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Counting carbon: historic emissionsfrom fossil fuels, long-run measures ofsustainable development and carbondebtJan Kunnasa, Eoin McLaughlinb, Nick Hanleya, David Greasleyb, LesOxleyc & Paul Warded

a Division of Economics, University of Stirling, Stirling FK9 4LA, UKb School of History, Classics and Archaeology, University ofEdinburgh, Edinburgh, UKc Waikato Management School, University of Waikato, Hamilton,New Zealandd School of History, University of East Anglia, Norwich, UKPublished online: 07 May 2014.

To cite this article: Jan Kunnas, Eoin McLaughlin, Nick Hanley, David Greasley, Les Oxley &Paul Warde (2014): Counting carbon: historic emissions from fossil fuels, long-run measuresof sustainable development and carbon debt, Scandinavian Economic History Review, DOI:10.1080/03585522.2014.896284

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Counting carbon: historic emissions from fossil fuels, long-run measuresof sustainable development and carbon debt

Jan Kunnasa*, Eoin McLaughlinb, Nick Hanleya, David Greasleyb, Les Oxleyc andPaul Warded

aDivision of Economics, University of Stirling, Stirling FK9 4LA, UK; bSchool of History,Classics and Archaeology, University of Edinburgh, Edinburgh, UK; cWaikato ManagementSchool, University of Waikato, Hamilton, New Zealand; dSchool of History, University of EastAnglia, Norwich, UK

(Received 10 May 2013; accepted 15 January 2014)

This article examines how to account for the welfare effects of carbon dioxideemissions, using the historical experiences of Britain and the USA from the onsetof the industrial revolution to the present. While a single country might isolateitself from the detrimental effects of global warming in the short run, in the longall countries are unable to free ride. Thus, we support the use of a single globalprice for carbon dioxide emissions. The calculated price should decrease as wemove back in time to take into account that carbon dioxide is a stock pollutant,and that one unit added to the present large stock is likely to cause more damagethan a unit emitted under the lower concentration levels in the past. Weincorporate the annual costs of British and US carbon emissions into genuinesavings, and calculate the accumulated costs of their carbon dioxide emissions.Enlarging the scope and calculating the cumulative cost of carbon dioxide fromthe four largest emitters gives new insights into the question of who is responsiblefor climate change.

Keywords: environmental accounts; fossil fuels; carbon dioxide; carbon debt;genuine savings

1. Introduction

This article examines how to account for the welfare effects of carbon dioxideemissions, using the historical experiences of Britain and the USA as illustrations.Pollution adversely influenced the well-being of past generations, but pastpollution may also diminish the well-being of future generations. The long half-life of the greenhouse gases means global warming is influenced by emissionsaccumulated over past centuries. Thus, past polluters owe a ‘carbon debt’ to thefuture generations.

Both the costs of pollution to past and future generations are considered herewithin a ‘Green National Accounting’ (GNA) framework. Conventional measures ofnational income and wealth may mislead when economic activity results in environ-mental impacts.1 GNA adjusts net national product measures for the depletion of

*Corresponding author. Email: j.g.kunnas@stir.ac.uk1Vincent, ‘Greener National Accounts’ (2001).

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natural resources, pollution and environmental deterioration.2 Accounting for thecosts of greenhouse-gas emissions over time is an important example of a GNAenvironmental adjustment. GNA underpins the measures of the sustainability ofeconomic development which are deployed here to gauge carbon dioxide emissionscosts.

One such adjusted measure, Genuine Savings (GS) provides the starting point ofour analysis and we adjust the measure for carbon pollution to gauge the historicalcosts of pollution. GS provides a measure of net investment used by the World Bankto indicate if well-being will be sustained into the future.3 The key idea here is thatpollution equates to disinvestment that needs to be offset by other capital formationfor consumption to be sustained into the future. Hence GS indicates whether or notpast generations have saved enough, after taking account of carbon pollution, tosustain future consumption. However, GS does not fully measure any ‘carbon debt’to future generations, unless allowance is made for accumulated pollution. Hence wefurther extend the analysis by gauging the cumulative effects of historical carbonemissions to show how these might diminish the well-being of future generations.

This investigation of pollution-adjusted GS and ‘carbon debt’ considers the cases ofBritain and the USA over the periods 1760–2000 and 1800–2000, respectively.4 GSsums the value of year-on-year changes in each element of the capital stock of a country.GS values, in theory, changes in capital stock using shadow prices which reflect themarginal value product of each stock in terms of its contribution to future welfare,defined as the present value of aggregated utility over infinite time. Changes in the stockof carbon can be included using marginal damage costs to value current-periodemissions of changes in the stock. One major challenge is to account for the multipleenvironmental costs of the use of fossil fuels, both in time and place, to human healthand the delivery of vital ecosystem services.5 In other words, pollution from fossil fuelshas both immediate flow and long-lasting cumulative stock effects on local, regional andglobal scales. The long-lasting effects may give rise to ‘carbon debts’ which are not fullyreflected in measures of GS. Much has been written of the possible costs to society frompresent and prospective emissions of carbon dioxide. In contrast, gauging how weshould price, and thus value the cost of past emissions has been relatively neglected. Theprice we put on past emissions is central to the calculations of GS and ‘carbon debt’.Hamilton and Clemens price CO2 in their GS calculations according to its globaldamages on the assumption of a universal property right to a clean environment: ‘forexample [they] are assuming that the Comoros Islands have the right not be inundatedas a result of CO2 emissions elsewhere’. They adopt a constant damage of $20 per tonneof carbon from Fankhauser, but do not provide any rationale.6 Lindmark and Acar, incontrast, discount their carbon price, reasoning: ‘Since the social cost of carbon is timedependent (the damage is not immediate, but occurs in the future), we adjust thehistorical price by calculating the historical discounted unit cost based on a 2-percent

