7. The Social Cost of Carbon

The social cost of carbon is a useful guide for the appropriate level of carbon prices, although an incomplete one.  

A youtube video on the Social Cost of Carbon covering much of the material on this page is available via the video tab on the home page, or here:

It is a well-established principle of environmental economics that emissions of pollutants should be priced according to the damage they cause.  This broad principle is commonly discussed in terms of Pigouvian taxes or the Polluter Pays Principle.  This principle implies that carbon prices should reflect the level of the costs of the damages caused by greenhouse gas emissions.  This cost of damages is usually referred to as the Social Cost of Carbon (SCC).

The calculation depends on four main things.

1. What changes to the climate result from additional emissions?
2. What damages result from these changes to the climate?
3. The cost of these additional damages, and
4. How we balance costs now and in the future, this is how do we estimate a present cost of future damages?

In practice the Social Cost of Carbon is usually estimated by assuming a base case emissions track, modelling the impacts of the climate change and resulting damage associated with this emissions track, and estimating the financial cost of the resulting damages, for example due to rising sea levels.  This process is repeated adding an additional (say) a billion tonnes of extra emissions and calculating the additional damages that result.  The (discounted) additional cost per tonne of additional emissions is derived from this.  The calculations are usually done using elaborate (but not necessarily accurate) models that seek to capture the impacts of modelled climate change Integrated Assessment Models (IAMs).

Estimating the SCC involves many uncertainties about the nature, extent and cost of damages, and the value that should be placed on non-market effects, including many changes to ecosystems.  These uncertainties are compounded by the damage being determined by the stock not the flow of GHGs, and even by the cumulative effect of the stock over time, with effects depending on how long a given concentration of GHGs is present in the atmosphere.  Furthermore the effects of changing the stock are likely to be highly non-linear, leading to dependence on the assumed reference emissions track.  There is also considerable uncertainty about the discount rate that should be used in weighting current and future costs, and the adjustments necessary to account for effects across people at very different levels of income (equity weighting).  These uncertainties lead to a wide range estimates of the SCC.

The US Environmental Protection Agency (EPA) published new estimates of the SCC in 2015.  These are intended for use is assessing the cost effectiveness of policies such as fuel efficiency standards for vehicles.  Because many damages are large but occur in the distant future the choice of discount rate has a particularly large effect on the results, so the results are presented for a range of discount rates.  Values in $2011 range from $12 to $116/tCO2 in 2015 rising over time by roughly 2% p.a. in real terms.  This range, covering an order of magnitude, is fairly typical of surveys of the SCC, though some have argued for much higher values, and a few for lower values[1].

Social Cost of CO2, 2015-2050

Social Cost of CO2, 2015-2050 a (in 2014 Dollars per metric ton CO2)
Source:  Technical Update of the Social Cost of Carbon for Regulatory Impact Analysis Under Executive Order 12866 (May 2013, Revised July 2015)

	Discount Rate
Year	5% Average	3% Average	2.5% Average	3% 95th percentile
2015	$12	$40	$62	$120
2020	$13	$47	$69	$140
2025	$16	$51	$76	$150
2030	$18	$56	$81	$170
2035	$20	$61	$87	$190
2040	$23	$67	$93	$200
2045	$26	$71	$99	$220
2050	$29	$77	$110	$240

Source: US Environmental Protection Agency http://www3.epa.gov/climatechange/EPAactivities/economics/scc.html

While this is useful and well founded set of estimates that is probably as good as can be expected at the moment, many of the limitations of the modelling suggest that there are good reasons to suppose that these are likely to be underestimates of the SCC, especially at the lower end.

More recent modelling has tried to address these difficulties, but the remain intractable.

Discount rates.  A low estimate often follows from the application of a constant, continuously compounded discount rate of 5%.  It is likely to be more appropriate to use a discount rate that falls over time, which would reduce the effect of discounting and so increase the estimated SCC towards the higher values in the table.  A workshop held by the EPA acknowledges this as a consensus view, and that this approach is the adopted by the UK and France[3].

