Main

The major cause for climate change, elevated atmospheric CO2 concentration, did not happen overnight, but is the result of past CO2 emissions. These past CO2 emissions brought economic wealth for the emitting countries, but have caused and will cause climate damage worldwide in the past, present and future. In an inclusive wealth (IW) perspective1, an intact climate system is a valuable asset, and the climate damages caused by CO2 emissions reduce the wealth associated with this asset, the ‘climate wealth’. Past CO2 emissions generated economic wealth at that time, at the expense of reduced climate wealth, and in that sense they have been borrowed from climate wealth. To capture this, we propose the concept of climate wealth borrowing (CWB), which is the present value, in consumption equivalents, of climate damages caused by all historical CO2 emissions.

Countries have been differing considerably in their amounts and time profiles of past CO2 emissions2. While from a cumulative emissions perspective, the emissions time profile does not matter3, it does from a welfare-theoretic perspective4, due to (1) increasing marginal damages of CO2 emissions and (2) discounting. (1) Whereas each ton of CO2 contributes similarly to global warming5,6, climate damages increase more than proportionally with the temperature increase4. Hence, marginal damages, that is, the extra climate damages due to an extra ton of emissions, were considerably smaller at lower atmospheric CO2 concentrations in the past. (2) However, having emitted CO2 in the past also means that these emissions have caused damages already in the past and thus had ‘more’ time in accumulating impacts on wealth. The CWB concept includes both of these effects and allows a welfare-theoretically sound assessment of past CO2 emissions.

In this analysis, we apply the CWB concept in the context of IW and comprehensive investment assessments7,8,9. The IW approach defines the inclusive (or comprehensive) wealth as the aggregate value of all natural and human-made capital stocks7. The IW approach is applied in the UN IW reports10,11,12 and the United States have recently launched a new draft National Strategy to improve its statistical description of economic activity and development by accounting for the wealth contributions of water, air, and other natural assets following the IW approach13. The application of the IW approach allows one to measure how human activities, such as emitting CO2, affect the various natural and human-made capital stocks and therefore IW over time. As, in particular, natural capital stocks provide various services that are either not traded on markets or accrue outside the national accounting system, and therefore lack price information, the appropriate valuation approach is carried out by means of shadow prices, which capture both use and non-use values of capital stocks14,15. CO2 emissions enter such calculations as cost, anticipating the negative effects of future climate change on most countries around the globe16. The associated shadow price of atmospheric CO2 is coined the social costs of carbon (SCC). Whereas the SCC can be meaningfully derived for any emissions trajectory (for example, any representative concentration pathway), they coincide only with the optimal (Pigouvian) carbon tax along an optimal emission trajectory16. Here we compute a SCC time series and use it to quantify CWB for the historical, non-optimal CO2 emissions. CWB can be compared with investment in (manufactured) capital17. The former reduces global IW (in almost all countries around the globe), and the latter increases IW, through the increase in the investing country’s wealth. We put country-specific CWB into perspective with private accumulation of IW arising from the increase of manufactured capital stocks as measure how CWB affects sustainable development of countries.

Deriving the SCC since 1950

To obtain a historical SCC time series and to assess the impact of countries’ past CO2 emissions on global wealth, we calibrate a globally aggregated neoclassical growth model to match observed global economic development, global CO2 emissions, atmospheric CO2 concentration and global mean temperature increase from 1950 to 2018. The model structure is based on the integrated assessment model (IAM) DICE4. We impose until 2018 the observed paths for investment and CO2 emissions abatement and consider optimal policies thereafter, as standard in the integrated assessment literature4. Two important determinants of the SCC are future economic impacts of climate change and the social discount rate (SDR). In addition to the estimates of economic climate impacts used in DICE4, we consider alternative climate impact functions based on Weitzman18 and Howard and Sterner19. The latter has been shown to support an ambitious temperature stabilization target comparable to the one set out in the Paris Agreement20. We calibrate the central parameters determining the SDR, namely the pure rate of time preference (δ) and the marginal elasticity of utility (η), to match the historical path of investment from 1950 until 2018. This results in an SDR of 6.75% per year for that period. An alternative parameterization derives from the expert survey by Drupp et al.21, which translates into an SDR of 3.74% per year for that period. Accordingly, we refer to the former as the calibrated, rather high SDR and to the latter as the expert-based, rather low SDR.

