Clean Techn Environ Policy DOI 10.1007/s10098-015-0978-x

ORIGINAL PAPER

The impact of time horizon on integrated climate assessment models Kum Yeen Wong1 • Joon Huang Chuah2,3 • Chris Hope1

Received: 2 October 2014 / Accepted: 20 May 2015 Ó Springer-Verlag Berlin Heidelberg 2015

Abstract The PAGE09 model is a revised version of the earlier PAGE2002 and PAGE95 integrated assessment models (IAMs) that have been extensively used to evaluate climate change impacts and the social costs and benefits of different abatement and adaptation policies under uncertainty. This paper investigates the use of the latest PAGE09 model as a policy-oriented tool in determining an efficient climate change policy that internalises the mean social cost of carbon dioxide (SCCO2). We show that the choice of final analysis year, time horizon and the carbon dioxide (CO2) emissions pathway in the PAGE09 model do significantly affect the model results for the SCCO2 and its trajectory over time and so the prescriptions of future climate policy. Further analysis shows that a constant time horizon and a slight modification of the penultimate analysis year which is currently fixed in the default model help avoid the underestimation of the SCCO2 in future years. This paper also highlights the potential benefit of a consensus position on the specification of time horizon for the development of future IAMs to aid policy making. Keywords Integrated assessment models  Time horizon  Social cost of carbon dioxide  Climate policy

& Kum Yeen Wong [email protected] 1

Judge Business School, University of Cambridge, Trumpington Street, Cambridge CB2 1AG, UK

2

Division of Electrical Engineering, Department of Engineering, University of Cambridge, 9 JJ Thomson Avenue, Cambridge CB3 0FA, UK

3

Department of Electrical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia

Introduction The implementation of climate policies has always been difficult and controversial due to the inevitable uncertainties surrounding climate science (Fullerton et al. 2010; IPCC 2007; Kalkuhl and Edenhofer 2010; Nordhaus 2007a; Roughgarden and Schneider 1999). In order to develop good and sustainable climate policy responses, it is important that policymakers around the world obtain the best possible understanding of the economic and noneconomic impacts of climate change under uncertainty (Stanton et al. 2008). To provide such insights, one of the popular analytical tools used is the integrated assessment model (IAM), a model that combines interdisciplinary economic, environmental and social knowledge to inform and contribute to a better and clearer understanding of the current climate policy debate (Ingwersen et al. 2014; Nordhaus 2011; Stanton et al. 2008). Ever since the first pioneering attempt to determine the social cost of carbon in the early 1980s (Nordhaus 1982), several IAMs with varying complexity, structures and numerical values of key parameters have been introduced to assist in setting climate research priorities, and to help policy analysis and formulation (Clarkson and Deyes 2002; Nordhaus 2011). The aim of this paper is to investigate the use of the PAGE09 model, a well-known IAM, in estimating the marginal social cost of carbon dioxide (SCCO2) that sets the optimal price of carbon dioxide (CO2) for policymaking purposes. Specifically, the original model is enhanced to discover the impact of changing the time horizon specification on the mean SCCO2 and its future trajectory under two future scenarios; the A1B businessas-usual (BAU) and the 2016. R5 low-emissions scenarios.

123

K. Y. Wong et al.

The social cost of carbon dioxide Some studies in the past had suggested that climate change will have only minor economic impacts and had proposed modest controls on greenhouse gas (GHG) emissions. However, Roughgarden and Schneider (1999) pointed out that many of these modest-control policy recommendations were based on best guess point estimate values and thus failed to inform policy makers of risky and potentially catastrophic outlier events. Indeed, in contrast to studies that have examined the economic and non-economic impacts of climate change separately, research that has incorporated both aspects including possible impacts due to an abrupt system change has found that the magnitude of the SCCO2 increases, including the mean SCCO2 of US$85/tCO2 estimated in the Stern Review (IPCC 2007; Stern 2006; Yohe and Tirpak 2008). While Ackerman et al. (2009) suggested that the Stern Review understates the climate change damages, a comparison of studies over the last 12 years shows varying estimates of the marginal impacts of CO2, ranging from US$0.4 to US$445.0/tCO2 as presented in Table 1. With differing approaches and assumptions with regard to the key variables such as the discount rates and damage functions, each IAM gives different estimates of the SCCO2 reflecting the inherent uncertainty surrounding climate change (Bowen and Ranger 2011; Edenhofer and Kalkuhl 2010; Stanton et al. 2008; Stern 2006). Nevertheless, the issue is not which IAM is right, but what policy insights can be gained by comparing between scenarios and models with a clear understanding of the underlying assumptions within the models (Schneider 1997). For instance, despite the difficulty in projecting the future, a general consensus exists that the SCCO2 increases over time as illustrated in Fig. 1 as larger incremental damages are expected as a result of future emissions (Clarkson and Deyes 2002; Interagency Working Group on Social Cost of Carbon 2010).

Existing carbon dioxide prices A review of the existing CO2 prices implemented in various pioneering political economies shows that the rates have been relatively modest (except for Sweden’s high standard rate) as illustrated in Fig. 2. Most of the CO2 prices had been introduced in pioneering developed political economies with an objective to induce conservationbased behaviour and promote overall mindfulness towards energy consumption (Corfee-Morlot and Jones 1992). As mentioned by one of the respondents in the survey by Ekins et al. (2002), ‘‘by putting a value on it, it gives financial justification for doing something’’.

123

Although many European countries introduced taxes on energy products as an instrument to combat climate change in the 1990s, the proposal for a harmonised EU-wide CO2 tax for competitiveness reasons was unsuccessful (Fullerton et al. 2010; Hasselknippe and Christiansen 2003). While the Eu-emissions trading system (EU-ETS), introduced in 2005, is the most substantial application to date, it has failed so far to deliver an adequate stable CO2 price (Ares 2012; Shell International BV 2011). As of 15 August 2012, permits in the EU-ETS Phase II were selling for €7.49 (US$9.96 based on IMF’s 2010 average €/US$ exchange rate of 1.33)/tCO2, that is nearly 90 % lower than the mean SCCO2 of US$85/tCO2 estimated in the Stern Review (Barchart.com Inc. 2012; IntercontinentalExchange, Inc. 2012; Stern 2006). Even though fiscal neutrality is not essential to achieving the objectives of a new CO2 tax policy, most of the countries that had imposed CO2 taxes have their other tax policies adjusted downwards or phased out in order to offset the regressivity of the CO2 tax and avoid the distortionary impact of existing taxes on labour and capital markets (Corfee-Morlot and Jones 1992; Fullerton et al. 2010; Sumner et al. 2009). Instead of a single uniform rate, some countries vary the CO2 tax rates according to the types of energy products and activities being taxed, well illustrating the political compromises that surround the introduction of CO2 taxes (Commission of the European Communities 2005; Ekins et al. 2002).

