The Role of Scenario Uncertainty in Estimating the Benefits of Carbon Mitigation

The benefits of carbon mitigation are subject to numerous sources of uncertainty and accounting for this uncertainty in policy analysis is crucial. One often overlooked source uncertainty are the forecasts of future baseline conditions (e.g., population, economic output, emissions) from which carbon mitigation benefits are assessed. Through, in some cases highly non-linear relationships, these baseline conditions determine the forecast level and rate of climate change, exposed populations, vulnerability, and way in which inter-temporal tradeoffs are valued. We study the impact of explicitly considering this uncertainty on a widely used metric to asses the benefits of carbon dioxide mitigation, the social cost of carbon (SCC). To explore this question a detailed integrated assessment that couples economic and climate systems to assess the damages of climate change is driven by a library of consistent probabilistic socioeconomic-emission scenarios developed using a comprehensive global computable general equilibrium model. We find that scenario uncertainty has a significant effect on estimates of the SCC and that excluding this source of uncertainty could lead to an underestimate of the mitigation benefits. A detailed decomposition finds that this effect is driven primarily through the role that uncertainty regarding future consumption per capita growth has on the value of inter-temporal tradeoffs through the consumption discount rate.


Introduction
Climate change is one of the most important, but also vexing, problems of our time.Despite the complexity of the issue, inherent uncertainty, and considerable knowledge gaps policy makers are still left with the burden of having to make decisions as to the timing and magnitude of emission mitigation activities.To assist decision makers the research community has developed tools that seek to convey the current state of knowledge about potential welfare losses associated with greenhouse gas (GHG) emissions.These tools serve as only a single input into the process, but provide valuable information about the quantifiable tradeoffs between policy alternatives.The social cost of carbon (SCC) is one of the mostly widely studied and used tools for this purpose.The SCC is a measure of society's willingness to pay to prevent the future damages that will arise from an incremental unit of carbon dioxide (CO 2 ) emissions (typically one metric ton) being emitted in a given year.In principal the SCC summarizes the impacts of CO 2 emissions on all relevant market and non-market sectors, including agriculture, energy production, water availability, human health, coastal communities, biodiversity, and so on.The SCC is of course limited by our knowledge of these complex systems, and is heavily influenced by the uncertainty surrounding the information we do have.An important role for policy analysts is to ensure that the central estimates and distributions of the SCC presented to policy makers correctly capture the known and quantifiable uncertainties associated with the problem.Substantial effort has gone into understanding the role of uncertainty in the climate response to anthropogenic emissions (e.g., Newbold and Daigneault, 2009;Weitzman, 2009) and economics systems (e.g., Anthoff and Tol, 2013) in determining the benefits of CO 2 mitigation as represented by the SCC.However, an often overlooked source of uncertainty are the economic, demographic, and emissions forecasts that define the baseline state of the world under which the impacts of climate change are being assessed.Through, in some cases highly non-linear relationships, these baseline conditions determine the forecast level and rate of climate change, exposed populations, vulnerability, and the way in which inter-temporal tradeoffs are valued.In many cases estimates of the SCC are based on a single socioeconomic-emissions scenario, determined to be representative of the possible states of the world (e.g., Hope (2013), Nordhaus (2010)).In other cases sensitivity analysis has been performed and the SCC estimates have been presented for multiple scenarios without a presumption of which might be more likely (e.g., Waldhoff et al. (2011)).
In others cases the SCC is estimated along multiple scenarios which are then, either explicitly or implicitly, given probabilities to generate an overall distribution (USG, 2010(USG, , 2013)).What has not been studied in a formal way is the specific impact that uncertainty surrounding future socioeconomic and emissions forecasts has on the benefits of carbon mitigation policies, as measured by the SCC.This paper seeks to fill that gap.
While a detailed analysis of the impact of scenario uncertainty on the benefits of carbon mitigation has not been previously conducted, there have been a few studies that incorporate a general representation of such uncertainty within a larger uncertainty analysis of the SCC.Newbold et al. (2013) and Anthoff and Tol, 2013 both include adhoc representations of uncertainty around exogenous scenario forecasts though they take very different approaches.Newbold et al. (2013) specify probability distributions over the rate at which key socioeconomic variables, such as population and economic output per capita, will converge to deterministic long run values.Anthoff and Tol (2013), on the other hand, allow the initial rate of growth in the state variables to be equal across potential scenarios and instead specify distributions for the long run differentiation in socioeconomic conditions.In both cases the distributions that define uncertainty in future socioeconomic conditions are defined as independent for simplicity with the potential for internal inconsistencies arising in some simulations.Nordhaus (2011) offers slightly more consistency by defining distributions over key parameters (total factor productivity growth, population growth, carbon intensity of economic output) within a basic exogenous growth model to incorporate uncertainty about future socioeconomic conditions and CO 2 emissions into estimates of the SCC.
As noted by Newbold et al. (2013), a preferred approach would be to generate a set of probabilistic scenarios using a comprehensive computable general equilibrium (CGE) model that is capable capturing key feedbacks and interdependencies across the sources of uncertainty.Assigning probabilities to a set of scenarios developed using a CGE model ex post will be, at least in part, an inherently arbitrary process.To define a defensible set of probabilities for scenarios one must account for the underlying uncertainty within the economic, social, and political systems in a systematic way and allow those assessments to determine the relative likelihood across a consistent set of forecasts.
Recently Abt (2012) undertook such an exercise as a followup to the work of Webster et al. (2002).Using empirical assessments and expert elicitation to characterize key parametric and stochastic uncertainties associated with scenario development, they calibrated MIT's Emission Prediction and Policy Analysis (EPPA) global CGE model to develop sets of socioeconomic-emissions scenarios with explicit probabilities.
We update these libraries of scenarios for use with the Climate Framework for Uncertainty, Negotiation, and Distribution (FUND) integrated assessment model (IAM), which couples climate and economic systems to assess the monetized damages associated anthropogenic GHG emissions.Using these libraries of probabilistic scenarios in conjunction with the FUND model we assess the impact of uncertainty in socioeconomic-emissions forecasts on estimates of carbon mitigation benefits, as measured by the SCC.Specifically we conduct a series of simulations, each of which considers different sources of uncertainty associated with climate damage assessment.This series of experiments allows us to disentangle the effect of different types of uncertainty on the SCC and any possible interaction between those sources.Specifically we consider uncertainty in baseline socioeconomic conditions, non-U.S.climate policy, sensitivity of climate systems to GHG concentrations and the mapping of climate change to human welfare.We find that incorporating uncertainty about future socioeconomic conditions significantly increases the expected benefits of carbon mitigation and that this effect is mainly through a desire for risk adverse agents to hedge against damages in cases of lower than expected per capita income growth.Furthermore, we find that uncertainty surrounding baseline socioeconomic conditions may be more important for the SCC than uncertainty about the sensitivity of the climate to GHG emissions.
Uncertainty in future GHG emissions is driven by uncertainty in both future socioeconomic conditions and potential climate polices.Therefore it would be appropriate for a nation estimating the benefits of mitigations actions to consider a baseline in which there is uncertainty over future climate policies that are independent of the actions being analyzed.For example, when assessing the benefits of CO2 mitigation the U.S. government currently considers the possibility that in the baseline other nations/regions will adopt climate policies conditional on no further U.S. action beyond what is currently written into law.We specifically analyze the effect of such uncertainty on the SCC by further utilizing the work of Abt (2012) which used an expert elicitation to develop probability distributions over the effective carbon price in regions outside of the U.S. conditional on the assumption that the U.S. takes no further actions to significantly mitigate domestic emissions.We find that the low probability of meaningful action outside of the U.S. conditional on no further domestic action has a negligible effect on the SCC that should be used in U.S. benefit cost analysis.
The remainder of the paper is structure as follows: Section 2 describes the set of probabilistic scenarios and the IAM used in our study, Section 3 presents the main results, and Section 4 provides concluding remarks.