CWB

SCC in 1950 have been fairly low compared with SCC in 2018, but clearly positive, reflecting the long-lasting climate effects of past CO2 emissions. Over time, the current-value SCC increase, reflecting increasing marginal damages (Fig. 1a). From the present-day perspective (2018 in our computations), past CO2 emissions are valued relatively high, due to the reversed discounting effect: The earlier one would have avoided the emissions and the damage associated, the better from the present value perspective due to the compounding effect. This effect is more pronounced for the higher, calibrated SDR; for the expert-based, lower, SDR, the two opposing effects of compounding and increasing marginal damages almost fully offset each other, resulting in an almost constant present value SCC over time (Fig. 1b). In turn, for the expert-based SDR, CWB scales linearly with cumulative CO2 emissions (Fig. 1c). For the calibrated, higher, SDR, the compounding effect dominates and historically earlier CO2 emissions result in higher CWB than more recent CO2 emissions, which is indicated by the declining present value SCC (Fig. 1b). However, even for a high SDR, the relationship between CWB and cumulative CO2 emissions is linear with good approximation (Fig. 1c). Thus, valuing cumulative past carbon emissions at current SCC would provide a robust first-order approximation to CWB. Such an approach, that is, using a constant, current SCC estimate to assess past CO2, is applied in the IW Reports, which assess the cumulative CO2 between 1990 and 2014 with a constant SCC (for example, ref. 12). Our results show that this approach is a reasonable approximation to the welfare-theoretically sound CWB assessment based on historical SCC.

Fig. 1: SCC and CWB 1950–2018.
figure 1

a,b, The solid lines show the mean SSC in current values at the year of emission (a) and present value in 2018 (b), with bands indicating 95% CIs of the mean (N = 18). c, The dots show the relationship between cumulative fossil and industrial-process CO2 emissions (in Gt CO2) and the CWB (in trillion USD) for all countries (labels only for the five countries with the largest cumulative emissions and CWB). The error fences display the 95% CIs of the mean (N = 18). For the five largest emitters, the relative shares are displayed in the data table in c. The dashed lines show a linear model fit on the relationship between cumulative emissions and CWB. All results are presented for the two specifications of the SDR, the expert-based SDR obtained from Drupp et al.21 (red, δ = 1.1% per year and η = 1.35) and the calibrated SDR (blue, δ = 4.4% per year and η = 1.2). USA, the United States; CHN, China; RUS, Russia; DEU, Germany; JPN, Japan.

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Mean aggregate CWB amounts to 40.05 (95% confidence interval (CI) ±1.44) and 87.92 (95% CI ±3.23) trillion USD (in 2017 purchasing power parity (PPP) prices) for the calibrated and expert-based SDR, respectively (note that these figures include all fossil and industrial CO2, for example also international bunker fuel emissions; if we restrict the CO2 emissions to those attributed to countries, the two figures would drop to 38.86 (95% CI ±1.40) and 85.30 (95% CI ±3.12) trillion USD). The United States and China are responsible for close to 40% of mean aggregated CWB since 1950: the mean United States share is 24.55% (95% CI ±1.25%) and 22.84% (95%CI ±1.15), China’s mean share is 12.07% (95% CI ±0.68%) and 14.64% (95% CI ±0.88%) for the calibrated and expert-based SDR specification, respectively. These shares relate to the shares in the cumulative fossil and industrial-process CO2 emissions (1950–2018) of the United States and China, 22.67% and 14.95%, respectively. Results for all countries can be found in Supplementary Table 1.

Country-specific CWB is the present value of all damages caused by historical CO2 emissions by that country. This can be compared with the present value of damages resulting from the fraction of atmospheric CO2 that can be attributed to a country. Based on the FaIR-Geoffroy climate carbon cycle model, only 54% of the United States cumulative emissions between 1950 and 2018 are still in the atmosphere in the year 2018. In comparison, the fraction for China is 63%. Valuing the stock of atmospheric CO2 attributable to cumulative emissions of the United States at current SCC gives estimates that are 73.90% (95% CI ±21.45%) or 50.14% (95% CI ±14.34%) lower than the emission-based CWB for the calibrated and expert-based SDR specification, respectively. For China the corresponding figures are 59.53% (95% CI ±17.33%) and 40.68% (95% CI ±11.72%) (Extended Data Fig. 1).

