AUTHOR ACCEPTED MANUSCRIPT

Transcription

1 AUTHOR ACCEPTED MANUSCRIPT FINAL PUBLICATION INFORMATION Strategic Climate Policy wit Offsets and Incomplete Abatement : Carbon Taxes Versus Cap-and-Trade Te definitive version of te text was subsequently publised in Journal of Environmental Economics and Management, 66(2), Publised by Elsevier THE FINAL PUBLISHED VERSION OF THIS MANUSCRIPT IS AVAILABLE ON THE PUBLISHER S PLATFORM Tis Autor Accepted Manuscript is copyrigted by World Bank and publised by Elsevier. It is posted ere by agreement between tem. Canges resulting from te publising process suc as editing, corrections, structural formatting, and oter quality control mecanisms may not be reflected in tis version of te text. You may download, copy, and distribute tis Autor Accepted Manuscript for noncommercial purposes. Your license is limited by te following restrictions: (1) You may use tis Autor Accepted Manuscript for noncommercial purposes only under a CC BY-NC-ND 3. IGO license ttp://creativecommons.org/licenses/by-nc-nd/3./igo/. (2) Te integrity of te work and identification of te autor, copyrigt owner, and publiser must be preserved in any copy. (3) You must attribute tis Autor Accepted Manuscript in te following format: Tis is an Autor Accepted Manuscript by Strand, Jon Strategic Climate Policy wit Offsets and Incomplete Abatement : Carbon Taxes Versus Cap-and-Trade World Bank, publised in te Journal of Environmental Economics and Management66(2) CC BY-NC-ND 3. IGO ttp://creativecommons.org/licenses/by-nc-nd/3./ igo/ 218 World Bank

2 Strategic Climate Policy wit Offsets and Incomplete Abatement: Carbon Taxes versus Cap-and-Trade* Jon Strand Development Researc Group, Environment and Energy Team Te World Bank Wasington DC 2433, USA and Department of Economics, University of Oslo Journal of Environmental Economics and Management, fortcoming, 213 Abstract: Tis paper provides a first analysis of a policy bloc of fossil fuel importers wic implements an optimal coordinated climate policy, faces a (non-policy) fringe of oter fuel importers, and a bloc of exporters, and purcases offset from te fringe. We compare a carbon tax and a cap-andtrade sceme for te policy bloc, wic in eiter case is accompanied by an efficient offset mecanism for reducing emissions in te fringe. Te policy bloc is ten sown to prefer a tax over a cap, since only a tax leads to a lower fuel export price and by more wen te policy bloc is larger. Offsets are also more favorable to te policy bloc under a tax tan under a cap. Te optimal offset price under a carbon tax is below te tax rate, wile under a cap and free quota trading te offset price must equal te quota price. Te domestic carbon and offset prices are bot iger under a tax tan under a cap wen te policy bloc is small. Wen te policy bloc is larger, te offset price can be iger under a cap. Fringe countries gain by mitigation in te policy bloc, and more under a carbon tax since te fuel import price is lower. JEL Classification: Q31; Q38; Q54; Q58; H23 Key words: Climate policy; carbon taxes, cap-and-trade scemes; carbon emissions; strategic trade policy. *I wis to tank, witout implicating, Lawrence Goulder, Micael Toman, Ian Parry, Saule Siddiqui, and seminar participants at several institutions, plus two referees and an editor of tis journal for elpful comments to previous versions. I in particular tank te arrangers of and participants at te Environmental Protection and Sustainability Forum at te University of Exeter, were te paper was first presented. Te views expressed in tis paper are tose of te autor only and sould not be taken to represent tose of te World Bank, its management, or member countries. 1

3 1. Introduction Today, only countries under Annex 1 of te Kyoto Protocol wo ave extended te validity of te Protocol up to 22, at KOP18 in Doa, in December 212, ave policies wic include formal climate policy targets. Tese countries migt at later stages be joined by oter igincome countries (including Canada, Japan and te U.S.), and peraps also by some major emerging economies (among wic Cina and Sout Africa ave already signaled a willingness to impose greenouse gas (GHG) pricing in te relatively near future). Wat seems not acievable, anytime soon, is a set of compreensive and coordinated climate policies for all GHG emitters globally. Te countries wit formal climate policies ave agreed to binding emissions caps for te period ; but tese countries comprise less tan 2 percent of global GHG emissions. Current policy includes two offset scemes. Te most important of tese is te Clean Development Mecanism (CDM), wereby abatement of carbon emissions, to comply wit te overall cap, can be purcased from countries tat do not ave a climate policy. 1 An objective of te CDM is to make it easier (and less costly) for emitters in te policy countries to abide by teir emissions caps. A climate policy could, alternatively, take te form of a carbon tax. No compreensive carbon tax policy is so far used or seriously contemplated. 2 Most observers see little difference between a climate policy involving a carbon tax, and a cap-and-trade (c-a-t) sceme wit (expected) 1 Te oter sceme is Joint Implementation wic involves some Annex B countries purcasing offsets from oter countries witin tis bloc. 2 A few smaller nations, including te Scandinavian countries already from te early 199s, ave enacted unilateral and relatively compreensive carbon taxes. But tese countries constitute a too small fraction of global emissions to matter globally. 2