Methods
In this section we describe the methods and tools used to study the effects of scenario uncertainty on estimates of the SCC.We begin by presenting the suite of probabilistic socioeconomic-emissions scenarios used, followed by a brief description of the FUND IAM.The section concludes with a discussion of the techniques used to adjust the suite of probabilistic scenarios to be compatible with the FUND model.

Probabilistic Scenario Libraries
The foundation for the probabilistic socioeconomic-emissions scenarios are a set of libraries developed using MIT's Emission Prediction and Policy Analysis (EPPA) model by Abt (2012) and available from the National Center for Environmental Economics at U.S. Environmental Protection Agency. 1 EPPA is a recursive dynamic global CGE model designed to generate projections of economic growth and anthropogenic emissions of greenhouse gases and aerosols (Paltsev et al., 2005).The model includes 16 economic regions connected through international trade, and relatively high resolution in the energy sector.To develop the libraries of probabilistic scenarios Abt (2012) defined probability distributions for key parameters of the model including: elasticities of substitution, labor productivity growth, autonomous energy efficiency improvement, fossil fuel resource availability, population growth, urban pollutant trends, future energy technologies, non-CO 2 GHG trends, capital vintaging, and carbon prices outside of the U.S. The probability distributions were derived from a combination of empirical analysis and expert elicitation.To populate the scenario libraries the EPPA model was run 400 times using Latin-Hypercube sampling from the parameter distributions.Two separate libraries of potential baseline scenarios were developed: one with no additional climate policy in any region, and one with the possibility of non-U.S.climate action conditional on no new U.S. mitigation policies.
Detail information about the development of the probabilistic scenarios are available from Abt (2012).
Efforts to estimate the SCC have typically relied on deterministic socioeconomic-emissions scenarios, such as those from in the Special Report on Emissions Scenarios from the Intergovernmental Panel on Climate Change (Nakicenovic et al., 2000) or those developed during exercises by the Stanford Energy Modeling Forum (EMF) (see Clarke et al. (2009) for a description of EMF-22).For example, both the 2010 and 2013 estimates of the SCC by the U.S. federal government were based on a set of five scenarios derived from the EMF-22 exercise (USG, 2010(USG, , 2013)).These scenarios include four reference (business as usual) runs from the IAMGE, MESSAGE, MiniCAM -BASE, and MERGE Optimistic models.The fifth scenario was an average of the 550 ppm CO 2 -e stabilization without overshoot runs from the same set of four models.Each of the five scenarios was given equal weight (20% probability) in developing the final SCC estimates.Figure 1 provides a comparison between the library of probabilistic socioeconomic-emissions scenarios derived from the EPPA model and the five deterministic scenarios from the EMF 22 exercise used by the U.S. government. 2We present this comparison to provide context for the uncertainty captured within the libraries of probabilistic scenarios.
In general the EPPA model is more optimistic about economic growth during the beginning to middle of the century, though a number of the EMF 22 scenarios project higher economic growth during the later part of the century bringing levels in line by 2100.The five deterministic scenarios track the mean population projection in the EPPA library, but their range is very narrow relative to the 95% confidence interval contained within the probabilistic scenarios.The policy case used in the USG SCC estimates is substantially below even the lower end of the 95% confidence interval for the probabilistic scenarios suggesting the probabilistic scenarios place a far smaller probability on the possibility of substantial international climate action absent of further U.S. action.For the probabilistic scenarios Abt (2012) determined the likelihood of non-U.S.climate policy through an expert elicitation from which regional and temporal conditional distributions for carbon prices outside of the U.S were derived.The probability of significant mitigation policies being adopted outside of the U.S., under the condition of no further U.S. action, was deemed to be quite low by the expert panel and therefore the two libraries of probabilistic scenarios are relatively similar.Figure 2 compares the projected global CO 2 emissions with and without the potential for non-U.S.carbon mitigation policies.The potential for such non-U.S.policy does not notably change the distribution of economic output forecasts and is assumed to have no effect on population.The inclusion of policy uncertainty has a small, but less than for CO 2 , impact on global CH 4 emissions but the effect on other GHG emissions is negligible.