Per-capita CWB

While the country-specific CWB is highest and of similar magnitude for the United States and China, the per-capita figures are quite different. Whereas mean per-capita CWB (at current population size) in the United States is 30,061.01 (95% CI ±1,085.80) and 61,399.96 (95% CI ±2,136.10) USD (in 2017 PPP prices) for the calibrated and expert-based SDR; the corresponding figures for China are 3,386.80 (95% CI ±145.10) and 9,014.09 (95% CI ±432.28) USD. Accordingly, on per-capita basis, the United States rank third among all countries of the world (behind Estonia and Luxembourgh), while China falls to the 83rd and 80th place, for the calibrated and expert-based SDR specification, respectively (of 174 countries assessed on per-capita basis). The per-capita assessments confirms the dominant responsibility of industrialized countries for climate change (Fig. 2 displays the mean per-capita CWB for all countries for the expert-based SDR; the corresponding information for the calibrated SDR is shown in Extended Data Fig. 2).

Fig. 2: Per-capita CWB for the expert-based SDR, in 2017 PPP USD.
figure 2

The figure has been created using Wolfram Research, Inc., Wolfram∣Alpha Knowledgebase, Champaign, IL (2021).

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Relationship to manufactured capital wealth investments

Sustainable development, defined as non-declining human wellbeing, requires that IW does not decline7. IW is the aggregate social value of all natural and human-made capital stocks. Whereas CWB is a reduction of IW, investments in manufactured capital increase IW. To assess country-specific contributions to sustainable development in the IW sense, we compare country-specific CWB with the corresponding welfare measure of country-specific manufactured capital (K) wealth investments (KWI), that is, the present value, in consumption equivalents, of all historical investments in manufactured capital.

Global CWB relative to global gross KWI is 0.52% (95% CI ±0.02%) and 3.71% (95% CI ±0.14%), and relative to net investment, 0.91% (95% CI ±0.03%) and 6.95% (95% CI ±0.26%), for the calibrated and the expert-based SDR (Fig. 3a,b, respectively). The 20 countries with the largest cumulative emissions differ substantially. The United States, China and India exceed the global ratio (gross and net), while several European countries with large emissions in the past are below the global ratio of CWB to KWI. In particular France and Italy have rather low CWB relative to their capital investments; their CBW relative to net KWI is even lower than the global ratio of CWB to gross KWI. It is the other way around for Poland and South Africa. Results for all countries are presented in Supplementary Table 1.

Fig. 3: CWB relative to manufactured capital wealth investments (KWI).
figure 3

a,b, Mean CWB relative to gross and net KWI and 95% CIs, based on the time period from 1950 to 2018, for global CWB (dashed lines) and for the largest 20 countries in terms of cumulative CO2 emissions. As for Russia, Ukraine and Kazakhstan investment time series do not start before 1990, these countries are omitted. c,d, Mean CWB relative to gross and net KWI and 95% CIs, for the entire period from 1950 to 2018, and for the three periods, 1950–1974, 1975–1999 and 2000–2018, for global CWB (dashed lines) and for the five largest countries terms of cumulative CO2 emissions (excluding Russia). USA, the United States; CHN, China; DEU, Germany; JPN, Japan; IND, India; GBR, the United Kingdom; CAN, Canada; FRA, France; ITA, Italy; POL, Poland; ZAF, South Africa; MEX, Mexico; IRN, Iran; AUS, Australia, KOR, South Korea; BRA, Brazil; SAU, Saudi Arabia; ESP, Spain; IDN, Indonesia; TUR, Turkey.

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Applying the calibrated SDR results in a considerable smaller ratio (globally and across countries) not only because CWB is considerably lower (see above) but also because the rather high SDR implies a stronger compounding effect for investments in manufactured capital. Accordingly, periods with still rather low emissions, but high capital investments, like in the 50s and 60s have a higher weight in the aggregated figures. In turn, countries differ in their deviation from the global ratio of CWB to KWI across the two SDRs, depending also on the time profile of their CO2 emissions and manufactured capital investments.