This matches well with intuition.  A constant discount rate reduces very distant effects to low values at high discount rates.  For example even at a 3% discount rate a value declines by a factor of 100 in just over a century and a half.  This has the consequence, for example, that very large scale damage beginning two centuries hence with a Present Cost of $1 trillion (and thus worth up to investing $1 trillion to avoid) would be worth only investing $10 billion to avoid if it were in three and a half centuries rather than two. This does not appear to be a good guide to decision making.

Omitted costs.  Many of the costs of climate change are omitted from models, essentially assuming that they are zero.  Some costs are dealt with only partially, because they are difficult to estimate reliably [3], or difficult to measure as a financial loss.  For example, non-market damages are particularly difficult to estimate because it is difficult, and in many ways impossible, to develop adequate costings for the loss of major ecosystems.  Indirect costs, for example the risks of displacement of people by climate change, may also be omitted, even though the potential economic and humanitarian costs may be large.

Difficulties in estimating the effects of large temperature changes.  Models designed to estimate the cost of damages for a temperature change of one or two degrees may be become highly misleading if used to estimates the costs of larger temperature changes.  Damages may increase only quite slowly with small temperature changes, but are likely to increase quite rapidly thereafter, and perhaps catastrophically when certain thresholds are reached [4].  This is often not represented adequately in models.  For example, the widely used DICE model shows GDP only approximately halving with a temperature rise of 19 degrees centigrade.  This is unlikely to be realistic, and indeed the model’s author has cautioned against its use for temperature changes above around 3 degrees.  But temperature changes above 3 degrees would be very likely under a business as usual emissions scenario, and the effects of such large temperature changes are a major cause for concern.

Indeed, the discontinuities likely to arise with larger temperature changes raise fundamental challenges to the concept of marginal damage from a tonne of emissions.  This is one reason that the SCC can only ever by a guide for action.

Treating GDP growth as exogenous.  Most models assume that the drivers of GDP growth are largely unaffected by even very severe climate change.  Over a century, even slow growth (anything above 0.7% p.a.) more than doubles GDP, and so more than offsets the costs of warming even if GDP is assumed to halve from the level it would otherwise reach.  Even with a temperature rise of 19 degrees over a century people appear, on average, better off than today, because the benefits of growth (more than doubling GDP) outweigh the costs of climate change (halving GDP).  Calling this result counterintuitive is something of an understatement.

A recent study including the effect on GDP of climate change showed that including the effect on GDP increases estimates of the SCC by a factor of nearly 6 from the EPA’s value, to $220/tCO2.

Role of risks.  Analysis often excludes some risks which are difficult to model, for example some types of climate feedbacks.  This effectively assumes that they won’t happen and so won’t cause any damage, ignoring the risks.  Indeed, even attempting to set a single average cost of damages fails to address the question of willingness to tolerate the chance of a cost much larger than the estimated average (due to low probability high impact events).  The EPA does estimate of the cost in the upper tail of the damage distribution, and some other modelling explicitly includes a range of sensitivities.  However these approaches, at best, go only part way towards addressing the problem of the risk of catastrophe outcomes, especially in view of the other limitations I’ve outlined.

Finally, the process of assessing policy measures needs to take account of all costs and benefits.  Measures to reduce emissions often have valuable co-benefits for health which need to be factored in to decision making.  And analysis needs to take account of future benefits for emissions reduction, for example in promoting early stage technologies.

 There are some who have argued that the uncertainties are so great that such analysis is all but useless for policy making[6].  However this seems to go too far.  Although wide, this range is a useful guide for decision making because it gives some guidance for appropriate levels for the carbon price, at least as a lower bound.  For example, the current EUETS price is currently below the lower end of the range shown in the table above, and the values in the table are quite likely to be biased downwards by omissions of some damages.  This gives strong guidance that the EUETS price is too low to adequately price damage due to greenhouse gas emissions [7].