2Daly/Cobb, Common Good (1989); Repetto et al., Wasting Assets (1989); United Nations,Handbook (2003).3World Bank, Wealth (2006) and Changing Wealth (2011).4The emissions of carbon dioxide are usually expressed as the amount of carbon emitted, andwe are following this convention, and thus also using carbon as a short-hand for carbondioxide emissions.5UK NEA, UK National Ecosystem Assessment (2011).6Fankhauser, ‘Evaluating’ (1994); Hamilton/Clemens, ‘Genuine Savings’ (1999), 342.

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interest rate’. They further discuss if CO2 emissions should be priced according to itsglobal or national damage, deciding in favour of a global measure in the absence ofdamage cost estimates for Sweden.7

This article scrutinises the literature on pricing carbon damages, and shows howalternative approaches to pricing influence the measures of GS and ‘carbon debt’ forBritain and the USA from 1760 and 1870, respectively. Section 2 discusses whetheremissions should be priced according to their local or global effects. Section 3assesses the pricing of historical emissions and the use constant or discounted carboncosts. We show in Section 4 how the damages from historical carbon dioxideemissions can be incorporated into GS measures of sustainable development toprovide more robust signals about the long-run economic development possibilitiesof a country. A particular focus of the paper is the calculations in Section 5 of thecumulative cost of carbon, which throw light on the responsibility for climatechange. Yet, while ‘carbon debt’ is a legacy of fossil-fuel-driven industrialisation, itssize will be determined by future abatement as well as past emissions.

2. Spatial effects: where and how damages should be counted?

The geographic scope of pollution has major implications for national wealthaccounting. Some pollutants have chiefly local effects, for example particulates suchas PM10 impose a cost on the citizens of the emitting country. Other pollutants canbe exported onto neighbour countries or regions, for example by building highersmokestacks. We consider that only damages that impact on the national well-beingof a country should be included in the accounts of that country. The theory ofnational accounting focuses on the well-being of the economy whose production andconsumption activities are being measured. In the case of British SO2 emissions,Norway would show the cost of acidification from the imported emissions in itsnational accounts, but the cost would not be in the British accounts.8

The emission of carbon dioxide impinges on the local, regional and global economy.The long-time delay between emissions and impacts make carbon dioxide particularlydifficult to cost. The initial effect is for the emissions of individual countries to be dilutedinto the global commons. Carbon dioxide is both non-visible and nontoxic. Thus, thenoticeable effects of the carbon dioxide emissions of the emitting country are similar inthe short run to those of exported regional emissions such as SO2. In the long term,however, the combined emissions of all individual countries are relevant, if theconcentrations of carbon dioxide and other greenhouse gases exceed critical thresholds.

A carbon dioxide threshold of 350 parts per million (ppm) is generally consideredthe ‘safe’ level.9 This threshold has already been surpassed and the seasonallyadjusted annual figure is estimated to reach 400 ppm in the spring of 2014 or 2015.10

The often mentioned 450 ppm target is a political compromise between risks and thecosts of emission reductions – a compromise that might be detrimental for example,to coral reefs, which are estimated to be in rapid and terminal decline worldwide

7Lindmark/Acar, ‘Sustainability’ (2013); Brännlund, Växthusgasernas (2008); Tol, ‘SocialCost’ (2008); Price, Social Cost (2007); Stern, Stern Review (2007), 304.8cf. Atkinson/Hamilton, ‘Progress’ (2007).9Rockström et al., ‘Planetary Boundaries’ (2009).10http://www.economist.com/news/science-and-technology/21577342-carbondioxide-concentrations-hit-their-highest-level-4m-years-measure (Accessed 10.5.2013).

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from multiple synergies arising from mass bleaching, ocean acidification and otherenvironmental impacts.11 Many estimates of the costs of greenhouse-gas emissionsuse even higher concentrations than 450 ppm. For example, Eyre et al., Price et al.and the Interagency Working Group on Social Cost of Carbon assume a doubling ofgreenhouse gases from a preindustrial level to 550 ppm carbon dioxide equivalents,which implies a stabilisation of CO2-only concentrations at around 425–484 ppm.12

The safe upper concentration level could be interpreted as a nonrenewable naturalresource, the carrying capacity of the atmosphere. Below the safe level, increasingconcentrations of greenhouse gases mean that the remaining size of this resource isdecreasing. Concentrations above that level, as in the current situation, can beinterpreted as an ‘overdraft’. More emissions, regardless of whether we are under orover the assumed safety level, are disinvestments, as they reduce the room for futureemissions or increase the emission cuts needed to remain below this safe upper level.