4 emissions as under a tax. Some differences are still widely recognized; tey all speak in favor of a tax over a cap. 3 Tis paper focuses on differences between taxes and caps tat ave so far been less widely discussed. First, carbon taxes and c-a-t work differently wen policy countries are net fossil fuel importers, and exporters beave strategically. Secondly, offset scemes may work differently under te two policies. Bot differences, it is sown, tend to favor taxes over c-a-t for te countries implementing (or benefiting from) a climate policy. In my model it is assumed tat all countries can be split into two main groups, importers and exporters of fossil fuels. Most countries belong to te first group, including virtually all countries tat may wis to establis a climate policy. Te exporting group is smaller, notably te OPEC countries, and Russia including some previous Soviet republics. Importers consist of a policy bloc wic pursues a climate policy (tose Annex 1 countries tat ave extended te Kyoto Protocol); and a fringe wit no policy (te rest of te world ). Te latter group acts witout coordination, eac perceiving no market power in fuel markets. Te producer and policy blocs are eac assumed to coordinate teir policies fully witin teir bloc, but not across blocs. Te solution concept is static non-cooperative Nas Equilibrium (NE) in simultaneous strategies, for bot models treated (in sections 2 and 3 respectively), in focusing 3 Under uncertainty te effects differ as only emissions vary under a tax, and only te emissions price under a cap. From Weitzman (1974), wen uncertainty takes te form tat benefits (in terms of reduced climate cange) of mitigation policy are less uncertain tan costs in te sort run (wic, arguably, is te case in practice), a tax solution is preferred. See also Hoel and Karp (21, 22), Pizer (22), and Karp and Costello (24) for dynamic analyses. Secondly, te government s ability to recuperate income may be greater under a tax as many or most emissions permits are anded out for free to emitters under a cap. A tird, politically important, difference is in terms of transparency of gains and losses to different affected parties. Under c-a-t it is easier to obscure tese distributional implications. Tis may be a political reason wy many countries seem to opt for c-a-t solutions, despite of te drawbacks pointed out. 3

5 on sort-run demand and supply relations. In bot models te exporter sets a fuel export tax. In te first model, te policy bloc sets a carbon tax and offset price; and in te second model te policy bloc sets an emissions cap. Dynamic issues, in particular te exaustibility of fossil fuels and te dynamics of climate cange, are not studied. 4 Sinn s (28) green paradox argument tat carbon pricing could lead to increased emissions in te sort run, is also not addressed. 5 Te policy bloc establises an offset sceme for inducing abatement in te fringe, wit two potential motivations. First, overall emissions can tus be furter reduced, peraps more ceaply tan troug mitigation in policy countries alone. Secondly, reduced fuel demand in te fringe may elp reduce aggregate fuel demand and tus te fuel export price. Under c-a-t, I assume tat te market for quotas is competitive wit te same trading price for te policy bloc and fringe. Fringe country emitters are ten paid an amount per abated emissions equal to te quota price facing policy country emitters. Under a carbon tax, it is less obvious ow an offset market sould be modeled. I assume tat offsets are purcased from fringe countries by te policy bloc at a given offset price, set by tis bloc, wic clears te offset market in fringe countries. Tis offset price could, in principle, be eiter iger or lower tan te carbon tax carged to policy bloc emitters. Importantly also, we assume no informational problems in implementing offsets and tat all offsets are additional. 4 Tis requires a dynamic model for a more complete analysis. A large literature ere exists; see e g Bergstrom (1982), Karp (1984), Karp and Newbery (1991), Wirl (1994), Rubio and Escrice (21), Salo and Tavonen (21), Rubio (25), Liski and Tavonen (24); and more recently Karp and Zang (21) and Wirl (212). 5 Te profile of future carbon taxes is ere important. Wen te future carbon tax is expected to increase rapidly, an increase in te general level of carbon taxation could induce Sinn s paradox by raising emissions in te sort run. Also, if climate policy partly implies supporting development of backstops for replacing fossil fuels, emissions may be worsened in te sort run; see e g Strand (27), Hoel (21), and Ploeg and Witagen (213). 4

6 Te preference for taxes over c-a-t for fuel importers as been sown in earlier papers by Berger, Fimreite, Golombek and Hoel (1992), and Berg, Kverndokk and Rosendal (1997). Strand (211) considers two fuels, one imported (oil) and one produced by consumer countries. Importers oil demand is ten somewat elastic under a cap, allowing some rent extraction by importers. A tax ere still dominates a cap for fuel importers. A possible objection to te current model is its static nature; tis issue is elaborated furter in te final section, wit reference to follow-up work. 2. Model 1: Te Policy Bloc Sets a Carbon Tax 2.1 Basics Assume te following aggregate utility function related to fossil-fuel consumption for countries wit a climate policy (te policy bloc ): (1) 1 γ 2 W1 = R1 R1 pr1 cr q1 R F, 2 were γ >, and identifies te relative size of te policy bloc in total fuel demand, wile te complement, 1-, represents te relative size of te fringe. Te policy bloc and fringe are assumed to be identical apart from teir relative sizes, represented by. An increase in implies a proportional increase in bot equilibrium fuel demand for given import prices, and in te externality cost experienced from GHG emissions. An interpretation is tat all individuals preferences are identical, and represents te sare of te global fuel-demanding population tat resides in te policy bloc. Wile not by itself very realistic (and see comments at te end of section 5), tis assumption facilitates te analysis of canges in relative sizes of policy bloc and fringe, a igly policy-relevant issue. 5

7 p is te fossil fuel import price. R 1 is te fossil-fuel consumption for te policy bloc, R is global fossil-fuel consumption, wile c represents te climate externality cost per unit of global fossil fuel consumption for policy bloc countries. Equation (1), and oter demand and supply functions, take linear-quadratic forms standard in te literature (and as in related work by Strand (211), Karp, Siddiqui and Strand (213); and Wirl (212)). We assume (wit little loss of generality) tat fossil-fuel importers produce no fuels, and tat producer countries consume no fossil fuels and export all teir production. Let R F denote fuel consumption in te fringe. Te last term in (1) represents an assumption tat te countries in te policy bloc are able to induce a reduction of te fringe s fossil fuel consumption and tus carbon emissions, below te business-as-usual level, troug a subsidy (or offset price ) q 1 to tose units of fossil fuel consumption in te fringe wit te smallest net productive yield (implying tat abatement in te fringe is efficient). Tis term gives te net outlay by te policy bloc, related to incentive payments from te policy bloc to te fringe, given tat all offsets in te fringe are purcased at price q 1, posted by te policy bloc. Suc payments represent a mecanism under a carbon tax sceme tat corresponds closely to an offset market under a c-a-t sceme (suc as te CDM). q 1 sould owever be interpreted somewat differently from te trading price under a c-a-t sceme. In particular, it need not be identical to te domestic tax on emissions. Under c-a-t, market arbitrage will ensure identical carbon trading prices for all carbon units, wic does not necessarily old in te tax case. In model 1 te policy bloc uses two instruments. First, it sets an excise tax, t 1, per unit of te imported fossil fuel. Tis leaves te consumer fuel price in tese countries at p+t 1. Fossil fuels are imported and consumed by many small competitive agents. Te public demanding fossil fuels in tis group of countries maximizes 6