Estimates of the cost of damage from greenhouse gas emissions remain useful inputs into decision making.  They can be useful in ruling policy measures in – if a policy measure has a cost per tonne below even a cautious estimate of the cost of damages then it is very likely cost-effective.  But they are much less useful for ruling measures out.  It is probably worth paying a good deal more to reduce the risks of large changes to the climate than the conventional estimates of damage costs suggest.  And in any case judging which risks are acceptable will always be a matter of political and ethical debate, rather than a simple matter of costings.

Updated 19th April 2015

[1] Comparing estimates of the SCC from different sources presents a number of difficulties, including the currency and year in which the estimates are quoted (US$ 2011 here), the date of the estimates and the assumptions made, all of which are sometimes unclear.  However, most estimates seem to imply values roughly within the US EPA range.  For a discussion of a variety of issues see: https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/42502/sei-scc-report.pdf.  Also see: L. Johnson and C. Hope, “The social cost of carbon in U.S. regulatory impact analyses: an introduction and critique” Journal of Environmental Studies and Sciences.  September 2012, Volume 2, Issue 3, pp 205-221.  More recent work by C. Hope and M. Hope (“The Social cost of CO2 in a low growth world” Nature Climate Change, August 2013) points out that with lower growth estimates of the SCC rise as future generations are correspondingly poorer (essentially this is an aspect of the discount rate issue).  A few calculations by others in the past have produced very low and even occasionally negative values for SCC (implying GHG emissions are beneficial), due, for example, to increased agricultural productivity, but these do not seem a plausible reflection of current circumstances and understanding.   For estimates giving higher values see:

http://www.e3network.org/papers/Climate_Risks_and_Carbon_Prices_executive-summary_full-report_comments.pdf, which explicitly critiques the US EPA analysis.

[3] http://www.rff.org/Publications/Resources/Pages/183-Benefits-and-Costs-in-Intergenerational-Context.aspx

[4] A good survey of omissions from calculations of the SCC is given by a recent report co-sponsored by the US NGOs the Environmental Defense Fund and National Resources Defence Council:  http://costofcarbon.org/blog/entry/missing-pieces

[5] A good review of the limits of modelling can be found in Nicholas Stern, The Structure of Economic Modelling of the Potential Impacts of Climate Change, Journal of Economic Literature 2013.  This includes the reference to damages at very large temperature changes, quoting work by Ackerman, Stanton and Bueno: Fat tail, Exponents, Extreme Uncertainty:, Simulating Catastrophe in DICE, Ecological Economics 69, 2010

[6] See http://web.mit.edu/rpindyck/www/Papers/Climate-Change-Policy-What-Do-the-Models-Tell-Us.pdf  The author argues that the assumptions, especially on the damage function, cannot be sufficiently robust to base conclusions on.  However he acknowledges the pragmatic value of such results as a possible marker for a carbon price.

[7] The marginal price signal is at too low a level, so some economically efficient abatement is not being signalled.  It is possible that an inefficient mix of abatement is being purchased, even though the level of abatement is efficient.  This could be the case if, for example, there was too much expensive abatement through renewables programmes.  In this case the appropriate response would be to reduce the expensive abatement under other programmes, in which case the price floor in the ETS would still be appropriate but might not bind.  Alternatively, renewables programmes may recognise the presence of other market failures, notably those associated with failure to recognise spill-over effects from innovation, and the policies in place are appropriate.  In this case the cap is too loose.  Some mix of these explanations is of course possible, although the latter seems the more plausible.  In either case a floor to maintain an efficient marginal price signal remains appropriate. 

[8] Temperature impacts on economic growth warrant stringent mitigation policy, Frances C. Moore and Delavane B. Diaz, Nature Climate Change 5, 127-131 (2015)