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Page 1: Stochastic carbon sinks for combating carbon dioxide emissions in the EU

Energy Economics 34 (2012) 1523–1531

Contents lists available at SciVerse ScienceDirect

Energy Economics

j ourna l homepage: www.e lsev ie r .com/ locate /eneco

Stochastic carbon sinks for combating carbon dioxide emissions in the EU

Ing-Marie Gren ⁎, Mattias Carlsson, Katarina Elofsson, Miriam MunnichDepartment of Economics, Swedish University of Agricultural Sciences, Box 7013, 750 07 Uppsala, Sweden

⁎ Corresponding author.E-mail addresses: [email protected] (I.-M.

[email protected] (M. Carlsson), Katarina.elo(K. Elofsson), [email protected] (M. Munnic

0140-9883/$ – see front matter © 2012 Elsevier B.V. Alldoi:10.1016/j.eneco.2012.07.002

a b s t r a c t

a r t i c l e i n f o

Article history:Received 28 March 2010Received in revised form 15 January 2012Accepted 3 July 2012Available online 14 July 2012

JEL classification:C61D80H23Q48Q54

Keywords:Carbon sequestrationEU emission trading and nationalcommitmentsStochastic emissions and carbon sinkChance constrained programmingCost effectiveness

This paper carries out numerical calculations on the potential of carbon sinks in the EU Emissions TradingScheme (ETS) and national commitments under conditions of stochastic carbon dioxide emissions from fossilfuels and carbon sequestration by forests. Chance constraint programming is used to analyze the role ofstochastic carbon sinks for national and EU-wide compliance costs. The analytical results show that theinclusion of the carbon sink option can reduce costs for low enough marginal cost and risk discount, butalso that costless carbon sinks as by-products from forestry are not part of a cost-effective solution under ahigh reliability concern. Cost savings are reduced due to risk discounting under a reliability concern, inparticular when assigning Chebyshev's inequality as compared with a normal probability distribution. It isalso shown that the supply of forest sinks on the market depends on the differences in marginal abatementcost between the trading and the non-trading sectors, and in risk discounting between achievements of theETS cap and the national commitment. Relatively low marginal abatement cost in the non-trading sector andhigh risk discounting of national commitment achievements increase the supply of sinks in the market and,hence, reduces the equilibrium price. The empirical application illustrates the importance of risk discountingfor the magnitude of cost savings obtained from introducing forest carbon sinks in the EU ETS and nationalcommitments.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Carbon sequestration is regarded as a promising option for meetingclimate change targets as it would decrease the total control cost formeeting overall abatement targets (e.g., Bosetti et al., 2009; Lubowskiet al., 2006; Stavins, 1999). For example, Lubowski et al. (2006) showthat approximately one-third of the US carbon abatement commitmentwould be achieved by forest carbon sequestration in a cost-effectivesolution. In 2008 the United Nations launched a collaborative programcalled Reducing Emissions from Deforestation and forest Degradation(REDD) to facilitate projects in developing countries (UN, 2011).An emission trading system for forest carbon sequestration was also in-troduced in New Zealand in 2008 (MAF, 2011).

In spite of the potential cost advantages of carbon sequestration andthe international activities promoting this measure, it is currently notallowed in EU climate policy programs. One argument put forward isthe risk of cheap credits in the EU Emissions Trading Scheme (ETS),which would reduce the incentives for technological innovation (EC,2008). Bosetti et al. (2009), Murray et al. (2009), and Sohngen (2009)have questioned this argument, but on different grounds. Murray et

Gren),[email protected]).

rights reserved.

al. (2009) and Sohngen (2009) find it unlikely that flooding of cheapcredits would occur because sinks are estimated to contribute at most30% of the emission cuts needed internationally. Bosetti et al. (2009)show that investments as well as research and development in new en-ergy technologies could be reduced by only 1% to 10% due to the possi-bility of using mitigation options in the REDD program. It can also beargued that any relatively cheap abatement optionwould reduce the al-lowance price and the incentives for further technological develop-ment, and thus would not be specific for carbon sinks. Another majorargument against sequestration is the specific uncertainty of carbonsequestration compared with reductions in emissions to the atmo-sphere (EC, 2008). Considering that forest areas cover approximatelyone-third of the total territorial area of EU countries, carbon sequestra-tion may play an important role in achieving reduction targets alsounder conditions of uncertainty. This study aims to analyze and calcu-late the potential of carbon sequestration in the EU 2020 program,with explicit consideration given to the stochastic nature of carbon se-questration relative to that of carbon dioxide emissions from fossilfuels. We derive conditions for inclusion of carbon sinks in a cost effec-tive program and illustrate the magnitude of cost savings in an empiri-cal application.

Despite the political concern over carbon sequestration and thelarge scientific literature on this subject, there are no empirical studies,to the best of our knowledge, on the role of land as a stochastic sink forcontrol costs and market design in the EU ETS. On the other hand,

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1524 I.-M. Gren et al. / Energy Economics 34 (2012) 1523–1531

uncertainty plays a key role in the literature on climate policy, wherethe environmental impacts of climate change have been the mainstochastic parameter (see surveys in Golub et al., 2011; Kann andWeyant, 2000; Peterson, 2006). In principle, three approaches touncertainty in numerical models of climate policy can be identified:Monte-Carlo simulation, stochastic dynamic programming, and realoption analysis (Golub et al., 2011). Monte-Carlo simulations accountfor simultaneous analyses of multiple uncertainties; these can beapplied to complex models and are used extensively (Cline, 1992;Dietz et al., 2011; Gerst et al., 2010; Nordhaus, 2008; Pizer, 1999; Tol,1999). Stochastic dynamic programming allows the modeler to includethe possibility that parameters that are uncertain today may be knowntomorrow (Lorenz et al., 2011; Nordhaus and Popp, 1997). The realoption value method has some similarities to stochastic dynamic pro-gramming with the assumption of future learning, and is mainly usedfor evaluating whether benefits, including the value of maintainingflexibility in the short term with regard to future policy choice, exceedcosts (see, e.g., Anda et al., 2009; Dixit and Pindyck, 1994).

In contrast to the approaches in the above studies, which mainlyfocus on uncertainty about the damage that will follow a futureincrease in atmospheric carbon concentration, cost effectiveness andcredibility are crucial components when countries develop nationalor regional policies (Barrett and Stavins, 2002; Stavins, 1997). Nationalpolicy-makers are therefore likely to be concerned with the choice ofabatement portfolio and the ability to achieve targets in order tomaintain trust in international cooperative agreements. Applied studieson national and regional policies reflect this joint concern for cost effec-tiveness and risk management, in particular for policies that go beyondemission reductions in the fossil fuel sector, such as technology devel-opment (Baker and Solak, 2011), adaptation measures (Kato et al.,2009), and agricultural and forest measures (Couture and Reynaud,2011; Kim and McCarl, 2009). When decision-makers hold a relativelystrong aversion against deviations from a target or threshold, safety-first decision rules can be particularly useful. The safety-first criteriacan, in turn, be formulated in different ways, which in general giverise to different outcomes (e.g., Bigman, 1996; Pyle and Turnovsky,1970). This paper applies the safety-first criterion originally sug-gested by Tesler (1955), which allows for the adoption of relativelyeasy and accepted decision rules and minimization of costs underemission constraints, where the emission constraint is formulatedin probabilistic terms.