The PAGE09 model The PAGE09 model is an enhanced version of the earlier PAGE2002 and PAGE95 IAMs that have been extensively used to evaluate climate change impacts and the social costs and benefits of different abatement and adaptation policies under uncertainty (Asian Development Bank 2009; Eliasch 2008; Hope and Watkiss 2010; Stern 2006). The benefit of using the PAGE09 model is its ability to simulate complex results from specialised scientific and economic models using simple equations (Hope 2011d). Also, the PAGE09 model has been updated to incorporate the latest published information (for example, from the 2007 IPCC report) of the possible damages from climate change for eight world regions (Hope 2011b). To account for the large uncertainties in the estimates of climate damages, the PAGE09 model uses a Latin Hypercube Sampling scheme, as compared to ‘‘random’’ Monte Carlo sampling, as the former provides a better coverage of the underlying probability density functions (PDFs) (Hope 2011c). Functional forms are assumed to be known with certainty, while each of the uncertain model parameters is expressed as triangular probability

The impact of time horizon on integrated climate assessment models Table 1 Past literature on marginal impact of CO2 Literature

Emissions year

Marginal impact of CO2 (Mean) US$/tCO2

Assumptions

Ackerman and Stanton (2012) (in US$2007)

2010

445.0

H-W RCP2.6 scenarioa, 1.5 % discount rate

118.0

N-N RCP2.6 scenarioa, 1.5 % discount rate

96.0

H-W RCP2.6 scenarioa, 3 % discount rate

28.0

N-N RCP2.6 scenarioa, 3 % discount rate

51.0

Base socioeconomic scenario, 0.1 % pure time preference rate (‘‘PTP’’)

Anthoff et al. (2011) (in US$1995)

2010

8.3

Base socioeconomic scenario, 1 % PTP

3.3b

A1 scenarioc, 1 % PTP

0.4

Base socioeconomic scenario, 3 % PTP

Hope (2011a) (in US$2005)

2010

106.0 ± 1.5, Interval [12.0, 290.0]

A1B scenarioc, 1 % mean PTP

Nordhaus (2011) (in US$2005)

2015

150.3b 27.8b

Hotelling rentsd on carbon until 2255, then optimal policy, catastrophic damages at tipping point of 3°C Optimal policy, 0.1 % social discount rate

35.1e

EMF-22 scenariof, 2.5 % discount rate

Interagency Working Group on Social Cost of Carbon (2010) (in US$2007)

2010

Nordhaus (2010) (in US$2005) Tol (2010)

e,

21.4 Interval [N/A, 64.9]

EMF-22 scenariof, 3 % discount rate

2010

17.4b 8.9b

2°C temperature target Optimal scenario, no climatic constraints

N/A

20.7b

Meta analysis of mean estimates from 232 published estimates, 0 % PTP

1.4b

Meta analysis of mean estimates from 232 published estimates, 3 % PTP

Weyant et al. (2006) (in US$2000)

2025

27.6b,f

The reference case was defined by each of the 19 modellers’ own assumptions about economic and population growth, future energy prices and rates of technological improvement without considering the Kyoto Protocol’s emission targets

Stern (2006) (in US$2005)

2001

85.0

BAU scenario towards stabilisation at 550 ppm CO2e, 0.1 % PTP

Hope (2006) (in US$2000)

2000

5.0, Interval [1.1, 13.9]b

A2 scenarioc, 3 % PTP

a

Based on the IPCC RCP3-PD emissions scenario (Ackerman and Stanton 2012)

b

Price per tonne carbon divided by 3.7 (44/12)

c

Based on the emission scenarios of the IPCC Special Report on Emission Scenarios (‘‘SRES’’) (IPCC 2007)

d

Time path of maximum value energy resources extraction (Nordhaus 2011)

e

Calculated using combination of all outputs from all emission scenarios and 3 models (DICE, PAGE and FUND)

f

Based on the emission scenarios of Stanford Energy Modeling Forum (Interagency Working Group on Social Cost of Carbon 2010)

g

Mean result of the 19 models used in the study

distributions defined by a minimum, mode and maximum value. All the input parameters and assumptions in the study are unaltered from the default PAGE09 model unless mentioned otherwise. The detailed technical descriptions of the default input parameters, assumptions and equations used in the model are fully documented in Hope (2006, 2011c, d). As in most IAMs, the PAGE09 model defines damage from climate change as a non-linear function, essentially computed as a combination of specified damage functions for

(a)

(b)

(c) (d)

The economic impacts, such as impacts on marketed output and income in sectors such as agriculture and energy use, that are directly included in GDP; The environmental impacts, such as impacts like health and wilderness areas which are not directly included in GDP; The sea-level rise impacts; and The discontinuity impacts, such as the increased risks of climate catastrophe due to the melting of the Greenland or West Antarctic Ice Sheet. The occurrence of such a discontinuity is determined in a

123

K. Y. Wong et al. Fig. 1 Carbon prices1 (price per tonne CO2 multiplied by 3.7) over time estimated by other IAMs. Adapted from Edenhofer and Kalkuhl (2010)

Fig. 2 Existing CO2 prices calculated based on IMF (2012) 2010 average exchange rates and the implementation year. Adapted from Ares (2012), Barchart.com Inc. (2012), Commonwealth of Australia (2012), Environmental Administration (2012), Intercontinental Exchange, Inc. (2012), Ministry of Finance (2011) and Sumner et al. (2009)

US$/tCO2 150.0 126.3 100.0 62.9 50.0

16.0

0.0

1990

Finland

1991

The effect of the changes in societal structure and technology is captured through the economic and non-economic impacts as a polynomial function of the regional temperature the same range as in Ackerman et al. (2009). The total damages of climate change are capped at the statistical value of civilisation as suggested in Weitzman (2009). For the purpose of the study, the determination of the CO2 price that would compensate the marginal impact of CO2 for a given emissions scenario and its trajectory over time was made based on the methodology established in Hope (2011a). Using the PAGE09 model, the total net present value (NPV) of the economic, environmental and social impacts of climate change for ten time periods was calculated by injecting an extra spike of 100 GtCO2 emissions in a given year on top of the following scenarios: A1B BAU baseline emissions scenario that is based on projected balanced use of energy sources and an emission scenario as summarised in IPCC Special Report on Emission Scenarios (SRES), with constant emissions (‘resource steady state’) after year 2100 (IPCC 2007; Nordhaus 1991) and

123

1991

1992

Sweden Sweden Norway (Standard) (Industry) (Highest)

(b)

Norway (Lowest)

Denmark

25.0

22.6

2012

Proposed

10.0

4.1

probabilistic manner and becomes more likely with higher temperature rises (temperature itself is determined probabilistically).

