Banking permits: Economic efficiency and distributional effects

Journal of Policy Modeling 31 (2009) 382–403

Available online at www.sciencedirect.com

Banking permits: Economic efficiencyand distributional effects

Valentina Bosetti a,∗, Carlo Carraro b, Emanuele Massetti c

a Fondazione Eni Enrico Mattei, Corso Magenta 63, 20121 Milano, Italyb Fondazione Eni Enrico Mattei, University of Venice, CEPR, CESifo and CEPS, Italy

c Fondazione Eni Enrico Mattei and Catholic University, Milan, Italy

Received 23 April 2008; received in revised form 8 September 2008; accepted 2 December 2008Available online 25 December 2008

Keywords: Emission trading; Banking

1. Introduction

In a multi-period market for pollution rights, the possibility to transfer emission allowancesto the future is referred to as banking of emission units. The early use of allowances issued inthe present for later periods is instead referred to as borrowing of emission units. A market ofpermits where both banking and borrowing of emission rights are allowed is characterised by fullintertemporal flexibility. In this market, the so-called “when flexibility” is therefore added to theso-called “where flexibility” (achieved when different countries trade pollution rights). A fullyflexible market is shown to be superior, in terms of efficiency, to a market in which the transferof pollution rights is restricted, in either dimension (see, for instance, Leiby & Rubin, 2001). Theimportance of the “when flexibility” is also recognised by the Kyoto Protocol, which specifies thatin the event that a Party has a surplus of carbon allowances at the end of the first commitment period,a portion of these permits may be carried-over to a subsequent commitment period after 2012.1

Despite its relevance, banking is rarely considered in the empirical literature that quantifies thecosts of mitigation policies. In a few cases, intertemporal flexibility is introduced, but the numberof permits that are moved across time, and the future use of the extra-allowances, is exogenouslydetermined by the modeller (Manne & Richels, 2001; Babiker, Jacoby, Reilly, & Reiner, 2002;Springer, 2003; Carraro & Galeotti, 2004).

∗ Corresponding author.E-mail address: [email protected] (V. Bosetti).

1 Cf. Article 3(13) of the Kyoto Protocol.

0161-8938/$ – see front matter © 2008 Society for Policy Modeling. Published by Elsevier Inc. All rights reserved.doi:10.1016/j.jpolmod.2008.12.005

mailto:[email protected]

dx.doi.org/10.1016/j.jpolmod.2008.12.005

V. Bosetti et al. / Journal of Policy Modeling 31 (2009) 382–403 383

The theoretical literature on emission trading is instead rich in contributions on banking. Thesecontributions generally show that a permit system with intertemporal flexibility increases welfare.2

However, the assumptions commonly made in these papers are far from being realistic and do notmimic the conditions under which a carbon market with intertemporal flexibility is reasonablyexpected to operate.

For this reason, one of the objectives of this paper is to introduce a fully endogenous marketof carbon permits with banking in WITCH – the integrated assessment climate-economy hybridmodel used in this paper – and to assess the welfare impacts of a fully intertemporal emissiontrading scheme for various allocation rules. The functioning of pollution permit markets withintertemporal flexibility can thus be analysed under some realistic assumptions that cannot be ingeneral imposed in analytical models for tractability reasons.

In their seminal paper, Cronshaw and Kruse (1996) set up the standard framework along whichresearch on banking of tradable permits has developed so far.3 Their work is characterised by thefollowing crucial assumptions: (i) there is a constant number of profit-maximising firms actingwith perfect foresight in a competitive market for permits. Firms damage the environment byreleasing pollutants as a side effect of their production activity; however, they can also acquireinputs to mitigate emissions. Each firm receives an (ii) equal endowment of permits for eachperiod and can buy from or sell permits to other firms at a given price. Permits can be transferredacross time by either banking them for future use or (iii) by borrowing future allowances for usein the present. The authors show that, at the equilibrium, the present value permit prices mustbe non-increasing over time. Were discounted prices increasing, firms could (iv) buy from themarket today to sell in future periods (speculative banking) thus increasing profits. This wouldlead to an unboundedly large demand for permits in the first period that would increase today’sprice. Hence, this cannot be an equilibrium. Thus, assuming that (v) marginal abatement costsare constant over time, banking takes place if and only if permit prices rise over time with theinterest rate, i.e. discounted prices are constant.

This result represents a very useful benchmark, but it relies on a set of assumptions whichtypically do not hold in the case of carbon markets induced or established by climate policy.To begin with, marginal abatement costs can hardly be constant over time. They are usuallynon-linear, with a time profile that reflects the alternating predominance of two opposite forces:on the one hand, diminishing returns tend to increase abatement costs over time; on the otherhand, technological change works in the opposite direction and lowers abatement costs over time.Secondly, contrary to what assumed by Cronshaw and Kruse, climate policy can be realisticallyexpected to become increasingly tighter over time, with a time-varying, rather than constant,endowment of annual emission permits. Thirdly, and most importantly, it is highly unrealisticthat any future regulation of carbon trading will allow “speculative banking”, i.e. the possibilityof buying and banking emission permits for pure speculation on the future price of carbon. TheKyoto Protocol explicitly forbids this type of banking, thus ruling out one of the pillars that supportCronshaw and Kruse’s result. Finally, borrowing is also likely to be partly restricted since it hasthe potential to become a serious threat to the achievement of ambitious stabilisation targets andan incentive to defect from the climate agreement.