Unlike climate change economics, there is a relatively large bodyof theoretical and empirical literature on the design of emissionpermit markets with heterogeneous stochastic emission sourcesapplied to water quality management under safety-first criterion (e.g.,Byström et al., 2000; Elofsson, 2003; Gren, 2008, 2010; McSweenyand Shortle, 1990; Shortle, 1990). Following this literature, chanceconstraint programming is used to analyze the role of the differentabatement options. To the best of our knowledge, this method hasbeen used in a climate change context only by Held et al. (2009), whoidentify optimal investment strategies under stochastic climate andtechnological change at the global scale, and Schmidt et al. (2011),who argue that themethod is unsuitable for the analysis of damage un-certainty if it is possible to learn about climate sensitivity. Unlike thosestudies, we focus on the need among national policy-makers for jointconsideration of cost effectiveness and risk management in the choiceof abatement portfolio.

The empirical calculations in this paper consist of cost savings of un-certain carbon sequestration from forest and conversion of agricultureland to forest under probabilistic constraints for the EUETS and nationalcommitments. Similar to several empirical studies on the evaluation ofthe costs of carbon trading, a partial equilibrium model is constructedbased on marginal control costs for emission reduction and carbon se-questration in different countries (e.g., Böhringer and Löschel, 2009).Limitations are made by including only carbon dioxide emissions relat-ed to fossil fuels, which account for approximately 80% of total carbon

emissions in the EU. The emission control costs for each country arethen calculated as changes in consumer surplus from decreases in useof different types of fossil fuel products: oil products, coal, and naturalgas. The costs to convert arable land to forest are calculated as decreasesin producer surplus from arable land. Uncertainty is quantified based ondata on mean and standard deviations in carbon sequestration fromforests and in carbondioxide emissions from fossil fuels.We then followa similar approach for uncertainty discounting of carbon sequestrationas applied by Kim and McCarl (2009) and Kurkalova (2005).

In our view, the main contribution of this paper is the applicationof safety-first decision rules in terms of chance constraint program-ming, much used in water quality management, to climate changemanagement. To our knowledge, there is only one numerical analysisusing this method in the climate change literature (Held et al., 2009),but there is no study on the design of emission permit markets. Dueto the use of deterministic equivalents, the method is straightforwardto use in larger numerical models. The chosen certainty requirementdetermines the stringency of policies, the uncertainty-adjusted abate-ment effect of each measure, and, consequently, the optimal portfolioof measures.

The paper is organized as follows: in Section 2 we describe thesimple model with stochastic carbon sinks and probabilistic con-straints, which builds on the EU 2020 targets. Data sources are brieflydescribed in Section 3. Section 4 presents the results. The paper endswith a brief summary and some tentative conclusions.

2. The model

EU countries face different regulations with regard to carbon diox-ide emissions. In this paper we focus on two directives: the EU ETS(Official Journal, Directive, 2009/29/EC) and national commitments(Official Journal, Decision 406/2009/EC). The EU ETS is the cornerstoneof the EU's strategy for fighting climate change. It is the first and largestinternational trading system for carbon dioxide emissions in the worldand has been in operation since 2005. In addition to the EU ETS, mem-ber states face individual targets expressed as reductions in percentfrom the 2005 emission level. In this paper, carbon sequestration isintroduced as an offset that can be used as an emission reductionoption by the trading and the non-trading sectors.

For each country, we allow for two main strategies to reduce theatmospheric content of carbon: mitigation of carbon dioxide emissionsat source, such as reductions in oil or coal consumption, and the use ofcarbon sequestration. The emission of carbon dioxide from fossil fuelcombustion is determined by use of energy, Xij where i=1,…,m EUcountries and j=1,…,n energy types, and their conversion into carbondioxide. The conversion into carbon dioxide is based on calorific con-tent in the energy types, the calculation of which differs amongreporting organizations (Macknick, 2009). This means that the re-ported energy uses as measured in physical unit may be exactly thesame for different organizations but the associated carbon dioxideemissions differ. We therefore allow for uncertainty in the calculationof CO2 from given quantities of energy uses.

The use of energy is divided among the trading and the non-trading sectors, Xij

ETS and XijNETS, respectively. Total carbon dioxide

emissions from a fossil fuel in a country, Eij, is then written as

Eij ¼ Eij XETSij þ XNETS

ij ; εij� �

ð1Þ

where εij is the uncertainty associated with the conversion of fossilfuel j into carbon dioxide. In addition to reductions in carbon dioxideemissions, the trading and the non-trading sectors are allowed to buycarbon sequestration from land owners by paying the associated costfor areas of land use, Aik

ETS and AikNETS, where k=1,…,o land-use op-

tions. Carbon sequestration from a certain land use k in country i,

Page 3: Stochastic carbon sinks for combating carbon dioxide emissions in the EU

1525I.-M. Gren et al. / Energy Economics 34 (2012) 1523–1531

Sik, is then defined as a function of the sum of areas of land use of thetwo sectors and a stochastic term according to

Sik ¼ Sik AETSik þ ANETS

ik ;νik

� �; ð2Þ

where νik is a stochastic term. It is assumed that Sik is increasing inAik.Total emissions from the sectors in the ETS in each country are then

TETSi ¼

Xn

j¼1

EETSij −Xo

k¼1

SETSik ; ð3Þ

and the emission from the non-trading sectors in each county iswritten as

TNETSi ¼

Xn

j¼1

ENETSij −Xo

k¼1

SNETSik : ð4Þ

The control costs for emission reductions from the business-as-usual(BAU) emission levels are calculated as the associated decrease in con-sumer surplus, Cij(Xij), which are assumed to be decreasing and convexin Xij. This is the only possibility for reducing carbon emissions from fos-sil fuel combustion as long as the different carbon capture technologiesare in their early development stages and not available for firms as acontrol option. The costs for carbon sinks are assumed to be determinedby themanagement and opportunity cost of the area of forest or perma-nent crop land, Cik(Aik), which are assumed to be increasing and convexin Aik.

The decision problem under the EU 2020 scenario is now formu-lated as the minimization of total costs under a probabilistic restric-tion on total emissions, where ρ is the chosen probability forachieving a certain maximum level of total emissions in the ETS,TETS

, and total emissions from the non-trading sectors in eachcountry, T

NETSi . Due to the static nature of our model it is further

assumed that the energy sources cannot be reduced completely, i.e.,the use of fossil fuel must be larger than or equal to a predefinedlevel, Xij, ensuring economies without large structural changes.Furthermore, there is a restriction on the availability of land suitablefor carbon sequestration, Aik.

