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Catastrophic risks and the value of health projects
Mark Freeman
Centre for Health Economics, York
7th December 2017
Mark Freeman (University of York) Risk & Valuation December 2017 1 / 20
What is appropriate for valuing healthcare in LMICs?
Risk matters
Macroeconomic risk has a different valuation implication
(precautionary saving) than project uncertainty (risk premium)
Risk should not be measured by standard deviation alone. Higher
moments matter
Low probability, but potentially catastrophic, economic outcomes can
significantly influence valuations
Risk premiums can be negative, increasing healthcare project
valuation
National or international perspective?
Mark Freeman (University of York) Risk & Valuation December 2017 2 / 20
Risk-free or risk-adjusted discounting?
Risk-free discounting
Many governments value all social projects using the simple Ramsey rule
(e.g. UK for horizons < 30 years). Based on the Arrow-Lind theorem
Risk-adjusted discounting
Others (e.g. French, Dutch and Norwegian), explicitly allow for risk in
valuation, as project benefits generally relate to the overall
macro-economy (non-zero ‘beta’).
Central ground
Some argue that risk premiums are too small to concern us. The US
discounts at 7% and 3% (2.5%, 3% & 5% climate change, 3% health).
Mark Freeman (University of York) Risk & Valuation December 2017 3 / 20
Stylistic example
Binomial process for consumption
Current aggregate consumption c0 = $1, 000. Consumption in 10 years of
cu (probability π) or cd (probability 1 − π).
Parameterizing
We set cu, cd and π so that future (10-year) consumption has an
expectation of $1,200 with a standard deviation of $300.
Vary π, let the mean and standard deviation determine cu and cd .
Mark Freeman (University of York) Risk & Valuation December 2017 4 / 20
The consumption process
0
500
1,000
1,500
2,000
2,500
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Futureconsumption
Probability of being in the up state
Consumption in the up state
Consumption in the down state
Low probability of severe
consumption catastrophe
Mark Freeman (University of York) Risk & Valuation December 2017 5 / 20
An LMIC healthcare project
Another binomial process
Healthcare project with monetized benefit of bu or bd in ten years:
Pro-cyclical: bu occurs iff cu occurs; probability π
Counter-cyclical: bu occurs iff cd occurs; probability 1 − π
Also look at risk-free and acyclical projects.
Parameterizing
bu and bd set so the expected benefit is $2, with standard deviation to $1.
They depend on π.
Mark Freeman (University of York) Risk & Valuation December 2017 6 / 20
Cyclical benefits
-1
0
1
2
3
4
5
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Benefit
Probability of being in the up state
benefit in up state (pro-cyclical)
benefit in down state (pro-cyclical)
Mark Freeman (University of York) Risk & Valuation December 2017 7 / 20
Counter-cyclical benefits - Mirror image
-1
0
1
2
3
4
5
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Benefit
Probability of being in the up state
benefit in up state (counter-cyclical)
benefit in down state (counter-cyclical)
Low probability of
consumption catastrophe
associated with high project
benefits
Mark Freeman (University of York) Risk & Valuation December 2017 8 / 20
Valuing the healthcare project
Equilibrium
Social planner gets time separable utility e−ρtU(ct) from aggregate
consumption. In equilibrium, the present value, p, of the project:
U(c0 − p) + e−ρt
E[U(ct + b)] = U(c0) + e−ρt
E[U(ct)]
The utility function
Power utility with relative risk aversion = 2, rate of pure time preference
ρ = 1%.
