Time Varying SDRs Time Varying Social Discount Rates: Ben Groom Individual Time Accounting for the timing of costs and bene…ts in the evaluation Preferences of health projects relevant to LMICs The Social Discount Rate Time Varying Social Discount Rates Ben Groom (LSE) Estimating the Parameters of the SDR Conclusion Harvard Club, Boston, September 14th, 2017 Additional Materials
The Social Discount Rate Risk Free Projects Time Varying SDRs Ben Groom Discounted Utilitarian SWF Individual Time Preferences W 0 = u ( c 0 ) + exp ( � δ ) u ( c 1 ) + .... exp ( � δ T ) u ( c T ) + ... The Social Discount Rate Time Varying Ramsey Rule Social Discount Rates Estimating the SDR = δ + η g c Parameters of the SDR g c = consumption growth Conclusion Additional Materials 2 consumption side arguments for discounting, 3 parameters ( δ , η , g c ) 1 Utility discounting: pure time preference, δ . 2 Societal ‘Wealth E¤ect’: η g c
The Social Discount Rate Risk Free Projects Time Varying SDRs Ben Groom Production side, opportunity cost arguments: SDR = r Individual Time Preferences Risk free projects: Risk-free interest rate, cost of borrowing The Social Discount Rate Risky Projects (systematic risk): Asset prices or consumption Time Varying related equivalent Social Discount Rates Estimating the Parameters of the Equilibrium SDR Conclusion r = δ + η g c (=STP) Additional Materials 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
Time Varying SDRs for Risk Free Projects 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 Figure: Source Groom and Hepburn (2017)
Time Varying SDRs: Uncertainty in growth Risk Free Projects Time Varying SDRs General Growth Uncertainty Ben Groom SDR lower re‡ecting precautionary saving Individual Time � � Preferences η , σ 2 c , H , σ 3 c , H , σ 4 SDR H = δ + � f η ¯ g The Social c , H Discount Rate Wealth E¤ect Precautionary Savings E¤ect Time Varying Social Discount Rates Estimating the Term Structure of SDR Parameters of the SDR Conclusion Depends on the expected di¤usion of consumption growth Additional Materials Growth Di¤usion: examples Independent growth shocks: Brownian Motion Persistence : drift, parameter uncertainty, regime switches See Gollier 2013
Time Varying SDRs: Uncertainty in growth Risk Free Projects Time Varying SDRs Ben Groom Example: Brownian Motion Individual Time � � Preferences µ , σ 2 ln ( c t + 1 / c t ) = ˜ x , ˜ x � N The Social c Discount Rate � 0 . 5 η ( η + 1 ) σ 2 SDR = δ + η ¯ g Time Varying c Social Discount Wealth E¤ect Prudence E¤ect Rates lower SDR, ‡at term structure Estimating the Parameters of the SDR Conclusion Example: Parameter Uncertainty Additional Materials i.i.d. shocks, but uncertainty about the mean parameter µ i � � µ i , σ 2 x i � N ˜ ( i = 1 , 2 , ... n ) c SDR H = δ + H � 1 ln [ E exp ( � η ˜ g H H )]
Time Varying SDRs: Uncertainty in growth Time Varying � � � � SDRs g L g L g H g H Ben Groom ¯ 1 , ¯ = ( 1 %, 3 % ) ; ¯ 1 , ¯ = ( 0 %, 3 . 5 % ) ; 2 2 Individual Time = 1 %, η = 2 δ 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) Time Varying SDRs Ben Groom rH )] ! R H = � 1 Individual Time exp ( � R H H ) = E [ exp ( � ˜ H ln E [ exp ( � ˜ rH )] Preferences The Social Discount Rate Time Varying Social Discount Rates Estimating the Parameters of the SDR Conclusion Additional Materials Gamma Discounting (Weitzman Time series applications of 2001, American Economic Review). Weitzman (1998) ENPV approach
Time Varying SDRs: Heterogeneity Di¤erences in expert opinion, or heterogeneous time preferences Time Varying SDRs Ben Groom Individual Time 8 . .2 Preferences The Social Discount Rate .15 6 . Time Varying Social Discount Density .1 y t Rates i 4 s n . e D Estimating the Parameters of the .05 SDR 2 . Conclusion 0 0 10 20 30 Additional 0 0 2 4 6 8 Materials Weitzman Gamma Rate of societal pure time preference (in %) Weitzman’s ‘Gamma’ Distibution of Pure rate of time preference, δ . the SDR for Climate Change Discounting Expert Survey by (Weitzman 2001) Drupp et al. (2015)
