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Time Varying SDRs Time Varying Social Discount Rates: Ben Groom Individual Time Accounting for the timing of costs and benets in the evaluation Preferences of health projects relevant to LMICs The Social Discount Rate Time Varying

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Time Varying Social Discount Rates:

Accounting for the timing of costs and bene…ts in the evaluation

  • f health projects relevant to LMICs

Ben Groom (LSE) Harvard Club, Boston, September 14th, 2017

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

The Social Discount Rate

Risk Free Projects

Discounted Utilitarian SWF W0 = u (c0) + exp (δ) u (c1) + .... exp (δT) u (cT ) + ... Ramsey Rule SDR = δ + ηgc gc = consumption growth 2 consumption side arguments for discounting, 3 parameters (δ,η, gc)

1 Utility discounting: pure time preference, δ. 2 Societal ‘Wealth E¤ect’: ηgc

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

The Social Discount Rate

Risk Free Projects

Production side, opportunity cost arguments: SDR = r Risk free projects: Risk-free interest rate, cost of borrowing Risky Projects (systematic risk): Asset prices or consumption related equivalent Equilibrium r = δ + ηgc (=STP) Debate: which is appropriate when distortions exist (e.g. Burgess and Zerbe 2014; Moore et al 2013; Spackman 2017) Shadow cost of capital approach: convert to consumption and discount using STP

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Time Varying SDRs for Risk Free Projects

Figure: Source Groom and Hepburn (2017)

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Time Varying SDRs: Uncertainty in growth

Risk Free Projects

General Growth Uncertainty SDR lower re‡ecting precautionary saving SDRH = δ + η ¯ g

Wealth E¤ect

f

  • η, σ2

c,H, σ3 c,H, σ4 c,H

  • Precautionary Savings E¤ect

Term Structure of SDR Depends on the expected di¤usion of consumption growth Growth Di¤usion: examples Independent growth shocks: Brownian Motion Persistence : drift, parameter uncertainty, regime switches See Gollier 2013

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Time Varying SDRs: Uncertainty in growth

Risk Free Projects

Example: Brownian Motion ln (ct+1/ct) = ˜ x, ˜ x N

  • µ, σ2

c

  • SDR = δ +

η ¯ g

Wealth E¤ect

0.5η (η + 1) σ2

c Prudence E¤ect

lower SDR, ‡at term structure Example: Parameter Uncertainty i.i.d. shocks, but uncertainty about the mean parameter µi ˜ xi N

  • µi, σ2

c

  • (i = 1, 2, ...n)

SDRH = δ + H1 ln [E exp (η ˜ gHH)]

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Time Varying SDRs: Uncertainty in growth

  • ¯

gL

1 , ¯

gL

2

  • =

(1%, 3%) ;

  • ¯

gH

1 , ¯

gH

2

  • = (0%, 3.5%) ;

δ = 1%, η = 2

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Time Varying SDRs: Uncertain interest rates

Expected Net Present Value (Weitzman 2001, Newell and Pizer 2003, Freeman et al 2015)

exp (RHH) = E [exp (˜ rH)] ! RH = 1 H ln E [exp (˜ rH)] Gamma Discounting (Weitzman 2001, American Economic Review). Time series applications of Weitzman (1998) ENPV approach

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Time Varying SDRs: Heterogeneity

Di¤erences in expert opinion, or heterogeneous time preferences

.05 .1 .15 .2 Density 10 20 30 Weitzman Gamma

Weitzman’s ‘Gamma’ Distibution of the SDR for Climate Change (Weitzman 2001)

. 2 . 4 . 6 . 8 D e n s i t y 2 4 6 8 Rate of societal pure time preference (in %)

Pure rate of time preference, δ. Discounting Expert Survey by Drupp et al. (2015)

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Time Varying SDRs: Heterogeneity

Heterogeneous pure time preference and the representative agent (Heal and Millner 2013, PNAS, Gollier and Zeckhauser 2005, Freeman and Groom 2015)

Welfare function with heterogeneous agents (H&M 2013) W (C (t) , t) = ∑i wiU

  • c

i (C (t) , t)

  • exp (δit)

c

i is the optimised path for agent i.