8 (2) 1 γ V = R R ( p+ t ) R wit respect to R 1, yielding te demand level 1 p t1 (3) R1 =. γ γ / is te inverse demand sensitivity of fossil fuels wit respect to price in te policy bloc. Te fringe of fuel-importing countries wit no climate policy (wit subscripts F) as aggregate utility function (given no transfers from te policy bloc) (4) 1 γ 2 WF = RF RF prf (1 ) cr, 21 were subscript denotes no transfers. (1-)c is te climate-related externality of global fossil fuel consumption for te fringe. Tese countries in aggregate beave competitively. In te absence of transfers tese countries would maximize (5) 1 γ V = R R pr 21 2 F F F F wit respect to R F, yielding te first-order condition (1 )(1 p) (6) RF =, γ were γ/(1-) is te inverse demand sensitivity for te fringe. Te slope of te (global) aggregate demand function is 1/γ. 7

9 Te second instrument of te policy bloc is to pay a subsidy q 1 per unit of offsets ( foregone fossil fuel consumption ) in te fringe; i. e., te difference between te fuel consumption tat would ave materialized ad it not been for tis subsidy, and actual fuel consumption in te fringe. 6 Te fringe tus reduces its fossil fuel consumption below te bencmark (6). Te fuel price at te margin for te fringe equals p+q 1, were te policy bloc makes up tis difference troug a subsidy to fringe fuel consumers. Te induced fuel consumption in te fringe is ten 1 (7) RF = (1 p q1 ). γ Te subsidy is assumed to be paid only on te amount of fuel consumption avoided in te fringe by te incentive payment, called ΔR F = R F R F, given by 1 (8) RF = q1. γ Aggregate fossil-fuel demand, from bot blocs combined, is now 1 p t 1 p q 1 p t (1 ) q = + = + =. γ γ γ (9) R R1 RF (1 ) Assume a single (unified) producer country or region wit aggregate utility function (1) W2 =Π 2 + sr 1 cr 2, were П 2 is net profit of its petroleum producers, s 1 R is excise tax revenue for fuel exporting countries, wile c 2 R denotes negative emissions externalities for te exporter bloc. Individual fuel exporters are price takes wit profit functions 6 Tis requires full additionality; see comments in section 5. 8

10 (11) Π 2 = ( p s1) R pr φr, were p is a lower bound on marginal fuel extraction cost. Maximizing (11) wit respect to R yields te fossil-fuel supply function (12) p= p + s1+ φr. φ (> ) represents te (inverse) supply sensitivity of petroleum output. Te externality cost of one unit of carbon emissions is c for te policy bloc, and (1-)c for te fringe. Individual fringe countries are small and ignore tis factor in teir own decisions. Te global externality cost per fossil fuel unit equals c+c 2, wic would correspond to a Pigou tax imposed by a benevolent global regulator, given tat markets are oterwise competitive. Solving (9) and (12) for R and p as functions of te tax parameters t 1, q 1 and s yields 1 p s t (1 ) q R =, γ + φ (13) γ φ ( ) (1 (1 ) ). γ + φ γ + φ (14) p = p + s1 + t1 q1 We derive fuel demand for eac bloc as functions of s, t 1 and q 1, as follows: γγ ( + φ) (15) R = [ γ(1 p s ) ( γ + (1 ) φ) t + (1 ) φq ] γγ ( + φ) (16) R = [ γ(1 p s ) + φt ( γ + φ) q ] F

11 A iger q 1 increases R 1 (but lowers R), since p is reduced tus incentivizing iger policy bloc fuel demand. Indeed, tis is te basic purpose for te policy bloc of subsidizing offsets in te fringe. 2.2 Te policy bloc solution An autority representing te entire policy bloc sets t 1 and q 1 to maximize W 1 in (1), considering its own fuel demand response (15), te aggregate fuel demand response (13), and te export price response (14), to canges in t 1 and q 1 ; wile te exporter tax, s 1, is taken as exogenous. Te solution concept is (static) non-cooperative Nas Equilibrium (NE) were te policy bloc sets carbon tax and offset price, and te exporter bloc sets a fuel export tax; eac taking te oter s strategy variable(s) as exogenous. Appendix 1 now sows te following result. Proposition 1: Te static NE solution in t 1 and q 1 for te policy bloc is given by te following solutions, expressed as functions of s 1 : 2γ (17) t1 = [ φ(1 p 2 2 s1) + ( γ + φ) c] 2( γ + φ) (1 + ) φ γ 1 q1 = p 2 2 s1 + + c = t1. 2( γ + φ) (1 + ) φ 2 (18) [ φ(1 ) ( γ φ) ] q 1 < t 1 is ere a general result. More specifically, our ratio of one-to-two follows from te linearquadratic structure of te model and is not general. Wen is small, t 1 and q 1 are bot small: te policy bloc ten neiter carges ig domestic carbon taxes nor induces muc offsets in te fringe, for two separate reasons. First, wit low, te climate externality for te policy bloc, c, 1