FUND Integrated Assessment Model
The FUND Integrated Assessment Model (IAM) couples basic representations of atmospheric and climate systems with economic systems in order to estimate the monetized welfare impacts of climate change (Anthoff and Tol, 2013).
FUND has a spatial resolution of 16 national or multi-national regions and damage sectors spanning: agriculture, forestry, sea level rise, cardiovascular and respiratory mortality and morbidity due to extreme temperatures, malaria, dengue fever, schistosomiasis, diarrhea, energy consumption for space heating and cooling, water resources, biodiversity loss, and tropical and extra-tropical storms.In this paper we use version 3.8 of the model, for which the source code is available at http://www.fund-model.orgalong with more detailed technical information.
The model is run from 1950 onwards to initialize the model in terms of both the climate and economic systems.For the economic systems this allows the model to resolve important lagged effects whereby the rate of climate change is important for understanding agents' ability to react.In the majority of cases the model's parameters are defined by probability distributions and therefore Monte Carlo simulations are use to estimate a sampling distribution of net present value of climate change damages (the SCC).In this case we use 10,000 simulations, which provide standard errors that are on the order of less than 2% of the mean SCC.
We maintain all of the default assumptions for the model's parameters except for the socioeconomic-emissions scenarios (including the starting regional population and economic growth), the endogeneity of emissions pathways, equilibrium climate sensitivity distribution, and the coastal protection algorithm.By default FUND is designed to estimate regional anthropogenic CO 2 emissions as proportional to economic output, where the proportion is based on the time period's energy and carbon intensity of production for the region.The growth rate of economic output, regional energy, and carbon intensity of production are specified exogenously, however, within the model the level economic output is adjusted based on the level of climate change induced damages in market sectors.This leads to realized emissions that are slightly different from the "no damage" emissions scenario that would be projected solely based on the exogenous inputs.This specification is potentially problematic as it does not take into account how climate change may alter the carbon intensity of production.For example, one of the most important damage categories within FUND is the increased demand for space cooling (Anthoff and Tol, 2013).It is likely that the carbon intensity of the production offset by increased expenditures on space cooling would be relatively lower and therefore overall CO 2 would increase (Cian et al., 2007).However, the FUND model by default would assume that these changes lower emissions.Incorporating a more complete framework for endogenous emissions is beyond the scope of this paper, and therefore we chose to impose the emissions scenarios exogenously.We note that whether or not emissions are endogenized in the default manner used by FUND has a negligible effect on the mean SCC (significantly less than 1% in a default FUND run).
A key factor in determining the benefits of carbon mitigation is the response of the climate to GHG emissions.
This characteristic of the climate is commonly represented through the equilibrium climate sensitivity which measures the increase in mean global and annual temperature in equilibrium from a sustained radiative forcing equivalent to a doubling of atmospheric carbon dioxide over pre-industrial levels.Measuring the aggregate strength of the numerous climate feedbacks is inherently uncertain and the distribution over potential values is often subject to a large variance and slowly diminishing upper tail (Roe and Baker, 2007).It has been shown that in some settings, even with only a small probability, the chance of a strong climate response to increasing atmospheric GHG concentrations has significant implications for the benefits of carbon pollution mitigation (Weitzman, 2009).To represent the equilibrium climate sensitivity we use a inverted truncated normal distribution as proposed by Roe and Baker (2007)  The other modification we make to the FUND model is with respect to the algorithm used by the model to determine the behavior of regional decision makers in building coastal protections in response to expected sea level rise.
By default FUND assumes highly myopic decision makers that respond instantaneously to any annual change in the relevant state variables based on the assumption that these deviations from past trends will persist into perpetuity.This representation can lead to instability when considering scenario uncertainty that is, in part, determined by stochastic shocks. 4Without modification some runs show regional decision makers moving from protecting a large proportion of their coast in one year, to stopping nearly all coastal protection programs in the next year, only to reverse that decision in the following year.We choose to avoid this instability by modeling regional decision makers as using a 20 year moving average of state variable trends when forecasting future conditions to determine coastal protection efforts.Appendix A has further details about adjustments made to the coastal protection algorithm and damages from sea level rise.requires specifications for the regional population and gross domestic product (GDP) per capita growth rates.All specifications must cover the years 1950 onwards, in annual time steps.The probabilistic scenario libraries described in Section 2.1 provide projections for all of these variables for the 16 EPPA regions between 1997 and 2100 in five year time steps starting in 2000.To use the libraries of probabilistic scenarios with FUND we need to map the projections from EPPA regions to FUND regions, construct pathways for the variables from 1950 to 2000, and extrapolate the scenario past 2100.We discuss each of these steps in turn.