In a similar fashion, Dasgupta and Mäler argue that when a country adds to theatmosphere’s carbon content, it reduces the value of this common property resource.They suggest two possibilities to calculate the value of the changes to this globalresource in the country’s national accounts:13 First, to attribute to each country thefraction of the earth’s atmosphere that reflects the country’s size relative to the worldas a whole. Second, to regard the global common as every country’s asset. In thatcase, the entire cost of global warming inflicted by a country would be regarded asthat country’s loss. A third way to calculate the cost of climate change for a countrywould be to estimate only the cost directly incurred in that country, such as the costsdue to a drier climate or more storm damages, in that country alone.14

Our argument in support of the second approach – to regard the global commonas every country’s asset – is that in the case of a global phenomenon such as humaninduced climate change, there is in the long term no possibility for a single country toisolate itself from the impacts of climate change. Every country will be affected tosome degree, say from increases in food prices if climate change has negative impactson global food production.15 Net exporters of food might, in the short run, receivesome benefits from such developments, but at the expense of consumers. Moreover,countries that are less affected by climate change will also have difficulty isolatingthemselves from people migrating from areas that are becoming uninhabitable dueto climate change or conflicts induced by climate change. Brown16 argues that thecommonly cited estimate by Myers and Kent of 200 million people displaced whenglobal warming takes hold could easily be exceeded. Even this estimate would meanan eight-fold increase over today’s entire documented refugee and internallydisplaced populations.17 From Mexico alone between 1.4 and 6.7 million personsare predicted to migrate as a result of the effect of climate change on decliningagriculture production by 2080.18 Ethically speaking, the use of a global damage cost

11Veron et al., ‘Coral Reef Crisis’ (2009).12Eyre et al., Global Warming (1999); Price et al., Social Cost (2007); Interagency WorkingGroup on Social Cost of Carbon, Social Cost (2010).13Dasgupta/Mäler, ‘Wealth’ (2001).14Ackerman et al., What We’ll Pay (2008).15FAO, Impact (2005); Easterling et al., ‘Food’ (2007).16Brown, Migration (2008); Myers/Kent, Environmental Exodus (1995).17UNHCR, Global Trends (2011).18Feng et al., ‘Linkages’ (2010).

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indicates a belief that we are all in the same lifeboat when it comes to the long-termeffects of climate change. Our second argument for the global damage approach ispractical: using one single carbon cost per tonne for all countries makes internationalcomparisons easier.

Summing up, no country in the long term will be able to isolate its economy fromclimate change and the costs it will inflict. Avoiding the worst outcomes of climatechange will require significant emission reductions worldwide. However, theemission reductions needed in the future depend on past emissions, which causehigher costs in the future. Past emissions can be attributed to individual countries,and thus imply a ‘carbon debt’.

3. Pricing of carbon dioxide emissions

So far we have established that the costs of carbon dioxide emissions should beincluded in national accounts, and that costs should reflect global damages. Next weneed to establish the price of such emissions. Here, we first consider differentestimates of the social costs of carbon; second, we discuss whether we should use aconstant damage cost or a price that changes over time; and finally, we examine howto estimate the historical prices of carbon emissions.

3.1. Costing carbon dioxide emissions

Among the first researchers to provide a monetary quantification of the damage tosociety from global warming due to emissions of carbon dioxide and othergreenhouse gases were Nordhaus, Cline, Titus and Fankhauser.19 Henceforth, wewill call this the social cost of carbon (SCC), the monetised value of the marginalbenefit of reducing one tonne of CO2 measured by its carbon content. This isdetermined by the marginal value of avoided damages. Over time, the models usedto calculate this cost have become more sophisticated, but the general approach hasremained the same. They start with projections of economic growth and technolo-gical improvements affecting the society’s ‘carbon intensity’, which are then used toproject the development of greenhouse-gas emissions into the future. Based on this,climate models predict changes in the concentration of greenhouse gases in theatmosphere and the resultant changes in global temperature, and regional climatepatterns. Economic harms from predicted temperature increases are then estimatedusing damage functions which include aspects such as changes in net agriculturalproductivity, human health and property damages from sea-level rise and increasedflood risk. Finally these future damages are discounted back to the present, to give apresent value of future damages per tonne of emissions.

Hamilton and Clemens and Bolt et al. use the damage cost calculated byFankhauser. He used Monte Carlo simulations with a stochastic greenhouse damagemodel that accounts for future emissions, and the accumulation of emissions in theatmosphere, radioactive forcing and the temperature increases the annual damagewill lead to. His results lead to damage costs of emissions rising over time, from$20.3 per tonne of carbon between 1991 and 2000 to approximately $28/tC in the

19Nordhaus, ‘To Slow’ (1991); Cline, Economics (1992); Titus, Cost (1992); Fankhauser,‘Global Warming’ (1992).

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decade 2021–2030.20 This rising path of for the SCC recognises the fact that eachextra tonne emitted causes more damage as the stock of greenhouse gas in theatmosphere increases.

A review of the literature compiled for the UK Department for Environment,Food and Rural Affairs (DEFRA) in 2002 suggests using a point estimate for theSCC emissions of £70/tC for policy in UK, with an associated sensitivity range, witha lower bound of £35 and an upper bound of £140, for emissions in 2000, and thenraised by £1/tC for each subsequent year.21 These costs are taken from Eyre et al.,who used the The Climate Framework for Uncertainty, Negotiation and Distribu-tion (FUND) 1.6 and the Open framework 2.2 models. Despite differences in themodels they gave very similar results, with a 3%/year discount rate the FUND modelreturned marginal damages of €70/tC, and the Open Framework €74/tC in 1995.22 Areview of the DEFRA paper undertaken in 2005 suggested slightly lower SCC: £56/tC in 2000, £68/tC in 2010 and an increasing growth rate thereafter.23

Finally, a DEFRA paper published in 2007 suggested using a shadow price ofcarbon (SPC) instead of the SCC. The SPC is based on the SCC for a givenstabilisation goal, but can be adjusted to reflect estimates of the marginal abatementcost (costs of mitigating carbon emissions) required to take the world onto thestabilisation path and other factors that may affect the UK’s willingness to pay forreductions in carbon emissions, such as a political desire to show leadership intackling climate change. They suggested a SPC of £18.6 per tonne of carbon dioxideequivalent in 2000 (£68.2/tC), with an increase to £25.5/tCO2e (£93.6/tC) in 2007 and£28.1/tCO2e (£103.1/tC) by 2012.24 These values were taken from the Stern review,and are based on the Policy Analysis of the Greenhouse Effect (PAGE) 2002 modelwith the damage experienced under an emissions scenario which leads to stabilisationat 550 ppm CO2e.

