While your question is from a theoretical point of view, maybe this article about the legal aspects of integrating SCC in CBA might give you some insights? Overall, the choice of social discount is generally relatively arbitrary, in the sense that it is provided by national regulators. As well the measured SCC is dependent of model assumptions and by nature does not take into account all the sources of uncertainty.

As the authors argued: "while there continues to be debate about the size of the SCC, there is overwhelming evidence that the costs of climate change are substantial and that whatever the true value of the SCC, it is clearly not zero. Ignoring the SCC—i.e., using a value of zero in benefit–cost analysis—would restrict climate regulations to those that can be justified solely by their cobenefits (e.g., reductions in local pollution such as particulate matter or mercury) and is inconsistent with the best available

science."

 I am not qualified to say if it is a double discounting but my intuition is that SCC takes into account international emissions while your specific project is local, so the SCC is used to introduce an approximation of the costs, which, in absence of more accurate measure, gives you the more probable expectation, but not weighted by uncertainties.

Integrated Assessment Models and the Social Cost of Carbon: A Review and

Assessment of U.S. Experience

Gilbert E. Metcalf and James H. Stock

Review of Environmental Economics and Policy, volume 11, issue 1, Winter 2017, pp. 80–99 doi:10.1093/reep/rew014

Dear Sébastien, thanks for the response. I am aware that in practice both SCCs and social discount rates are suggested by national regulatory bodies, and these are rather arbitrary. In theory, uncertainty can be accounted for in social discount rates (see especially the work by Christian Gollier on that, for example his book Pricing the Planet's Future). The estimation of SCC definitely has a lot of problems of its own; still, in this case I am specifically interested in the (purely) theoretical question whether using SCC, which is the result of an IAM that includes a social rate of discount, in a CBA involving social discounting is correct.

well, to my knowledge the question has not been answered theoretically (Pizer et al 2014 10.1126/science.1259774). But in practice extrapolated SCC are introduced into CBA with discounting, sometimes even without using the same social discounting.

So if you manage to prove whether it is wrong or not, you'll have your paper published in Science ;)

Hello, Bartosz.  You pose an insightful question.  I am a little bit surprised you have only 3 answers after 26 days.

First, may I ask whose SCC calculation you are using? The USA EPA outlines their method of calculating/using the SCC at the following link: https://www.epa.gov/climatechange/social-cost-carbon

The EPA description suggests that the SCC applied to a unit of carbon emitted/mitigated in a particular year in a cash flow relates to the PV of damages into the future discounted back to that specific year.  Call that PVcn.  Thus, to get a PV at year zero (that is, PVco) the PVcn must be discounted by a factor of “n”.  So the answer is “yes” – an already-discounted value is then discounted again.

First, please keep in mind that this is not the only time this occurs in CBA.  Anytime you have a capital or ‘stock’ entry in a cash flow after year zero, you are doing something similar. In financial economics (and in the Arrow-Debreu model), values of stocks result from capitalizations of flows.  Think about the value that is entered (and then discounted to PVo) for vehicles replaced in the 7th year of a project cash flow, for example.  This applies the general equilibrium concept that capital values result from capitalization of the future values of their marginal products in use (VMP). So the SCC in the above description is a stock value at a point in time rather than a flow value at that point in time.

At the above EPA site, the suggested PV for carbon emissions is provided at a range of discount rates and at different points in time.  If your CBA uses a discount rate not matched to the SCC value chosen from there, then – yes – different discount rates would be in play in that CBA. [Note that the above site also shows social cost of methane estimates.]