For these reasons, this paper proposes a more articulated set-up to analyse the role of bankingin carbon markets, thus overcoming limitations imposed by analytical approaches. The analysis of

2 See Newell, Pizer, and Zhang (2003), for a survey.3 For further developments see Rubin (1996), Kling and Rubin (1997), Liski and Montero (2005). For an analysis with

uncertainty see Godby, Mestelman, Muller, and Welland (1997) and Innes (2003).

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the role of banking will be carried out by using WITCH, a regional model of the world economyin which twelve macro-regions have agreed on a mitigation policy based on tradable emissionrights. Regions differ in population, technology, income, energy demand, etc. They can buy andsell permits in a competitive world carbon market, which sets marginal abatement costs equalworldwide. First, we study regions’ optimal choices – i.e. their investments, R&D expenditures,net demand of permits, etc. – when there is no “when” flexibility. Then, we introduce “when”flexibility by allowing banking (but not borrowing) of carbon emissions. Speculative banking isnot permitted either. Finally, we examine the effect of banking on the price of permits, on the timepath of CO2 abatement, on optimal investments, on the diffusion of technical change, etc.

This paper has a final additional objective. An important issue in the present debate on climatepolicy is the participation of developing countries in the cooperative effort to reduce globalGHG emissions. These countries’ decision crucially depends on the way in which the burden ofcontrolling GHG emissions is shared among all countries and regions. The burden-sharing issue isequivalent to the allowance allocation issue if the policy adopted worldwide to control emissionsis a global carbon market. Therefore, in this paper, we analyse the efficiency and distributionalimplications of banking for three different allocations of carbon rights, and investigate the roleof banking under these distribution rules. By changing the distribution of permits among regions,we stress the effect of asymmetries among players in determining optimal banking decisions andthe consequent price of permits over time.

From a policy perspective, we find that banking is a key instrument to comply with increasinglystringent emission reduction targets. Significant cost savings are indeed possible by allowinggreater intertemporal flexibility. A more original result is that banking provides relevant incentivesto the early adoption of cleaner technologies, thus inducing a positive intertemporal spillovereffect. This effect is stronger when the allocation rule is such that mostly OECD countries find itoptimal to bank permits. The reason is that, in this case, banking also fosters a positive internationaltechnology spillover effect.

Our findings only partly confirm what is predicted by the analytical literature on the efficiencyof “when” flexibility. Some new results – for example on the relationship between banking andtechnological change, on the implications of banking for the choice of the allocation rule, andalso on the future equilibrium path of the permit price – are presented in this paper. In particular,contrary to what stated by Cronshaw and Kruse (1996), we find that a discounted permit priceincreasing over time is perfectly consistent with a well-defined carbon market. Moreover, discon-tinuities in the price path may arise, due to discontinuities in the evolution of marginal abatementcosts and in the total number of emission allowances.

This paper is organised as follows. Section 2 illustrates the basic set-up of the WITCH modelemployed for our numerical analysis. Section 3 presents our results on banking of carbon rightsand how (partial) “when flexibility” affects carbon emissions, the carbon market and the permitprice. Section 4 discusses how banking changes optimal investment and R&D decisions, withconsequent impacts on the speed of diffusion of technical change. Section 5 shows the effectsof banking on stabilisation costs for three emission rights allocation rules. A concluding sectionsummarises the most important findings of our analysis and outlines some policy implications.

2. The WITCH model and climate policy scenarios

The WITCH – World-Induced Technical Change Hybrid – model is a regional integratedassessment model that captures the channels of transmission of climate policy into the economicsystem and provides normative information on the optimal responses of world economies to


climate damages and policy (for a complete list of model equations the reader is referred toAppendix A). It is a hybrid model because it combines features of both top-down and bottom-upmodelling. The top-down component consists of an inter-temporal optimal growth model of theworld economy. Within this framework, the energy input of the aggregate production function hasbeen expanded to provide a bottom-up like description of the energy sector. World countries aregrouped in 12 regions that strategically interact. A game-theoretic approach is used to describethese interactions. A climate module and a damage function provide the feedback on the economyof carbon dioxide emissions into the atmosphere.

WITCH top-down framework guarantees a coherent, fully intertemporal allocation of invest-ments that have an impact on the level and cost of mitigation—i.e. R&D efforts, investments inenergy technologies, fossil fuel expenditures. The regional specification of the model and the pres-ence of strategic interaction among regions – through CO2, exhaustible natural resources, carbontrading and technological spillovers – allows us to account for free-riding incentives. Investmentstrategies are optimised by taking into account both economic and environmental externalities.Optimal strategies belong to the open-loop Nash equilibrium of the dynamic game defined by themodel.

By endogenously modelling fuel (oil, coal, natural gas, uranium) prices, as well as the costof storing the CO2 captured, the model can be used to evaluate the implications of mitigationpolicies on the energy system in all its components.4

In this paper, WITCH is used to analyse the cost of stabilising concentrations of CO2 emissionsin the atmosphere at 450 ppmv by the end of the century. This stabilisation target is in generalconsidered to be quite stringent. It limits global mean warming to less than 3 ◦C (see the analysisby the Working Group III in Metz, Davidson, Swart, & Pan, 2001), thus making the achievement ofthe often-cited 2 ◦C target possible. Stabilising emissions at this level is supposed to significantlyreduce or even avoid many of the impacts listed for 3 ◦C warming or more, and lead to much higherenvironmental benefits than stabilisation at higher levels.5 For simplicity and without affectingthe main conclusions of the paper, we assume that all countries and regions agree to achievethe stabilisation objective by establishing a world carbon market that allows regions to exchangecarbon rights. Banking of emission permits is allowed. “Speculative banking”, i.e. buying andbanking permits at the same time, as well as “borrowing”, are not allowed.