25 These are considerably higher costs of carbon comparedto estimates cited earlier, which is mainly due to the use of a lower discount rate(1.4%/year) for future climate change damages. The PAGE-model has recently beenupdated, but so far a comparable scenario with a stabilisation at 550 ppm CO2e

using the updated PAGE09-model has not been presented. Its Business as Usualscenario provides slightly higher costs, with a mean estimate of $106 per tonne ofcarbon dioxide (£389/tC), compared to the $85/tCO2 (£312/tC) Business as Usual(BAU)-scenario in the Stern report (in year 2001 in year 2000 dollars).26

Tol gathered 103 SCC estimates in 2005 from 28 published studies, andcombined them to form a probability density function. He found the range ofestimates strongly right-skewed: the mode of all studies combined was $2/tC (1995US$), the median was $14/tC, the mean $93/tC and the 95th percentile $350/tC. Heconcluded that: ‘Using standard assumptions about discounting and aggregation, themarginal damage costs of carbon dioxide emissions are unlikely to exceed $50/tC

20Hamilton/Clemens, ‘Genuine Savings’ (1999); Bolt et al., Manual (2002); Fankhauser,‘Evaluating’ (1994).21Clarkson/Deyes, ‘Estimating’ (2002).22Eyre et al., Global Warming (1999).23Watkiss et al., Social Costs (2005).24Price et al., Social Cost (2007). The SPC for 2007 and 2012 in 2007 price level, and 2000 inthat year’s price level.25Stern, Stern Review (2007).26Hope, ‘Critical Issues’ (2013); ‘Social Cost’ (2011).

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(31.7 £/tC), and are probably much smaller’.27 Tol updated his estimate three yearslater as the number of estimates had roughly doubled, with approximately half of theestimates from work by Tol and his co-authors. In the update the mean was $23/tC,and there was a 1% probability that the SCC is greater than $78/tC.28 This surveywas utilised by the US Department of Transportation for a new set of fuel economystandards, and by the US Department of Energy setting energy efficiency standardsfor fluorescent lamps and incandescent reflector lamps.29

A more recent estimate was undertaken in 2010 by Interagency Working Groupon SCC set by the US government to establish the SCC to use when assessing thebenefits of regulations that would limit emissions of carbon dioxide. The interagencygroup ran three commonly used models (FUND, The Dynamic Integrated ClimateChange (DICE) and PAGE) using standard baseline projections of economic growthand technological development giving each model equal weight. For the costs in2010, they produced a wide range of estimates ranging from $17.2 to $238 per metrictonne of carbon (in 2007 dollars). The central value is the average SCC across modelsat the 3%/year discount rate, which is, for example, $78.5 per metric tonne of carbonin 2010, increasing to $164.6/tC in 2050.30 The working group updated its estimate in2013 using updated versions of the assessment models. More complex carbon cyclemodels and updated damage functions with a better reflection of the damage causedby sea-level rise lead to considerable higher estimates of the costs. The central valuein the update was $121.1 (in 2007 dollars) per metric tonne of carbon in 2010,increasing to $260.6/tC in 2050. Discounted to 2000 this would return values almostas high as in the 550 ppm stabilisation scenario in the Stern report.

3.2. What are the costs of past carbon emissions?

All the above estimates suggest that the SCC should increase in the future, as futureemissions are expected to produce larger damages as physical and economic systemsbecome more stressed in response to greater climatic change, and as the stock in theatmosphere increases. In this section we will discuss whether carbon costs shouldaccordingly decrease as we go back in time, or remain constant, as suggested byHamilton and Clemens and Bolt et al.,31 when included in an environmentalaccounting measure such as GS.

We offer three major arguments against using a constant damage cost for theemissions of carbon dioxide (that is, a cost per tonne which does not vary as eitherthe level of emissions or the global stock of atmospheric CO2 changes). The firstarises from a general feature of stock pollutants such as CO2. One unit of a stockpollutant added to an already large stock is likely to cause a higher damage than aunit emitted under a low concentration level. In other words, ‘a ton of CO2 added to

27Tol, ‘Marginal damage’ (2005). $50/tC was also used by Arrow et al., ‘Sustainability’ (2012)although their source was Tol, ‘Economic Effects’ (2009).28Tol, ‘Social Cost’ (2008).29Masur/Posner, ‘Climate Regulation’ (2011).30The original values were presented as costs per metric tonne of carbon dioxide, these havebeen transformed to costs per metric tonne of carbon by multiplying with 3.67 (the molecularweight of CO2 divided by the molecular weight of carbon 44/12 = 3.67).31Hamilton/Clemens, ‘Genuine Savings’ (1999); Bolt et al., Manual (2002).