Probabilistic Scenario Libraries for FUND
3 Specifically the equilibrium climate sensitivity distribution is defined as λ / (1 − f ), where λ = 1.2 C is the reference (grey-body) climate sensitivity and f is a normal random variable with mean 0.696 and standard deviation 0.389 truncated from above at 0.88.This provides a mean of 3.22 C and allows for approximately 66% of the mass to lie between 1.5 C and 4.5 C. 4 The stochasticity is introduced in the development of the scenarios with EPPA and not within the FUND model itself.The projections in the original library of scenarios described in Section 2.1 are available for the 16 regions modeled within EPPA.These regions are not the same as the 16 regions modeled within FUND.Table 1 lists the regions in each model.In some cases EPPA regions are a direct, or fairly comparable, match to a region in FUND.These include the United States, Canada, Western Europe, the Former Soviet Union, China Plus, and Australia and New Zealand.In the case of Western Europe there are some small discrepancies, such as whether the Channel Islands are included, but these differences are negligible relative to the region.In the case of China Plus, FUND includes Macao, Mongolia, and North Korea whereas those are listed in the "Rest of World" region in EPPA.Since these countries represent a negligible percentage of the region's level in any of the scenario variables we consider them sufficient to be considered a direct mapping.For the remainder of the FUND regions we adopt the mapping in the last column of Table 2.This represents the most parsimonious mapping possible.
In order to calibrate the mapping parameters we use country level projections for the scenario variables (population and GDP per capita growth).This data is aggregated up to the regional scale for both the FUND and EPPA regions and used to directly solve for a set of mapping parameters.To calibrate the population and GDP per capita mapping parameters we use the CEPII database reflecting country level projections out to 2050 (Foure et al., 2012).The parameters we use in our regional mapping are defined as the average projected in the CEPII database between the years 2000 and 2050.This approach implicitly assumes that shifts in the regional variables will be spread evenly across  the countries within the EPPA regions. 5The specific estimates for the mapping parameters are presented in Table 3.
Since the climate model in FUND is resolved based on global emissions we do not specify mapping parameters for emissions data.

Historic Scenario
In order to calibrate the historic  population we use the United Nations Population Division database (UN, 2013) to derive estimates of the population growth rate for the FUND regions.These growth rates are used to define the historic population scenario based on the regional populations in 1997 as derived in Section 2.3.1.To calibrate historic GDP we use the time series of GDP and population estimates from Maddison (2003) to derive GDP per capita growth rates for the FUND regions.These growth rates are then applied to the 1997 levels of population and GDP derived in Section 2.3.1 to produce a historical GDP scenario.For consistency we use the historical emissions data from Asadoorian et al. (2006) which was designed to match up with emissions forecasts from the EPPA model.
Since the FUND climate model is resolved from global emissions no further assumptions about regional mappings are required.

Extrapolation Past 2100
The EPPA scenario libraries are only computed out to the year 2100 but given the long term nature of the climate change problem we run the FUND model out to 2400 to capture the long term impacts of carbon emissions.This process requires extrapolating the scenarios past 2100.We adopt reasonable central assumptions that have been used elsewhere in the climate economics literature, but note that clearly any forecast out this far in time will be fraught with uncertainty.Therefore we examine the sensitivity of our results to these assumptions by considering uncertainty over these extrapolations as represented by wide uninformed priors.
It has often been noted that in the long term there are reasons to expect a decline in the global GDP per capita growth rate relative to current conditions.Some have argued this on the basis that current rapid growth in (some) developing nations, in part fueled by knowledge and technology transfers, will converge to that of developed nations (Lucas, 2000;Helpman, 2009).Others have suggested that finite supplies of natural resources will ultimately place constraints on perpetual economic growth (Meadows et al., 2004).Following Newbold et al. (2013) we assume a long run GDP per capita growth rate of 1%, which we implement through a linear decline from 2100 to 2300.When considering uncertainty over the long term GDP per capita growth rate we use a uniform distribution ranging from 0% to 2% with the lower bound being consistent with the assumptions of USG (2010) and an upper bound representative of the average global growth rate over the past six decades (Maddison, 2003).This range is also inclusive of the assumptions made in other climate economics studies (e.g., Nordhaus, 2010, Anthoff andTol, 2013 ).
Long term exogenous population projections, used in climate economics and elsewhere, tend to be based on reaching a replacement fertility rate where the population growth rate ultimately becomes zero.While there seems to be some comfort with this general assumption, with Cohen (1995) going so far as to suggest that it is "the one irrefutable proposition of demographic theory," the point in time at which the replacement rate is reached can vary widely between projections.For our central tendency we follow USG (2010) in assuming the population growth rate will reach zero in 2200, an assumption similar to the projection of Nordhaus (2010).For simplicity, we implement this assumption as a linear decline from the 2100 growth rate.When considering uncertainty over this assumption we use a uniform distribution ranging from 2150 to 2250.The lower end of this range is similar to assumptions by Anthoff and Tol (2013) and the upper end is consistent with an extrapolation of an exponential decline in the population growth rate based on projections by the The World Bank (2013).
Changes in the CO 2 emissions intensity (CO 2 per unit of economic output) are the result of numerous factors including relative energy trends, technological change, and governmental policies.As noted by Nordhaus and Boyer (2000), in the long run baseline CO 2 emissions intensity will be driven by the escalating price of carbon based fuels due increasing scarcity and extraction costs and the declining price of non-emitting energy sources due to technological advancements.Following Nordhaus (2010) we assume that CO 2 emissions intensity reaches zero in 2250 as nonemitting technologies become cheaper than the remaining fossil fuel resources.For simplicity we implement this transition from the 2100 CO 2 emissions intensity linearly.When considering uncertainty over this assumption we use a uniform distribution over the year in which the economy reaches decarbonization in the baseline with a range of 2150 to 2350.For non-CO 2 emissions we assume that they remain constant at their 2100 levels as this assumption has little effect on the mean social cost estimates compared to alternative assumptions.
We recognize that there is the potential for correlations between these distributions and the potential for further study to provide improved assessments of the underlying distributions of these extrapolation assumptions.We do not present these assumptions as a state of the art assessment or the most defensible approach to extrapolate socioeconomic and emissions projections far out into the future.Instead we suggest that these assumptions are a reasonable approach to scope out the impact of such uncertainty where the results may be used to inform the value of future efforts to study alternative approaches and calibrations.