In order to contribute to the burden-sharing debate, we compute stabilisation costs and theirgeographical distribution for three different allocation rules: Equal Emissions per Capita, Con-traction and Convergence and Sovereignty. These are the most commonly studied allocation rulesin the environmental economics literature. Independently of the allocation scheme and to gain inrealism, we assume that until 2030 the whole abatement effort is undertaken by High Income (HI)regions alone, while Low Income countries are allocated their baseline emissions.6 We followhere the recent literature on post-Kyoto architectures (see, for example, the six chapters in Aldy

4 Model equations and variables are listed in Appendix A at the end of this article. For a thorough description of themodel see Bosetti, Carraro, Galeotti, Massetti, and Tavoni (2006), Bosetti, Carraro, Massetti, and Tavoni (2008), Bosetti,Carraro, Massetti, and Tavoni (2007a), and Bosetti, Massetti, and Tavoni (2007b).

5 Note, however, that there would still be the risk of impacts associated with mean warming of less than 3 ◦C.6 High Income regions are: USA, OLDEURO, NEWEURO, KOSAU (South Korea, South Africa and Australia), CAJAZ

(Canada, Japan, New Zealand). Low Income regions are: TE (Transition Economies), MENA (Middle East and NorthAfrica), SSA (Sub-Saharan Africa), SASIA (South Asia), CHINA, EASIA (East Asia) and LACA (Latin America andthe Caribbean). The aggregation of world regions is discussed in detail in Bosetti et al. (2007a, 2007b). For an analysis ofthe distributional impacts of climate policy see Bosetti et al. (2007a, 2007b).


and Stavins (2002) and related comments). In most of this literature, no binding commitment isassumed for developing countries until they reach some ability to pay and/or a significant shareof world emissions in per capita terms.

In the Equal Emissions per Capita (EPC) scenario, allowances are distributed among regionsin proportion to their population, so that each individual is endowed with the same CO2 emissionrights. This scenario turns out to be very stringent for industrialised countries, because of theirmodest share of world population, which will further decline over the next century.

The Sovereignty (SOV) allocation scheme has opposite implications: allowances are distributedto each region according to their present share of total emissions. Developing regions may bepenalised because of rapid population and economic growth, while industrialised countries mayreduce emissions at moderate costs.

The Contraction and Convergence allocation scheme (CC) stands between these two extremes.According to this widely discussed policy option, emission rights are first distributed according tothe sovereignty rule in order not to constrain industrialised economies excessively; then, greaterweight is given to the equal emissions per capita allocation rule, eventually switching to a fullapplication of this rule by the end of the century.7

The reference scenarios are the stabilisation scenarios without “when” flexibility (one for eachallocation rule) and, for the estimate of stabilisation costs, the benchmark is the WITCH Baselinescenario, in which no climate policy is imposed.

3. Banking, emissions, and carbon prices

As described in the previous section, in our scenarios, from 2030 on, all countries cooperateto stabilise GHG concentrations at 450 ppm (while HI countries undertake all the required effortfor the first decade). The consequent optimal strategic choices in all countries and regions aredescribed in this section. These choices include the optimal investment profile for all energytechnologies, the optimal R&D investments, the net demand of permits and the number of permitsto be banked in each period of time. Let us start by analysing this latter variable.

3.1. Banking of carbon rights

At the equilibrium, a considerable number of permits is banked in the first decades of the cen-tury under all allocation schemes (see Fig. 1). The largest number of banked permits throughoutthe century is recorded under the Sovereignty rule (20 GtC, or 4.2% of total emission allowances).Under the EPC and CC rules, the number of banked permits is lower but still significant (14.63 GtC,or 3.1% of total emission allowances and 14.93 GtC, or 3.2% of total emission allowances,respectively).

The banking of permits during the first decades of the century, and the consequent forwardtransfer of allowances, generates lower emissions in the first decades of the century, as shown inFig. 2 and Table 1. However, since all banked emissions must be used by the end of the century,the situation is reversed from 2042 to 2052 onward, when CO2 emissions in the atmosphere growat a faster rate, with respect to the no-banking scenario. Both emission paths, with and withoutbanking, ensure compliance with the stabilisation target.

7 The Contraction and Convergence allocation scheme was first proposed by the Global Commons Institute in the early1990s.


Fig. 1. Savings of Carbon Permits (GtC, average per year). Positive values indicate banking, negative values indicatereleasing of banked permits.

Fig. 2. CO2 emissions from energy consumption under different allocation schemes with and without banking.

However, banking smoothes the transition path to an economy with a lower carbon intensity byredistributing the effort from later to earlier periods. This causes an overall welfare improvement(Section 5 contains a detailed discussion of welfare effects). Banking is particularly useful forcountries endowed with a surplus of allowances (with respect to their needs). As shown in Fig. 1,banking is highest under the SOV scenario. The SOV allocation scheme is indeed the one underwhich the two groups of countries – High Income and Low Income – are alternatively endowed

Table 1Variations of CO2 emissions from energy consumption with Banking relative to the No Banking case.

SOV CC EPC

2002–2031 −9% −8% −8%2032–2051 −4% 0% 0%2052–2071 13% 11% 12%2072–2097 2% 5% 5%2002–2097 0% 0% 0%


Table 2Variations of trade of carbon permits when Banking is allowed, relative to the No Banking case.