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an already large stock of atmospheric CO2 is likely to cause a higher damage than aton emitted under a low concentration level’.32

The second reason comes from the different proximities to future damages due toclimate change at different points in time. Price et al.33 argue that: ‘As time goes on,the damage comes closer, and is discounted less heavily; so its present value rises,increasing the social cost of carbon’. By analogy, therefore, as we go back in time,the damage is further away, which should also be reflected in the damage cost.

The third argument relies on the claim that human induced climate change wasinitially positive. Ruddiman claims that: ‘…Earth should have undergone a largenatural cooling during the last several thousand years, and that at least a smallglaciation would have begun several millennia ago had it not been for greenhouse-gas releases from early human activities’. The human activities Ruddiman refers toare the slow rise in CO2 concentrations that started 8000 years ago when humansbegan to cut and burn forests in China and the rise of methane concentrations thatbegan 5000 years ago when humans began to irrigate land for rice farming and tendlivestock in unprecedented numbers.34

One can argue that as long as global warming generated benefits for humans,emissions of greenhouse gases can be seen as a positive addition to GS, and onlythereafter as a disinvestment. Tol (2013) argues that: ‘Most rich and most poorcountries benefitted from climate change until 1980, but after that the trend isnegative for poor countries and positive for rich countries’.35 The biggest benefits ofclimate change in his calculations come from impacts on agriculture, and are entirelydue to carbon dioxide fertilisation which makes crops grow faster as it stimulatesphotosynthesis and relieves drought stress.36 It could thus be argued that carbondioxide released from the burning of fossil fuels was the first chemical fertiliser,having a substantial impact on increasing agricultural yields in the nineteenthcentury.

Ackerman et al.,37 however, argue that recent research has cast doubts on anyagricultural benefits of climate change. Possible positive effects of CO2 fertilisationcan be counter-acted by the negative effects of a warmer climate and changes inprecipitation. Lobell et al. created models linking the yields of the four largestcommodity crops to weather trends from 1980 to 2008. At the global scale, maizeand wheat exhibited global net losses of 3.8% and 5.5%, respectively, relative to whatwould have been achieved without the climate trends.38

Hamilton and Clemens and Bolt et al.39 suggested using a constant carbon price,but provide no justification for this approach. One such justification is provided byKunnas and Myllyntaus, as they note that over the past 200 years the oceansabsorbed about a half of the total carbon dioxide emissions, but this has not beenfree of environmental impacts; when carbon dioxide dissolves in seawater it formscarbonic acid responsible for a decrease by 0.1 unit from preindustrial levels of the

32Fankhauser, Valuing Climate (1995), 60–61.33Price et al., Social Cost (2007), 9.34Ruddiman, Plows (2005), 105 and ‘Anthropogenic Greenhouse’ (2003).35Tol, ‘Economic Impact’ (2013).36McGrath/Lobell, ‘Independent Method’ (2011).37Ackerman et al., What We’ll Pay (2008), 17.38Lobell et al., ‘Climate Trends’ (2011); Ziska, ‘Climate Change’ (2011).39Hamilton/Clemens, ‘Genuine Savings’ (1999); Bolt et al., Manual (2002).

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average pH of the oceans, with an exponential decrease of nearly 0.8 pH unitforecasted by 2300. This could have major effects on calcifying marine biota, such ascalcareous plankton and coral reef communities.40 Thus it can be argued that thisdelay of global warming has been at the expense of the oceans, as it has used up theaccumulative capacity of the oceans.

3.3. Estimating the costs of historical carbon dioxide emissions

Given a conclusion that the costs of carbon emissions decline as one movesbackwards in time, this raises the question on how to set the rate at which the price isdiminishing. We could start by locating the point in time where climate change mightstop being a ‘good thing’ and turns into a ‘bad thing’. That is, however, not enough.Another question is the long lifetime of greenhouse gases, especially carbon dioxide,which means that emissions emitted before climate change switched from enhancingto degrading human well-being are still warming the climate. Archer suggests 300years and a 25% tail that lasts forever as the best approximation for the lifetime offossil-fuel CO2.

41 If we were to agree that 1980,42 for example, is the turning point,and climate change is on average a good thing before that date and bad thereafter,then emissions before 1681, 300 years from that point, could be considered harmless.We could then let the carbon price diminish from its present value, whatever wedecide that to be, to zero by this time point. This method is, however, heavilydependent on both the ‘correct’ location of the point in time where climate changestops being a good thing and turns into a bad thing, and the approximation for thelifetime of CO2. A different approach is suggested by Lindmark and Acar. Theydepart from Brännlund’s survey of the peer-reviewed estimates included in Tol anduse a value of SEK 300/tonne based on Price et al. For historic emissions, Lindmarkand Acar discount the 2000 price by 2%/year, based on average long-run economicgrowth rate as suggested by Rabl.43 To avoid exchanging values back from Swedishcrowns, we take our price straight from Price et al. and Stern: £18.6 and $30 in 2000(in 2000 prices) per tonne of CO2 in 2007. Expressed as the price per tonne of carbonthis means £68.2/tC and $110/tC. This method gives costs diminishing as we gofurther away from future damage due to climate change without the need to fix apoint in time when climate change becomes a ‘good thing’, as the costs approachzero asymptotically.