Results
Uncertainty surrounding the benefits of mitigating CO 2 emissions arises from a number of sources in addition to the forecasts of future socioeconomic and emission trajectories.Two of the most notable sources are the strength of the climate response to GHG emissions and the mapping of climate change to human well being.As discussed previously, the FUND model incorporates uncertainty over the strength of the climate response through the equilibrium climate sensitivity distribution and uncertainty over the welfare impacts of climate change by defining probability distributions for most of the parameters in the model's damage functions.Given these multiple sources of uncertainty we consider a set of 9 cases that allow us to understand the relative effects of the different sources of uncertainty (socioeconomic, climate sensitivity, damage parameters, and non-U.S.carbon policy) and the interactions between them.Table 4 presents the sources of uncertainty included in each of the 9 cases.Case 1 is a fully deterministic case with all variables set to their means, while cases 2-4 introduce a single source of uncertainty each.Cases 5-7 consider interactions between two sources of uncertainty and case 8 considers uncertainty over all non-policy parameters.In the final run, case 9, we add uncertainty over non-U.S.climate policy conditional on no further U.S. action.We

Included Features Case Number
1 2 3 4 5 6 7 8 9 10 Socioeconomic Uncertainty X X X X X X Climate Sensitivity Uncertainty X X X X X X Damage Parameter Uncertainty X X X X X X Policy Uncertainty X Extrapolation Uncertainty X Table 4: Case Definitions note that uncertainty in socioeconomic conditions will also lead to uncertainty in emissions but refer to this source as socioeconomic uncertainty to denote the difference from policy uncertainty.
Given the important role of discounting in the estimation of the SCC we consider a series of five specifications to understand important interactions between the underlying assumptions of social preferences and the sources of uncertainty.The per period consumption rate of discount, r t , used in estimating the SCC is defined based on the Ramsey formula where ρ is the pure rate of time preference, 1/η is the elasticity of intertemporal substitution, and g t is the growth rate of per capita consumption in period t.We consider four variable discount rates based on commonly applied values for ρ (1% and 0.1%) and η (1.0 and 1.5).We also consider a constant discount rate of 3% (mathematically represented as ρ = 0.03 and η = 0) to understand how the correlation between the consumption rate of discount and socioeconomic conditions influences the impact of scenario uncertainty on the SCC.
The main results of this paper are presented in Table 5, which lists the mean SCC estimates in 2015 for each of the 10 cases along with their standard errors.In comparing cases 1 and 2 one is presented with the impact of adding in socioeconomic uncertainty to an otherwise deterministic model.The role of socioeconomic uncertainty in estimating the SCC may be understood by noting that the relative effect is strongly driven by the value of η, such that for the constant discount rate introducing scenario uncertainty has no effect, a 5-10% effect for a value of η = 1.0, and an effect of 25-30% in the case of η = 1.5.These results suggest that the primary effect of considering uncertainty in forecasts of baseline conditions occurs through its role in determining the effective consumption discount rate.
Uncertainty over future income growth leads to an increases in the willingness to sacrifice in the current period to hedge against the potential that additional damages (in this case from climate change) will be born in future periods with lower than expected per capita consumption growth (Gollier, 2008).This leads to an increase in the estimate of the mean SCC.Because the parameter η serves a measure of risk aversion in this setting, the relative effect of socioeconomic uncertainty increase with η as suggested by the theoretical work of (Gollier, 2007).0 65 71 (0.6) 63 (0.6) 137 (1.2) 72 (1.1) 127 (1.7) 150 (1.8) 140 (2.5) 136 (2.3) 141 (2.9)  0.030 0.0 11 11 (0.0) 11 (0.0) 25 (0.2 To further examine this effect of socioeconomic uncertainty we follow Weitzman (1998) and consider the certaintyequivalent forward rate for discounting between adjacent periods where E [P t ] is the expected discount factor where r s is the consumption discount rate as defined in (1).We then define the certainty equivalent consumption discount rate for discounting period t back to the present as rt = 1 t ln t ∏ s=0 exp (r s ) .
Figure 3 presents the certainty equivalent consumption discount rate for the deterministic case 1 along with case 2 where socioeconomic uncertainty is introduced for ρ = 0.001 and η = 1.5. 6Even though case 1 represents a completely deterministic setting the consumption discount rate still declines over time due to a population growth rate that is higher than the economic growth rate, leading to declining consumption per capita growth over the time horizon.However, with the inclusion of uncertainty over socioeconomic forecasts the certainty equivalent discount rate is significantly lower.By 2200 the certainty equivalent discount rate is 10% lower when socioeconomic uncertainty is considered.This decrease in the effective discount rate results in the main source of the increase in the estimates of the mean SCC seen in Table 5.