SOV CC EPC

2002–2031 −26% −19% −18%2032–2051 −52% −3% −1%2052–2071 36% 28% 20%2072–2097 23% −20% −20%2002–2097 −1% −3% −1%

with large amounts of “hot air”: before 2030 Low Income countries and after 2030 High Incomecountries. Of course this extreme scenario is very unlikely but it represents a useful benchmarkfor the purpose of our analysis. The presence of extra allowances leaves wide margins for theintertemporal reallocation of permits, and thus for high banking activity. In particular, with theSOV allocation scheme, High Income countries switch from a tight climate policy before 2030,to a mild one after 2030 (because in 2030 a binding target is introduced also for Low Incomecountries).

3.2. Carbon market

Banking also affects the size of the emission trading market. The number of emission rightstraded over the whole century is rather constant (slightly lower with reductions of 1.4%, 3.0%and 1.5% for SOV, CC and EPC, respectively), but significant variations are recorded on shortertime periods. Banking reduces the market size in the first decades, while it increases the numberof permits exchanged in later periods.

Table 2 shows the variations in the number of traded permits induced by banking. Thesechanges are modest if we consider the whole century, but they significantly change the size ofthe market year by year. Banking is thus likely to have a strong effect on the market of emissionpermits. Let us therefore analyse the implications for the time profile of the permit price.

3.3. Carbon price

Without the possibility to transfer permits intertemporally, the quantity of carbon emitted ineach period must be the same under all three allocation scenarios. Indeed, from the well-knownCoase theorem, the price of carbon does not depend on the distribution of permits (Coase, 1960).However, when intertemporal transfer of permits is allowed, the amount of emissions in each timeperiod is not independent of the distribution of permits. As a consequence, the price of carbonneeds not to be the same under different initial allocations of permits. This is clearly visible fromFigs. 3 and 4. Different time paths for carbon prices will in turn imply different optimal investmentstrategies and different total stabilisation costs, as we will see in detail in the next sections.

As shown above, in the presence of “when” flexibility, emission rights are initially banked,supply drops and prices in the carbon market go up. Banking induces a strong increase in the carbonprice in the first decades of the century, up to 227% higher, as shown in Fig. 5. It should also benoticed that, given the assumption of full convergence to an equal per capita allocation by 2050, theContraction and Convergence and the Equal per Capita allocations imply a very similar price path.

Subsequently, banked allowances are released, supply increases and the price goes down. Sincecarbon prices are very high in the second half of the century, the apparently small percentage varia-tions imply massive drops in carbon prices. As a result, banking induces a smoother intertemporal


Fig. 3. Price of carbon for different allocation schemes (2002–2047).

Fig. 4. Price of carbon for different allocation schemes (2052–2097).

Fig. 5. Change of carbon price, in the banking case with respect to the no banking one.


Fig. 6. Rate of growth of the carbon permit price in the sovereignty case.

path of the carbon price, as predicted by the analytical models. Although expected, it is importantto highlight that this result comes out from a numerical and realistic simulation model, as thesmoothing effect is often questioned in the policy debate. The rate of growth of carbon prices isstrongly reduced, as Fig. 6 portrays.

A well established result in the literature, which draws back to Hotelling (1939), requires thatthe rate of growth of carbon price be equal to the rate of interest. This result cannot be tested inour set-up because in WITCH regional capital markets are not integrated. As a consequence, themodel yields twelve distinct time patterns for the interest rate.8

Table 3 displays, for selected years, the difference between the interest rate and the rate ofgrowth of carbon price together with banked permits, for all regions of WITCH.9 In High Incomeregions interest rates are always lower than the rate of growth of carbon price while in Low Incomeregions there are periods of fast growth in which the interest rate is higher than the rate of growthof carbon price. If we look at banking activity, we can confirm that the arbitrage condition betweensavings and selling permits in the carbon market – which rules out banking when the interest rateis higher than the rate of growth of carbon prices – holds.10

A second interesting feature of the carbon market with banking is synthesised by Fig. 7, whichrefers to OLDEURO, again under the SOV scenario. The growth rate of the carbon price is higherthan the interest rate throughout the century. Why then are not all the saved allowances releasedat the same time in the last period?

There are two explanations for a gradual release of saved permits. First, without an internationalfinancial market, it is impossible to finance earlier consumption so as to spread the extra revenuesfrom permit sales over the last period of trade. In our macroeconomic, aggregated, context, thereare only two ways to smooth consumption over time: through savings, embodied in capital goods,and through savings of emission allowances. Since both work only forward, allowing to postpone

8 For all regions, in both cooperative and non-cooperative settings, the interest rate is always greater than the intertem-poral discount rate. Per capita consumption is rising for all countries.

9 Assuming that consumption is not affected, sales of permits at time T will increase the capital stock and deliver returnsat time T + 1. For this reason, at time T, the interest rate that is relevant for the intertemporal arbitrage condition thatgoverns the allocation of permits between banking and the carbon market is the interest rate of time T + 1.10 The only exception to this conclusion refers to EASIA. This is explained by the numerical approximations in our

solution algorithm.

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Table 3Interest rates and the rate of growth of the price of carbon.