12 and te related Pigou tax, is small. Secondly, market power of te policy bloc in te fossil fuel market is ten small. Te reason wy te offset incentive price, q 1, is lower tan te domestic carbon tax t 1 in te policy bloc, is tat offset payments go to foreigners, wic reduces te attractiveness of foreign offsets, relative to domestic mitigation via te carbon tax t 1. Te policy bloc acts as a monopsonistic purcaser of offsets from fringe countries (wic act non-cooperatively), and limits its offset purcases to maximize its net return from suc purcases. Wen te offset price instead is exogenous (and not necessarily optimal), we ave (19) 2 t1 = [ γ ( γ + φ) c+ γφ(1 p s1) + (1 ) φ q1]. ( γ + φ) φ Wen q 1 is iger (corresponding to a larger volume of offsets), t 1 is set iger in response. Intuitively, more offsets in te fringe leads to a lower fuel export price wic makes a iger carbon tax in te policy bloc advantageous. 2.3 Te exporter solution Te exporter bloc maximizes bloc welfare, W 2, wit respect to its fuel export tax s 1, given te supply function (12) from its individual producers, and te price relation (14). Still invoking te NE concept, t 1 and q 1 are taken as given by te exporter. I now solve for s 1, p and R, as functions of te carbon tax t 1 and offset subsidy rate q 1 set by te policy bloc. Te following result emerges, sown in Appendix A. Proposition 2: Te static NE solution for s 1 is te following function of t 1 and q 1 : γ γ + φ 2γ + φ 2γ + φ (2) s 1 = (1 p t 1 (1 ) q 1) + c 2. 11

13 As expected, s 1 is reduced in response to increased t 1 and q 1. Tis effect is stronger for t 1 (q 1 ) wen > (<) ½, so tat te fraction of te policy bloc in total fuel demand is greater (smaller) tan one alf. Interestingly, wen offsets are used (q 1 >), te exporter s fuel tax is lower. 2.4 Overall Nas Equilibrium Simultaneously solving (17), (18) and (2) for t 1, q 1 and s 1 gives te following result. Proposition 3: Te simultaneous, static, NE for te non-cooperative tax-setting game between te policy bloc and te fuel exporting bloc is caracterized by 2γ φ γ φ D (21) t1 = [ (1 p c2) + (2 + ) c] = 2q1 1 1 = [2 ( + ) (1 + ) ](1 ) + [2( + ) (1 + ) ] (1 + ), D (22) s { γ γ φ γφ p γ φ φ c 2 γ c } 1 were D1 = ( γ + φ)[2(2 γ + φ) (1 + ) φ]. To interpret tese expressions we rely on simulations based on simplifying parametric assumptions; and comparative-static results; all presented in section 4. Two furter features are considered. First, te incentivized emissions level describes net emissions as an outcome of incentive mecanisms applied (t 1, and q 1 ), bot in te policy bloc and in te fringe. Tis emission level corresponds notionally to a cap discussed under model 2 in te next section. It can be defined by 1 1 (23) RI1 = R1 RF = (1 p) (1 + t ) 1 γ 2. 12

14 Tis magnitude is simulated in section 4, in some parametric cases. In all cases studied, R I1 > (optimal emissions in te policy bloc always exceed emissions offset by te fringe). Te second feature is abatement in te policy bloc versus fringe (in terms of reducing R), via te tax and offset policies applied. From (13) (noting tat t 1 = 2q 1 ), R is reduced more (less) in te policy bloc tan in te fringe given tat > (<) 1/3. Tus in particular, wen = 1/3 it is optimal for te policy bloc to implement equally muc abatement in eac of te two blocs. 3. Model 2: Te Policy Bloc Uses Cap-and-Trade 3.1 Basics In te second model, te policy bloc sets a cap on its emissions, still taking fringe demand as exogenous. Tis cap can be acieved in part troug offsets purcased from te fringe by te policy bloc, wic give room for iger emissions witin te policy bloc for a given cap. Call te cap R P, and te amount of offsets R FP. Emissions by te policy bloc, R 1, are ten given by R P + R FP (offsets allow for policy-bloc emissions above te cap). Denote fringe emissions by R F, and fringe emissions in te (counterfactual, but ere still well defined) case wit no offsets by R F ; ten R F = R F R FP. Total emissions, R, are given alternatively as R 1 + R F, or R P + R F. I assume free trading of emissions rigts witin te policy bloc at a single quota price t 2 (applying parallel symbols wit te tax case). As a condition for offset market equilibrium in te quota market, emission offsets need to be purcased from te fringe at price t 2 : domestic emitters in te policy bloc must be indifferent between abating one unit of emissions, and purcasing one unit of offsets wereby abatement is avoided. Te equilibrium concept is simultaneous NE were te policy bloc determines te quantity of fuel demand and te exporter sets te fuel export tax. In calculating its optimal fuel demand 13

15 (including any offsets), te policy bloc takes te export tax as given, as in model 1. Te main difference from model 1 is tat te exporter, in setting its optimal export tax, takes net fuel demand by te policy bloc (incorporating any demand reduction induced in te fringe by te offset policy), and not te carbon price, as given. I put two constraints on te number of allowable offsets, R FP. First, R FP must be non-negative. Secondly, R FP cannot exceed abatement in te fringe, given a uniform carbon price t 2 enforced in te fringe. A carbon price no greater tan t 2 would ten implement te offset quota R F. As under model 1, I assume efficient offsets: for emissions tat are offset troug incentive payments from te policy bloc to te fringe, te mitigation cost is lower tan for any one unit of residual emissions (were offsets are not taking place). 7 We can treat te strategy of te policy bloc as setting te quota trading price of emission rigts (or tax) witin te bloc, wic is dual to te quantity solution. Te basic strategy of te fringe is also te same in tis case as under policy. A consequence is tat te amount of offsets in te fringe, to be financed by te policy bloc, is still given by (8). Te offset price is owever different ere. Use of c-a-t (and wit no quota discounts for offsets as discussed in te final section) requires te offset price in te fringe to equal te domestic quota price in te policy bloc countries (equivalent to te tax t 2 ) as a condition for market clearing in te quota market. In te last expression in (1), q 2 is ten replaced by te domestic trading price in te policy bloc, t 2. No similar constraint on te offset trading price was imposed in model 1, were te policy bloc implemented offsets directly via transfer payments to fringe countries, and te offset trading price could be set freely. 3.2 Importer solution 7 Tis is not an obvious outcome, since te unit incentive pay by policy bloc emitters to te fringe, t 2, is generally iger tan te carbon price tat would oterwise implement te actual offsets taking place in te fringe. 14