To put this effect in context we note that the impact of adding only uncertainty over the equilibrium climate sensitivity to the deterministic model (case 3 compared to case 1) yields a relatively smaller impact in most cases.The inclusion of uncertainty over the equilibrium climate sensitivity places a small amount of downward pressure on the mean SCC.This stems, in part, from the fact that FUND forecasts some benefits in low levels of warming due to increased productivity in the agricultural and forestry sectors and reduced demand for space heating.As a result the annual damages in FUND are decreasing with respect to the equilibrium climate sensitivity parameter in the near term, an effect which helps net out future increases in damages from higher levels of warming due to discounting. 7t is the incorporation of uncertainty over the parameters of the damage functions that has the greatest impact on the mean SCC estimates.Moving from the deterministic case (case 1) to one in which only damage function uncertainty is considered (case 4) increases the mean SCC estimate by 110-140%.
The interaction cases of 5-7 provide similar intuition to the earlier runs.In case 5 we take the socioeconomic uncertainty run of case 2 and add in uncertainty over the equilibrium climate sensitivity parameter.As was the case earlier, this addition results in a slight decrease in the mean SCC.Similarly in case 6 we take the damage function uncertainty run in case 4 and add in uncertainty over the equilibrium climate sensitivity parameter, and again find a slight decrease in the mean SCC, though the effect is greater with uncertainty over the damage function parameters.In case 7 we include uncertainty over both the damage function parameters and socioeconomic conditions.The resulting mean SCC is higher than the case with only uncertainty over the damage function parameters (case 4) and again the increase is absent for the constant discount rate and, as a percentage, increases with η.This suggests that even with uncertainty over the damage function parameters the primary role of uncertainty in socioeconomic conditions is through the effective discount rate.In similar fashion, adding climate sensitivity uncertainty (case 8) results in a small decrease in the mean SCC relative to the case with uncertainty over the damage function parameters and socioeconomic conditions (case 7).
Our core finding, that uncertainty over the forecast of the socioeconomic scenarios affects the SCC primarily through the consumption discount rate, can be further illustrated by considering the simulated SCC distributions.
We compare the typical case studied with uncertainty over equilibrium climate sensitivity and damages function parameters (case 6) to the addition of socioeconomic uncertainty (case 8). Figure 4 presents the simulated 2015 SCC distributions for both the case of a variable discount rate (Figure 4a) and a constant discount rate (Figure 4b).As may seen, in the case of the constant discount rate there is no significant change in the shape of the distribution and in turn the mean SCC.However, in the case of the variable discount rate there is a significant increase in the variance of the SCC estimates.This is evident by the increase in the mass at both the upper and lower tails of the distribution.In terms of there effect on the mean SCC the increase in the upper end of the tail dominates.
In case 9 we add in the probability of climate policy outside of the U.S. conditional on no additional GHG mitigation policies within the U.S. as described in Section 2.1.Given the very low probability assigned by the expert panel to the possibility of significant mitigation action outside the U.S., the results in Table 5 are as expected with the additional non-U.S.climate policy uncertainty having only a small affect on the mean SCC.This result is relatively constant across the entire SCC distribution as is shown in Figure 5.In most cases there is a slight decrease in the mean SCC when the non-U.S.climate policy uncertainty is included, but this difference is close to the standard error in magnitude except for case with a relatively low effective discount rate.
In Case 10 uncertainty over the post-2100 extrapolation assumptions in introduced to Case 8 which included uncertainty over the socioeconomic, equilibrium climate sensitivity, and damage function parameters.This additional uncertainty increases the expected SCC estimates by less than 2% despite the wide range of scenario uncertainty introduced.Furthermore in all discounting specifications the increase in the mean SCC is within the standard error of the estimates.It is important to note that this results does not suggest that the events past 2100 are irrelevant for estimating the SCC.In both Case 8 and Case 10 the 50-85% of the mean SCC estimates are due to the perturbation's incremental damages past 2100 depending on the discounting specification (the majority of this is due to damages prior to 2200).Instead this result suggests that for the purpose of estimating the benefits of of near term CO 2 mitigation on the margin, uncertainty over the baseline socioeconomic and emissions conditions past 2100 may not have a significant role in determining the mean SCC estimates.

