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Discounting future healthcare costs and benefits(Part 1)

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CHE Seminar presentation 7 December 2017 by Ben Groom, Associate Professor of Environment and Development Economics, LSE

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Discounting future healthcare costs and benefits(Part 1)

  1. 1. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying Social Discount Rates: Uncertainty, Heterogeneity and Project Risk Ben Groom (LSE) Centre for Health Economics, University of York December 7th, 2017
  2. 2. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Impatience, self-control and hyperbolic discounting
  3. 3. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Impatience, self-control and hyperbolic discounting Figure: Source: The New Yorker.
  4. 4. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials The Social Discount Rate Risk Free Projects
  5. 5. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 ) + ...
  6. 6. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 ) + ...
  7. 7. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  8. 8. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  9. 9. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  10. 10. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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.
  11. 11. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  12. 12. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  13. 13. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  14. 14. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  15. 15. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 Equilibrium r = δ + ηgc (=STP)
  16. 16. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 Equilibrium r = δ + ηgc (=STP) Debate: which is appropriate when distortions exist (e.g. Burgess and Zerbe 2014; Moore et al 2013; Spackman 2017)
  17. 17. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 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
  18. 18. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs for Risk Free Projects Figure: Source Groom and Hepburn (2017)
  19. 19. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertainty in growth Risk Free Projects
  20. 20. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertainty in growth Risk Free Projects General Growth Uncertainty
  21. 21. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  22. 22. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  23. 23. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  24. 24. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  25. 25. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  26. 26. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  27. 27. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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, ‘jump risk’
  28. 28. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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, ‘jump risk’ See Gollier (2012)
  29. 29. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertainty in growth (risk free)
  30. 30. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertainty in growth (risk free) Example: Brownian Motion ln (ct+1/ct ) = ˜x, ˜x N µ, σ2 c
  31. 31. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertainty in growth (risk free) 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
  32. 32. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertainty in growth (risk free) 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
  33. 33. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertainty in growth (risk free) 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
  34. 34. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertainty in growth (risk free) 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: Jump Risk Suppose that GDP loss % of λ with probability p
  35. 35. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertainty in growth (risk free) 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: Jump Risk Suppose that GDP loss % of λ with probability p SDRH = δ + H 1 ln [p(1 λ) + (1 p)E exp ( η ˜gH H)]
  36. 36. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertainty in growth (risk free) 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: Jump Risk Suppose that GDP loss % of λ with probability p SDRH = δ + H 1 ln [p(1 λ) + (1 p)E exp ( η ˜gH H)]
  37. 37. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertainty in growth (risk free) 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: Jump Risk Suppose that GDP loss % of λ with probability p SDRH = δ + H 1 ln [p(1 λ) + (1 p)E exp ( η ˜gH H)] Example: Parameter Uncertainty i.i.d. shocks, but uncertainty about the mean parameter µi
  38. 38. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertainty in growth (risk free) 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: Jump Risk Suppose that GDP loss % of λ with probability p SDRH = δ + H 1 ln [p(1 λ) + (1 p)E exp ( η ˜gH H)] Example: Parameter Uncertainty i.i.d. shocks, but uncertainty about the mean parameter µi ˜xi N µi , σ2 c (i = 1, 2, ...n)
  39. 39. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertainty in growth (risk free) 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: Jump Risk Suppose that GDP loss % of λ with probability p SDRH = δ + H 1 ln [p(1 λ) + (1 p)E exp ( η ˜gH H)] 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 + H 1 ln [E exp ( η ˜gH H)]
  40. 40. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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, p1 = 1/3, p2 = 2/3
  41. 41. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertain interest rates Expected NPV (Weitzman 2001, Newell and Pizer 2003, Freeman et al 2015) exp ( RH H) = E [exp ( ˜rH)] ! RH = SDRH = 1 H ln E [exp ( ˜rH)]
  42. 42. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertain interest rates Expected NPV (Weitzman 2001, Newell and Pizer 2003, Freeman et al 2015) exp ( RH H) = E [exp ( ˜rH)] ! RH = SDRH = 1 H ln E [exp ( ˜rH)] Gamma Discounting (Weitzman 2001, American Economic Review).
  43. 43. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Uncertain interest rates Expected NPV (Weitzman 2001, Newell and Pizer 2003, Freeman et al 2015) exp ( RH H) = E [exp ( ˜rH)] ! RH = SDRH = 1 H ln E [exp ( ˜rH)] Gamma Discounting (Weitzman 2001, American Economic Review). Time series applications of Weitzman (1998) ENPV approach
  44. 44. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs: Heterogeneity Di¤erences in expert opinion, or heterogeneous time preferences 0.05.1.15.2 Density 0 10 20 30 Weitzman Gamma Weitzman’s ‘Gamma’Distibution of the SDR for Climate Change (Weitzman 2001) 0.2.4.6.8 Density 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)