16 (1)-(16) from model 1 are still valid. Te fuel demand functions of te policy bloc and te fringe, as viewed by eac, are still given by (3) and (6), were t in (3) is interpreted as te quota price witin te c-a-t sceme in te policy bloc. Policy-bloc fuel demanders (and emitters) still maximize profits given te fuel price including te quota price, serving as a tax witin te policy bloc. Te strategy of te policy bloc itself can also be viewed as very similar to model 1. Tis is because te tax and c-a-t solutions are formally identical for fuel consuming countries facing a given fuel import price, under full certainty and wit full auctioning of emissions quotas. (15) can be interpreted, alternatively, as te condition for optimal energy demand R 1, or for optimal quota price t, in eiter case taking te fuel import price, p, from (12), and s as exogenous. Proposition 4: Wen te importer bloc uses a c-a-t policy wit optimal offsets and assuming free offset trading, te constrained optimal quota price, t 2, expressed in terms of te exporter tax, s 2, equals te offset price and is given by 2 γ t2 = (1 p s2) + ( + ) c = q2. ( γ + φ) φ (24) { φ γ φ } Moreover, te solution entails (25) p+ t2 = m were m is te marginal productivity of energy use in bot te policy bloc and te fringe. Proof: See te appendix. Te appendix demonstrates tat te constrained optimal solution for te importer takes te form of a corner solution were a maximum number of offsets is utilized for te given offset price, 15

17 wic equals te carbon trading price witin te c-a-t sceme in te policy bloc. Tis result as a simple intuitive explanation: For a given cap (wic effectively constrains energy consumption witin te policy bloc) and given tat offsets and quotas are sold at te same price, te policy bloc wises to consume as muc fossil energy as possible wic means tat it uses offsets to te maximum extent (for given offset price). Tis is different from Section 2, were te offset price was independently optimized, and set lower tan tat tax. Te offset amount was ten also lower for any given (policy bloc-internal) carbon price. Comparing (24) to (17), t 2 < t 1 (for any given export tax s); but te difference is small wen is close to one. Wen is low, by contrast, te difference is greater; and t 2 /t 1 tends to zero as goes to zero. All net offset market rent is ere captured by fringe emitters. Tis follows from te assumption of perfect competition and free arbitrage in te offset market, so tat all units in tat market (weter domestic in te policy bloc or purcased from te fringe) need to be traded at a uniform price. Offsets are in general more costly to te policy bloc in tis case tan under model 1 (were tey could be bougt at a discount relative to te domestic carbon tax t 1 ); ere tey must be paid at full cost t 2. But tis also serves to reduce te internal carbon price witin te policy bloc, t 2, below t 1 in model Exporter solution For fuel exporters, c-a-t is more dramatically different from a carbon tax solution for te policy bloc. Exporters no longer face an importer tax, but instead a cap by te policy bloc, in amount R P. Instead of (9), te exporter faces te aggregate fuel demand function 16

18 1 p (26) R= R1+ RF = RP + RF = RP + (1 ) γ R P, te emissions cap set by te policy bloc, includes possible offsets purcased by te policy bloc from te fringe, so tat actual policy bloc emissions may exceed R P by te amount of offsets. Te exporter now takes R P as fixed, and only te baseline demand by te fringe, R F, as variable. We ave te following result, sown in te appendix: Proposition 5: Wen te policy bloc cooses a c-a-t solution, te optimal strategy of te exporter bloc is to set its export tax s according to γ (1 )( γ + φ) (2 ) γ + (1 ) φ (2 ) γ + (1 ) φ (27) s2 = (1 p t2 (1 ) q2) + c2. Comparing (27) to (2), we find s 2 > s 1 (from model 1) for any given t 2 and q 2. Te exporter is (muc) more aggressive in setting its export excise tax wen te importer cooses a c-a-t policy, tan wen it cooses a tax policy. Te difference is greater wen (te sare of te policy bloc among all fuel demanders) is larger. Simulations, discussed in section 4 below, also indicate tat s 2 > s 1 more generally. Te export price, p, can be expressed as γ + (1 ) φ (1 ) γ (2 ) γ + (1 ) φ (2 ) γ + (1 ) φ (28) p p = (1 p t2 (1 ) q2) + c2 Comparing to te carbon tax case, p is greater ere for any given t (were t = t 1 is te carbon tax in model 1, and t = t 2 te quota price in model 2). We find: 17

19 (29) 2 dp γ (1 ) d( t2) (1 p 2 t2 (1 ) q2 c2) γ + = φ d [ γ + (1 )( γ + φ)] γ + (1 )( γ + φ) d Tis expression is always positive for given t 2 (so tat t 2 falls proportionately). But it is also positive wen t 2 increases in, provided tat te first term dominates te second. Tis is always so wen is initially small; t 2 is ten also small (from (3) below); and d(t 2 ) must consequently be small. We tus find tat wen is small at te outset, te export price always increases wen te policy bloc comprises a larger fraction of total fuel demand ( increases). Tis is diametrically opposite to te conclusion under model 1, were te policy bloc used a carbon tax. We find, in te simulations in section 4 below, tat p can increase in, also for larger values (wen c is low). It is important to stress tat te beavior of te policy bloc is formally identical in te two models (except for te constraint t 2 = q 2 only in model 2); despite te fact tat te policy bloc sets a tax in te first, and a cap in te second model. It occurs because te two problems, maximizing wit respect to te cap, and to te tax, yield te same result for given beavior of te exporter. It follows from duality of te tax and cap solutions: bot implement te same allocation under competitive conditions. Te difference between te two models lies in te response of a non-competitive exporter to te cosen policy bloc strategy, tax or cap. 3.4 Overall Equilibrium Overall equilibrium is found by solving (24) and (27) for t 2 and s 2 (noting tat q 2 = t 2 ). Proposition 6: Given tat te importer bloc uses a c-a-t policy wit free offset trading, and te exporter sets an optimal fuel export tax, te static NE (t 2, s 2 ) combination is given by 18