USA OLDEURO NEWEURO KOSAU CAJAZ TE MENA SSA SASIA CHINA EASIA LACA

Difference between the rate of growth of carbon price and the interest rate2012 6.48% 5.91% 2.12% 5.87% 5.86% 2.44% 4.43% 4.27% −0.78% 0.05% −0.14% 4.52%2032 3.11% 2.61% −0.32% 2.18% 2.54% −0.02% 1.16% 1.16% −0.24% 0.68% 0.01% 1.30%2052 1.68% 1.45% 0.01% 1.45% 1.45% 0.52% 1.09% 0.11% 0.21% 0.75% 0.50% 1.28%2072 1.57% 1.57% 0.44% 1.04% 1.51% 0.77% 0.33% −0.21% 0.90% 1.22% 1.16% 0.81%2092 1.89% 1.37% 0.53% 0.77% 1.24% 0.84% 0.02% −0.54% 1.01% 1.28% 1.27% 0.61%

Banking (GtC). Positive values indicate banking of permits, negative values indicate releasing of banked permits2012 0.070 0.012 0.000 0.000 0.000 0.000 0.186 0.022 −0.067 0.397 0.059 0.1672032 0.458 0.244 0.000 0.056 0.110 0.000 −0.280 −0.070 0.000 −0.064 0.000 0.0002052 0.318 −0.091 0.000 −0.109 −0.113 0.000 −0.109 0.000 0.000 0.000 0.000 −0.1982072 −0.363 −0.156 0.000 0.000 −0.023 0.000 0.000 0.000 0.000 0.000 0.000 0.0002092 −0.180 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000


Fig. 7. Carbon market: OLDEURO.

Fig. 8. Carbon market: USA without Banking.

consumption but not to anticipate future positive income shocks, it is not possible for regions tosell at the most convenient moment and to anticipate consumption in earlier times. Second, anextremely high supply of permits in a single time period would make the carbon price sink;11 ascan be inferred from Fig. 1, the amount of permits banked is substantial and if concentrated onlyin a single time period it would outweigh demand by a factor of two, or more. Thus, contrary towhat would be optimal for a single firm with open access to permit markets and with virtually noimpact on prices, regions release banked emission permits gradually through time.

A closer look at banking decisions of single regions gives additional useful insights. Considerthe behaviour of the US and of CHINA when permits are distributed according to the Sovereigntyrule. Under this rule, the first region is predominantly a seller of permits, while the secondis predominantly a buyer. Fig. 8 shows the US optimal decisions in the permit market in theno-banking scenario. It pictures the emission constraint faced by the US, its actual emissions,

11 It is important to note that this happens in a perfectly competitive market. Even if regions behave as price takers, thesolution algorithm for the market of permits (a Walrasian tatônnement process) gives a price feedback signal that inducesthe choice of a new optimal supply (demand) of allowances, until market clearance.


Fig. 9. Carbon market: USA with Banking.

purchases and sales of emission rights. Despite the effort to reduce GHG emissions with respectto the baseline, the steep decline of emissions imposed by the stringent climate policy can only befulfilled by purchasing emission rights in the market. However, when the burden of reducing GHGemissions starts to fall also on Low Income countries, the peculiar distribution of permits impliedby the Sovereignty principle rewards the early efforts of High Income countries and leaves spacefor net sales of permits. Fig. 8 clearly shows the US effort to smooth the emission path throughoutthe century using the market instrument.

The picture changes significantly with the introduction of banking (Fig. 9). Emissions arefurther smoothed over the century: between 2007 and 2017 there is a sudden drop of emissions,no purchases and instead saving of allowances. The uneven path of emissions during these twotime periods is due to the “no-speculation” rule imposed to prevent regions from buying andsaving permits at the same time. From 2017 till 2032 there are again purchases of emission rights,but in a smaller quantity compared to the no banking scenario. Starting from 2032 until 2052,emission rights in excess are saved for use in later periods, instead of being sold in the market.Indeed, the emission path remains lower than what recorded in the no-banking case until 2047.This implies that an extra effort is made to reduce emissions and the incentive to use them in laterperiods is stronger than the incentive to sell them in the market when banking is not allowed.From 2052 onward banked emissions are sold in the market and are used to cover extra emissions.

Also net buyers bank permits. Consider the case of CHINA. Until 2032 Low Income countriesparticipate in the climate agreement without any constraint on emissions, but they are allowedto trade permits if they reduce emissions below their BAU level. With banking, CHINA hasthe incentive to save some emission rights for later periods when the price of carbon increases.Figs. 10 and 11 show optimal trading and saving decisions both with and without banking. Theextra-sales between 2022 and 2031 are possible thanks to the emission rights stored beforehand. Anextra amount of savings is released in 2032, when the emission target becomes binding for China aswell: without banking China is a buyer of permits, with banking a seller. With banking, emissionsare lower from 2002 until 2041, but are higher from 2042 onward, thanks to a lower carbon price.

4. Investments in energy R&D and in renewables

As shown in Section 3, when banking is allowed, prices are higher in the first part of the centuryand lower in the second part, with some differences that depend on the adopted allocation rule.


Fig. 10. Carbon market: CHINA without Banking.

How does the modified price path affect technological change? Does it increase energy efficiencyand/or foster the adoption of low carbon energy sources? The answer is positive. Banking indeedstimulates earlier investments in energy R&D, in R&D to lower the cost of advanced biofuelsand in Wind and Solar electricity generation technologies (W&S). As an example, let us analysewhat happens to investments in Energy R&D (see Fig. 12). With respect to the corresponding no-banking scenarios, R&D investments increase substantially in the first decades of the century andthen decrease. However, Energy R&D investments over the whole century decline in all bankingscenarios because the increased flexibility in the carbon market lowers the need for R&D-drivenenergy efficiency. The stocks of R&D capital follow the movement of R&D investments with asmall time delay (see Fig. 13). It is worth noting that the inertia is increased by the presence ofintertemporal R&D spillovers in the R&D sector. Similar results also hold for investments in allcarbon-free technologies that are modelled in WITCH.

