s : Accounting for the timing of costs and bene ts in the evaluation of health projects relevant to LMICs (LSE) Harvard Club, Boston, September 14th, 2017
The Rate Risk Free Projects s Discounted Utilitarian SWF W 0 = u (c 0 ) + exp ( δ) u (c 1 ) +... exp ( δt ) u (c T ) +... Ramsey Rule = δ + ηg c g c = consumption growth 2 consumption side arguments for discounting, 3 parameters (δ,η, g c ) 1 Utility discounting: pure time preference, δ. 2 Societal Wealth E ect : ηg c
The Rate Risk Free Projects s Production side, opportunity cost arguments: = r Risk free projects: Risk-free interest rate, cost of borrowing Risky Projects (systematic risk): Asset prices or consumption related equivalent Equilibrium r = δ + ηg c (=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
s for Risk Free Projects s Figure: Source Groom and Hepburn (2017)
s: Uncertainty in growth Risk Free Projects s General Growth Uncertainty lower re ecting precautionary saving H = δ + ηḡ f η, σ 2 c,h, σ3 c,h, σ4 c,h Wealth E ect Precautionary Savings E ect Term Structure of 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
s: Uncertainty in growth Risk Free Projects s Example: Brownian Motion ln (c t+1 /c t ) = x, x N µ, σ 2 c = δ + ηḡ 0.5η (η + 1) σ 2 c Wealth E ect Prudence E ect lower, at term structure Example: Parameter Uncertainty i.i.d. shocks, but uncertainty about the mean parameter µ i x i N µ i, σ 2 c (i = 1, 2,...n) H = δ + H 1 ln [E exp ( η g H H)]
s: Uncertainty in growth s ḡ1 L, ḡ 2 L = (1%, 3%) ; ḡ1 H, ḡ 2 H = (0%, 3.5%) ; δ = 1%, η = 2
s: Uncertain interest rates Expected Net Present Value (Weitzman 2001, Newell and Pizer 2003, Freeman et al 2015) s exp ( R H H) = E [exp ( rh)]! R H = 1 ln E [exp ( rh)] H Gamma Discounting (Weitzman Time series applications of 2001, American Economic Review). Weitzman (1998) ENPV approach
Density 0.05.1.15.2 Density 0.2.4.6.8 s: Heterogeneity Di erences in expert opinion, or heterogeneous time preferences s 0 10 20 30 Weitzman Gamma Weitzman s Gamma Distibution of the for Climate Change (Weitzman 2001) 0 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)
s: Heterogeneity Heterogeneous pure time preference and the representative agent (Heal and Millner 2013, PNAS, Gollier and Zeckhauser 2005, Freeman and Groom 2015) s Welfare function with heterogeneous agents (H&M 2013) W (C (t), t) = i w i U c i (C (t), t) exp ( δ i t) c i is the optimised path for agent i. Is there a Representative Pure Time Preference? Answer: Yes! h δ η (H) = i δ i (w i exp ( i h δ i H)) η 1 / i (w i exp ( Declines to the lowest value of δ i as H goes to in nity i δ i H)) η 1
s: Heterogeneity Heterogeneous pure time preference and the representative agent (Heal and Millner 2013, PNAS, Gollier and Zeckhauser 2005, Freeman and Groom 2015) s Figure: Representative Pure Time Preference: δ
s with Risky Projects Gollier (2012, 2012b) s Consumption CAPM Growth is i.i.d r (β) = δ + ηµ η 2 σ 2 c + βησ 2 c Prudence Project Speci c Risk Premium Growth is Persistent: e.g. Parameter Uncertainty r 0 (β) = δ + η µ + ησ 2 (β 0.5η) δ + ηµmin + ησ r (β) = 2 (β 0.5η) if β 0 δ + ηµ max + ησ 2 (β 0.5η) if β > η Term Structure of Risky Discount in CCAPM Precautionary e ect and the risk premium work in opposite directions in most public investment cases: β > 0
s with Risky Projects s Figure: Term structure of Discount for Risky Projects by β. Source: Gollier (2012b)
Utility discount rate, Elasticity of Marginal Utility, growth and interest rates s Utility 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, g c and rates of return r Historical data, econometrics (N&P 2003) Expert surveys (Drupp et al. 2015, Pindyck 2017)
Estimating Parameters Utility discount rate as a survival rate (Fenichel et al. 2017) s Figure: Demographic δ : Survival hazard rate aggregated across the population (Function of mortality rate and life expectancy at each age)
Estimating Parameters Revealed preference measures of the elasticity of marginal utility, UK (Groom and Maddison 2017) s 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
Estimating Parameters Long-term discount rate: Evidence from housing ownership (Giglio et al 2015; Fesselmeyer et al. 2017) s Figure: Declining Discount in housing tenure: (Fesselmeyer et al. 2017)
Estimating Term Structures Gollier and Mahul 2017 s Figure: Term Structure of Risk Free Rate (left) and Aggregate Risk Premium (right) (Gollier and Mahul 2017).
Estimating Term Structures Gollier and Mahul 2017 s Figure: Term Structure of Risk Free Rate (left) and Aggregate Risk Premium (right) (Gollier and Mahul 2017).
Project Appraisal in LMICs s Declining Discount for risk free projects TVs? Empirics: persistence? variability? risk prefs? Prudence and high variability: large prudence e ects Low growth, low : Liberia, DRC, (-2%) etc. High growth, high : 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 important (country speci c), but so is valuation Empirical work exists
s: Uncertainty in growth: Parameter uncertainty Example from previous French Guidelines (Lebegue 2005, p 102) s ḡ 1 = 0.5%, ḡ 2 = 2%, δ = 1%, η = 2
Estimating Parameters using Expert Opinion: Economists Drupp et al (2015) Discounting Disentangled. Density 0.2.4.6.8 Density 0.1.2.3 s 0 2 4 6 8 Rate of societal pure time preference (in %) 0 2 4 6 8 10 Real (in %)
0.2.4.6.8 1 Density Estimating Parameters using Expert Opinion? Drupp et al (2015) Discounting Disentangled. s 1% 2% 5 0 5 10 15 Lower Bound of Range 3% range 2% range 0% Range (point value) 92% of economists agree on long run between 1% and 3%
Estimating Parameters using expert opinion: Economists s 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 () 2.27 1.62 2.00 2.00 0.00 10.00 lower bound 1.12 1.62 1.00 0.00-3.00 8.00 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
Estimating Parameters: Which Experts? or Public Opinion? s Table: Disagreement between Experts and Members of the Public? (%) Source 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
ing: References s Drupp, M.A., Freeman,M.C.,Groom,B., Nesje,F., 2015. Discounting Disentangled: An Expert Survey on the Determinants of the Long-Term 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.
ing: References s 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... 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. Journal of bene t-cost analysis, Vol. 6.2015, 1, p. 6-32
ing: References s 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 ing... 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.