In this paper we follow a similar approach and explore it further adding a lowerand a higher carbon price to the comparison, in constructing a series for the shadowcost of carbon emissions over the time period 1760–2000 presented in Figure 1. Ourlow price of $23/tC in 1995 comes from Tol’s (2008) meta-analysis referred to above,and the high price $312/tC in 2001 in year 2000 prices, from the BAU-scenario in theStern Review. Tol argues that this high price is an outlier in the literature, on theother hand, Ackerman and Stanton argues that Tol’s meta-analysis introduces biasesin favour of low estimates. We discounted all prices with the same 2%/year asLindmark and Acar. For comparison, we have also included a constant $20/tC, as

40Kunnas/Myllyntaus, ‘Forerunners’ (2008); see also Sabine et al., ‘Oceanic Sink’ (2004);Caldeira/Wickett, ‘Anthropogenic carbon’ (2003); Orr et al., ‘Anthropogenic Ocean’ (2005).41Archer, ‘Fate’ (2005).42See Tol, ‘Economic Impact’ (2013).43Rabl, ‘Discounting’ (1996).

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suggested by Hamilton and Clemens and Bolt et al.44 For reasons of simplicity wepresent it in 2000 prices which give £13.2/tC.45

To ascertain the costs of historical carbon emissions, for Britain and the USA,the next stage involves multiplying by these four different estimates of the unit pricefor past emissions. Figures 2 and 3 are constructed by multiplying the selected unitcosts of carbon by British emissions of carbon as taken from McLaughlin et al.,which were based on data from Boden et al. and Warde, and US emissions fromBoden et al.46 The highest annual costs at the end of the series arise when using theBAU-price from the Stern report, which gives in 2000 over 12 times higher totalannual carbon costs than the Tol price and over 15 times higher costs than theconstant for both Britain and the USA. Even the lower price from Stern, utilised byLindmark and Acar returns 4–5 times higher annual costs than the Tol and constantprice estimates. Prior to 1863, the constant cost approach generated the highest costs.

It might be more instructive, however, to show the costs of carbon dioxideemissions as a share of GDP. This shows how much lower annual GDP would be, iffuture generations bearing the costs of climate change could demand compensationfor this externality. As we can see from Figures 4 and 5 this changes the outcomeconsiderably. Using a constant cost of carbon the peak will be when the carbonintensity of the economy was at its highest. In Britain the peak was at 1.4% of GDP

Figure 1. Estimates of the shadow costs of carbon per tonne (2000 prices), 1760–2000.

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Sources: Lindmark/Acar, ‘Sustainability’ (2013); Stern, Stern Review (2007); Tol, ‘Social Cost’ (2008);Hamilton and Clemens, ‘Genuine Savings’ (1999); Bolt et al., Manual (2002).

44Tol, ‘Social Cost’ (2008); Stern, Stern Review (2007); Ackerman/Stanton, ‘Climate Risks’(2012), Hamilton/Clemens, ‘Genuine Savings’ (1999); Bolt et al., Manual (2002).45Officer, Dollar-Pound (2013).46McLaughlin et al., ‘Testing’ (2012); Boden et al., Global (2012); Warde, Energy (2007).

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Figure 3. Annual costs of carbon dioxide emissions in US, (2000 prices), 1800–2000.

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Sources: Lindmark/Acar, ‘Sustainability’ (2013); Stern, Stern Review (2007); Tol, ‘Social Cost’ (2008);Hamilton/Clemens, ‘Genuine Savings’ (1999); Bolt et al., Manual (2002); Boden et al., Global (2012).

Figure 2. Annual costs of carbon dioxide emissions in Britain, (2000 prices), 1760–2000.

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Figure 5. USA carbon dioxide costs as a percentage of GDP, 1869–2000.

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Sources: Figure 3, and GDP from Williamson, ‘What Was the U.S.’ (2013b).

Figure 4. British carbon dioxide costs as a percentage of GDP, 1760–2000.

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Sources: Figure 2, and GDP 1760–1870 from Broadberry et al., ‘British Economic’ (2011) and 1870–2000from Williamson, ‘What Was the U.K.’ (2013a).

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in 1873 at the beginning of the coal-driven second industrial revolution. In the USA,larger wood resources delayed this peak until 1917 at 1.6% of GDP. Usingdecreasing carbon costs postpones this peak to the eve of the first oil crisis, to1971 for Britain at 0.3%, 1.5% or 4.3% of GDP depending on which price we use,and to 1973 in the USA at 0.4%, 1.9% and 5.4%. Even the highest price used is notenough to turn economic growth into decline. Modern growth still continues, but atleast to some degree at the expense of future generations.

4. Genuine savings measures and carbon costs over time

Next we incorporate the annual cost of British and US carbon emissions into GSscalculations over time, using our four different prices. As will be recalled, GS is anindicator of sustainable development which tracks the year-on-year changes in acountry’s capital stocks, including natural capital. The global accumulative capacityfor greenhouse-gas emissions is one of these stocks. The results are presented inFigures 6 and 7. According to this methodology, carbon emissions, regardless of theprice used, have little influence on the overall trend of sustainable development inBritain and the USA. The ups and downs in GS for the whole period under scrutinyis driven by a range of other changes in capital, for example, investments in humancapital. For the sake of clarity, we left out the Tol price, as from Tables 1 and 2 wecan see that this has a minor impact. These tables present the average GS rates of thefull period and selected sub-periods. Even when accounting for carbon emissions,British and US GS measures are overwhelmingly positive, apart from the two world

Figure 6. British GS and GS with carbon, 1765–2000.

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Sources: Figure 2 and Greasley et al., ‘Testing’ (2014).