(a)

29.1

27.8

26.6

2008

Canada

2008

EU-ETS Australia (Phase II)

France

Country

2016.R5 low-emissions scenario that requires global emissions to peak in year 2016 and reduce on an annual basis by 5 % in order to provide a 50 % chance of limiting global average warming to 2°C relative to pre-industrial 1990 levels (Bowen and Ranger 2011).

Figure 3 shows the total global CO2 emissions in the A1B baseline trajectory and the 2016.R5 low-emissions policy projections. A spike of 100 GtCO2 instead of 1 or 10 Gt was used in the study in line with the results of the previous sensitivity analysis conducted by Hope (2011c) which indicated that this is the appropriate level to estimate the climate change impact resulting from a marginal change from the current emissions level. By dividing the NPV differential by 100 billion, the price that internalises the impact caused by the addition of one more tonne of CO2 emissions in a given analysis year was obtained. The discount rate in the study discounts according to an equity weighting scheme that converts changes in consumption into utility giving more (less) weight to consumption per capita in poorer (richer) regions and time periods and then by the rate of PTP (Hope 2011d). The equity weighting scheme is dependent on the elasticity of marginal utility of consumption which is inserted as a triangle distribution of (0.5, 1, 2). Following the equity

Global CO2 Emissions (Gt)

The impact of time horizon on integrated climate assessment models A1B

70.00

2016.R5

60.00 50.00 40.00 30.00 20.00 10.00 2000

2050

2100 Year

2150

2200

Fig. 3 Global CO2 emissions by date. Adapted from PAGE09 model, includes fossil fuel use and land use change

weighting, the damages are further discounted at the annual rate of PTP, which is entered as a triangle distribution of (0.1, 1, 2). To capture the uncertainty in the SCCO2, the @Risk 5.7 analysis software was used to run the model 100,000 times and calculate the range and expected value (Palisade 2012). The mean was deemed to be the most appropriate summary statistic to be used given the right-skewed distribution and the theoretical basis of the PAGE09 model of calculating the expected utility (Hope 2011a; Schoemaker 1982; Watkiss 2005; Watkiss and Downing 2008). The data were also presented as PDFs to provide policy makers the opportunity to consider a strategic hedging of the low-probability, but policy-relevant, outcomes (Cucchiella et al. 2013; Roughgarden and Schneider 1999; Schneider 1997).

Findings In the next sections, the paths over time of the SCCO2 under the A1B and 2016.r5 scenarios are investigated and discussed using the default PAGE09 model with a constant final analysis year (YLAST) of 2200 and an enhanced version of PAGE09 model.

where r is the sample standard deviation and n is the sample size, 100,000 (Mendenhall et al. 2012). 90 % of the SCCO2 values lie in the range of US$11.8 to US$291.6/ tCO2. The shape of the distribution is clearly asymmetric and strongly skewed to the right, displaying a few very high SCCO2 values with 0.1 % of the values being above about US$3,600/tCO2. The finding of these low-probability but high-impact figures was not surprising as the PAGE09 model takes into account the possibility of a large discontinuity such as the significant sea-level rise due to the irreversible melting of the Greenland or West Antarctic ice sheets occurring (Hope 2011a). When the timing of the additional CO2 emissions was changed to develop a schedule of CO2 prices over time as suggested by Watkiss and Downing (2008), the estimated mean SCCO2 increases in real terms at an exponential rate of about 2.0 % per year as illustrated in Fig. 5. This reflects growing climate change damages due to population and income growth and the fact that later emissions will cause a greater incremental damage as they are emitted when climate change is expected to be more severe. Although the shape of the marginal damage contrasts with Clarkson and Deyes’s (2002) analysis of the SCCO2 results of studies conducted between 1991 and 2000 which showed a more or less linear increase of damage costs over time, a review of more recent climate change publications shows almost similar accelerating trajectories with 2–3 % optimal CO2 price increase per year in real terms (Nordhaus 2007b; Yohe et al. 2007). The results from the PAGE09 model suggest that a 2010 SCCO2 of around US$106.4 ± 1.7/tCO2 (95 % CI) in 2005 prices—rising to around US$231.9 ± 3.8/tCO2 (95 % CI) in 2050—would efficiently capture the marginal impacts of climate change under the A1B scenario. This high tax level is consistent with the Stern Review’s report on the severity of damages from global warming (Fullerton et al. 2010).

Estimating the level of SCCO2 using the default model

Low-emissions scenario: default model

Under the A1B scenario, the price that internalises the SCCO2 in the year 2010 has an estimated mean value of US$106.4 ± 1.7/tCO2 [95 % confidence interval (CI)] (in constant US$2005 prices) as shown in Fig. 4. On average, 95 % of the time, the interval [104.7, 108.1] contains the true mean value. The ±1.7 margin of error at a 95 % confidence level is derived using the following formula: r 95 % margin of error ¼ 1:96  pffiffiffi n

When a 2016.R5 scenario is assumed, the default PAGE09 model suggests that the SCCO2 has an estimated mean value of US$52.4 ± 1.3/tCO2 (95 % CI) (in constant US$2005 prices) in the year 2010 as shown in Fig. 6. 90 % of the SCCO2 values lie in the range of US$5.5 to US$129.5/tCO2. This lower estimated mean value of SCCO2, about half of the US$106.4 ± 1.7/tCO2 predicted in the A1B scenario, reflects the importance of lowering GHG emissions to reduce the chance of a large discontinuity (Hope 2011c).