A second problem with the SCC is now under discussion in the USA and at the USAID (where US government money is used to fund projects on behalf of other countries/citizenry).  That is the issue of what Charles (Chuck) Howe in 1974 referred to as “the accounting stance” of CBA.  The accounting stance issue relates to the jurisdiction and citizenry for whose welfare the numeraire of the CBA is denominated.  The numeraire commonly used comes from the welfare theory underlying the Arrow-Debreu model of general equilibrium and is referred to as the AGGREGATE CONSUMPTION NUMERAIRE. The accounting stance then defines the limits of whose consumption values (WTP) go into the benefit and cost accounts. If you are doing a CBA for your country (to whom the costs in the CBA are accounted) but the SCC covers damages related to the entire globe, then the accounting stance for one part of the calculations is inconsistent with the CBA numeraire. [Howe’s monograph can be found here: http://onlinelibrary.wiley.com/doi/10.1002/9781118665657.ch2/summary ]

Keep up the good work.  All best wishes.  Bill Ward

Dear Bill, thanks a lot for your very detailed response. The question was purely hypothetical, not linked to any specific project (I am not working on CBA currently) - call it scientific curiosity. Thanks for pointing out that the problem is related to cash-flow valued stocks in general. I still do not really know what the (theoretical) consequences of all this are: what would a theoretically consistent CBA look like and how much would it be different from a conventional, theoretically inconsistent one...? Thanks also for referring to the accounting stance issue, it's new to me.

https://www.jstor.org/stable/23594772?seq=1#page_scan_tab_contents

https://19january2017snapshot.epa.gov/climatechange/social-cost-carbon_.html

This is an excellent question. Time discounting carbon by a Decision Maker (DM) does not result in the double-discounting of carbon. Furthermore, the DM is not engaging in a CBA (the DM is engaging in a cost or a benefit analysis, not in a cost and benefit analysis) in discounting the Social Cost of Carbon. The DM Is simply discounting the value of the damage of carbon. This yields a social-discounted carbon tax, or subsidy, depending on whether atmospheric carbon is being increased or drawndown by the project that you are working on; but the discount is only of the damage caused by carbon, or benefit of preventing such damage.

The issue is the time lag between the release/drawdown of the carbon and the actual damage that It does/prevents.* You are not double discounting because your CBA project is discounting the time period between today and the time that you pay for and the carbon and the carbon tax and presumably "release" the carbon or remove the carbon and receive the subsidy and are assumed to drawdown atmospheric carbon, but the carbon tax is discounting from the time that you pay the carbon tax/receive the subsidy until the damage/damage prevention from your "use" of the carbon has occurred (say in ten years later).**

So if your CBA involves removing carbon from the soil in ten years (t=10), then you discount the tax that you will pay at that time to its present value (in t=1), while the DM will have discounted the carbon you release in ten years from ten years after that from that future (t=10) time period, when the carbon you release actually does most of its damage. You are discounting t=1-10, while the DM is discounting 10-20, though from the DM's perspective your t=10 is t=1 and your t=20, the DM's t=10. There is no "double counting" because you are discounting t=1 through t=10, and the DM is discounting t=10 through t=20. (Though from the DM"s perspective, again, your t=10 is the DM's t=1 and so on.)

Any disparity between your and the DM's discount rate means that present and future agents (' lives) will be relatively affected differently then if your discount rate matched the DM's and differently still if the DM's matched yours. The difference lies only in the net effective discount rate produced by your time period until you buy/emit the carbon and the DM's time period from your time of emission until it damages the environment.

What the most effective rate is cuts to the primordial question in time discounting: what is the correct rate? As far as carbon release/release-prevention, the answer to that is zero, other things being equal. It is only if economic growth occurs and there is elasticity in marginal utility, there is an actual risk of the exogenous extinction of the Earth, or some other empirical factor that actually changes the value of damage to the environment caused by carbon release as a function of time.

Any of these real values must be either known or very accurately estimated; if any of them are not--if "imaginary" or subjective values are used to discount-values that do not effect the actual experience of future generations, then it is inefficient and untechnical to positively discount environmental damage because current generations are simply destroying future generations without compensation, while they "benefit" materially from the increase in (say) carbon emission.

As far as the discounting of your CBA, outside of the values that are not compensating for an effect on actual experience, their might be an ethical case for positive time discounting, but it would still be inefficient. The inefficiency in any "unreal," subjective discounting results from the welfare loss that occurs when distribution is based on the mismeasurement of welfare that discounting causes. At any given moment, all utility is fully enjoyed, but time-discounting measures its value as if it were less than it actually is: the result is generally inefficient distribution of resources across generations.