Chance constrained programming is applied, where it is assumedthat the objective of the policy-maker is to minimize total abatementcosts for achieving a probabilistic target constraint for maximum al-lowable emissions (see e.g., Birge and Louveaux, 1997; Charnes andCooper, 1964). A predetermined pollution target, E , must then beobtained with a minimum level of a chosen probability ρ∈(0, 1). Itis assumed that the countries have the same reliability concern fortheir national commitments as for the EU ETS. The decision problemis then formulated as

MinXij ;Aik

TC ¼Xm

i¼1

Xn

j¼1

CETSij XETS

ij

� �þ CNETS

ij XNETSij

� �h iþXo

k¼1

CETSik AETS

ik

� �þ CNETS

ik ANETSik

� �h i0@

1A

ð5Þ

subject to

Xij≥Xij for all i ¼ 1;…;m and j ¼ 1;…;n ð6Þ

∑kAik≤Ai for all i ¼ 1;…;m and k ¼ 1;…; o ð7Þ

Pr TETS≤T ETSh i

≥ρ ð8Þ

Pr TNETSi ≤T

NETSi

h i≥ρ for all i ¼ 1;…;m ð9Þ

where T ETS is the total cap on emissions for the trading sectors in the27 EU member states, and TNETS

i is the emission targets set by the na-tional commitments.

A number of studies have used the formulations in Eqs. (8) and (9)to include probabilistic constraints in decision models (e.g., Byströmet al., 2000; Elofsson, 2003; Gren, 2008, 2010; Kataria et al., 2010;McSweeny and Shortle, 1990; Shortle, 1990). The basic approach isto transform Eqs. (8) and (9) into deterministic equivalents. Sincethis is made in the same way for both Eqs. (8) and (9), we presentthe transformation in the following only for Eq. (8), which is writtenas

Pr½ TETS−Exp TETSh i

Var TETS� �1=2 ≤

T ETS−Exp TETSh i

Var TETS� �1=2 �≥ρ ð10Þ

where Exp is the expectation operator and the termTETS−Exp TETS½ �Var TETSð Þ1=2 shows

the number of standard errors, ϕ, that TETS deviates from the mean. Bythe choice of ρ, there is a level of acceptable deviation, and the ex-pression within brackets in Eq. (10) then holds only if

Exp TETSh i

þ ϕρVar TETS� �1=2≤T ETS

: ð11Þ

The left hand side of Eq. (11) shows that reliability in achievingthe target is achieved at a cost, which is increasing in reliability con-cern, i.e. in ϕρ, and in Var(TETS). The variance in Eq. (11),Var(TETS)=Var(EETS)+Var(SETS)−Cov(EETS,SETS), has an interestinginterpretation. When Cov(EETS,SETS)>0 the forest sink acts as a hedg-ing device and reduces total risk (e.g. Byström, et al., 2000; Gren,2010). On the other hand, a negative co-variation increases totalrisk. In principle, we might not expect much correlation betweenthe stochastic terms because uncertainty in forest sink is largelydetermined by climate factors and uncertainty in emission coeffi-cients from fossil fuel depends on calculations of the calorific contentin different energy types. If this is the case the co-variation term iszero.

The parameter ϕρ in Eq. (11) can be quantified in twoways. One is toassumea specific probability distribution.Whenanormal probability dis-

tribution is assignedϕρ is a standard number such that∫ϕρ

f ϕð Þdϕ¼ρ

−∞, whereϕ

is the standardized distribution of E and f(ϕ) is the probability densityfunction for ϕ (see e.g., Taha, 1976). This approach is frequently appliedin the literature on policy instruments for stochastic water pollution(Byström, et al., 2000; Gren, 2010; McSweeny and Shortle, 1990;Shortle, 1990). The other way of quantifying ϕρ is a more flexible, butless used, approach that is based on Chebyshev's inequality where noassumptions are made with respect to the probability distribution(e.g., McCarl, 2010). The value of ϕρ is then determined where ϕρ=(1−ρ)−1/2.

There are no a priori expectations on the probability distributions ofcarbon sink from the included land uses, which would favor the appli-cation of the flexible approach in this paper. On the other hand, thisflexibility is achieved at a high cost of risk discounting. For example,for ρ=0.9, the value of ϕρ is 1.28 under normal distribution and 3.16with Chebyshev's equivalence. Calculations are made in Section 4 forboth approaches.

The optimal allocations of Xij and Aik are determined by thefirst-order conditions according to

∂CETSij

∂XETSij

¼ −λ∂Exp TETS

h i

∂EETSij

þ ψ∂Var TETS

� �

∂EETSij

0@

1A ∂EETSij

∂XETSij

−βij ð12Þ

∂CNETSij

∂XNETSij

¼ −γi

∂Exp TNETSh i

∂ENETSij

þ ηi∂Var TNETS

� �

∂ENETSij

0@

1A ∂ENETSij

∂XNETSij

−βij ð13Þ

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1526 I.-M. Gren et al. / Energy Economics 34 (2012) 1523–1531

∂CETSik

∂AETSik

¼ λ∂Exp TETS

h i

∂SETSik

−ψ∂Var TETS

� �

∂SETSik

0@

1A ∂SETSik

∂AETSik

þ θik ð14Þ

∂CNETSik

∂ANETSik

¼ γi

∂Exp TNETSi

h i

∂SNETSik

−ηi∂Var TNETS

i

� �

∂SNETSik

0@

1A ∂SNETSik

∂ANETSik

þ θik ð15Þ

where ψ ¼ ϕρVar TETSð Þ−1=2

2 ; ηi ¼ϕρVar TNETS

ið Þ−1=2

2 , and βij, θik, λ, and γi arethe Lagrange multipliers for the lower bounds on energy use, areaof land for carbon sequestration, the overall emission target for thetrading sectors, and the national commitments. The left-hand sidesof Eqs. (12) to (15) show the marginal costs of each of the carbon di-oxide mitigation options. The right-hand sides of the same equationspresent the marginal impacts on the targets, T ETS and TNETS

i , respec-tively. The impact consists of two main parts: the marginal impact onexpected emission and on variance in emissions. Carbon sinks are thenincluded in a cost effective program for relatively low marginal costand variability in marginal impact, and high marginal reduction inexpected emissions.

Since we are interested in evaluating the potential of carbonsequestration as a by-product from forestry in Europe, it is useful toinvestigate under what conditions sequestration will be implementedin the ETS or in national commitment programs and the allocation ofsink in these two programs. Setting the marginal cost of carbonsequestration to zero, it can be seen from Eqs. (14) and (15), in the ex-pressions within parentheses, that sinks are included in the solution forlow-enough risk discount. The first term within parentheses definitelyacts in favor of introducing an option with zero marginal cost, but for ahigh-enough marginal impact on the total or national variance and riskdiscount the expressions on the right-hand side become zero. Underconditions of separability between variances in emission from fossilfuels and carbon sink among countries, the marginal impact on thevariance is the same for the market and the national commitment.This implies that the risk discount is higher for national commitmentthan for the tradingmarket since the country variancewithin parenthe-ses in Eq. (15) is lower than the corresponding variance in Eq. (14),which implies that ηi>ψ.

From Eqs. (14) and (15) we can also identify the allocation of sinksbetween the market and national commitments. Since the marginalimpact on expected sequestration is the same regardless of whatpurpose the sink is used for, the condition for a positive supply on themarket is

λγi

>Α−ηiΒΑ−ψΒ

ð16Þ

where Α ¼ ∂Exp TETS½ �∂SETSik

¼ ∂Exp TNETS½ �∂SNETSik

and Β ¼ ∂Var TETSð Þ∂SETSik

¼ ∂Var TNETSð Þ∂SNETSik

. Thus, for

each country there is a switch point where forest sinks are supplied onthe market, which is determined by the relative marginal abatementcosts for the trading and the non-trading sectors and the relationbetween ηi and ψ. When uncertainty in carbon sink is neglected, thesupply is determined only by the marginal abatement costs, and sinksare offered when the marginal cost at the market is higher than thatfor achieving the national commitment. This condition is relaxedwhen uncertainty is introduced when ηi>ψ and, hence, the right-hand side of Eq. (16) is less than unity. Sinks are then offered at themarket even when the marginal cost of the national commitment ishigher because of the relatively high risk discount for achieving thenational commitment.