Concluding Remarks
The benefits of carbon mitigation are subject to numerous sources of uncertainty, and accounting for this uncertainty in policy analysis is crucial.One often overlooked source uncertainty are the forecasts of future baseline conditions from which carbon mitigation benefits are assessed.Baseline characteristics of concern include regional assessments of economic activity, population growth, and emissions of GHGs and tropospheric aerosols.Through, in some cases highly non-linear relationships, these baseline conditions determine the forecast level and rate of climate change, exposed populations, vulnerability, and way in which inter-temporal tradeoffs are valued.We study the impact of explicitly considering this uncertainty on a widely used measure for the benefits of CO 2 mitigation, the SCC.We use a detailed IAM that couples economic and climate systems to assess the damages of climate change in conjunction with a library of consistent probabilistic socioeconomic-emission scenarios to explore this question.
Our results show that assuming a deterministic central estimate for the future socioeconomic state of the world may lead to a significant underestimate of the expected benefits of carbon mitigation.We find that the error introduced by ignoring uncertainty about future socioeconomic conditions could be larger than than the error associated with excluding uncertainty about the sensitivity of the climatic response to GHG emissions.Furthermore, we find that the uncertainty about future socioeconomic conditions may be substantially more important for assessing intertemporal tradeoffs, as defined by the effective consumption discount rate, as opposed to assessing the vulnerability of regions and sectors to forecast climate changes.The relative impact of this effect is higher for cases where a greater rate of relative risk aversion is assumed, as there is a greater desire to hedge against the possibility of climate damages occurring in cases of lower than expected income per capita growth.
We also consider the impact of allowing for the possibility of additional regional or international carbon policy conditional on the assumption that the U.S. takes no further action to significantly reduce GHG emissions.Allowing for this additional policy uncertainty has little to no effect on the distributions of economic activity and population, and only a minimal change in global CO 2 emissions.Our results suggest that the expected SCC estimates are not affected by the inclusion, or conversely the exclusion, of such uncertainty.The small size of the effect is primarily driven by the low conditional probability placed on significant international action absent U.S. involvement by the expert panel that was convened by Abt (2012) to develop the set of probabilistic scenarios.Given the negligible quantitative effect of such uncertainty, the inherent issues associated with assessing the conditional regional carbon price distributions, and the resulting nation specific SCC estimates it may be preferable to exclude such policy uncertainty in estimates of the SCC.
The FUND model used in this paper represents a detailed accounting of what we currently know and can reasonably quantify about the potential damages associated with future climatic changes.For this reason it has been widely used throughout the academic community (Tol, 2008) and by governments (USG, 2013).However, it is only one of a handful of models that have been proposed to estimate the SCC.A main difference between models is that FUND is based on a detailed sectoral accounting of damages where as other models, such as those by Nordhaus (2010) and Hope (2013), estimate damages as a proportion of regional GDP.In such cases uncertainty over socioeconomic conditions may have additional effects.It is also worth noting that while it is widely recognized that IAMs provide valuable information about the potential welfare losses associated with GHG emissions they do not represent a complete accounting of the welfare risks, particularly when it comes to difficult to assess unmanaged systems such as ecosystems, tropical cyclones, and oceans (Nordhaus, 2013).However, it is unlikely that such omissions would affect our finding that scenario uncertainty through its impact on the effective consumption discount rate has a significant effect on the expected benefits of CO 2 mitigation.Though, it may be the case that such omissions are important for understanding the relative effects of different sources of uncertainty.