20 2 γ (3) t = {[(2 ) γ + (1 ) φ] c+ (1 ) φ(1 p c )} 2 2 D2 (31) s (1 )[( γ+ φ) φ] c2 + γγ [ + (1 ) φ](1 p) γc = D 2 were D = ( γ φ)[2 γ (1 ) φ] [( γ φ) φ ] t 2 ere tends to c as tends to one. t 2 is always rising in for low, but could fall or rise for larger ; tis is found in comparative static results, and in simulations in section 4 below. s 2 = s 1 from model 1 for = and no climate policy. Wen >, s 2 > s 1 and more so wen is iger. Te exporter adopts a more aggressive taxation strategy te iger is, since te fuel demand elasticity faced by te exporter is lower (as less of fuel demand is variable). Consider implications of te overall solution for te optimal cap to be set, analogously to te amount of incentivized emissions (from (23)) under model 1. Te optimal cap, R C2, is 1 (32) RC2 = R1 RF = [ (1 p ) t2 ]. γ Simulations in section 4 sow tat R C2 > independent of. Tis is similar to wat was found in model 1. Te intuition is also ere tat for low (were, conceivably, te cap could be negative) te emissions price is too low to really matter in terms of emissions reductions. Compare also ere te amounts of abatement taking place in te policy bloc versus in te fringe. From (13), (15) and (16) and inserting q 2 = t 2 we now simply ave 19

21 (33) R1 = (1 s t2) = R 2 1 (34) RF = (1 s t2) = (1 R ). 2 Tus in tis case fuel demand in te policy bloc and fringe are proportional to bloc size. Tis is simply a consequence of fuel consumption being efficiently allocated across fuel-consuming countries in tis case, from (25). 8 4.Comparative Statics wit Simulations I will now discuss some key comparative-static results given canges in two key exogenous parameters, (te sare of fuel importers wit a climate policy) and c (te global externality of GHG emissions for fuel importers). 9 Tese are illustrated by model simulations in a simple numerical example were p = c 2 = (te exporter s fuel supply function as intercept at zero, and no negative climate impacts on te exporter), and γ = φ = 1 (demand and supply functions for fossil fuels are equally sloped). 1 In figures 1-8, all model 1 variables are in blue (except q 1 wic is in green), and all model 2 variables are in red. Figures 1-3 illustrate solutions as functions of (te fraction of te fuel demand market represented by te policy bloc), for tree alternative values of c: = (no climate concern); = ¼ ( medium climate concern); and = ½ ( ig climate concern). Five variables are sown in figures 1-3: clockwise from upper left t and q (te carbon tax and offset price); s (te exporter fuel tax); p (fuel export price); and R 8 Tis is an idealized model were te offset markets are assumed to function perfectly; in particular, all units of excess emissions in te fringe are perfectly offset using te offset price t 2. Tis is clearly not realistic; see te discussion of tis issue in te conclusion below. 9 I tank Saule Siddiqui for invaluable elp in creating te simulations and figures. 1 Te exact comparative-static results are not reproduced; tey can be obtained from te autor upon request. 2

22 (consumed amount of te resource); all as functions of (te policy bloc as sare of fueldemanding countries). Wen c = (figure 1), everyting is driven by strategic concerns. As noted, q 1 = ½ t 1. Bot are iger tan q 2 (= t 2 ). Wile t 1 and q 2 (= t 2 ) differ also for small, te difference is greater for larger. 11 Te carbon price of te policy bloc is dramatically iger under a carbon tax tan under c-a-t wen is ig. Wile te carbon tax increases strongly in, te quota price in te c- a-t case also increases in up to a certain point, but is reduced wen increases furter. Two factors give opposite effects on t 2 : a iger makes te policy bloc more collusive and more aggressive in its pricing; but a iger also makes te exporter (muc) more aggressive wic reduces te scope for rent extraction by te policy bloc. Interestingly, te policy bloc s carbon price is always positive even as tere is no climate concern in tis case Figure 1 in about ere Fossil fuel consumption drops in, only sligtly in te tax case, and more dramatically in te cap case, as te exporter price ten increases drastically. Te tax case is good for importers as te import price is substantially reduced wen increases. Figures 2 and 3 ( intermediate and ig climate concern) differ more from figure 1 as grows. Tis is because a climate concern of te policy bloc affects policy very little wen is small, but muc more wen is ig: te carbon tax and quota price are ten also muc iger. In particular, te quota price under c-a-t rises uniformly in. q 2 now (sligtly) exceeds q 1 for ig (greater tan about.65 for c = ¼; and greater tan about.6 for c = ½). Tis more 11 As noted, owever, te model is less suitable for describing wat appens under a cap solution for ig values. 21

23 aggressive carbon pricing strategy of te policy bloc leads to a greater reduction in bot te import price, and total fossil fuel consumption, wen increases Figures 2 and 3 in about ere Generally, t 1 > t 2 for all values of and c. Tis difference is owever not uniformly greater wen is iger. Two main factors explain tis. First, s 2 > s 1 always, and te difference is greater wen is iger. Te importer s optimal response is to set t 1 > t 2 (wen te exporter tax, and tus te export price, is lower). 12 Te second factor is related to te functioning of te offset market. In te tax case, under model 1, te domestic carbon tax in te policy bloc is independent of te offset price (effective witin te fringe); tere is no direct effect of te offset market on te domestic carbon tax. In model 2, by contrast, te offset carbon price must equal te carbon price witin te policy bloc. Tis puts downward pressure on te carbon price wen te policy bloc is small and te fringe is large ( small), and te offset market is a large sare of total abatement. Wen te fringe is small ( large), by contrast, tis factor is less important (as te offset market is also less important). Tere is ten less downward pressure on te carbon price from an offset market under te cap. Tese two factors work in opposite directions wit respect to Δt = t 1 - t 2 wen increases. Wen c =, Δt increases strongly in. Wen c = ¼, Δt increases but more slowly over a large range for. Wen c = ½, Δt is reduced for iger. 12 In te limit as tends to unity, under a cap te NE solution in tis model entails te exporter setting te export price at its maximal level coking off demand. Te carbon quota price is ten equal to zero. Tis is an unrealistic economic model; see Strand (21) for elaboration and discussion of alternative equilibrium concepts. 22