The equilibrium price of permits in the trading market is deter-mined by λ. Under deterministic conditions, the carbon emissionfrom energy sources can be traded on an equal basis with carbon

sinks at the equilibrating permit price. This is not the case when theimpact on the variance of marginal changes in Xij

ETSand/or AikETSis

non-zero. Disregarding capacity constraints, exchange rates can bedetermined from Eqs. (12) and (14) by the marginal impacts of thetwo classes of measures. Using a certain emission reduction ascommon denominator, the exchange rates for carbon sink, TrSik, andemission reduction, TrEij in optimum are written as

TrSik≡−∂Exp TETS

h i

∂SETSik

−ψ∂Var TETS

� �

∂SETSik

: ð17Þ

TrEij≡∂Exp TETS

h i

∂EETSij

−ψ∂Var TETS

� �

∂EETSij

ð18Þ

The results in Eqs. (17)–(18) are similar to that of several studies onwater quality management, which show that carbon sink or emissionreduction may entail a relative cost advantage/disadvantage whenthe variance is decreasing/increasing in its argument (e.g., Shortleand Horan, 2008). However, whether or not the marginal impacts onthe variances are negative depend on the probability distributionsand the functional relations between carbon dioxide emission andfossil fuels and emission and sequestration. In the empirical applica-tion in Section 4, linear functions are assumed for the impact of themeasures on the atmospheric load. The variances are then increasingin sequestration and fossil fuels. However, as shown by Försund andNaevdal (1998), among others, whether or not the cost-effective so-lution is achieved when trading ratios are endogenous depends onthe initial distribution of carbon dioxide allowances. Initial allow-ances are assumed to be distributed so that a cost-effective solutionis achieved.

3. Data retrieval

For each of the EU member states, three types of data sets arerequired for the calculations of cost-effective solutions in the nextsection; abatement costs, mean and variance of carbon sequestrationof different land uses, and mean and variance of carbon dioxide emis-sions from energy-related sources. Since the focus of this paper is onthe role of stochastic carbon sinks on the costs of EU ETS and nationalcommitment targets, we present data for calculations of carbon sinksand quantification of uncertainty in more detail than for the otherclasses of data. Gren et al. (2009) give a detailed presentation of alldata on abatement costs for reductions in energy-related emissionsand calculations of emissions from different energy sources.

3.1. Calculation of carbon sink and emission from fossil fuels

Several studies calculate the potential of terrestrial ecosystems forcarbon sequestration at the global scale, but few studies cover Europeancountries (e.g., Janssens et al., 2005; Ovando and Caparros, 2009; Schulpet al., 2008). In principle, the carbon net uptake in the terrestrial bio-sphere is a combination of photosynthesis and vegetation rebound,which differs for different land uses (Janssens et al., 2005). Calculationsof carbon sequestration include changes in carbon stocks in both soiland biomass for different land uses. These are, in turn, calculated fordifferent types of biomass compartments in forests and agriculturalland, which requires the application of a combination of numericalmodels and measurements of biomass productivity and decompositionof carbon in soils. Such calculations are carried out by Janssens et al.(2005), who report estimates of carbon sequestration per unit of areafor forests, arable land, and permanent crops for European countries.Moreover, they quantify uncertainty in these estimates as standarddeviations in sequestration per unit land area. According to their

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1527I.-M. Gren et al. / Energy Economics 34 (2012) 1523–1531

estimates, forests and permanent crop land act as carbon sinks andarable land as carbon sources for almost all countries (see Table S1 inSupplementary data). Themean emission coefficients vary considerablyamong countries, between 0.10 and 3.25 tC/ha and year for forests.

In addition to the sequestration obtained from forestry as aby-product we allow for the conversion of agriculture land into forest.Given the short period until 2020, afforestation requires fast-growingtree varieties to provide carbon sequestration. Assuming this can be ac-complished, the corresponding net effect on carbon sequestration perunit of land area is calculated as the difference in emission coefficientsbetween the land uses displayed in Table S1 in the Supplementarydata. An additional assumption is that the coefficients of variation ofcarbon sequestration for these planted forests are the same as thosefor current forest. The static design of our numerical model alsorequires restrictions on the areas of agriculture land that can beconverted to forests. For all EU countries, land use is affected by anumber of common policies, such as the common agricultural policyand by national interests for food security, rural development, andcountryside amenities. Taking these considerations into account,Ovando and Caparros (2009) report from a survey of different studiesthat the potential conversion of agriculture land into other land usesranges between 5% and 27% of total agriculture land in EU countries.Since actual agriculture land as a share of total territorial area differsconsiderably between the countries, the potential increases will alsovary (see Table S2 in supplementary data). However, country-specificinvestigations of maximum conversion of agriculture land in a shorttime perspective are not available, and it is therefore assumed thatthe maximum conversion of agriculture land into other uses is 20% ofthe actual land area in all countries. Sensitivity analyses are carriedout for other constraints.

Expected carbon dioxide emissions from different types of fossil en-ergy are calculated by use of data on energy uses and emission coeffi-cients (Gren et al., 2009). Uncertainty in emissions are obtained fromMacknick (2009)whomade a review of the literature on carbon dioxide

Table 1CO2 emission from fossil fuel (thousand tons), forest carbon sink (thousand tons), allocatio

Emissions in 2006 fromfossil fuel

Forest sink:actual conversion

Austria 69,675 27,632 6642Belgium 128,396 1412 373Bulgaria 46,934 17,803 4847Cyprus 8441Check Republic 117,617 14,274 4327Germany 816,432 84,416 21,559Denmark 60,944 5480 1267Estonia 14,851 5785 3324Spain 355,472 16,665 4270Finland 67,425 31,697 14,066France 383,634 52,313 14,431Greece 103,986 2407 2311Hungary 53,547 12,790 3525Ireland 47,363 1646 402Italy 446,523 35,129 10,662Lithuania 13,149 9163 4023Luxembourg 12,383Latvia 8788 11,609 5654Malta 2709Netherlands 225,081 2952 770Poland 310,308 36,626 11,948Portugal 58,795 5995 2984Romania 93,080 49,331 12,543Sweden 52,514 49,230 26,435Slovenia 15,613 10,597 2403Slovakia 35,411 23,043 5502United Kingdom 567,793 9520 2192Total 4,116,864 489,883 159,818

Source: calculations based on Tables S1, S2, S3, and S4 in Supplementary data.a CoV: coefficient of variation of all CO2 emissions from fossil fuel and all forest sink, resp

emissions from fossil fuel and found upper and lower limits of the emis-sion coefficients from coal, natural gas and crude oil (see Table S4 inSupplementary data). Standard deviations in emission coefficients arecalculated by assuming that 95% of all outcomes fall within the reportedranges,which gives 0.019, 0.030, and 0.031 as coefficients of variation inemission coefficients of coal, natural gas, and crude oil. The estimatedcoefficient of variation for crude oil is applied to all oil products.