123

K. Y. Wong et al.

Fig. 4 Marginal impact of CO2 in the year 2010 with BAU emissions. Adapted from PAGE09 model 100,000 simulation runs with the A1B scenario

231.9

250.0 CCT (US$ t/CO2)

Fig. 5 Estimated mean of SCCO2 over time with the final year fixed at default year 2200 and BAU emissions. Adapted from PAGE09 model 100,000 simulation runs with the A1B scenario

195.7

200.0

164.0 y = 6E-16e0.0198x

133.3

150.0 106.4 100.0

103.7

50.0 0.0 2000

2010

2020

2030

2040

2050

Year

Fig. 6 Marginal impact of CO2 in the year 2010 with low emissions. Adapted from PAGE09 model 100,000 simulation runs with the 2016. R5 scenario

Changing the year in which the additional tonne of CO2 is emitted resulted in higher values of SCCO2 up to US$104.5 ± 2.7/tCO2 (95 % CI) in year 2050, with a slightly slower growth rate than under the A1B scenario of 1.8 % per year in real terms as illustrated in Fig. 7.

123

Enhancing the PAGE09 model In the default PAGE09 model, the original base year is 2008 while YLAST is fixed at year 2200. When the analysis year, in which the extra spike of CO2 emissions is superimposed (YSCC), was changed to model different

The impact of time horizon on integrated climate assessment models

150.0

CCT (US$ t/CO2)

Fig. 7 Estimated mean of SCCO2 over time with the final year fixed at year 2200 and low emissions. Adapted from PAGE09 model 100,000 simulation runs with the 2016. R5 scenario

104.5 90.6

100.0 76.6

y = 2E-14e0.0177x

63.4 52.4 50.0

50.9

0.0 2000

2010

2020

2030

2040

2050

Year

possible policy implementation years up to 2050, the time horizon therefore shortened from 192 to 150 years for emissions in 2050. With a shorter time horizon for the later implementation years, there is a risk that the model underestimates the impacts from emissions in these years and so gives a biassed estimate of the SCCO2 growth rate. The uncertainty and effect of the GHG emissions scenarios become even more important over longer time horizons (IPCC 2007). In estimating the SCCO2 using a multi-model approach, the US Interagency Working Group on Social Cost of Carbon (2010) had run each of the three models through 2300 which they considered far enough into the future to capture all the significantly relevant climate change damage effect. Thus, in order to test the robustness and validity of the PAGE09 model results when an emission year different from 2010 is considered, the paper examined the impact of using (a) (b) (c)

A constant time horizon of 192 years (TH192); A constant YLAST of 2300 (YLAST2300) and; A constant time horizon of 292 years (TH292).

By changing the model specification as shown in Table 2. Business-as-usual scenario: enhanced model By running simulations using the experiments shown in Table 2 above, it was found that the estimated mean SCCO2 in real terms increases over the years at a higher rate than when using the default model shown as D in Fig. 8 et seq, up to 2.3 % per annum in experiment A, as shown in Fig. 8. Also, when experiments B and C were performed, that is, with a longer time horizon, the estimated mean SCCO2 is about one quarter higher than the default mean value of US$106.4/tCO2 in 2010 with growth rates of 2.2 and 2.0 % per annum, respectively. By examining 22 studies of SCCO2, Anthoff et al. (2011) found that majority of the studies had shown accelerating growing SCCO2, increasing at an average rate of

2.3 % per year, with the highest estimate at 4.1 % and the lowest one at 0.9 % per annum. Our finding implies that the standard deviation of 0.9 % and the corresponding margin of error in the survey by Anthoff et al. (2011) could be potentially lowered if the various studies had assumed a homogeneous and comparable time horizon and discounting period, thereby increasing the accuracy and usefulness of the SCCO2 annual growth rates surveyed. Low-emissions scenario: enhanced model Under the 2016.R5 scenario, the estimated mean SCCO2 in real terms also increases over the years at a higher rate than when using the default model, up to a maximum rate of 2.0 % per annum as shown in Fig. 9. Whilst it may seem obvious to the naked eye that the SCCO2 values under the four experiments are different especially in the later years, it is necessary to test whether these differences are statistically significant. To do so, a Kolmogorov–Smirnov two-sample one-tailed test was performed by using. Dm;n ¼ max½Sm ð X Þ  Sn ð X Þ; where Sm (X) is the observed cumulative distribution for one sample (of size m),Sn (X) is the observed cumulative distribution for the other sample (of size n) and m = n = 100,000 with the following hypotheses: H0 There is no difference in the cumulative distributions of the SCCO2 based on a constant time horizon with the estimated SCCO2 based on a constant YLAST. HA The estimated SCCO2 values based on a constant time horizon are stochastically larger than the ones based on a constant YLAST. (Siegel and Castellan 1988). The data for all the years were cast in two cumulative frequency distributions which are then graphically reproduced in charts for analysis. By visually inspecting the

123

K. Y. Wong et al. Table 2 Inputs to test the impact of a later final analysis year and a constant time horizon

Model specification

Default (D)

Experiment

YLAST2200

(A) TH192

(B) YLAST2300

(C) TH292

Time horizon for YSCC 2009

191

192

291

292

2010

190

192

290

292

2020

180

192

280

292

2030

170

192

270

292

2040

160

192

260

292

2050

150

192

250

292

2009

2200

2201

2300

2301

2010

2200

2202

2300

2302

2020 2030

2200 2200

2212 2222

2300 2300

2312 2322

2040

2200

2232

2300

2332

2050

2200

2242

2300

2342

YLAST for YSCC

Penultimate year (YPENUL)a for YSCC 2009

2150

2150.5

2200

2200.5

2010

2150

2151

2200

2201

2020

2150

2156

2200

2206

2030

2150

2161

2200

2211

2040

2150

2166

2200

2216

2050

2150

2171

2200

2221

a

In order to ensure a consistent time step algorithm in the PAGE09 model when YLAST is changed, YPENUL which is fixed as year 2150 in the default model was changed to be midway between the antepenultimate year (YAPEN) (i.e. year 2100) and YLAST. To illustrate, when YSCC is 2050, YLAST was reset to 2242 and YPENUL was adjusted to 2171. This revision was consistent with concentrating the computational effort in the earlier years as the level of uncertainty surrounding the emissions forecasts increases over time (Hope 2006)

310.8 300.0 CCT (US$ t/CO2)

Fig. 8 The effect of changing the time horizon and YLAST on the mean of the SCCO2 with BAU emissions. Adapted from PAGE09 model 100,000 simulation runs with the A1B scenario

200.0

100.0

0.0 2000

yC = 5E-16e0.02x

261.5

171.4 176.7 165.2 134.4 133.9 130.5 138.6 108.4 129.2 133.3 106.4 104.3 103.7

2010

2020

202.6

2030

292.6

249.4 263.2

209.8

yB = 2E-17e0.0215x

216.3

yA = 2E-18e0.0226x yD = 6E-16e0.0198x

231.9 195.7

164.0 MeanB_TH292 MeanC_YLAST2300 MeanA_TH192 MeanD_YLAST2200 2040

2050

Year

charts, the differences between the two sample distributions (e.g., between scenarios B and C) at the various mean intervals were recorded. With the Dm,n value obtained from the largest of these differences, the value of X2 was computed using the following equation:

123

X 2 ¼ 4D2m;n

mn mþn

(Siegel and Castellan 1988). The probability associated with X2 with a degree of freedom (df) of 2 was obtained using Excel’s CHIDIST

The impact of time horizon on integrated climate assessment models 150.0

142.5 128.3 118.0

118.8 CCT (US$ t/CO2)

Fig. 9 The effect of changing the time horizon and YLAST on estimated mean of SCCO2 with low emissions. Adapted from PAGE09 model 100,000 simulation runs with the 2016. R5 scenario

110.7

101.0

100.0 80.8

50.0

0.0 2000

65.2 62.4 62.8 67.5 61.652.7 52.4 50.9 50.8

2010

94.9

78.9

97.5 90.6

yB = 2E-16e0.0202x yC = 1E-14e0.0179x yA = 9E-17e0.0203x yD = 2E-14e0.0177x

104.5

81.4 76.6

63.4 MeanB_TH292 MeanC_YLAST2300 MeanA_TH192 MeanD_YLAST2200

2020

2030

2040

2050

Year

formula function and compared against an online Chi square calculator developed by the Department of Statistics at Texas A&M University (Department of Statistics 2009). The results for the tests are presented in Table 3. In all the analysed cases except for the years 2009 and 2010 in both experiments, and year 2020 for a YLAST of 2300 versus a constant time horizon of 292 years, the probability associated with X2 is p \0.0001. Hence, the tests suggested that the H0 if there is no difference to the mean SCCO2 when the default final year is adjusted should be rejected in favour of HA at a 0.1 % significance level for YSCC greater than. a. b.

2010 where the default YLAST of 2200 is assumed and; 2020 in situations where a later YLAST of 2300 is assumed.

So there is statistical evidence at the 99.9 % confidence level that the PAGE09 model is sensitive to the time horizon assumption. The estimated mean SCCO2 values for later emissions years are not independent of the length of time over which the values are calculated. This finding is consistent with the suggestion of Watkiss and Downing (2008) that curtailing the time horizon to a century could substantially lower the SCCO2 estimate for current emissions.

Discussion Our results show that the choice of final analysis year, time horizon and CO2 abatement emission pathway do influence the level of SCCO2. The Kolmogorov–Smirnov two-sample one-tailed test shows that there should be more discourse on the marginal impacts of CO2 based on different time horizons to arrive at a general consensus on what constitutes an ideal time frame for the determination of the

CO2 price. This raises an area for further investigation as to what constitutes an ideal time frame for the determination of the CO2 price. Although there are more than 300 different estimates of SCCO2 in the literature, the discussion on the marginal impacts of CO2 based on different time horizons is limited (Anthoff et al. 2011). What seems to be agreed is that a long time horizon of at least a century is needed to capture the inertia, time lags or spill-over effects of the CO2 emissions and the anticipated climate change damages and potential discontinuities (Downing et al. 2005; Nordhaus 2011; Sterman 2000; Watkiss 2005; Weyant and Olavson 1999). However, the question is how long is long enough. Nordhaus (2011) contended that it is extremely difficult to provide reliable estimates of climate change damages over a long period of time. Trajectories over several centuries may go outside the range of plausibility resulting in misleading findings (Sterman 2000). From a policy decisionmaking perspective, an analysis based on an infinite time horizon is not practical and is unlikely to yield any incremental useful benefits given the fact that predictions and decisions regarding climate change in the future will be made under conditions of even greater uncertainty. A rule of thumb proposed by Sterman (2000) is to set the time horizon several times as long as the longest time delays between taking a decision and its effects on the state of the system. At the other extreme, when a low discount rate is used in a model, Anthoff et al. (2011) suggested that only a time horizon of about 1000 years is long enough for the model to properly take into account the impact of discounting. Meanwhile, Ford (2009) and CCE (2012) suggested that two models are developed instead; the first dealing with the short-run policy point of view (1–2 decades) and the second with the long-run ecological point of view (centuries). The results of the short-run model are then used to support the relationships in the long-run model.

123

K. Y. Wong et al. Table 3 Kolmogorov–Smirnov test results

Analysis year

A1B Max Dm,n=100,000

2016.R5 2

X , df = 2

p value

Max Dm,n=100,000

X2, df =2

p value

YLAST2200 versus TH192 2009

0.002

0.8

0.6703

0.002

0.8

2010

0.004

3.2

0.2019

0.002

0.8

0.6703 0.6703

2020

0.014

39.2

\0.0001

0.010

20.0

\0.0001

2030

0.026

135.2

\0.0001

0.018

64.8

\0.0001

2040

0.036

259.2

\0.0001

0.026

135.2

\0.0001

2050

0.048

460.8

\0.0001

0.036

259.2

\0.0001

YLAST2300 versus TH292 2009

0.001

0.2

0.9048

0.001

0.2

0.9048

2010

0.002

0.8

0.6703

0.002

0.8

0.6703

2020 2030

0.008 0.011

12.8 24.2

0.0017 \0.0001

0.008 0.012

13.0 28.8

0.0017 \0.0001

2040

0.016

51.2

\0.0001

0.014

39.2

\0.0001

2050

0.020

80.0

\0.0001

0.024

115.2

\0.0001

Based on the literature review of other IAMs, it is found that the time horizons used for SCCO2 analysis vary from 60 to 1050 years as shown in Table 4. To examine further the impact of a longer time horizon, YLAST in the PAGE09 model was varied from 2200 to 3000 under the two emission scenarios, with YPENUL adjusted accordingly, as in Experiment B. The results are illustrated in Fig. 10. In the A1B trajectory, the level that internalises the SCCO2 in the year 2010 has an estimated mean value that ranges from US$108.4 ± 1.7/tCO2 for a final year of 2200 to a level that is 136 % higher at US$255.8 ± 4.9 for a final year of 3000. In contrast to the marginally concave CO2 prices over time in the A1B scenario, a linear relationship was observed in the 2016.R5 scenario where the estimated mean of SCCO2 in the year 2010 varies from US$52.7 ± 1.3 to US$135.9 ± 5.4/tCO2. This constitutes an increase in the level of SCCO2 of about 158 %. The pattern of slightly concave SCCO2 observed under the A1B scenario when a longer time horizon was considered could be due to the use of very low non-symmetrical triangular distributions for the PTP [0.1, 1, 2] in the PAGE09 model (Fankhauser 1994; Fankhauser 1995; Thureson and Hope 2012). To test this hypothesis, simulations using a fixed PTP at 3 % were performed under different time horizon assumptions. This value, which was benchmarked against the empirical estimate of 3 % PTP in the study by Anthoff et al. (2011), was simply illustrative, not definitive, of the many possible estimates. The shape of the graph changes to one that is linearly rising, with lower levels of SCCO2 for all time horizons as expected as shown in Fig. 11. This is due to the impact of discounting over a very long time period with the last three