24 As noted, t 1 = 2q 1, wile t 2 = q 2. Still, q 2 < q 1 for low and/or low c; but q 2 > q 1 wen bot and c are ig. Wen is low, te dominating factor is te drag (toward low carbon prices) from te constraint t 2 = q 2 under c-a-t. Wen is ig, by contrast, te offset market is small and pricing in tat market means little for efficiency witin te policy bloc. Wen c is ig (and te quota price ig under c-a-t for ig ), q 2 = t 2 ten implies q 2 > q 1 in suc cases. Te more general comparative-static results sow tat t 1 rises, wile bot s 1 and R in model 1 fall, wen bot and c increase. 13 Te same olds wen c canges in model 2. Effects of on t 1 and s 2 as are sligtly more complex. Wen c is small, dt 2 /d > always wen is small; and dt 2 /d < always wen is large. Wen c is ig, t 2 rises uniformly in. s 2 always rises in wen c is small, and always falls in wen c is ig and already ig. Tis confirms te main results from te simulations in figures 1-3. Figure 4 sows incentivized quotas R I1 in (23), and R C2 in (32) for te simulated example. Under my numerical example tese two expressions are found as 1 (23a) R I1 = 1 s1 (3 t ) (32a) RC 2 = (1 s2 R) t2. R C2 corresponds to te optimal quota (accounting for offsets) set by te policy bloc in model 2. R I1 as a similar interpretation in model 1 (except tat a government-managed offset sceme is ere assumed instead of a free offset trading sceme). Optimal quotas are similar in te two models for low (sligtly greater in model 2); but are muc smaller in model 2 for ig. 13 Analytical results can be obtained from te autor upon request. 23

25 ----- Figure 4 in about ere Figures 5-7 sow welfare levels for te policy bloc, fringe and exporter bloc under models 1-2. Most strikingly, for bot policy bloc and fringe, utility is everywere iger in model 1 tan in model 2. As is easily verified, tis result olds generally and does not rely on te cosen parameter values. For te policy bloc, te difference in outcome under te two models grows wit, as seen from te figures. In a relevant example, = ¼ (as for Annex B under te Kyoto Protocol), te difference in utility for te policy bloc is small, and it matters little to te policy bloc weter a tax or a c-a-t solution is cosen. Wen te policy bloc is larger, te difference can be large, and te coice of policy regime a major concern for te policy bloc. 14 Exporter welfare is greater wit c-a-t ten wit carbon taxes, for values up to a maximum point. For even iger values, te aggression in exporter fuel price setting (as fuel demand becomes less elastic) backfires, as fuel output tends to zero wen tends to one Figures 5-7 in about ere We finally simulate net welfare of fringe countries due to offsets (disregarding climate effects), expressed by B F, wic takes te form (35) B F = q, were q is te generic offset price, given by t 1 /2 from (21) under model 1, and by t 2 from (3) under model 2. Simulations for tree alternative values of c (=, ¼, and ½) are sown in figure 8. For moderate values of (<.6) te welfare gain to te fringe from an offset market is 14 For suc c values or iger, utilities tend to be negative in te model, for bot fuel-consuming blocs. Tis is due to te large negative externalities from emissions. It would ten ave been better to ave no fossil fuels available at all. Tis is not realistic, but follows from my assumption tat te coke price of fossil fuels is quite low (= 1 and tus only twice te externality value for c =.5), and te demand function linear. 24

26 everywere greater under a tax tan under c-a-t. Tis mirrors results for q from figures 1-3: werever q 1 > (<) q 2 welfare gains from offsets are greater (smaller) under model Figure 8 in about ere Conclusions and Final Comments Tis paper as analyzed a carbon tax versus an emissions cap wit free quota trading (c-a-t) as alternative climate policy strategies for a fossil fuel-importing climate policy bloc facing a fuel-importing group of countries (a fringe ), wit no climate policy, and a fuel-exporting bloc wic sets its fuel export tax optimally. Te optimal carbon price in te policy bloc is influenced by bot a climate ( Pigouvian ) motive, and a strategic motive wereby te policy bloc influences te exporter s fuel price troug its tax or cap. A positive carbon tax leads to a lower fuel import price, wic benefits all fuel importers including te fringe. Te tax is set iger wen te policy bloc is larger, for two reasons: te Pigou element is ten greater; and te strategic element, wereby te tax reduces overall fuel demand and te fuel export price, is greater. I find tat a carbon tax is always preferred over a c-a-t policy by fuel importers, mainly because fuel exporters carge a lower fuel price under a carbon tax tan under c-a-t. Under c-a-t, once a cap as been set, overall fuel demand is less sensitive to te fuel export price tan under a carbon tax. Tis gives a monopolistic exporter an incentive to set its export price iger under c-a-t tan under a carbon tax, and tis urts all importers. Having an offset market is also more advantageous to te policy bloc under a carbon tax in my model, because te offset price can be set lower tan te tax, wile unified trading makes price differentiation between domestic quotas and offsets infeasible under c-a-t. Te fringe also fares better under a carbon tax, and more so 25