It is assumed that there is no co-variation in emissions and carbonsequestration among countries and the total risk is then calculated asthe sum of all country variances, which corresponds to a coefficient ofvariation of 0.11. Approximately 70% of this total risk is allocated toforests in Germany, France, Sweden, and Romania (see Table 1).

In total, maximum carbon sequestration amounts to 15.1% of totalcalculated forecasted emissions in the target year 2020, which isconsiderable when compared with the target reduction of 20% (seeTable S3 in Supplementary data). For some countries, namely, Finland,Lithuania, Latvia, Romania, Sweden, Slovenia, and Slovakia, carbon se-questration accounts for more than one-half of the forecasted emissions.

It is also interesting to relate the carbon sinks reported in Table 1to the EU 2020 targets and commitments, which declare reductions in2020 by certain decreases in percent from the 2005 total and nationalemission levels (see Table S3 in Supplementary data). In total, anunchanged land-use allocation during 2006 and 2020 would contrib-ute by two-thirds to the fulfillment of the overall carbon dioxidereduction target. For several countries – Austria, Bulgaria, Estonia,Spain, Finland, the Netherlands, Portugal, Romania, Sweden, Slovenia,and Slovakia – the carbon sink from actual land use exceeds the na-tional commitments as measured by required reductions from theforecasted 2020 emission levels.

3.2. Carbon sequestration and emission reduction costs

The carbon sink from actual forest land cover reported in Table 1 isobtained as a by-product of conventional forestry and is therefore

n of risk, and maximum share of sink of forecasted emissions in 2020.

Share of maximum total risk, %:emission sink

Maximum sinks in % offorecasted emission in 2020

0.45 3.59 42.61.71 0.01 1.50.09 1.46 43.30.00 0.000.27 0.97 16.324.86 33.53 13.10.18 0.15 13.30.00 0.16 40.311.80 1.35 5.50.18 4.99 66.215.68 13.08 17.50.63 0.02 4.50.27 0.76 25.50.18 0.01 3.914.95 5.84 8.90.00 0.39 114.70.00 0.000.00 0.63 150.20.00 0.005.77 0.04 1.91.98 6.51 14.10.36 0.17 12.20.54 11.62 51.40.45 11.23 109.60.00 0.53 69.20.09 2.51 64.219.55 0.42 1.9100 100 15.1CoVa:0.003 CoVa=0.083

ectively.

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Fig. 1. Total costs for achieving the ETS target and national commitments with andwithout carbon sink, with uncertainty in fossil fuel emission and/or carbon sink by for-ests, and for normal (norm.) and Chebychev (Cheb.) probability distributions.

1528 I.-M. Gren et al. / Energy Economics 34 (2012) 1523–1531

assumed to entail zero management cost. The carbon sink canincrease, and hence incur costs, by changing the allocation of landfrom low- to high-sink land intensities, which entails costs (see vanKooten et al., 2005, for a review andmeta-analysis of carbon sequestra-tion options and costs). Ideally, cost functions for providing carbonsequestration would be available for each country, showing theallocation of sequestration by different options minimizing costs foreach sequestration level. Unfortunately, this is not the case. We there-fore calculate conversion costs based on data on rental value and sup-ply elasticities of agriculture land. Table S2 in the Supplementary datapresents the rents from arable land per unit of land use area. Thereare no supply elasticities for agriculture land for each EU memberstate, but only for Western Europe (Meil et al., 2005), which are usedin this study. The estimates vary between 0.05 and 0.20, and we usethe average value of 0.125.

The costs of emission reductions are calculated as correspondingdecreases in consumer surplus derived from energy demand func-tions for three main classes of energy products: oil products (heavyfuel oil, light fuel oil/heating oil, gasoline, diesel, and jet kerosene),coal (hard coal and lignite), and natural gas. These demand functionsare, in turn, assumed to be linear and are calculated by means of dataon input price elasticities, price level, and input use for the year 2006.For each of the energy inputs we distinguish between the trading andthe non-trading industry sectors, the power sector, and the house-holds. However, data are not available on price elasticities for thetrading and non-trading sector, and the relative difference in margin-al abatement costs between these sectors are therefore assumed to bethe same as those reported in Böhringer et al. (2009); approximatelyfour times higher in the non-trading sector.

4. Minimum cost solutions with alternative carbon sink options

According to the target set by EU 2020, the trading sectors in theEU ETS need to reduce total emissions by 21% and each countryfaces caps on its emission from the non-trading sector within thenational commitment directive. Table S3 in the Supplementary datapresents the required reductions in percent to achieve the nationalcommitments. Given these targets, the model framework, and all as-sumptions, minimum costs are calculated under different scenarioswith respect to inclusion of carbon sinks and size of the tradingmarket.We also carry out sensitivity analysis for changes in parameter valueson uncertainty and provision of forest sinks. We use GAMS' solverConopt2 for all calculations (Brooke et al., 1998).

Fig. 1 shows the minimum costs for achieving the target for thetrading sector by 21% and the national commitments with and withoutcarbon sinks under different reliability levels. Total control costs areshown for six different options: i) no sink, ii)with sink and uncertaintyin both sink and fossil fuel emissions, and iii)with sink and uncertaintyonly in forest sink with the assumption of a normal probability distri-bution or Chebyshev's inequality. The first and third cases allow forthe separation of impacts on costs from uncertainty in emission fromfossil fuel and in carbon sink. The second option constitutes the refer-ence case when both uncertainties are acting.

The total cost for reaching the EU emission targets under determin-istic and no sink cases is found for the probability of 0.5 for the normaldistribution; it amounts to 98 billion Euro/year which corresponds toapproximately 0.9% of total GDP in the EU countries in 2006. The asso-ciated allowance price is 46 Euro/t CO2 emission. When we comparethese estimates with the results of other studies, we note that theyfall in the upper level of the range (e.g. Böhringer et al., 2009; Caproset al., 2008; Stankeviciute et al., 2008). The total estimated costs inCapros et al. (2008), who used a general equilibrium model of the EUcountries, range between 75 and 111 billion Euro/year, which corre-spond to approximately 0.6% and 1% respectively of the sum of GDPin all EU countries in 2006. The associated allowance prices varybetween 22 and 47 Euro/t CO2. Stankeviciute et al. (2008) used a

partial equilibrium model of sectors in the energy system and estimat-ed costs under different scenarios for the EU 2020 target and they gotan allowance price that varies between 25 and 57 Euro/t CO2.Böhringer et al. (2009) compared the results of three different generalequilibrium models and found considerable differences in allowanceprices and welfare impacts. Allowance price can be as low as approxi-mately 17 Euro/t CO2 emission but also reach a level of 68 Euro/t andcalculated welfare losses (measured as Hicksian Equivalent or Com-pensating Variation) range between approximately 1% and 2.5%.

The total cost without the forest sink option is approximatelythree times as large as when carbon sink is included and the chosenprobability of achieving the targets is 0.5 under the assumption of anormal probability distribution. This gain from carbon sinks is re-duced to one-third when Chebyshev's equivalence is applied. Athigher reliability levels the gains are reduced, and disappear at aprobability level of 0.9 and 0.99 for Chebyshev and normal probabilitydistributions, respectively. Control costs increase at higher levels of ρmainly due to the high risk discounts for national commitments, asdiscussed in Section 2.