A.1 Wetland and Dry Land Loss
In the model of Fankhauser (1995) the change in wetlands was due to annual inland migration of existing wetlands on an unprotected coastline increasing their area over time and an inundation due to sea level rise which reduced their area.The damages associated with changes in the area of wetlands was W L = ∆W t,r R W t,r , where ∆W t,r [km 2 ] is the change in wetland area and R W t,r [$/km 2 ] is the value of ecosystem services from wetlands.In the approach taken by Fankhauser (1995) ∆W t,r was used to represent cumulative change in wetland area through period t and R W t,r represented an annual flow of consumption equivalent welfare per square kilometer of wetland.In FUND R W t,r was chosen to account for the present value of all future services that would have been provided by a unit of wetlands at the time it is lost.The value of wetlands is assumed to be increasing in the region's per capita income, y r,t , and population density, d r,t [people/km 2 ] and decreasing in the region's existing wetland area, W t,r .Specifically where α [$/km 2 ] represents the present value of ecosystem services associated with a km 2 in the base year τ and W τ,r [km 2 ] is the area of wetlands present in the region in the base year.8 To ensure cohesion with this approach the FUND model uses ∆W t,r to represent not the cumulative change in wetlands through period t but instead the change in wetland area in period t.Therefore in FUND the change in wetlands is based not on the cumulative level of sea rise, S t , but instead the annual change in sea level, ∆S t .For every meter of sea level rise in a given year it is assumed that ω s r square kilometers of wetlands will become inundated and in turn lost forever.It is also assumed that if the region's coast were unprotected the wetlands would migrate such that ω m r additional square kilometers of wetlands would be gained per meter of sea level rise that occurred that year.It is further assumed that this gain will be limited by coastal protections in a perfectly proportional manner to the fraction of the coastline protected, following Fankhauser (1995).Therefore the total area of wetlands lost in a given year due to sea level rise is where Wr [km 2 ] is the area of the region's wetlands that are exposed to sea level rise, and θ t,r ∈ [0, 1] is the fraction of the coastline that is assumed to be protected from current years increase in sea level.The min operator ensures that the region cannot lose more wetlands than those that are exposed to changes in sea level.
The general differences between FUND and the model of Fankhauser (1995) are similar in the case of dry land as they were for wetlands.The damages associated with changes in the area of dry land was DL = ∆D t,r R D t,r , where ∆D t,r [km 2 ] is the change in dry land area and R D t,r [$/km 2 ] is the value of dry land.In the approach taken by Fankhauser (1995) ∆D t,r was used to represent cumulative loss of dry area through period t and R D t,r represented an annual flow of consumption equivalent welfare per square kilometer of dry land.Analogous to the case with wetlands, in FUND R D t,r was chosen to account for the present value of all future services that would have been provided by a unit of dry land at the time it is lost.The value of dry land is assumed to change over time only with changes in the region's income density, such that where φ [$/km 2 ] is the baseline value of dry land for the reference level of income density Λ [$/km 2 ], Y t,r [$] is the region's GDP, A t,r [km 2 ] is the region's area net of land loss to date, and ζ is the elasticity of dry land value with respect to income density.One important difference to note between FUND and the model of Fankhauser (1995) is that in the later it was assumed that regional decision makers would choose to build sea walls such that they protect the most valuable land first.Therefore the value of dry land was decreasing in the fraction of the coast line protected.
In FUND the value of dry land per km 2 is assumed to be independent of the level of coastal protections.
In FUND the annual area of dry land lost, ∆D (∆S t , θ t,r ) = ∆D t,r [km 2 ], occurs simply due to the inundation of land by the sea, and is assumed to be a power function with respect to sea level rise in a given year.Specifically if no coastal protections are erected in year t the area of dry land lost is min Dr − where Dr represents the total are of dry land in the region that is exposed to sea level rise.However, since the region has the ability to erect coastal protections that can protect the threatened land such that the actual loss of dry land will be A.2 "Optimal" Level of Coastal Protection In FUND the cost of coastal protections are similar to those used by Fankhauser (1995).In FUND it is assumed that the cost for a region to protect its entire coastline for one meter of sea level rise in a given year, π r [$/m], will be constant over time and sea level.It is assumed that if the region erects coastal protections for any part of their coastline they will do so as to protect against the full increase in sea level for that year.Furthermore, it is assumed that the cost will scale proportionally with the fraction of the coastline protected such that the total cost of protection in a given year will be θ t,r π r ∆S t .
In FUND, as with the work by Fankhauser (1995), the optimal level of coastal protection is said to be chosen through a simple cost benefit analysis used to mimic the behavior of regional decision makers.The FUND documentation does not provide the details of the objective function used by the regional decision makers, but does posit that the solution is equivalent to the form derived by Fankhauser (1995).Specifically the FUND model assumes the "optimal" solution to be for interior solutions and θ * r = 0 otherwise.Based on (9) the cost of protecting the coastline is The lost value of inland wetland migration due to sea level rise that would be lost from coastal protections is derived from (4) and ( 5) such that W G (θ t,r , ∆S t ) = θ t,r ω m r ∆S s R W r,t .
The value of lost dry land due to sea level rise is derived from ( 6) and ( 7) such that DL (θ t,r , ∆S t ) = (1 − θ t,r ) min Dr − As noted above, in FUND the simplifying assumption is made that regional decision maker's expectation in every period is that future income per capita growth and sea level rise will be equivalent to what is being experienced in the current period, such that g s,r = g t,r ∀s ≥ t and ∆S s = ∆S t ∀s ≥ t.It is also assumed that the regional decision maker is choosing the "optimal" level of protection as if it will be constant from the current period into the future, θ s,r = θ t,r ∀s ≥ t.Given this assumption (10) may be rewritten as where w t−1 represents the growth of wetlands such that, This solution as implemented in the model's source code is potentially problematic as it does not solve the correct objective function described in the model.Given the description of the coastal protection problem described above the minimization problem for the regional decision maker may be written as Noting the assumption that regional decision maker in any given period will expect the future conditions (e.g., growth of sea level, income growth, etc.) to be the same as the current period means that everything in the problem is constant except for the exponent on the discounting component and expected changes to the value of wetlands and dry land.
Therefore the problem in ( 16) may be rewritten as min

Figure 1 :
Figure 1: Comparison with the EMF 22 Scenarios based on the nature of the underlying uncertainty.The parameters of the distribution are calibrated based on the consensus statement by the Intergovernmental Panel on Climate Change in their Fifth Assessment Report (AR5) that the equilibrium climate sensitivity is "likely" between 1.5 C and 4.5 C (IPCC, 2007).Since the IPCC did not specify a central tendency in AR5 we refer to the analysis of the Coupled Model Intercomparison Project 5 by Forster et al. (2013) who found a mean equilibrium climate sensitivity of 3.22 C. 3 Figure 3: Certainty Equivalent Consumption Discount Rate (ρ = 0.001, η = 1.5) Figure 4: Effect of Scenario Uncertainty on the 2015 SCC Distribution

Table 1 :
Regions in the FUND and EPPA Models 2.3.1 Mapping Projections from EPPA to FUND Regions

Table 2 :
Regional Mapping from EPPA to FUND

Table 3 :
EPPA to FUND Mapping Parameters