The time profile of CWB relative to (gross and net) KWI for the five countries with the largest cumulative emissions (excluding Russia) indicates different trends for CWB/KWI over time (for the calibrated and expert-based SDR, Fig. 3c,d, respectively). While China had the highest CWB relative to its (gross and net) KWI in the early periods 1950–1974 and 1975–1999, this changed in the more recent past, if considering net investments. In the period 2000–2018, Japan, Germany and the United States had a higher CWB relative to KWI for both SDRs than China and China’s share even dropped below the global mean CWI/net KWI share. Hence, China’s more recent increase in CO2 emissions was less than proportional to its increase in investment. A similar development can be seen for India. On the other hand, ‘old’ industrial countries like Japan, Germany and the United States increased their CWB relative to gross and net KWI. While in the period 2000–2018, Japan’s and Germany’s CWB relative to gross KWI is still below the corresponding global value, this is not the case when considering net investments. This indicates that these countries have been investing a lot to maintain their manufactured capital basis, but were not able to sufficiently decarbonize their capital stock and production, showing an increasing challenge for sustainable development.

Discussion

Results on CWB are sensitive to the SDR applied. Calibrating the model to historical data leads to an SDR of 6.75% per year, which is higher than the SDR of 4.35% per year assumed by Nordhaus4. We contrast results for the calibrated SDR to an alternative, lower SDR that assigns higher weight to future climate impacts. The substantial differences of the SCC—both in current values at the year of emissions and in present values in 2018—for the two SDF are clearly visible in Fig. 1. Especially, the higher SDR assigns relatively more weight to past emissions, that is, the period where industrialized countries in Europe and the United States emitted already a substantial amount of CO2. The aggregated results show that the level of the SCC (that is accounting for climate impacts) dominates the compounding effect and, in turn, the lower SDR translates into higher CWB absolutely and also as share of manufactured capital investment. However, using the low, expert-based SDR leads to results inconsistent with the historical observations on investments in manufactured capital.

Results on CWB also strongly depend on the quantification of the economic impacts of climate change, which still are highly uncertain16,22,23. We contrast a rather shallow impact function provided by Nordhaus4 and a rather steep impact function, provided by Howard and Sterner19, complemented by a (for low temperature increases) modest impact function provided by Weitzman18. The uncertainty in economic climate impacts translates into large CIs for the mean SCC. For the Nordhaus-only impact function, the mean SCC in 2018 are 8.33 (95% CI ±0.43) and 33.14 (95% CI ±3.76) USD/tCO2 and for the Howard–Sterner-only impact function, the mean SCC in 2018 are 26.56 (95% CI ±1.45) and 99.04 (95% CI ±11.20) USD/tCO2, for the calibrated and expert-based SDR, respectively. Considering only the impact function provided by Howard and Sterner19 and the expert-based SDR, mean global CWB increases from 87.92 (95% CI ±3.23) to 150.57 (95% CI ±1.94) trillion USD (in 2017 PPP prices) and the share of CWB relative to the present value of manufactured capital investments increases from 3.71% (95% CI ±0.13%) and 6.94% (95% CI ±0.26%) to 6.36% (95% CI ±0.08%) and 11.90% (95% CI ±0.15%), for the expert-based SDR, for gross and net investments, respectively.

The impact functions we consider account neither for potential climate impacts on economic growth nor for the uncertainty of climate-change impacts triggered, for example, by tipping points24. The former could increase climate impacts tenfold16. However, the empirical evidence for the (persistent) impact of climate change on economic growth is inconclusive, while the estimated impact on economic output levels is consistent with the impact estimates of major IAMs25. Uncertain climate impacts are a major argument for the guardrail approach to temperature targets as adopted in the Paris Agreement. However, it would be normatively challenging to justify the evaluation of historical emissions with a policy target that was not introduced before 2015, and in turn a budget approach does not allow deriving welfare implications of past CO2 emissions. In contrast, the welfare-theoretic approach we propose here does allow such a derivation irrespective of the past or current climate policy framework due to the influence of past CO2 emissions on wealth.

Our analysis is (1) restricted to country-specific fossil and industrial-process CO2 emissions, (2) neglects the regionally uneven distribution of carbon sinks and (3) does not account for regional variation in climate change impacts. Due to (1) and (2), we probably underestimate CWB for countries with high agricultural emissions, whereas we overestimate the CWB for countries with large forest carbon sinks. Using consumption-based instead of territorial CO2 emission would allow to account for the CWB implications arising from trade. Furthermore, (3) implies that we do not distinguish between domestic and abroad CWB of a country’s CO2 emissions and only derive global CWB. Such an analysis would require country-specific SCC26. However, since country-specific SCC are small relative to the (global) SCC27, using the global SCC figure provides already a comprehensive quantification of CWB.