123

analysis years (YAPEN, YPENUL and YLAST) representing more than 59 % of the aggregation period when the time horizon was extended in the PAGE09 model. Again, the findings seem to concur with the suggestion of Anthoff et al. (2011) for the use of a very long time horizon when a low discount rate is used in a model to provide an unbiased estimate of SCCO2 growth rate and its pattern over time. The impact of using a lower discount rate (e.g., fixing the PTP at 0) can be surmised from Fig. 11 with even higher levels of SCCO2 for all time horizons.

Limitations and areas for future research A fundamental limitation of this study as in most IAMs based on mathematical modelling is the fact that the PAGE09 model does not, and could not, capture all the important factors surrounding climate change (Roughgarden and Schneider 1999). Some of the omitted factors include the effects of ocean acidification and socially contingent impacts such as possible war and large-scale migration (Hope 2011d; Shell International BV 2011). Despite the robustness of its data and results, the PAGE09 model does not provide anything close to absolute certainty in terms of the impacts for a given temperature rise (Hope 2011a). Also, this study involved the use of key subjective value-laden probabilities for the uncertain economic, environmental and social welfare input parameters that need to be considered in policy making in the real world but cannot be directly measured (Downing et al. 2005). In addition, the state of the art of IAMs seems to be gradually moving towards merging with earth system models (ESMs) (e.g., the coupling of the Global Change

The impact of time horizon on integrated climate assessment models Table 4 Time horizon used in other IAMs of climate change Study

Model characteristic

Years

Anthoff et al. (2011)

FUND: Regionally disaggregated welfare maximisation model that represents time evolution of the social cost of carbon

1050

Nordhaus (2010)

RICE-2010: Regionalised model that incorporates an end-to-end treatment of economic growth, emissions, climate change, damages and emissions controls based on Ramsey growth model

Nordhaus (2007b)

DICE-2007: Neoclassical model that views the economics of climate change from the perspective of economic growth theory

Weyant et al. (2006)

EMF-21: Multi-gas policy assessment using 19 energy–economic models such as AIM, AMIGA, PACE, etc.

100

Hope (2006)

PAGE2002: An updated version of the PAGE95 IAM that incorporates IPCC (2007) reasons for climate change concern for the determination of the marginal impact of CO2

200

Goulder and Mathai (2000) Goulder and Schneider (1999)

Decision on carbon abatement or investment timing to minimise cost or maximise benefit General equilibrium model of response to given carbon tax policy, with endogenous private R&D

200 60

Fig. 10 The impact of longer time horizon on the estimated mean of SCCO2 in the year 2010 with BAU and low emissions. Adapted from PAGE09 model 100,000 simulation runs with the A1B and 2016. R5 scenarios

100 95

300.0 255.8

242.8 250.0

226.3

CCT (US$/t CO2)

208.2 200.0 155.9

170.1

185.6 Mean_A1B Mean_2016.R5

134.4

150.0 108.4 100.0 50.0 52.7

65.2

71.3

2300

2400

84.6

89.9

104.4

112.0

2700

2800

126.2

135.9

2200

2500

2600

2900

3000

YLAST

300.0 250.0 CCT (US$/t CO2)

Fig. 11 The impact of higher PTP on estimated mean of CCT in 2010 using different time horizons with BAU emissions. Adapted from PAGE09 model 100,000 simulation runs with the A1B scenario

208.2 200.0 155.9

170.1

226.3

PTP=[0.1,1,2]% PTP=3%

108.4 100.0 50.0

20.3

255.8

185.6

134.4

150.0

242.8

29.0

32.2

35.0

39.1

45.4

25.7

41.9

22.5

2300

2400

2500

2600

2700

2800

2900

3000

2200

YLAST

Assessment Model (GCAM), an IAM with the Community ESM (CESM) as reported in Bond-Lamberty et al. 2014) and developing more sophisticated components. Successful

integration of these two historically independent modelling paradigms—IAMs with simplified representations of complex natural processes and ESMs with no economic or

123

K. Y. Wong et al.

energy system modelling—would permit an unprecedented and more comprehensive analyses and feedback of the interactions between climate policy options, economic trends and the physical climate and Earth system. Such a consolidation, while interesting and beneficial, is beyond the reach of this study. As reality is so complex and it is always difficult to be certain about the impact of a CO2 price among all the other policies and wider socioeconomic developments, the use of IAM alone is no less relevant than any other research methods or approaches (EJPE 2009). Within a positivistic view, a robust and transparent IAM can provide useful falsifiable evidence and insights via sensitivity analysis to better assist decision making under uncertainty, either with the attempt to ‘satisfice’ or to identify an optimal policy solution (Schneider 1997; Schoemaker 1982; Simon 1956). It has been shown here that the estimates of SCCO2 could differ considerably depending on simple modelling decisions with regard to the final analysis year, time horizon specification and the CO2 emissions pathway in the underlying model. Thus, future research in the area of IAM development could examine the impact and significance of a structural time horizon adjustment that is mutually agreed upon by all the stakeholders to fully address the question about the optimal level of SCCO2 for practical policy decision making and implementation.