Is there a Representative Pure Time Preference? Answer: Yes! δ

η (H) =

h ∑i δi (wi exp (δiH))

1 η

i / h ∑i (wi exp (δiH))

1 η

i Declines to the lowest value of δi as H goes to in…nity

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Time Varying SDRs: Heterogeneity

Heterogeneous pure time preference and the representative agent (Heal and Millner 2013, PNAS, Gollier and Zeckhauser 2005, Freeman and Groom 2015)

Figure: Representative Pure Time Preference: δ

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Time Varying SDRs with Risky Projects

Gollier (2012, 2012b)

Consumption CAPM Growth is i.i.d r (β) = δ + ηµ η2σ2

c Prudence

+ βησ2

c Project Speci…c Risk Premium

Growth is Persistent: e.g. Parameter Uncertainty r0 (β) = δ + η ¯ µ + ησ2 (β 0.5η) r∞ (β) =

  • δ + ηµmin + ησ2 (β 0.5η)

if β 0 δ + ηµmax + ησ2 (β 0.5η) if β > η Term Structure of Risky Discount Rates in CCAPM Precautionary e¤ect and the risk premium work in opposite directions in most public investment cases: β > 0

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Time Varying SDRs with Risky Projects

Figure: Term structure of Discount Rates for Risky Projects by β. Source: Gollier (2012b)

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Estimating the Parameters of the SDR

Utility discount rate, Elasticity of Marginal Utility, growth and interest rates

Utility Discount Rate Ethics: Impartial Consequentialism δ = 0 (Ramsey, Stern.. etc) Agent relative ethics δ > 0 (e.g. Arrow 1999) Catastrophic risk (e.g. Stern 0.1%), survival rates Calibration to the interest rate (Nordhaus, IAMs, 3%-1.5%) Elasticity of Marginal Utility: η Revealed Preference: risk or inequality aversion, smoothing c Experimental methods, expert surveys (which experts?) Growth, gc and rates of return r Historical data, econometrics (N&P 2003) Expert surveys (Drupp et al. 2015, Pindyck 2017)

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Estimating SDR Parameters

Utility discount rate as a survival rate (Fenichel et al. 2017)

Figure: Demographic δ : Survival hazard rate aggregated across the population (Function of mortality rate and life expectancy at each age)

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Estimating SDR Parameters

Revealed preference measures of the elasticity of marginal utility, UK (Groom and Maddison 2017)

Table: Revealed Preference estimates of η in the UK

Methodology η StDev Inequality Aversion Progressive Taxes 1.52 0.047 Progressive Taxes (historical) 1.57 0.48 Consumption Smoothing Euler Equation 1.58 0.21 Product Substitution Frisch Parameter 3.56 2.19 Risk Aversion Insurance Demand 2.19 0.24 Subjective Well-being Happiness survey 1.32 0.17 Pooled Estimate Fixed E¤ects 1.53 Parameter Homogeneity Chi-sq(5) = 9.98 (p=0.076) Source: Groom and Maddison 2017

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Estimating SDR Parameters

Long-term discount rate: Evidence from housing ownership (Giglio et al 2015; Fesselmeyer et al. 2017)

Figure: Declining Discount Rates in housing tenure: (Fesselmeyer et al. 2017)

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Estimating SDR Term Structures

Gollier and Mahul 2017

Figure: Term Structure of Risk Free Rate (left) and Aggregate Risk Premium (right) (Gollier and Mahul 2017).

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Estimating SDR Term Structures

Gollier and Mahul 2017

Figure: Term Structure of Risk Free Rate (left) and Aggregate Risk Premium (right) (Gollier and Mahul 2017).

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Conclusion

Project Appraisal in LMICs

Declining Discount Rates for risk free projects TVSDRs? Empirics: persistence? variability? risk prefs? Prudence and high variability: large prudence e¤ects Low growth, low SDR: Liberia, DRC, (-2%) etc. High growth, high SDR: Botswana, South Africa (+4%), etc Risky Projects Term structure for risky projects depends on the ‘beta’ Risk premium rises with the time horizon for β > η Practical Advice SDR important (country speci…c), but so is valuation Empirical work exists

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Time Varying SDRs: Uncertainty in growth: Parameter uncertainty

Example from previous French Guidelines (Lebegue 2005, p 102)

¯ g1 = 0.5%, ¯ g2 = 2%, δ = 1%, η = 2

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Estimating SDR Parameters using Expert Opinion: Economists

Drupp et al (2015) ‘Discounting Disentangled’.