The main conclusion is that banking plays an important role in accelerating the adoption anddiffusion of energy efficient and/or carbon-free technologies. By inducing higher carbon pricesin the short term, banking provides the right incentives for firms to switch to climate friendlytechnologies earlier than in the absence of banking. This has important macroeconomic andenvironmental effects. Indeed, given the long lived nature of investments in the energy sector andthe lag time that separates R&D investments from commercialization of new technologies, banking

Fig. 11. Carbon market: CHINA with Banking.


Fig. 12. Change in Energy R&D investments, Banking case with respect to the No Banking case.

Fig. 13. Change in Energy R&D capital, Banking case with respect to the No Banking case.

could generate the necessary stimulus for an early start, thus averting the possibility of lockingthe system into a carbon-intensive technological path. Earlier adoption of new technologies canindeed reduce stabilisation costs and enhance the environmental effectiveness of climate policy.These issues will be discussed in the next section.

5. The cost of climate policy

Let us summarise all the results provided above by investigating how banking changes thecosts of stabilisation policy and the distribution of these costs among regions. Table 4 shows ourresults.

As expected, Table 4 shows that greater market flexibility, i.e. banking, reduces policy costs.Higher early carbon prices induce early investment in R&D and in low carbon technologies,thus producing an indirect benefit on future abatement costs that adds to the direct benefit frombanking. Savings in early periods are remarkable and suggest that banking might be a key optionfor reducing the total cost of climate policy. Table 4 suggests that the undiscounted aggregatecost, measured as Gross World Product (GWP) loss, declines from 5.57% to 4.74%, for the SOVallocation rule, from 5.52% to 4.97%, in the case of CC and from 5.38% to 4.82% for the EPC

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Table 4Stabilisation Cost, measured as changes in GDP with respect to baselinea.

USA OLDEURO NEWEURO KOSAU CAJAZ TE MEN A SSA SASIA CHINA EASIA LACA HI LI World

UndiscountedSOV −1.75% 0.18% −6.12% −3.79% −0.70% −10.24% −15.34% −10.71% −8.26% −9.70% −9.68% −7.66% −1.93% −9.78% −5.57%CC −4.20% −0.98% −8.06% −4.87% −1.76% −13.21% −14.68% 4.73% −4.23% −9.54% −8.56% −6.86% −3.61% −7.72% −5.52%EPC −10.04% −3.85% −13.01% −7.46% −4.29% −21.35% −12.79% 44.84% 5.61% −9.45% 5.94% −4.96% −7.76% −2.64% −5.38%Banking SOV −0.59% 0.42% −5.79% −3.49% −0.63% −10.08% −13.32% −9.31% −7.20% −8.73% −8.50% −6.45% −1.45% −8.54% −4.74%Banking CC −4.14% −0.48% −7.59% −4.36% −1.66% −12.57% −12.81% 3.55% −4.04% −8.79% −7.92% −5.27% −3.31% −6.88% −4.97%Banking EPC −9.39% −2.97% −12.00% −6.62% −3.91% −19.86% −11.24% 39.60% 4.77% −8.66% −5.57% −3.48% −6.99% −2.31% −4.82%

DiscountedSOV −1.48% −0.29% −4.49% −2.64% −0.67% −8.08% −11.07% −8.14% −6.17% −6.44% −7.06% −5.22% −1.50% −6.90% −3.59%CC −3.17% −0.99% −6.11% −3.49% −1.34% −10.33% −10.48% 7.82% −2.14% −6.22% −5.99% −4.54% −2.63% −4.97% −3.54%EPC −5.91% −2.26% −9.12% −4.98% −2.47% −15.04% −9.23% 37.69% 4.82% −6.08% −4.20% −3.37% −4.60% −1.60% −3.44%Banking SOV −1.48% −0.32% −4.38% −2.53% −0.72% −8.19% −9.37% −6.99% −5.28% −5.53% −6.19% −4.34% −1.52% −5.90% −3.21%Banking CC −3.28% −0.88% −5.79% −3.23% −1.35% −9.82% −8.92% 6.73% −1.88% −5.53% −5.43% −3.57% −2.57% −4.30% −3.24%Banking EPC −5.70% −1.98% −8.43% −4.53% −2.35% −13.94% −7.89% 33.10% 4.26% −5.38% −3.85% −2.47% −4.30% −1.31% −3.14%

a For discounted values, a discount rate of 3% decreasing over time has been applied; positive figures correspond to gains.


Table 5Distribution of undiscounted stabilisation costs.

HI LI

“SOV” 19% 81%“CC” 35% 65%“EPC” 77% 23%“Banking SOV” 16% 84%“Banking CC” 38% 64%“Banking EPC” 80% 22%

rule. This is equivalent to a net reduction of stabilisation costs of 15.0%, 10.0% and 10.4%, forSOV, CC and EPC, respectively. Discounted costs decrease by 10.5%, 8.5% and 8.6%, for SOV,CC and EPC, respectively. At a more disaggregated level, without discounting, all regions, exceptthe big sellers of permits in the CC and EPC scenarios, namely SASIA and SSA, are better offwith banking than without. Discounting changes the net position of those regions whose benefitscome late in the future.12

The distribution of the costs and benefits of climate change and climate change policy is ofgreat importance in determining both the feasibility and desirability of a specific architecture foragreement. The analysis of GDP changes for different world regions in the different scenarios mayoffer some indications as to what the distributional implications of climate change policies are,and highlights winners and losers under each scenario. Indeed, banking affects the distribution ofstabilisation costs. Our results (see Table 5) show that greater intertemporal flexibility provideslarger benefits to regions with the most favourable initial distribution of emission rights. HighIncome regions reduce their (already low) share of stabilisation costs when banking is allowedunder the SOV rule, as do Low Income regions when permits are distributed according to theEPC rule. Banking favours sellers of permits, which can maximise their revenues by optimallydistributing carbon rights across time.