As the IW framework, also CWB is based on a weak sustainability concept, according to which CO2 emissions can be compensated by investments in human-made capital stocks. Implications of climate change, in particular on various non-use values provided by natural capital stock, might favour an assessment under a concept of strong sustainability, which supposes limited substitution possibilities between capital stocks and/or investment in specific adaptation and restoration capital funds (28 and15, respectively). Focusing on cumulative CO2 emissions can be seen as related to such a strong sustainability assessment of climate change. However, our analysis has shown that both perspectives lead to similar conclusions when comparing country-specific cumulative emissions and CWB because the compounding (reverse discounting) effect balances the increasing marginal damage effect.

Conclusions

Past CO2 emissions, increasing atmospheric CO2 concentration, have caused and will cause climate damage worldwide in the past, present and future, and reduce global IW. We propose the concept of CWB to quantify the present value of climate damages from past CO2 emissions. From an IW perspective, CWB is the value of investments in human-made capital that is required to compensate for the wealth reductions from past and current CO2 emissions, to achieve sustainable development. We quantify CWB for the period 1950–2018, showing also how these reductions in IW compare with investments in manufactured capital. The latter allows assessment of the implications of CWB on sustainable development under a concept of weak sustainability, that is, considering the shadow-price aggregated change in capital stock. Still, the comparison of CWB with investments into manufactured capital indicates to which extent the cost countries impose on the global society by their CO2 emissions is accompanied with a strong increase in private, country-specific wealth. In turn, different fairness principles such as the polluter-pays or ability-to-pay principle would result in different responsibilities and potential financial burdens for climate change mitigation and adaption29. The concept of CWB and the methods developed here provide a quantitative basis to apply the different fairness principles. Furthermore, we show that the SDR influences the CWB not only by deflating future impacts but also by compounding past cost. A high SDR assigns a relatively larger responsibility to past emissions and hence to industrialized countries. However, we show that the two effects roughly offset each other. As a consequence, approximating CWB by applying constant, current SCC provides fairly accurate estimates. Accordingly, while in contrast to a CO2 budget approach, a welfare-theoretic perspective should account for the time profile of past CO2 emissions, in quantitative terms both approaches lead to similar results.

Methods

CWB

Our CWB approach builds on the discounted Utilitarian framework, which is standard in the climate economics literature30. We define the CWB by a country with emission path e = (e1950, e1951, …, e2018) as the present global wealth, measured in consumption equivalents at point in time t = 2018, that compensates for the climate damages caused by e. \(\,{{\mbox{CWB}}}\,\,\equiv \,{{\Delta }}{C}_{2018}=\mathop{\sum }\nolimits_{t = 1950}^{2018}{\mathrm{SCC}}_{2018,t}\cdot {e}_{t}.\) CWB is computed from the present values SCC2018 of past emissions, which are derived as: \({{{{\rm{SCC}}}}}_{2018,t}=\frac{\partial W/\partial {E}_{t}}{\partial W/\partial {C}_{2018}},\) where W denotes total welfare, and et, and Ct denote CO2 emissions and total consumption in year t, respectively, that is, the SCCs and CWB are measured in terms of consumption. We relate CWB to past investments in manufactured capital, which in contrast to CO2 emissions increase wealth. We distinguish between gross investments and net investments, the latter accounting for capital depreciation. The former is informative in terms of indicating a country’s savings, that is, directing output to wealth-increasing activities. The latter indicates whether investments are sufficient to at least maintain its capital base. As for CWB, we use a welfare measure, abbreviated KWI for capital (K) wealth investments, which captures the present value of all past investments in manufactured capital, and express the value of past investments in consumption equivalents in the year 2018. KWI is derived as the compensating surplus, in 2018 and with respect to global welfare, for the stream of investments that one country adds to the global economy. The present value equivalent surplus for the stream of investments 1950–2018 is \({{\Delta }}{C}_{2018}=\mathop{\sum }\nolimits_{t = 1950}^{2018}{{\Delta }}{C}_{2018,t}=\mathop{\sum }\nolimits_{t = 1950}^{2018}\frac{{(1+\delta )}^{-T}\,{U}^{{\prime} }({c}_{T})}{{(1+\delta )}^{-2018}\,{U}^{{\prime} }({c}_{2018})}\,{I}_{t}\), which can be equivalently expressed as \({{\Delta }}{C}_{2018}=\mathop{\sum }\nolimits_{t = 1950}^{2018}\frac{\partial W/\partial {C}_{t}}{\partial W/\partial {C}_{2018}}\,{I}_{t}.\) The formal derivation of CWB and KWI is detailed in Section 2 in Supplementary Information B.