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wars in Britain and the Great Depression and the Second World War in the USA.Except for the Business as Usual price, including carbon emissions has a marginaleffect on the GS indicator of sustainable development during most of the periodconsidered.

However, different conclusions emerge for more recent years. Considering theprospects of future sustainability the dip in the level of GS since the 1980s isespecially worrisome. With our highest price for carbon, this is enough to drop GSclose to zero in early 1980s, and negative in Britain for 1982 and in the USA for1980, 1982 and 1983. As the costs of carbon increase the closer we are to theanticipated damage, the possibility of GS remaining at a positive level in the future

Figure 7. USA GS and GS with carbon, 1869–2000.

–14

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Sources: Figure 3 and Greasley et al., ‘Comprehensive investment’ (2013).

Table 1. Mean British GS rates as a percentage of GDP.

GS nocarbon(%)

GS withcarbon

(constant) (%)

GS withcarbon(Tol) (%)

GS with carbon(Lindmark &Acar) (%)

GS withcarbon

(Stern) (%)

1765–2000 5.46 4.68 5.30 4.79 3.491765–1850 3.41 2.71 3.38 3.31 3.111850–1913 7.46 6.33 7.31 6.83 5.601914–1918 −2.50 −3.48 −2.73 −3.50 −5.451919–1938 3.65 2.78 3.38 2.52 0.311939–1945 −8.60 −9.26 −8.87 −9.72 −11.901946–2000 9.54 9.09 9.22 8.20 5.60

Sources: Figure 2 and Greasley et al., ‘Testing’ (2014).

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diminishes. These conjectures are highly dependent on the carbon price used toreflect the future costs of climate change. In turn this depends, in part, on theambitiousness of efforts to mitigate emissions of carbon dioxide and othergreenhouse emissions. Time matters as each 15-year delay in addressing rising CO2

emissions results in approximately ¾ degree Celsius long-term additional warming.47

Except for the high price taken from the Stern report, our three other estimates ofcosts of carbon are based on an assumption of restricting the increase of greenhousegases in the atmosphere to a doubling from a preindustrial level to 550 ppm carbondioxide equivalents or less. This would mean that only a fraction of the currentknown reserves of fossil fuels can be used. Current conventions of how to calculateGS do not answer how this should be taken into account. On one hand, it could beargued that this should not be accounted for as they are not extracted. One the otherhand, past emissions mean less absorptive capacity left in the biosphere for futureemissions from fossil fuel use, decreasing future possibilities of using fossil fuels andfuture prosperity. Another way to look at the question is that restricting emissions ofcarbon dioxide would mean that part of past investments in infrastructure related tofossil fuels will become obsolete ahead of their normal depreciation period, implyinga devaluation of some of past net investments in physical capital.

5. Cumulative costs of carbon emissions: calculating the carbon debt

In most cases, including carbon emissions had a marginal effect on measures of GS.However, that does not necessarily mean that emissions of carbon dioxide wouldhave a marginal effect on future prosperity. The annual effects of carbon dioxidemight be small, but the cumulative effects are not. This can be seen most effectivelyby reference to Figures 8 and 9, where we have calculated the accumulated costs ofcarbon dioxide, the ‘carbon debt’. For Britain the cumulative effects for 1800–2000range (depending on the choice of prices) from £100 to £1400 billion (in 2000 prices),with 75–96% of the debt accrued since 1900. The respective figures for the USA are$960 to $13,600 billion (in 2000 prices), with 96–99% of the debt occurring since1900. These values can be compared to the GDP of UK which was £916 billion in2000, and that of the USA which was $9951 billion.

Table 2. Mean USA GS rates as a percentage of GDP.

GS nocarbon

GS with carbon(constant)

GS withcarbon (Tol)

GS with carbon(Lindmark & Acar)

GS withcarbon (Stern)

% % % % %

1869–2000 10.31 9.51 6.73 9.02 10.021869–1913 16.52 15.65 16.40 15.90 14.801914–1918 10.73 9.22 10.36 9.15 6.341919–1938 5.31 4.12 4.95 3.73 0.921939–1945 0.95 0.12 0.62 −0.49 −3.061946–2000 8.21 7.67 7.82 6.52 3.52

Sources: Figure 3 and Greasley et al., ‘Comprehensive Investment’ (2013).

47Shoemaker/Schrag, ‘The Danger’ (2013).

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The big difference in cumulative costs between the BAU-scenario and scenarioswith active global climate policy shows clearly the interconnection between the pastand the future. The total ‘carbon debt’ depends on future climate policy and thestabilisation level as the carbon price is discounted from future damages. The morefuture emissions added to the accumulated stock of carbon in the atmosphere, thegreater the associated global warming and increase in the predicted damage fromclimate change, including changes in net agricultural productivity, human health andproperty damages from sea-level rise and increased flood risk. Thus future emissionswill increase the present value of future damages per tonne of emissions, as thesedamages are discounted back to present.

The accumulated costs can be compared to Ragueneau’s estimate that the‘carbon debt’ of industrialised countries since the beginning of the fossil-fuel-drivenindustrial revolution equals the total external debt of the developing countries ($3319billion vs. $3331 billion in 2006 in 2000 price level).48 With the Stern BAU-price, thecumulative costs of the US emissions alone would be quadruple this, and 1.5 timeswith the Lindmark & Acar price. The cumulative cost of the UK emissions would betwo-thirds of the external debt with the Stern price and one-quarter with theLindmark and Acar price. On the other hand, the Tol carbon cost would implycumulative costs for the US emissions of carbon dioxide equal to one-third of the

Figure 8. Cumulative cost of carbon (carbon debt) in Britain, 1800–2000.