The impact of uncertainty in emission from fossil fuel can be seen bycomparing costs under the no sink option and normal probability distri-bution, i.e. 98 billion Euro, with the costs under higher reliability levelsand under application of Chebyshev's inequality. Control costs increaseby amaximum of 30% under the normal probability distribution, and by40% under Chebyshev's inequality. The high risk discounting underChebyshev's inequality also implies that reliability levels exceedingρ=0.9 are infeasible given our assumptions of maximum emissionreductions. The corresponding effects of carbon sink are found bycomparing costs in the deterministic case of 28 billion Euro (whichare obtained for the normal probability distribution when ρ=0.5)with the control costs when only carbon sink is stochastic. Costs canthen increase by approximately three times under both probabilitydistributions. It is interesting to note that carbon sink is not includedin a cost effective solution under Chebyshev's distribution for ρ≥0.9 be-cause of the high risk discount. Control costs are then the same as in thedeterministic casewithout sinks, i.e. 98 billion Euro. The large impact ofuncertainty in carbon sink relative to uncertainty in fossil fuel emissionsis explained by the higher risk (see Table 1) and low cost of sinks asby-product from forestry.

The gains from the introduction of carbon sequestration are uneven-ly distributed among countries. We choose to present results for the in-dividual countries for ρ=0.9 since this is the largest probability forwhich feasible solutions are obtained for both probability distributions.It is also the level chosen by one of the few countries, Canada, wherereliability in carbon sequestration has been addressed and quantified(Kim and McCarl, 2009). All countries then make net gains under

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assumption of a normal probability distribution, in particular Germany,and Italy (see Table S5 in Supplementary data). Due to the high risk dis-count, the impacts of sink under Chebyshev's inequality on total and al-location of costs are negligible. The associated exchange rates for carbondioxide emission from coal, gas, and oil and carbon sink are presented inTables S6–S7 in Supplementary data,which show small effects of uncer-tainty because of the relatively low impact on total variance from amar-ginal change in carbon emission or sink from each country.

If the trading market is expanded to include all sectors, the totalcost for achieving the overall target is reduced considerably. The tar-gets set by the market for the trading sector and the national commit-ments on carbon dioxide reductions give an overall reduction of 15.5%in our model. This reduction is lower than the stipulated target by20% since the objectives of improved energy efficiency and renewableenergy are not included. Since the overall reduction of 15.5% is closeto the amount of the total carbon sink, the overall cost for meetingthe target without reliability constraints amounts to approximatelyone-fifth of the total cost without carbon sink. However, total costsincrease at higher reliability levels and are in the same order of mag-nitude as costs without sinks at probability levels of 0.99 if a normalprobability distribution is assumed (see Fig. 2). If we instead applyChebyshev's equivalence, the cost with sinks is the same as withoutsink at a reliability level exceeding 0.8.

Fig. 2 shows that overall costs are increasing rapidly for ρ>0.9under Chebyshev's inequality when carbon dioxide emissions from fos-sil fuel are stochastic, at the most from approximately 54 billion Euroto 210 billion Euro when carbon sinks are included. Corresponding in-crease in costs under a normal probability distribution is six-fold, fromapproximately 13 to 82 billion Euro. The gains from inclusion of carbonsinks are decreasing at higher reliability levels for both distributions, inparticular with Chebyshev's inequality where the gains disappear athigh reliability levels.

These results point at caution with respect to the evaluation ofcarbon sinks. For example, Michetti and Rosa (2011) estimated costswith and without carbon sinks obtained from forest management, de-forestation, and afforestation for a number of regions in the world,the EU being one of them. Their results point to cost savings for theEU of approximately 30%. Our results indicate higher cost savings inthe deterministic case, which are explained by our inclusion of actualcarbon sink and not only additional as in Michetti and Rosa (2011).On the other hand, these cost savings almost disappear at reliabilitylevels exceeding 0.8 when Chebyshev's inequality is used.

As reported in the Data retrieval section, data on mean andvariability in sequestration rely on studies carried out in the earlypart of the first decade of the 21st century. Moreover, the imposed re-striction on maximum areas of conversion of arable land representsan average of perceived capacity found in Ovando and Caparros(2009). It has also been assumed that carbon sequestration can be

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sink, Cheb

Fig. 2. Total costs for reducing CO2 by 15.5% with an EU wide emission trading marketwith and without carbon sink, with uncertainty in fossil fuel emission and/or carbonsink by forests, and for normal (norm.) and Chebychev (Cheb.) probability distributions.

fully implemented under both the ETS and the national commitmentdirectives. An ETS system for forestry was introduced in 2008 in NewZealand where measurement of sequestration during a period wasbased on changes in carbon pool from a certain baseline year (MAF,2011). Translated into EU climate change programs, this may implyless eligible carbon sink than the maximum potential displayed inTable 1. Furthermore, forecasted emissions in 2020 and associatedreduction requirements are uncertain as well as costs for reductionsin use of fossil fuels. Therefore, we carry out sensitivity analyses forchanges in these parameters: changes in sequestration and variability,afforestation area, amount of legible sequestration in the programs,fossil fuel reduction cost, and forecasted emissions. These are evaluatedbased on the EU 2020 targets on emission caps for the trading sectorand the national commitments for each country at a probability levelof 0.9 (see Fig. 3). A normal probability distribution is assumed sincesolutions are not feasible with Chebyshev's inequality for several ofthe parameter changes.

Changes in afforestation area by 25% had negligible impacts ontotal abatement costs as this option is relatively expensive; thus, as-sociated costs are not presented in Fig. 3. Other parameter changeshave considerable impacts on total abatement costs, in particularchanges in quantified uncertainty and forecasted emissions. Totalcontrol cost can then increase by approximately 50% when forecastedemissions increase by 5%. The change in total variance by 25% hassmaller cost effects, but increase at higher reliability levels.

5. Conclusions and discussion

Themain purpose of this paper has been to suggest amethod, chanceconstrained programming, for calculating cost effective reductions instochastic emissions from fossil fuels and for evaluating the potential ofincluding stochastic carbon sequestration in European forests as anabatement measure in the EU ETS program and as a way of meetingnational commitments. Carbon sequestration as a by-product of con-ventional forestry and afforestation on agriculture land was included asa carbon removal measure. A safety-first approach was used wheredecision-makerswere assumed to hold relatively strong aversions againstnon-attainment of the targets in the EU ETS and national commitment di-rectives. A simple partial equilibrium and chance-constrained model wasdeveloped where the control costs for reductions in energy use for allEU27 were calculated as decreases in consumer surplus of demand forfossil energy, and costs of afforestation as impacts on land owners' pro-ducer surplus.

The theoretical analyses derived conditions for when carbon sinksare included in a cost effective solution and when the equilibrium al-lowance price in the ETS market is affected. It was shown that carbonsink holds a relative advantage when marginal costs and risk dis-counts are low. The impact on the equilibrium permit price dependson the difference between abatement costs and risk impacts from

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Fig. 3. Total cost for the ETS and national commitments with forest sink and reliabilitylevel of 0.9 and normal probability distribution under different changes in parametervalues (costs are 78 billion Euro in the reference case).

