −0.59%

Same rate of abatement in all countries 1528 2170 4174 6419(in % of HFC) 0.01% 0.01% 0.02% 0.02%

Permits allocation proportional to population with trade −28,595 −39,824 −46,651 −61,907(in % of HFC) −0.19% −0.22% −0.21% −0.23%

markets, not technological change likely to play a significantrole only in the very long run), most often assume flexibilityof markets and full employment of factors.

Tax distortions is a more impalpable concept. We couldsay that there are tax distortions if the fiscal policy is notoptimal, but immediately the question is “with which avail-able fiscal tools and with respect to which targets, i.e., whichimplicit Social Welfare Function?”

In the case of a single consumer (by country), eitheran “aggregate” or a “representative” consumer, the issue isfairly simple. As was shown in the paper, it is possible toestimate, for a given CGE model, the curves of carbon taxand the curve of marginal abatement cost. The response isthen straightforward: there are tax distortions if the secondcurve deviates from the former, and the distance between thetwo curves is an indicator of the type (whether it is above orbelow) and the magnitude of the distortions. Determiningthese curves is anyway a fundamental exercise in order tofully understand the nature and the scope of the obtained re-sults.

With several categories of consumers (in each country),which is necessary in order to assess along with efficiencythe redistributive effects of a given climate change policy,the concept of tax distortion becomes more elusive becausevery different value judgments can be taken into account inpublic decision-making. The same observation applies tothe measurement of the marginal abatement cost, which canbe unequivocally measured only if the Social Welfare Func-tion is precisely defined. This is a challenge for the nextgeneration of CGE models, and more generally for the waysof thinking about and assessing policies in a domain whereequity considerations, both at the domestic and at the inter-national level, are so pervasive.

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Documents

Measuring the Welfare Cost of Climate Change Policies: A Comparative Assessment Based on the Computable General Equilibrium Model GEMINI-E3