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48Ragueneau, ‘CO2 Arithmethics’ (2009), Some alternative estimates of the carbon debt havebeen presented in Kunnas, ‘An Outline’ (2013).

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total external debt of developing countries, with the corresponding figure for Britainof around 5%.

This concept of the ‘carbon debt’ influenced the 2009 Climate ConventionConference in Copenhagen. Developed countries called for emission reductions indeveloping countries, while the latter use the former’s historical emissions as areason for inaction. Calculating the cumulative cost of carbon gives new insights intothe question of who is responsible for climate change. This can be seen in Figures 10and 11 where we have calculated the contribution of the countries with the biggestemissions in 2009, USA, China and India. For comparison’s sake sake we havetreated the EU as a single country, including Britain, as a Kyoto-protocol signatorywith a single emission target. As the starting year we have used 1902, which is thefirst year from which there is a continuous emissions series for China in the CDIAC-database used.49 For the carbon price we have used the constant $20/tC and themiddle of the range declining price from Lindmark and Acar assuming an annual 2%price increase since 2000.

The choice of price has a big influence on the accumulated costs, but it does notaffect the relative position of different countries. With both a constant price and adeclining price the USA has the highest cumulative cost of carbon emissions,contributing 24–27% of the cumulative global cost, followed by the EU with 17–19%. China is nowadays the biggest source of carbon dioxide, but the cumulative

Figure 9. Cumulative cost of carbon (carbon debt) in the USA, 1800–2000

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49Boden et al., Global (2012).

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costs of its emissions are still long behind with 10–12%. The combined cumulativecosts of the emissions of China and India are trailing behind even those of the EU, at13–16% despite their larger populations.

These calculations support the notion that the main reason for a warming climateis the historical greenhouse-gas emissions of developed countries; 41–47% of the costsare due to the cumulative emissions of carbon dioxide from the USA and the EUalone. On the other hand, the emissions of the big four major contributors account foronly 57–59% of the total cumulative costs, leaving over 40% to the rest of the world,supporting the need for a global treaty put forward by developed countries. Addingthe emissions from the nineteenth century would be unlikely to change the big pictureor the order of countries. Even in Britain, the first country to industrialise, the costs ofthe cumulative emissions from the nineteenth century were at most one-quarter ofthose from the twentieth century, as we can see from Figure 8.

It can be argued that the assumption that the costs of carbon dioxide emissionsdecrease as we go back in time gives a penalty to later-comer industrialisingcountries. On the other hand, using either a declining or a constant carbon pricedoes not change the order of countries related to the size of their carbon debt,although the declining price makes the relative size of China’s ‘carbon debt’bigger. Furthermore, this ‘penalty’ can be diminished by technology transfer ofcarbon efficient technology from countries that industrialised during lower carbondioxide concentrations in the atmosphere as a part of a global climate treaty.

Figure 10. Cumulative global costs of carbon, with constant $20 per tonne, 1902–2009.

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Source: Boden et al., Global (2012).

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The starting point for such treaty could be a mutual debt cancellation, developedcountries’ carbon debts offsetting developing countries’ conventional monetarydebt, leaving the dispute about historical responsibility behind.50

6. Summary and conclusions

In this paper we have examined how to incorporate the environmental effects offossil fuel use into the national accounts and the GS measure of sustainability. Thecosts of carbon emissions for Britain and USA have been calculated for the past twocenturies. The estimates have been used to adjust the measures of GS and to gauge‘carbon debts’. The choice of the carbon price has substantial effects on our findings.We favoured using a single global price for carbon dioxide emissions worldwide.This price decreases as we move back in time to reflect that carbon dioxide is a stockpollutant, and that one unit added to a larger stock is likely to cause a higherdamage than a unit emitted under the lower concentration levels in the past. Byimplication, the estimates of the unit cost of future emissions will increase, unless thestock declines.

Figure 11. Cumulative global costs of carbon, with Lindmark and Acar declining price, 1902–2009.

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50cf. Kunnas, ‘An Outline’ (2013).

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Including carbon emissions, except for the Business as Usual price, has onlymarginal effect on the historical estimates of GS for Britain and the USA. That doesnot mean, however, that emissions of carbon dioxide will have a marginal effect onfuture prosperity. The annual flow effects of carbon dioxide emissions are small, butthe cumulative stock effects are not. Our calculation of the cumulative cost ofcarbon, the ‘carbon debt’, gives new insights into the question of who is responsiblefor the costs of climate change. On the one hand, it supports the notion that the mainreason for a warming climate is the historical greenhouse-gas emissions of developedcountries. On the other, it shows the need for a global climate treaty to reduce futureemissions.

As current carbon emissions costs are determined by the discounted sum of totalemissions over time and the discounted damage costs, we cannot know what the‘right price’ for carbon is looking forward, since there are high levels of uncertaintyover both future damage costs and future emissions. For policy appraisal, however,any non-negative price is better than no price at all.

AcknowledgementsWe thank the Leverhulme Trust for funding this work. We are also thankful for commentsfrom participants at the Annual conference of the Modern British History Network June2012, Tampere FRESH meeting May 2012 and the departmental seminar at University ofStirling. Finally, a big thanks to the editorial team and referees for their patience and helpfulsuggestions.

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