27 wen te policy bloc is larger and te fringe smaller. A small fringe benefits more from being a free rider on a (relatively ig) carbon tax set by te larger policy bloc, wic puses te fuel export price down. To my knowledge tis paper represents te first attempt in te literature to analyze optimal offset policies in te context of a global model of strategic GHG mitigation policy. Being a first attempt, te analysis is stylized. Offset markets are assumed to be fully efficient, wit te best projects always implemented, and all offsets additional. My assumption tat wen te fringe faces an offset price equal to q, te mitigation in te fringe is te same as it would be wen facing tis level of carbon tax, is not realistic. Several problems wit te CDM ave been uncovered, including lack of additionality (many projects would ave been implemented even witout CDM financing; see Hagem (1996), Fiscer (25); Flues, Micaelowa and Micaelowa (21)), manipulation of baselines (Wirl, Huber and Walker (1998), Fiscer (25), Strand and Rosendal (212)), and leakage (Rosendal and Strand (211)); wic all limit te global abatement effects of CDM projects. Offset markets are assumed to be designed differently in te two cases. In te carbon tax case offsets are purcased directly by a central autority, wit a single offset price tat may differ from te carbon tax. In te c-a-t case, by contrast, te offset mecanism is market-based and of a standard CDM type. In my view tese are logical ways of organizing an offset market in te two cases; but tey are not te only ways. In one sense, my model can be seen as stacked against te c-a-t solution and in favor of te tax solution by allowing te policy bloc to price discriminate in te offset market only in te tax case. One migt alternatively consider ways in wic to differentiate te domestic and foreign markets under c-a-t, allowing for different prices in te two sub-markets also wit private trading. Some autors, including Castro and 26

28 Micaelowa (21), and Klemick (212), ave discussed offset discounts (te purcaser of an offset can increase its emissions by only a fraction of te purcase), wic migt be preferable wen offsets are not fully additional. Bargaining over net returns from individual CDM projects migt also be relevant. Wit project bargaining, market arbitrage will no longer old for offset quotas, wic will be priced lower, as discussed by Brécet, Ménière and Picard (211) wo stress tat a greater bargaining power to project sponsors makes offsets more attractive for te policy bloc. One may also question weter a totally separate sub-market for offsets (managed e g by governments) can provide te same degree of efficiency as an integrated, private, domestic and foreign c-a-t market. Te wider implications of alternative offset market mecanisms sould remain as a priority topic for future researc, given tat non-policy countries continue to play important roles for global GHG mitigation. In realistic cases, offsets migt ten be found to represent a less attractive option for a policy bloc, so tat teir optimal volume is smaller. However, given a large fringe, offsets migt still play a significant role. Considering te overwelming evidence in favor of tax over cap solutions, in tis and most oter modeling contexts, a natural question is, wy are c-a-t solutions at all used? I will not enter a deep discussion, only note tat in various policy contexts tere are strong biases against solutions tat put a direct price (or tax) on energy resources, and in favor of more roundabout and indirect, and less efficient, solutions. Heavy political economy issues often seem to lie beind: in te U.S. and many oter countries, biases against taxes in general; in te EU, succumbing to political pressure from industry lobbies to spare energy-intensive sectors from any burden of te EU-ETS (demanding c-a-t systems wit ig levels of free allocations); and in many oter countries strong populist pressure not to tax (but often rater subsidize) fuels and electricity. Hopefully, tis analysis can serve as an additional reminder tat energy tax solutions can be igly 27

29 beneficial, and were one key additional argument (relative to standard ones) is offered, namely te effects on fuel price setting and tus terms of trade wic, independently of oter factors, make tax solutions unambiguously favorable for fuel importers. My model is igly simplified and could be canged or expanded in oter ways tan tose already discussed. I ere only briefly mention a few possibilities. A) Static analysis, wile fossil energy extraction and climate cange are bot inerently dynamic processes. A key question is weter main results, suc as preference of a tax over a cap in climate policy for fuel importers, carries over to a dynamic context. Some ongoing researc indicates tat tey do. Wirl (212) as recently sown tat taxes are cosen over caps in a corresponding dynamic model of two monolitic blocs but no fringe. 15 Work is also in progress on te (analytically more intriguing) dynamic case wit a fuel importing fringe. See Karp, Siddiqui and Strand (213), wit results pointing in te same direction. 16 B) No fuel production in consuming countries, and no fuel consumption in fuel-producing countries. Canging tis would eliminate some extreme cases (including non-existence of positive resource extraction under c-a-t for = 1), but would oterwise leave main results intact. C) Only one fuel. Strand (211) considers two differentiated fuels in a model of two blocs only (exporters and importers). Tis canges conclusions sligtly, by making te ex post fuel demand function more elastic under c-a-t. Wile tis increases te attractiveness of te c-a-t solution, te basic preference for taxes still remains. 15 Wirl (212) sows tat taxes are dominant dynamic instruments also for exporters, as we ave assumed ere. 16 Te examples simulated in tis paper sow tat te exporter always cooses a tax; and tat te policy bloc in response cooses a tax for at least a long initial period (5-1 years). Note tat neiter Wirl (212) nor Karp, Siddiqui and Strand (213) include offset markets. A related, muc earlier unpublised paper is Karp (1988). 28

30 D) A monopolistic fuel exporter dictates te fuel export price; and tere is no fringe of competitive fuel suppliers. Starts of analysis incorporating competitive fringe fuel supply are found in Keutiben (21), and Karp, Siddiqui and Strand (213). E) All fuel-importing regions are equally averse to climate cange; and ave equal utility loss (relative to population size) per unit of carbon emissions. Wit different loss parameters, countries incentives to join te policy bloc will generally vary among countries. Te climate impact factor for te policy bloc, ere c, will ten also be a more complex function of. F) Climate costs are linear in total emissions. More plausibly, climate costs are strictly convex in emissions. Wit a quadratic cost function we would get an additional quadratic term in (1), reducing te optimal t 1 and t 2 ; and more so te larger is te policy bloc (and ). In oter respects, owever, little would cange. Also, since climate is a slow-moving variable, convexity is likely not to ave a serious impact on policy wen considering only relatively sort periods (suc as a year). In dynamic long-run models (Wirl (212) and Karp, Siddiqui and Strand (213)) convexity plays a larger role, making policy more restrictive over time. 29