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marginal reduction in fossil fuels in the trading and non-trading sec-tors. When abatement costs and risk impacts are relatively low foremission reduction in the non-trading sector, sinks are mainly usedfor fulfilling national commitments and the effect on allowanceprice is small. The empirical application showed that this can occur;the gains from introduction of carbon sinks are mainly attributableto the reduction in costs for fulfilling national commitments. Howev-er, cost savings can decrease considerably for high reliability levelsand uncertainty in carbon sink and/or emissions from fossil fuels, inparticular with application of Chebyshev's inequality. These resultspoint at caution with respect to the evaluation of carbon sinks whenreliability in reaching targets is a concern.

The uncertainty in carbon sequestration can be mitigated by im-proved monitoring and verification, which is costly. Antle et al.(2003) show that such costs depend on the sample size of measure-ment plots and can range between 1% and 30% of the cost for carbonsequestration in forests in a region in the United States. Antinori andSathaye (2007) report a monitoring and verification cost of approxi-mately 1 Euro/t CO2 sequestration, which is obtained from economet-ric analyses of a sample of actual projects in different countries.Sohngen (2009) provides an overview on the implementation of forestsequestration programs, which shows that the transaction costs arerelatively low. Our results indicate that the cost of probabilityconstraints can be considerable, and, hence, gains from monitoringprograms reducing uncertainty can be significant.

However, this paper considers only two sources of uncertainty inthe optimization: carbon sequestration by forests and carbon dioxideemissions from fossil fuels. Sensitivity analyses reveal relative highimpacts on costs for changes in quantified uncertainty. If carbonsinks are extended to include other land uses, such as grassland,arable land, and wetlands, a portfolio analysis would also consideruncertainty in carbon sequestration from these options. Such exten-sions require analyses of the co-variation between the sources of un-certainty. Depending on the signs of co-variations, carbon sinks mayhedge against or enforce overall uncertainty in reaching targets (seeByström et al., 2000, and Gren, 2008, 2010 for applications to waterquality management). It has also been assumed in this paper thatthe reliability concern, as expressed in terms of the probability ofachieving ETS and national commitment targets, is the same for allcountries. This may be a reasonable assumption for the commonETS, but it may not be true for the national commitments. Overallcosts increase if the reliability concern is relatively high in countrieswith large shares of total risk and high abatement costs.

Appendix A. Supplementary data

Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.eneco.2012.07.002.

References

Anda, A., Golub, A., Strukova, E., 2009. Economics of climate change under uncertainty:benefits of flexibility. Energy Policy 37, 1345–1355.

Antinori, C., Sathaye, J., 2007. Assessing transaction costs of project-based greenhousegas emissions trading. Lawrence Berkeley National laboratory Report. LBNL-57315.

Antle, J.M., Capalbo, S.M., Mooney, S., Elliot, E.T., Paustian, K.H., 2003. Spatial heterogene-ity, contract design and the efficiency of carbon sequestration policies for agriculture.J. Environ. Econ. Manag. 46, 231–250.

Baker, E., Solak, S., 2011. Climate change and optimal energy technology R&D policy.Eur. J. Oper. Res. 213 (2), 442–454.

Barrett, S., Stavins, R., 2002. Increasing participation and compliance in internationalclimate change agreements. Working paper, John F. Kennedy School of Government,Harvard University, Cambridge, Massachusetts, August 13.

Bigman, D., 1996. Safety-first criteria and their measures of risk. Am. J. Agric. Econ. 78,225–235.

Birge, J., Louveaux, F., 1997. Introduction to Stochastic Programming. Springer, NewYork.

Böhringer, C., Löschel, A., 2009. Market power in international emission trading. Theimpacts of US withdrawal from the Kyoto protocol. Discussion paper no 01-58.ZEW, Center for European Economic Research, Mannheim, Germany.

Böhringer, C., Rutherford, T., Tol, R., 2009. The EU/20/20/2020 targets: an overview ofthe EMF22 assessment. Energy Econ. 31, S268–S273.

Bosetti, V., Lubowski, R., Golub, A., Markandya, A., 2009. Linking Reduced Deforestation andGlobal Carbon Market: Impact on Costs, Financial Flows, and Technology Innovation.Fondazione Eni Enrico Mattei, Milano, Italy.

Brooke, A., Kendrick, D., Meeraus, A., 1998. GAMS. A User's Guide. The Scientific Press,San Francisco.

Byström, O., Andersson, H., Gren, I.-M., 2000. Economic criteria for restoration ofwetlands under uncertainty. Ecol. Econ. 35, 35–45.

Capros, P., Mantzos, L., Papandreou, V., Tasios, N., 2008. Model-based analyses of the2008 EU policy package on climate change and renewables. Report to the EuropeanCommission Directorate-General Environment.

Charnes, A., Cooper, W.W., 1964. Deterministic equivalents for optimizing and satisfyingunder chance constraints. Oper. Res. 11, 18–39.

Cline, W.R., 1992. The Economics of Global Warming. The Institute for Global Economy,Washington D.C.

Couture, S., Reynaud, S., 2011. Forest management under fire risk when forest carbonsequestration has value. Ecol. Econ. 70 (11), 2002–2011.

Dietz, S., Hope, C., Patmore, N., 2011. High impact, low probability? An empirical analysisof risk in the economic of climate change. Clim. Chang. 108 (3), 519–541.

Dixit, A., Pindyck, R., 1994. Investment Under Uncertainty. Princeton University Press,Princeton.

EC, 2008. Addressing the Challenges of Deforestation and Forest Degradation to TackleClimate Change and Biodiversity LossCOM(2008) 645 final at http://ec.europa.eu/environment/forests/pdf/com_2008_645.pdf (accessed February 21, 2011).

Elofsson, K., 2003. Cost effective reductions of stochastic agricultural nitrogen loads tothe Baltic Sea. Ecol. Econ. 47 (1), 13–31.

Försund, F., Naevdal, E., 1998. Efficiency gains under exchange-rate emission trading.Environ. Resour. Econ. 12 (4), 403–423.

Gerst, M., Howarth, R., Borsuk, M., 2010. Accounting for the risk of extreme outcomesin an integrated assessment of climate change. Energy Policy 38 (8), 4540–4548.

Golub, A., Narita, D., Schmidt, M., 2011. Uncertainty in integrated assessment modelsof climate change: alternative analytical approaches. Working Papers 2011.02.Fondazione Eni Enrico Mattei.

Gren, I.-M., 2008. Mitigation and adaptation policies for stochastic water pollution: anapplication to the Baltic Sea. Ecol. Econ. 66 (2-3), 337–347.

Gren, I.-M., 2010. Resilience value of constructed coastal wetlands for combatingeutrophication. Ocean Coast. Manage. 53 (7), 358–365.

Gren, I.-M., Munnich, M., Carlsson, M., Elofsson, K., 2009. A numerical model for costeffective CO2 mitigation in the EU with stochastic carbon sink. Working Paper No.2009:4. Department of Economics, SLU, Uppsala. Available at http://publikationer.slu.se/visa/results.cfm?pubid=P35063&f=hd&aktuelloid=178&ny=&rg=&ti=&px=&na=gren&in=&ty=1&mx=1000&ar=2009&lm=510&pe=50&ix=.