  45. 45. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 wi U ci (C (t) , t) exp ( δi t)
  46. 46. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 wi U ci (C (t) , t) exp ( δi t) ci is the optimised path for agent i.
  47. 47. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 wi U ci (C (t) , t) exp ( δi t) ci is the optimised path for agent i.
  48. 48. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 wi U ci (C (t) , t) exp ( δi t) ci is the optimised path for agent i. Is there a Representative Pure Time Preference?
  49. 49. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 wi U ci (C (t) , t) exp ( δi t) ci is the optimised path for agent i. Is there a Representative Pure Time Preference? Answer: Yes!
  50. 50. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 wi U ci (C (t) , t) exp ( δi t) ci is the optimised path for agent i. Is there a Representative Pure Time Preference? Answer: Yes! δη (H) = h ∑i δi (wi exp ( δi H)) 1 η i / h ∑i (wi exp ( δi H)) 1 η i
  51. 51. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 wi U ci (C (t) , t) exp ( δi t) ci is the optimised path for agent i. Is there a Representative Pure Time Preference? Answer: Yes! δη (H) = h ∑i δi (wi exp ( δi H)) 1 η i / h ∑i (wi exp ( δi H)) 1 η i Declines to the lowest value of δi as H goes to in…nity
  52. 52. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  53. 53. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  54. 54. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  55. 55. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  56. 56. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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)
  57. 57. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  58. 58. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  59. 59. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  60. 60. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Time Varying SDRs with Risky Projects δ = 0, η = 2, µ 2 [0%, 3%] , symmetric Figure: Term Structure of Discount Rates for Risky Projects by β. Source: Gollier (2012b)
  61. 61. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  62. 62. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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)
  63. 63. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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)
  64. 64. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  65. 65. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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%)
  66. 66. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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%)
  67. 67. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  68. 68. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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?)
  69. 69. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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?)
  70. 70. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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)
  71. 71. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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)
  72. 72. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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)
  73. 73. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  74. 74. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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)
  75. 75. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Project Betas French Guidelines (Gollier 2011) Sector Estimated consumption Beta Agriculture, Silviculture and Fisheries 0.85 Industry 2.09 Automobile Industry 4.98 Manufacture of Mechanical Equipment 3.00 Intermediate Industries 2.76 Energy 0.85 Construction 1,45 Transport 1.60 Administrative Services -0.09 Education 0.11 Health -0.24 Financial Services 0.15 Financial Intermediation 0.49 Assurance -0.36
  76. 76. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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).
  77. 77. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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).
  78. 78. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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?
  79. 79. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  80. 80. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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.
  81. 81. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  82. 82. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  83. 83. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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’
  84. 84. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 > 0
  85. 85. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 > 0
  86. 86. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 > 0 Practical Advice SDR important (country speci…c), but so is valuation
  87. 87. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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 > 0 Practical Advice SDR important (country speci…c), but so is valuation Empirical work exists to help guide decision makers
  88. 88. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  89. 89. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Estimating SDR Parameters using Expert Opinion: Economists Drupp et al (2015) ‘Discounting Disentangled’. 0.2.4.6.8 Density 0 2 4 6 8 Rate of societal pure time preference (in %) 0.1.2.3 Density 0 2 4 6 8 10 Real SDR (in %)
  90. 90. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Estimating SDR Parameters using Expert Opinion? Drupp et al (2015) ‘Discounting Disentangled’. 1% 2% 0.2.4.6.81 Density -5 0 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%
  91. 91. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  92. 92. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  93. 93. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects Estimating the Parameters of the SDR Conclusion Additional Materials Social Discounting: References Cropper, M.,Freeman,M.,Groom,B.,Pizer,W.,2014.Declining discount rates.Am.Econ.Rev.:Pap.Proc.104,538–543. 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.
  94. 94. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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
  95. 95. Time Varying SDRs Ben Groom Individual Time Preferences The Social Discount Rate Time Varying Social Discount Rates Uncertainty Heterogeneity Risky Projects 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.

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