Combining Expert Advice on Social Discounting Moritz A. Drupp 1 , - - PowerPoint PPT Presentation

Combining Expert Advice on Social Discounting

Moritz A. Drupp 1, Mark C. Freeman 2, Ben Groom 3, and Frikk Nesje 4

1 University of Kiel and University of Freiburg, Germany 2 University of York, UK 3 London School of Economics and Political Science, UK 4 University of Oslo and CREE, Norway

EAERE 2017, 29 June, 2017

Social discounting

Choosing the social discount rate (SDR) for long-term public project appraisal is “one of the most critical problems in all of economics” (Weitzman 2001 AER), not least because small changes in the SDR can substantially alter the recommended stringency of climate policy (Arrow et al. 2013 Science) How much would you invest now to avoid $1000 of climate damages a century from now? Stern’s (2007) SDR of 1.4% implies $250 Nordhaus’ (2008) long-term SDR of 4.5% implies $10

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This paper

Observation: There is substantial heterogeneity in opinion among experts on the appropriate balance between current and future net benefits, resulting both from uncertainty over the future as well as disagreement on value judgments

Drupp/Freeman/Groom/Nesje Combining Expert Advice on Social Discounting 3

This paper

Research questions: How should society aggregate widely varying expert advice into a single long-term SDR? What are the implications for the stringency of climate policies? More precisely: Based on data from Drupp et al. (2017 WP), we discuss different approaches to aggregating individual expert opinions and highlight their implications for climate policy in terms of the appropriate social cost of carbon (SCC) to be used for informing regulatory decision-making

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The expert survey data

Drupp et al. (2017 WP) present a survey of more than 200 experts that disentangles the long-term SDR into the component parts of the simple Ramsey Rule (SRR) The rate of pure time preference (δ) The wealth effect, which is composed of the growth rate of real, per-capita, consumption (g) and the elasticity of marginal utility of consumption (η) The forecasted real risk-free interest rate, as well as asking for the SDR directly. A prominent interpretation of the simple Ramsey Rule focuses on the trajectory of

• consumption. Under this reading, the SDR is given by SRR = δ + ηg

This approach is followed by Her Majesty’s Treasury (HMT 2003), for instance

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The expert survey data

Drupp et al. (2017 WP) find a mean recommended SDR of 2.3 percent with a wide divergence of individual recommendations, with values ranging from 0 to 10 percent The modal and median SDR of 2 percent receives the highest support when considering acceptable ranges The mean imputed individual SRR from these responses at 3.5 percent is higher than the average expert SDR

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The expert survey data

Variable Mean StdDev Median Mode Min Max N Real growth rate per capita 1.70 0.91 1.60 2.00

• 2.00

5.00 181 Rate of societal pure time preference 1.10 1.47 0.50 0.00 0.00 8.00 180 Elasticity of marginal utility 1.35 0.85 1.00 1.00 0.00 5.00 173 Real risk-free interest rate 2.38 1.32 2.00 2.00 0.00 6.00 176 Normative weight 61.53 28.56 70.00 50.00 0.00 100.00 182 Positive weight 38.47 28.56 30.00 50.00 0.00 100.00 182 Social discount rate (SDR) 2.27 1.62 2.00 2.00 0.00 10.00 181 SDR lower bound 1.12 1.37 1.00 0.00

• 3.00

8.00 182 SDR upper bound 4.14 2.80 3.50 3.00 0.00 20.00 183 Simple Ramsey Rule (SRR) 3.48 3.52 3.00 4.00

• 2.00

26.00 172

The SRR is imputed from the individual determinants

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Combining expert advice

The problem of the social planner is how to aggregate dispersed expert advice into a single representation of the discount rate, R(H), to apply when discounting a certainty-equivalent cash flow arriving at time H Let ri be either the imputed SRR or the recommended SDR of expert i ∈ [1, n]

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Combining expert advice: Weitzman (2001 AER)