Conclusions Although the findings seem to indicate that finite horizon solutions result in an ill-defined policy path, this is not necessarily a major obstacle to success for an active policy. Indeed, the PAGE09 model results do point towards a set of robust conclusions for policy making. Our findings suggest that: (a) One of the reasons why the range of estimates of the SCCO2 in the published literature varies widely could simply be the differing specification of the model time horizon. The finding of this paper offers a starting point for a discussion in the climate change arena for a relevant and coherent time horizon; one that is short enough to be accepted and useful for policy makers, but long enough from the present to be rigorous and establish significant results from a scientific perspective. For the PAGE09 model, it is suggested that a constant time horizon of about 200 or 300 years (for example, 192 years in Experiment A and 292 years in Experiment C) may be relevant and appropriate time frames to provide an unbiased estimate of the SCCO2; (b) The initial CO2 price for policy implementation should be at a level no lower than the mean SCCO2

123

(c)

(d)

(i) (ii)

(iii)

value of US$108.4 ± 1.7/tCO2 derived from the enhanced PAGE09 model (taking into account the adjustments to the YPENUL and a constant time horizon in Experiment A); This CO2 price should be increased over time to intensify decarbonisation (Barker 2008; Price et al. 2005; Sumner et al. 2009). On the other hand, the marginal impact of CO2 could be relatively lower if the world eventually moves onto a lower emissions path in the future, justifying a policy response of reducing the CO2 price in some time periods; this is consistent with the suggestion of Sinn (2008, 2007) for an initially high CO2 tax that would decline with the passage of time, albeit with a different reasoning; An effective climate policy must incorporate flexibility and be reviewed on a regular basis over time to take into account the.

Changing emissions pathway (Fankhauser 1994; Watkiss 2005); Low-carbon energy substitutes sources or ‘negative emissions’ technological development (Barker 2008; Loughlin et al. 2013; Nordhaus 2007a; Rout 2011) and; Better scientific and economic information regarding the impacts, particularly of the lowprobability but high-impact climate change catastrophe (Bowen and Ranger 2011; Murray et al. 2008; Schneider 1997).

References Ackerman F, Stanton EA (2012) Climate risks and carbon prices: revising the social cost of carbon. Economics 6:1–25 Ackerman F, Stanton EA, Hope C, Alberth S (2009) Did the stern review underestimate us and global climate damages? Energy Policy 37:2717–2721 Anthoff D, Rose S, Tol RS, Waldholf S (2011) The Time Evolution of the social cost of carbon: an application of fund. Economics the open-access, Open-Assess E J 1–21 Ares E (2012) Carbon price support. The House of Commons, London Asian Development Bank (2009) The economics of climate change in Southeast Asia: a regional review. ADB, Manila Barchart.com Inc. (2012) Futures. Barchart. http://www.barchart. com/quotes/futures/CKZ12. Accessed 16 Aug 2012 Barker T (2008) The macroeconomic effects of the transition to a low-carbon economy. The Climate Group, London Bond-Lamberty B, Calvin K, Jones AD, Mao J, Patel P, Shi XY, Thomson A, Thornton P, Zhou Y (2014) On linking an Earth system model to the equilibrium carbon representation of an economically optimizing land use model. Geoscientific Model Development, 7:2545–2555

The impact of time horizon on integrated climate assessment models Bowen A, Ranger N (2011) The costs of mitigating climate change: some results from the AVOID programme. Met Office Hadley Centre, Exeter CCE (2012) FAQs on CCE EIA. National Institute for Public Health and the Environment, Ministry of Health, Welfare and Sport. http://www.rivm.nl/en/themasites/cce/methods_and_models/faq sonCCEEIA/index.html. Accessed 15 Feb 2012 Clarkson R, Deyes K (2002) Estimating the social cost of carbon emissions. Department of Environment, Food and Rural Affairs, London Commission of the European Communities (2005), EUR Lex: Access to European Union law. http://eur-lex.europa.eu/LexUriServ/ LexUriServ.do?uri=CELEX:52005DC0525:EN:HTML. Accessed 29 March 2012 Commonwealth of Australia (2012) Implementation timeframe. Australian Government: Department of Climate Change and Energy Efficiency. http://www.climatechange.gov.au/en/govern ment/clean-energy-future/timeframe.aspx. Accessed 20 Mar 2012 Corfee-Morlot J, Jones T (1992) Designing a practical tax system for greenhouse gas emission abatement: an introduction. OECD climate change : designing a practical tax system. OECD, Paris Cedex, pp 15–23 Cucchiella F, D’Adamo I, Gastaldi M (2013) Financial analysis for investment and policy decisions in the renewable energy sector. Clean Technol Environ Policy, 1–18 Department of Statistics (2009) Home. Texas A & M University Department of Statistics. http://www.stat.tamu.edu/. Accessed 25 Jan 2012 Downing TE, Anthoff D, Butterfield R, Ceronsky M, Grubb M, Guo J et al (2005) Social cost of carbon: a closer look at uncertainty. Environment Policy Economics, Defra, London Edenhofer O, Kalkuhl M (2010) The green paradox revisited. Postdam Institute for Climate Impact Research, Montreal EJPE (2009) Cambridge social ontology : an interview with Tony Lawson. Erasmus J Philos Econ 2(1):100–122 Ekins P, Monkhouse C, Skinner I, Willis R (2002) Next steps for energy taxation: a survey of business views. Green Alliance, London Eliasch J (2008) Climate change: financing global forests. Office of Climate Change, UK Environmental Administration (2012) Environmentally related energy taxation in Finland, www.environment.fi: http://www.environ ment.fi/default.asp?contentid=147208&lan=en. Accessed 20 Mar 2012 Fankhauser S (1994) Evaluating the social costs of greenhouse gas emissions. Centre for Social and Economic Research on the Global Environment, University College London and University of East Anglia Fankhauser S (1995) Valuing climate change: the economics of the greenhouse. Earthscan Publication Limited, London Ford A (2009) Modeling the environment, 2nd edn. Island Press, Washington, DC Fullerton D, Leicester A, Smith S (2010) Environmental taxes. Institute for fiscal studies dimensions of tax design. Oxford University Press, Oxford, pp 428–549 Goulder LH, Mathai K (2000) Optimal CO2 abatement in the presence of induced technological change. J Environ Econ Manag 39:1–38 Goulder LH, Schneider SH (1999) Induced technological change and the attractiveness of CO2 abatement policies. Resour Energy Econ 21:211–253 Hasselknippe H, Christiansen AC (2003) Energy taxation in Europe: current status—drivers and barriers—future prospects. The Fridtjof Nansen Institute, Lysaker