Held, H., Kriegler, E., Lessman, K., Edenhofer, O., 2009. Efficient climate policies undertechnology and climate uncertainty. Energy Econ. 31, S50–S61.

Janssens, L., Freibauer, A., Schlamadinger, B., Ceulemans, R., Ciais, P., Dolman, A.,Heimann, M., Nabuurs, G.-J., Smith, P., Valentini, R., Schulze, E.-D., 2005. The carbonbudget of terrestrial ecosystems at country-scale a European case study. Biogeosciences2, 15–26.

Kann, A., Weyant, J.P., 2000. Approaches for performing uncertainty analyses in largescale energy/economic modeling. Environ. Model. Assess. 5, 29–46.

Kataria, M., Elofsson, K., Hassler, B., 2010. Distributional assumptions in chanceconstrained programming models of stochastic water pollution. Environ. Model.Assess. 15 (4), 273–281.

Kato, E., Ringler, C., Yesuf, M., Bryan, E., 2009. Soil and conservation technologies:a buffer against production risk in the face of climate change? Insights from theNile basin in Ethiopia. IFPRI Discussion paper 00871.

Kim,M.-K.,McCarl, B., 2009. Uncertainty discounting for land-based carbon sequestration.J. Agric. Appl. Econ. 41 (1), 1–11.

Kurkalova, L., 2005. Carbon sequestration in agricultural soils; discounting for uncertainty.Working Paper 05-WP388. Center for Agricultural and Rural Development, Iowa StateUniversity.

Lorenz, A., Schmidt, M.G.W., Kriegler, E., Held, H., 2011. Anticipating climate thresholddamages. Environ. Model. Assess., http://dx.doi.org/10.1007/s10666- 011-9282-2

Lubowski, R., Plantinga, A., Stavins, R., 2006. Land-use change and carbon sinks: econo-metric estimation of the carbon sequestration supply function. J. Environ. Econ.Manag. 51, 135–152.

Macknick, J., 2009. Energy and carbon dioxide emission data uncertainties. Interim ReportIR-09-032. International Institute for Applied Systems Analysis, Laxenburg, Austria.

MAF (Ministry of Agriculture and Forestry, New Zealand), 2011. Guide to Forestry in theEmission Trading SchemeAt http://www.maf.govt.nz/news-resources/publications.aspx?title=Guide%20to%20Forestry%20in%20the%20Emissions%20Trading%20Scheme (accessed October 21, 2011).

McCarl, B., 2010. McCarl and Spreen bookat http://agecon2.tamu.edu/people/faculty/mccarl-bruce/mccspr/new14.pdf (accessed January 3, 2011).

McSweeny, W.T., Shortle, J.S., 1990. Probabilistic cost effectiveness in agricultural non-point pollution control. South. J. Agric. Econ. 22, 95–104.

Meil, van H., Rheenen, van T., Tabeau, A., Eickhout, B., 2005. The impact of different pol-icy environments on agricultural land use in Europe. Agric. Ecosyst. Environ. 114(1), 21–38.

Michetti, M., Rosa, R.N., 2011. Afforestation and timber management compliance strate-gies in climate policy. A computable general equilibrium analysis. Nota di Lavoro04.2011. Sustainable Development Series. Fondazione Eni Enrico Mattei.

Murray, B., Lubowski, R., Sohngen, B., 2009. Including International Forest CarbonIncentives in Climate Policy: Understanding the Economics. Nicholas Institute forEnvironmental Policy Solutions at Duke University, USA.

Page 9: Stochastic carbon sinks for combating carbon dioxide emissions in the EU

1531I.-M. Gren et al. / Energy Economics 34 (2012) 1523–1531

Nordhaus, W.D., 2008. A Question of Balance—Weighing the Options on GlobalWarming Policies. Yale University Press, New Haven.

Nordhaus,W.D., Popp, D., 1997.What is the value of scientific knowledge? An applicationto global warming using the PRICE model. Energy J. 18 (1), 1–45.

Official Journal, 2009a. Decision No 406/2009/EC of the European Parliament and of theCouncil of 23 April 2009 on the Effort of Member States to Reduce Their GreenhouseGas Emissions to Meet the Community's Greenhouse Gas Emission ReductionCommitments Up to 2020. Published on 5 June 2009.

Official Journal, 2009b. Directive 2009/29/EC of the European Parliament and of theCouncil of 23 April 2009 Amending Directive 2003/87/EC so as to Improve andExtend the Greenhouse Gas Emission Allowance Trading Scheme of the Community.Published on 5 June 2009.

Ovando, P., Caparros, A., 2009. Land use and carbon mitigation in Europe: a survey ofpotentials of different alternatives. Energy Policy 37, 992–1003.

Peterson, S., 2006. Uncertainty and economic analysis of climate change: a survey ofapproaches and findings. Environ. Model. Assess. 11, 1–17.

Pizer,W.A., 1999. The optimal choice of climate change policy in the presence of uncertainty.Resour. Energy Econ. 21 (3–4), 255–287.

Pyle, D., Turnovsky, S., 1970. Safety-first and expected utility maximization in a mean–standard deviation portfolio analysis. Rev. Econ. Stat. 52 (1), 75–81.

Schmidt, M.G.W., Lorenz, A., Held, H., Kriegler, E., 2011. Climate targets underuncertainty: challenges and remedies. Clim. Change: Lett. 104 (3), 783–791.

Schulp, C., Nabuurs, G.J., Verburg, P., 2008. Future carbon sequestration in Europe— effectsof land use change. Agric. Ecosyst. Environ. 27, 251–284.

Shortle, J., 1990. The allocative efficiency implications of water pollution abatementcost comparisons. Water Resour. Res. 26, 793–797.

Shortle, F., Horan, R., 2008. The economics of water quality trading. Int. Rev. Environ.Resour. Econ. 2 (2), 101–133.

Sohngen, B., 2009. An Analysis of Forestry Carbon Sequestration as a Response to Cli-mate Change. Copenhagen Consensus Center, Copenhagen Business School,Frederiksberg, Denmark. http://fixtheclimate.com/component-1/the-solutions-new-research/forestry/.

Stankeviciute, L., Kitous, A., Criqui, P., 2008. The fundamentals of the future internationalemissions trading system. Energy Policy 11, 4272–7286.

Stavins, R.N., 1997. Policy Instruments for Climate Change: How can National Govern-ments Address a Global Problem? University of Chicago Legal Forum 1997, pp.293–329.

Stavins, R., 1999. The costs of carbon sequestration: a revealed-preference approach.Am. Econ. Rev. 89 (4), 994–1110.

Taha, H.A., 1976. Operations Research, an Introduction, Second edition. MacmillanPublishing, Inc., New York.

Tesler, L.G., 1955-56. Safety first and hedging. Rev. Econ. Stud. 23, 1–16.Tol, R.S.J., 1999. Safe policies in an uncertain climate: an application of FUND. Glob.

Environ. Chang. 9, 221–232.UN, 2011. UN-REDD ProgrammeAt http://www.un-redd.org/ 2011(accessed October

20, 2011).van Kooten, C., Eagle, A., Manley, J., Smolak, T., 2005. How costly are carbon offsets? A

meta-analysis of carbon forest sinks. Environ. Sci. Policy 7, 239–251.