Weitzman (2001 AER) takes, without explicit justification, the simple average of individual discount factors, e−HR(H) = 1 n

n

• i=1

e−Hri The difficulty with this approach is that it is not clear what weight to assign to each expert’s discount factor While Weitzman gives each response equal importance, this has been a controversial choice (e.g., Freeman and Groom 2015 EJ; Gollier and Zeckhauser 2005 JPE; Heal and Millner 2014 PNAS; Iverson 2013 JEEM; Jouini et al. 2010 JET; Millner and Heal 2017 WP; Weitzman and Gollier 2010 EL)

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Combining expert advice

We consider aggregation methods proposed by Jouini et al. (2010 JET) and Freeman and Groom (2015 EJ) and apply them to our data While we acknowledge that different approaches to aggregating SRRs exist (Millner 2016 WP) and that there is a literature on aggregating δ (e.g., Gollier and Zeckhauser 2005 JPE), the methods proposed by Jouini et al. (2010 JET) and Freeman and Groom (2015 EJ) are the more relevant for our exercise From now on, assume ηi = 1

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Combining expert advice: Jouini et al. (2010 JET)

Jouini et al. (2010 JET) assume that each expert took a normative position when responding to the survey, and propose a framework where the social planner resolves the disagreement over δi > 0 and gi in a hypothetical market between experts (with wi being the initial endowments of expert i) The discount rate is given by R(H) = − 1 Hln

• n
• i=1

wiδi n

j=1 wjδj

e−Hri

• Drupp/Freeman/Groom/Nesje

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Combining expert advice: Freeman and Groom (2015 EJ)

In the mixed normative-positive approach of Freeman and Groom (2015 EJ), δi is treated as a normative parameter and gi as a positive parameter. Growth forecasts are aggregated to say that g ∼ N(µ, σ2/N), where µ and σ2 are the sample mean and variance of growth forecasts and N is the effective number of independent expert observations The discount rate is given by R(H) = − 1 Hln n

i=1 δie−Hδi

n

i=1 δi

e−Hµ+0.5H2σ2/N

• Drupp/Freeman/Groom/Nesje

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Combining expert advice

0 ¡% ¡ 1 ¡% ¡ 2 ¡% ¡ 3 ¡% ¡ 4 ¡% ¡ 5 ¡% ¡ 0 ¡ 50 ¡ 100 ¡ 150 ¡ 200 ¡ 250 ¡ 300 ¡ 350 ¡ 400 ¡

Winsorised ¡

Gamma ¡discoun3ng ¡ Weighted ¡Gamma ¡discoun3ng ¡ Mixed ¡norma3ve-­‑posi3ve ¡ Gamma ¡discoun3ng ¡

(a)

0 ¡% ¡ 1 ¡% ¡ 2 ¡% ¡ 3 ¡% ¡ 4 ¡% ¡ 0 ¡ 50 ¡ 100 ¡ 150 ¡ 200 ¡ 250 ¡ 300 ¡ 350 ¡ 400 ¡

All ¡data ¡

Gamma ¡discoun3ng ¡ Weighted ¡Gamma ¡discoun3ng ¡ Data-­‑driven ¡

(b)

Figure (a) illustrates the time schedules of discount rates for (winsorized) SRR data. Figure (b) illustrates the time schedules of discount rates for SDR data. H (in years) is measured along the x-axis, while R(H) is measured along the y-axis.

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Implications for climate policy

0,002 0,004 0,006 0,008 0,01 0,012 0,014 0,016 0,018 0,02 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400

Percentage of the total cash flow arising each fifth year from DICE 2016 (Nordhaus 2017 PNAS). H (in years) is measured along the x-axis, while the percentage of the total cash flow arising in each fifth year is measured along the y-axis

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Implications for climate policy

Approach SRR SDR Gamma discounting 53.7 113.9 Weighted Gamma discounting 11.2 47.7 Mixed normative-positive Gamma discounting 8.0 . Data-driven . 28.2 The SCC is given in USD. Calculations are based on (winsorized) SRR data and SDR data. The data-driven approach is a 2 percent flat rate

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Conclusions

Overall, we find that the precise schedule of discount rates and the resulting SCC vary substantially with the data source as well as the aggregation approach employed Reported SCC estimates based on the SDR are higher than comparable estimates in the literature

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