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) Time Varying SDRs Ben Groom Individual Time Welfare function with heterogeneous agents (H & M 2013) Preferences � � The Social c � W ( C ( t ) , t ) = ∑ i w i U Discount Rate i ( C ( t ) , t ) exp ( � δ i t ) Time Varying c � i is the optimised path for agent i . Social Discount Rates Estimating the Parameters of the SDR Is there a Representative Pure Time Preference? Conclusion Additional Answer: Yes! Materials h i h i 1 1 δ � η ( H ) = ∑ i δ i ( w i exp ( � δ i H )) / ∑ i ( w i exp ( � δ i H )) η η Declines to the lowest value of δ i as H goes to in…nity
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) 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 Figure: Representative Pure Time Preference: δ �
Time Varying SDRs with Risky Projects Gollier (2012, 2012b) Time Varying Consumption CAPM SDRs Ben Groom Growth is i.i.d Individual Time Preferences r ( β ) = δ + ηµ � η 2 σ 2 βησ 2 + c c The Social Prudence Project Speci…c Risk Premium Discount Rate Time Varying Social Discount Rates Growth is Persistent: e.g. Parameter Uncertainty Estimating the Parameters of the µ + ησ 2 ( β � 0 . 5 η ) SDR r 0 ( β ) = δ + η ¯ � Conclusion δ + ηµ min + ησ 2 ( β � 0 . 5 η ) if β � 0 Additional r ∞ ( β ) = δ + ηµ max + ησ 2 ( β � 0 . 5 η ) Materials 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
Time Varying SDRs with Risky Projects 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 Figure: Term structure of Discount Rates for Risky Projects by β . Source: Gollier (2012b)
Estimating the Parameters of the SDR Utility discount rate, Elasticity of Marginal Utility, growth and interest rates Time Varying Utility Discount Rate SDRs Ben Groom Ethics: Impartial Consequentialism δ = 0 (Ramsey, Stern.. etc) Individual Time Preferences Agent relative ethics δ > 0 (e.g. Arrow 1999) The Social Discount Rate Catastrophic risk (e.g. Stern 0.1 % ), survival rates Time Varying Calibration to the interest rate (Nordhaus, IAMs, 3 % -1.5 % ) Social Discount Rates Estimating the Parameters of the Elasticity of Marginal Utility: η SDR Conclusion Revealed Preference: risk or inequality aversion, smoothing c Additional Materials 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 SDR Parameters Utility discount rate as a survival rate (Fenichel et al. 2017) 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 Figure: Demographic δ : Survival hazard rate aggregated across the population (Function of mortality rate and life expectancy at each age)
Estimating SDR Parameters Revealed preference measures of the elasticity of marginal utility, UK (Groom and Maddison 2017) Time Varying SDRs Ben Groom Table: Revealed Preference estimates of η in the UK Individual Time Preferences Methodology StDev η The Social Inequality Aversion Discount Rate Progressive Taxes 1.52 0.047 Time Varying Progressive Taxes (historical) 1.57 0.48 Social Discount Rates Consumption Smoothing Estimating the Euler Equation 1.58 0.21 Parameters of the SDR Product Substitution Frisch Parameter 3.56 2.19 Conclusion Risk Aversion Additional Materials 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 SDR Parameters Long-term discount rate: Evidence from housing ownership (Giglio et al 2015; Fesselmeyer et al. 2017) 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 Figure: Declining Discount Rates in housing tenure: (Fesselmeyer et al. 2017)
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