. 2 . 4 . 6 . 8 D e n s i t y 2 4 6 8 Rate of societal pure time preference (in %) . 1 . 2 . 3 D e n s i t y 2 4 6 8 10 Real SDR (in %)

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Estimating SDR Parameters using Expert Opinion?

Drupp et al (2015) ‘Discounting Disentangled’.

1% 2% .2 .4 .6 .8 1 Density

  • 5

5 10 15 Lower Bound of Range 3% SDR range 2% SDR range 0% SDR Range (point value)

92% of economists agree on long run SDR between 1% and 3%

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Estimating SDR Parameters using expert opinion: Economists

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

  • 2.00

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

  • 3.00

8.00 SDR upper bound 4.14 2.80 3.50 3.00 0.00 20.00 Number of quantitative responses Number of qualitative responses Total number of respondents

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Estimating SDR Parameters: Which Experts? or Public Opinion?

Table: Disagreement between Experts and Members of the Public? (%)

Source SDR PRTP η N Economists Mean 2.27 1.1 1.35 Median 2.00 0.50 1.00 186 StDev 1.62 1.47 0.85 Philosophers Mean 2.1 1.3 1.70 Median 2.00 0.00 2.00 16 StDev 1.43 3.46 1.51 Public Mean 1.85 1.43 1.67 Median 1.45 1.04 2.04 100 StDev 1.43 1.04 1.19

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Social Discounting: References

Drupp, M.A., Freeman,M.C. ,Groom,B., Nesje,F., 2015. Discounting Disentangled: An Expert Survey on the Determinants of the Long-Term Social Discount Rate. Grantham Research Institute Working Paper No.172. London School of Economics. Fenichel et al (2017). Even the representative agent must die!.... NBER Working Paper No. w23591 Freeman,M.C.,Groom,B.,2015. Positively gamma discounting: combining the opinions of experts on the social discount rate. Econ.J. 125,1015–1024. Freeman, et al, 2015. Declining discount rates and the Fisher E¤ect: in‡ated past, discounted future? Journal of Environmental Economics and Management, 73, pp. 32-39 Gollier, C., 2012. Pricing the Planet’s Future: The Economics of Discounting in an Uncertain World. Princeton University Press, Princeton.

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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Social Discounting: References

Gollier, Christian. 2013. “Evaluation of Long-Dated Investments Under Uncertain Growth Trend, Volatility and Catastrophes.” Toulouse School of Economics TSE Working Papers 12-361. Gollier, Christian. 2012b. Term Structures of discount rates for risky investments IDEI, mimeo. Groom B and Hepburn C (2017). Looking back at Social Discount Rates..... Review of Environmental Economics and Policy, Volume 11, Issue 2, 1 July 2017, Pages 336–356, https://doi.org/10.1093/reep/rex015 Groom, B., Maddison,D.J. ,2013. Non-Identical Quadruplets: Four New Estimates of the Elasticity of Marginal Utility for the

  • UK. Grantham Institute Centre for Climate Change Economics

and Policy Working Paper No.141. Harberger A.C. and Jenkins G (2015). Musings on the Social Discount Rate. Journal of bene…t-cost analysis, Vol. 6.2015, 1,

  • p. 6-32
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Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials

Social Discounting: References

Heal,G. and Millner, A.,2014. Agreeing to disagree on climate

  • policy. Proc. Natl. Acad. Sci. 111, 3695–3698.

Moore et al (2013). More Appropriate Social Discounting..... Journal of Bene…t-Cost Analysis, 2013, vol. 4, issue 1, 1-16 Newell R and Pizer W (2003). Discounting the bene…ts of climate change: How much do uncertain interest rates increase valuations? Journal of Environmental Economics and Management, 46(1), 52-74. Weitzman,M.L.,1998.Why the far-distant future should be discounted at its lowest possible rate. J.Environ.Econ.Manag.36,201–208. Weitzman,M.L.,2001.Gamma discounting. Am.Econ.Rev.91,260–271.