Hope C (2006) The marginal impact of CO2 from PAGE2002: an integrated assessment model incorporating the IPCC’s five reasons for concern. Integr Assess J 6(1):19–56 Hope C (2011a) Working Paper Series 9/2011 How high should climate change taxes be? Cambridge Judge Business School, University of Cambridge, Cambridge, UK Hope C (2011b) Working Paper Series 8/2011 New insights from the PAGE09 model: The social cost of CO2. Cambridge Judge Business School, University of Cambridge, Cambridge, UK Hope C (2011c) Working Paper Series 5/2011 The social cost of CO2 from the PAGE09 model. Cambridge Judge Business School, University of Cambridge, Cambridge, UK Hope C (2011d) Working Paper Series 4/2011 The PAGE09 integrated assessment model: a technical description. Cambridge Judge Business School, University of Cambridge, Cambridge, UK Hope C, Watkiss P (2010) The PAGE09 integrated assessment model. ClimateCost Project IMF (2012) IMF exchange rates. International Monetary Fund: http:// www.imf.org/external/np/fin/ert/GUI/Pages/Report.aspx?CT= ‘AUS’,’CAN’,’EMU’,’FIN’,’MYS’,’NOR’,’SWE’&EX=REP &P=DateRange&Fr=633979008000000000&To=6342935040 00000000&CF=Compressed&CUF=Period&DS=Ascending& DT=Blank. Accessed 22 Mar 2012 Ingwersen WW, Garmestani AS, Gonzalez MA, Templeton JJ (2014) A systems perspective on responses to climate change. Clean Technol Environ Policy 16:719–730 Interagency Working Group on Social Cost of Carbon (2010) Social cost of carbon for regulatory impact analysis under executive order 12866. U.S. Department of Energy, Washington, DC IntercontinentalExchange, Inc. (2012) Emissions. ICE: https://www. theice.com/emissions.jhtml. Accessed 23 May 2012 IPCC (2007) Summary for Policymakers. In Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt K, et al. Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA Kalkuhl M, Edenhofer O (2010) CESifo Working Paper No. 3044 Prices versus quantities and the intertemporal dynamics of the climate rent. CESifo: Munich Loughlin DH, Yelverton WH, Dodder RL, Miller CA (2013) Methodology for examining potential technology breakthroughs for mitigating CO2 and application to centralized solar photovoltaics. Clean Technol Environ Policy 15:9–20 Mendenhall W, Beaver RJ, Beaver BM (2012) Introduction to probability and statistics. Brooks/Cole: Cengage Learning, Boston Ministry of Finance (2011) Green taxes 2011. Ministry of Finance: http://www.regjeringen.no/en/dep/fin/Selected-topics/taxes-andduties/green-taxes-2011.html?id=609076. Accessed 8 April 2012 Murray BC, Newell RG, Pizer WA (2008) Balancing cost and emissions certainty. Resources for the Future, Washington, DC Nordhaus WD (1982) How fast should we graze the global commons? Am Econ Rev 72(2):242–246 Nordhaus WD (1991) To slow or not to slow: the economics of greenhouse effect. Econ J 101(407):920–937 Nordhaus WD (2007a) To tax or not to tax: alternative approaches to slowing global warming. Rev Environ Econ Policy 1(1): 26–44 Nordhaus W (2007b) The challenge of global warming: economic models and environmental policy. Yale University, New Haven Nordhaus W (2010) Economic aspects of global warming in a postCopenhagen environment. Yale University, New Haven

123

K. Y. Wong et al. Nordhaus WD (2011) Integrated economic and climate modeling. Cowles Foundation for Research in Economics. Yale University, New Haven Palisade (2012) @Risk. Palisade: http://www.palisade.com/risk/. Accessed 16 Aug 2012 Price L, Galitsky C, Sinton J, Worrell E, Graus W (2005) Tax and fiscal policies for promotion of industrial energy efficiency: a survey of international experience. The U.S Department of Energy, California Roughgarden T, Schneider SH (1999) Climate change policy: quantifying uncertainties for damages and optimal carbon taxes. Energy Policy 27:415–429 Rout UK (2011) Regional demand-pull scenarios and cost-effective emission mitigation. Clean Technol Environ Policy 13:719–729 Schneider SH (1997) Integrated assessment modeling of global climate change: transparent rational tool for policy making or opaque screen hiding value-laden assumptions? Environ Model Assess 2:229–249 Schoemaker PJ (1982) The expected utility model: its variants, purposes, evidence and limitations. J Econ Lit, 529–563 Shell International BV (2011) Shell energy scenarios to 2050 signals and signposts. Shell International BV, The Hague Siegel S, Castellan JN (1988) Nonparametric statistics for the behavioral sciences, 2nd edn. McGraw-Hill Book Company, London Simon HA (1956) Rational choice and the structure of the environment. Psychol Rev 63:129–138 Sinn H-W (2007) CESifo Working Paper No. 2087 Public Policies Against Global Warming. IIPF Annual Congress. CESifo, Warwick, pp 1–42 Sinn H-W (2008) Public policies against global warming: a supply side. Int Tax Public Financ 15:360–394 Stanton EA, Ackerman F, Kartha S (2008) Inside the integrated assessment models: four issues in climate economics. Stockholm Environment Institute, Somerville

123

Sterman JD (2000) Business dynamics: systems thinking and modeling for a complex world. Irwin McGraw-Hill, London Stern N (2006) Stern review on the economics of climate change. HM Treasury, London Sumner J, Bird L, Smith H (2009) Carbon taxes: a review of experience and policy design considerations. National Renewable Energy Laboratory, Colorado Thureson D, Hope C (2012) Is Weitzman right? The social cost of greenhouse gases in an IAM world. Swedish Business School, ¨ rebro O Tol RS (2010) The costs and benefits of EU climate policy For 2020. Copenhagen Consensus Center Watkiss P (2005) The social cost of carbon. Department for Environment, Food and Rural Affairs, London Watkiss P, Downing TE (2008) The social cost of carbon: valuation estimates and their use in UK policy. Integr Assess J 8(1):85–105 Weitzman M (2009) On modelling and interpreting the economics of catastrophic climate change. Rev Econ Stat 91(1):1–19 Weyant JP, Olavson T (1999) Issues in modeling induced technological change in energy, environment, and climate policy. Environ Model Assess 4(2–3):67–85 Weyant JP, Chesnaye FC, Blanford GJ (2006) Overview of EMF-21: Multigas Mitigation and Climate Policy. Energy J, 1–32 Yohe G, Tirpak D (2008) A research agenda to improve economic estimates of the benefits of climate change policies. Integr Assess J 8(1):1–17 Yohe GW, Lasco RD, Ahmad QK, Arnell NW, Cohen SJ, Hope C, Janetos AC, Perez RT (2007) Perspectives on climate change and sustainability. In: Parry ML, Canziani OF, Palutikof JP, van der Linden P, Hanson CE (eds) Climate Change 2007: Impacts, Adaptation and Vulnerability. Contribution of Working Group II to the Fourth. Cambridge University Press, Cambridge, pp 811–841