6. Conclusions

This paper provides new insights on the consequences of allowing permit traders to banktradable pollution rights. First, it shows the implications of banking for the market of carbonpermits, for carbon emissions and for carbon prices. We have seen that banking smoothes thetime profile of an emission path to stabilize CO2 concentrations in the atmosphere. It first createsan incentive to reduce at a faster pace and then to relax the stabilisation constraint in later years.We find that the number of permits traded in the market changes significantly when banking isallowed. Banking also induces early effort in R&D investments to enhance energy efficiency andhigher investments in renewable electricity generations technologies. These are certainly usefulinsights for market agents and regulators.

This paper challenges the analytical literature on intertemporal trading of emission permitsand shows that an increasing time profile for the discounted price of carbon is fully consistentwith banking. The gap between the interest rate and the rate of growth of carbon price is explainedby the absence of an international capital market. With heterogeneous interest rates and limits to

12 It is interesting to note that the climate policy hits China particularly hard, no matter which allocation rule is adopted.This happens because the peculiar dynamics of population, energy use and economic development in China all concur toshape an allocation of permits that is not sensitive to the distribution rules implemented in this paper.


the overall supply of permits, we find an equilibrium solution for which the rate of growth of thecarbon price is generally not in line with the interest rates that the market players face.

The absence of fully integrated capital markets is certainly a weakness of the model. However,a model with fully integrated capital markets would be considerably far from reality as well. Thus,despite its limitations, this paper provides a powerful insight on banking behaviour in a realisticsetting in which returns on investments differs internationally. It shows that, with a perfectlyintegrated carbon market, in countries with low returns to investment there will be an incentive tobank permits, while in countries with high returns to investment there might be low or no bankingof carbon permits. This explains part of the welfare gains that we find in our simulation exercises.

More challenging than the hypothesis of integrated capital markets is perhaps the hypothesis ofa perfectly integrated carbon market without national risk premiums. However, our results wouldchange only if the risk premium over carbon permits sold by some regions would change overtime, generating changes in the growth rate of carbon emission permits’ price from that region.

In our analysis, we rule out the possibility to borrow emission permits from future allocations.However, there exist emission markets in which borrowing is permitted and the same EU-ETS,despite with constraints, allows borrowing of carbon permits. Accordingly, an interesting area forfuture work will be the analysis of banking with different scenarios on restricted borrowing.

If the objective of climate policy is an ambitious GHG stabilisation target, our results showthat intertemporal flexibility, even if partial, substantially increases efficiency. Cost reductionsin terms of avoided GWP losses with respect to an inter-temporally rigid carbon market range– depending on the initial distribution of emission allowances – between 15% and 10% whendiscounting is not applied and between 10.5% and 8.5% when future losses are discounted.

Despite most of the world regions are better off with banking, independently of the initial dis-tribution of permits, we have shown that intertemporal flexibility provides a relative advantage tothose regions with a relatively more favourable distribution of emission rights. Banking empowerssellers more than buyers.

Finally, let us stress that we adopted more a normative approach than a descriptive one. Ourfindings belong to an ideal world in which all agents behave optimally and with perfect foresightover their future actions, the other agents’ decisions, and future states of the world. Nevertheless,we have been able to show that, when a richer framework of analysis is used, “when flexibility”yields some interesting unexpected results. We believe that these results can be useful both toeconomists – who will find a stimulus to build richer analytical models – and to policymakers –who may find in this paper useful information to design post-2012 carbon markets.

Acknowledgements

This paper is part of the research work being carried out by the Climate Change Modelling andPolicy Research Programme at the Fondazione Eni Enrico Mattei. Emanuele Massetti gratefullyacknowledges financial support from the project “Modelli matematici per le decisioni economico-finanziario-attuariali”, D.1 Sedi Padane 2007, Catholic University, Milan. Financial support fromthe Transust.Scan project is also acknowledged. The authors are grateful to Marzio Galeotti,Massimo Tavoni and three anonumous referees for their useful comments.

Appendix A. Model equations and list of variables

In this Appendix we reproduce the main equations of the model. For a full description of themodel please refer to Bosetti et al. (2007a, 2007b). The list of variables is reported at the end. In


each region, indexed by n, a social planner maximises the following utility function:

W(n) =∑t

U [C(n, t), L(n, t)]R(t) =∑t

L(n, t) {log [c(n, t)]}R(t), (A1)

where t are 5-year time spans and the pure time preference discount factor is given by

R(t) =t∏

v=0

[1 + ρ(v)]−5, (A2)

where the pure rate of time preference ρ(v) is assumed to decline over time. Moreover, c(n, t) =(C(n, t))/(L(n, t)) is per capita consumption.