IAM and calibration

We calibrate a global IAM based on DICE4 to quantify the SCCt time series. The IAM allows maximizing of welfare W, that is, the present value of aggregate utility Lt U(ct), which derives from the world population of size Lt and the level of per-capita consumption ct, by determining the optimal paths for CO2 emissions abatement and capital investment. However, the model also allows one to derive the shadow price information for given, that is, non-optimal, emissions abatement and capital investment paths. Unabated CO2 emissions from the production process increase atmospheric CO2 concentration and, in turn, global mean temperature, which reduces output (climate damages). The model structure is detailed in Section 3 in Supplementary Information B.

The IAM is calibrated to match observed global economic figures (output, capital stock, investment, depreciation and output elasticity of capital) from the Penn World Tables31 and to match observed, global fossil fuel and industrial CO2 emission from the Global Carbon Project2. The underlying deterministic economic growth framework of the IAM is not capable of reproducing business cycles in individual countries32, though can be calibrated so that global aggregated and therefore smooth output and investment time series are matched. The derived SCC and (global) consumption discount rate obtained from the model are then applied to derive the country-specific results.

Following Nordhaus4, we measure economic variables in PPP where our units are 2017 US$ (international dollars). Both capital stock and investments are denoted in output PPP since the conversion of capital data into PPP currencies uses a different PPP exchange rate than used for output in the Penn World Tables. For the investment time series, we use initial capital stocks in 1950 and calculate then a gross and net investment time series by using ‘share of gross capital formation at current PPPs’ and the depreciation rates, both obtained from the Penn World Tables. The calibration of economic output is detailed in Section 4.1 in Supplementary Information B. We replace the DICE carbon cycle and climate dynamics by the climate and carbon cycle model Finite Amplitude Impulse Response (FaIR)33 and the energy-balance model provided by Geoffroy et al.34 which have been shown to replicate historic CO2 concentration time paths and corresponding global mean temperature increase accurately35,36,37. The calibration of the carbon cycle and climate system is detailed in Section 4.2 in Supplementary Information B. As discussed in the main text, we consider three different climate damage functions, Nordhaus4, Weitzman18, and Howard and Sterner19. The damage functions and calibration of the abatement cost function are detailed in Section 4.3 in Supplementary Information B.

Until the year 2018 we impose the observed paths for investment and CO2 emissions abatement and derive optimal policies thereafter. Following Nordhaus4 we assume that certain properties such as population growth and development of non-CO2 forcing are exogenous and consider in addition to the baseline DICE specification, five further scenarios based on the baseline shared socio-economic pathways specification38. Accordingly, we consider in total 18 scenarios, that is, six scenarios for the three climate damage functions each. Accordingly, the presented results display if not indicated otherwise the mean over the 18 scenarios and 95% CI, implying that each climate impact function is assigned the same weight. The selection and calibration of the exogenous parameters are detailed in Section 4.4 in Supplementary Information B.

Discounting

We use two different model specifications with respect to discounting. In the first specification, we calibrate the parameters determining the SDR, the pure rate of time preference (δ) and the marginal elasticity of utility (η), to match the historical path of investment from 1950 until 2018 under optimal investment. We find that the observed path for the global capital stock is matched for combinations of δ and η that satisfy η = 3.268 − 0.47 ⋅ δ (in % per year). Numerically, the closest fit with the observed capital stock in the year 2019 is obtained with δ = 4.4% per year and η = 1.2. This calibration results in an SDR of 6.75% for that period. The second specification uses an expert-based parameterization from the survey by Drupp et al.21 with δ = 1.1% per year and η = 1.35, which translates into an SDR of 3.74% for that period. Note that a lower SDR would result in higher capital stocks in 2019 as the observed capital stocks if the IAM is optimized starting in 1950 since a lower SDR implies higher present value returns from capital investment and therefore less consumption. However, under both specifications we derive the SCC under given, that is, observed, levels of capital investment and CO2 emissions. The calibration of the SDR is detailed in Section 4.5 in Supplementary Information B.