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Discounting future healthcare costs and benefits(Part 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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
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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.
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E¤ect: in‡ated past, discounted future? Journal of
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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
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Groom, B., Maddison,D.J. ,2013. Non-Identical Quadruplets:
Four New Estimates of the Elasticity of Marginal Utility for the
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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.....
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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
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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.