A.1. Economic module

The budget constraint defines consumption as net output less investments:

C(n, t) = Y (n, t) − IC(n, t) − IR&D,EN (n, t) −∑

jIR&D,j(n, t) −

∑jIj(n, t)

−∑

jO&Mj(n, t) (A3)

where j denotes energy technologies.Output is produced via a nested CES function that combines a capital-labour aggregate and

energy; capital and labour are obtained from a Cobb-Douglas function. The climate damage Ωreduces gross output; to obtain net output we subtract the costs of the fuels f and of CCS:

Y (n, t) =TEP(n, p)

[α(n) ·

(K

1−β(n)C (n, t)Lβ(n)(n, t)

)ρ + (1 − α(n))ES(n, t)ρ]1/ρ

Ω(n, t)

−∑f

(Pf (n, t)Xf,extr(n, t) + P int

f (t)Xf,netimp(n, t))

− PCCS(n, t)CCS(n, t)

(A4)

Total factor productivity TEP(n,t) evolves exogenously with time. Final good capital accumu-lates following the standard perpetual rule:

KC(n, t + 1) = KC(n, t)(1 − δC) + IC(n, t). (A5)

Labour is assumed to be equal to population and evolves exogenously. Energy services are anaggregate of energy and a stock of knowledge combined with a CES function:

ES(n, t) = [αHHE(n, t)ρES + αENEN(n, t)ρES ]1/ρES . (A6)

The stock of knowledge HE(n,t) derives from energy R&D investment:

HE(n, t + 1) = aIR&D(n, t)bHE(n, t)c +HE(n, t)(1 − δR&D) (A7)

Energy is a combination of electric and non-electric energy:

EN(n, t) = [αELEL(n, t)ρEN + αNELNEL(n, t)ρEN ]1/ρEN . (A8)


Each factor is further decomposed into several sub-components (see Bosetti et al., 2006 for adetailed description of the energy sector). Factors are aggregated using CES, linear and Leontiefproduction functions.

For illustrative purposes, we show how electricity is produced via capital, operation andmaintenance and resource use through a zero-elasticity Leontief aggregate:

ELj(n, t) = min{μn,jKj(n, t); τn,jO&Mj(n, t); ςjXj,EL(n, t)}. (A9)

Capital for electricity generation technologies accumulates as follows:

Kj(n, t + 1) = Kj(n, t)(1 − δj) + Ij(n, t)

SCj(n, t), (A10)

where, for selected technologies, the new capital investment cost SC(n,t) decreases with the worldcumulated installed capacity by means of Learning-by-Doing:

SCj (n, t) = Bj(n)∑

t

∑nKj (n, t)

−log2PRj. (A11)

Operation and maintenance is treated as an investment that fully depreciates every year. Theresources employed in electricity production are subtracted from output in Eqs. (A3) and (A4).Their prices are calculated endogenously using a reduced-form cost function that allows fornon-linearity in both the depletion effect and in the rate of extraction:

Pf (n, t) = χf (n) + πf (n)

[Qf (n, t − 1)

Q̄f (n, t)

]ψf (n)

(A12)

where Qf is cumulative extraction of fuel f:

Qf (n, t − 1) = Qf (n, 0) +∑t−1

s=0Xf,extr(n, s). (A13)

Each country covers consumption of fuel f, Xf(n,t), by either domestic extraction or imports,Xf,netimp(n,t), or by a combination of both. If the country is a net exporter, Xf,netimp(n,t) is negative:

Xf (n, t) = Xf,extr(n, t) +Xf,netimp(n, t) (A14)

A.2. Climate module

GHGs emissions from combustion of fossil fuels are derived by applying stoichiometriccoefficients to the total amount of fossil fuels utilised minus the amount of CO2 sequestered:

CO2(n, t) =∑

fωf,CO2Xf (n, t) − CCS(n, t). (A15)

When a cap on emission (CAP) is included and banking is active we have an additional equation,constraining emissions, given the possibility to save, sell and buy permits:

CO2(n, t) = CAP(n, t) +NIP(n, t) − SAV (n, t) (A15′)


In addition, carbon permits revenues/expenses enter the budget constraint:

C(n, t) = Y (n, t) − IC(n, t) − IR&D,EN (n, t) −∑

jIR&D,j(n, t) −

∑jIj(n, t)

−∑

jO&Mj(n, t) − p(t)NIP(n, t) (A3′)

The damage function impacting output varies with global temperature:

Ω(n, t) = 1

1 + (θ1,nT (t) + θ2,nT (t)2). (A16)

Temperature increases through augmented radiating forcing F(t):

T (t + 1) = T (t) + σ1 {F (t + 1) − λT (t) − σ2 [T (t) − TLO(t)]} (A17)

which in turn depends on CO2 concentrations:

F (t) = η log

[MAT (t)

MPIAT

]/ log(2) +O(t), (A18)

caused by emissions from fuel combustion and land use change:

MAT (t + 1) =∑n

[CO2(n, t) + LUj(t)

] + φ11MAT (t) + φ21MUP (t), (A19)

MUP (t + 1) = φ22MUP (t) + φ12MAT (t) + φ32MLO(t), (A19)

MLO(t + 1) = φ33MLO(t) + φ23MUP (t) (A20)

Model variables are denoted with the following symbolsW welfareU instantaneous utilityC consumptionc per-capita consumptionL populationR discount factorY productionIc investment in final goodIR&D, EN investment in energy R&DIj investment in technology jO&M investment in operation and maintenanceTFP total factor productivityKc final good stock of capitalES energy servicesZ flow of new knowledgeΩ damagePj fossil fuel pricesXj fuel resourcesPCCS price of CCSCCS CO2 sequestered


HE energy knowledgeEN energyEL electric energyNEL non-electric energyKj stock of capital of technology jSCj investment costCO2 emissions from combustion of fossil fuelsNIP net import of carbon permitsSAV saved carbon permitsp price of carbon permitsMAT atmospheric CO2 concentrationsLU land-use carbon emissionsMUP upper oceans/biosphere CO2 concentrationsMLO lower oceans CO2 concentrationsF radiative forcingT temperature levelO exogenous radiative forcing of other greenhouse gases

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Banking permits: Economic efficiency and distributional effects

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