Mark Freeman (University of York) Risk & Valuation December 2017 9 / 20
Present value of the risk-free project
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Presentvalueoftheproject
Probability of being in the up state
PV (risk-free)
PV (risk-free, certain consumption)
Precautionary effect increases
price of risk-free projects
(extended Ramsey Rule)
Precautionary effect gets stronger
with catastrophic consumption
outcomes (Rietz 1988, Barro 2006 &
2009, Gabaix 2012)
Mark Freeman (University of York) Risk & Valuation December 2017 10 / 20
Present value of the pro-cyclical & acyclical projects
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Presentvalueoftheproject
Probability of being in the up state
PV (pro-cyclical)
PV (independent)
PV (risk-free)
Positive (zero) risk premium for
positive (zero) beta healthcare
project (CCAPM)
Risk premium high in the presence
of catastrophic risk (Rietz, 1988;
Barro 2006 & 2009; Gabaix 2012)
High sensitivity of valuation to precise
likelihood and outcome of catastrophe
(Martin, 2013; Gollier, 2016)
Mark Freeman (University of York) Risk & Valuation December 2017 11 / 20
Present value of the counter-cyclical project
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Presentvalueoftheproject
Probability of being in the up state
PV (counter-cyclical)
PV (risk-free)
Counter-cyclical projects more
highly priced than risk-free
assets (CCAPM)
Projects with strong payoffs in
catastrophic states are very highly
valued (e.g. Weitzman 2007 &
2009, Dietz 2011, Barro 2013,
Pindyck 2013). Discount rate here
negative.
Mark Freeman (University of York) Risk & Valuation December 2017 12 / 20
A counter-cyclical healthcare project
Healthcare projects in LMICs to protect against economic collapse
Consider an LMIC that, in the event of an economic collapse (low
probability event), expects a healthcare crisis (famine, malaria outbreak,
etc.).
Project to protect against this outcome
Since this project’s benefits are greatest in catastrophic states, it has very
high value.
Mark Freeman (University of York) Risk & Valuation December 2017 13 / 20
What is the ‘beta’ of a healthcare project
National or international perspective
The probability of catastrophic economic outcomes, and the relationship
with healthcare projects, within LMICs are greater/stronger on a national
than international perspective.
Proper international support would help mitigate national effects
Therefore, when undertaking these valuations, an assessment needs to be
made of the international policy response to a disaster
Mark Freeman (University of York) Risk & Valuation December 2017 14 / 20
Risk of future pandemic
Uncertain future risk
The number of deaths (as % population), N, in a future pandemic is
unknown. Both the policy maker and health expert think N is lognormally
distributed.
Different parameter values
E[N] = m for the policy maker and E[N] = M > m for the expert.
Var[N] = s2 for the policy maker and Var[N] = S2 for the expert.
Mark Freeman (University of York) Risk & Valuation December 2017 15 / 20
How does the policy maker respond to the expert advice
Bayesian learning
The policy maker hears the opinion of the expert and rationally Bayesian
updates her beliefs (e.g., French 1985; Lindley 1985; Genest and Zidek
1986).
Bayesian posterior
The Bayesian posterior of the expert is also lognormally distributed in N.
The mean and variance of this distribution, m , s 2 are known in closed
form as functions of m, M, s, S (messy!)
Mark Freeman (University of York) Risk & Valuation December 2017 16 / 20
Example
m = 2%, s = 2%, M = 3.2%, S = 2%. Then m = 2.46% and s = 1.23%
0
0.1
0.2
0.3
0.4
0.5
0 1 2 3 4 5 6 7 8 9 10
ProbabilityDensityFunction
N
Prior
Consensus
Posterior
Mark Freeman (University of York) Risk & Valuation December 2017 17 / 20
Economic damages
Consumption drops from ct to (1 − D(N))ct at some future time t in the
event of a pandemic. D(N) = 1 − exp(−θN2) for θ = 0.006585
0%
10%
20%
30%
40%
50%
60%
0 1 2 3 4 5 6 7 8 9 10
Economicdamages,D(N)
Percentage of population killed, N
Mark Freeman (University of York) Risk & Valuation December 2017 18 / 20
Main result
Expert opinion can result in decreasing WTP
After receiving expert opinion, a statistically and economically rational
policy maker with logarithmic utility will increase her expected value of N,
but reduce her willingness to pay to avoid the potential pandemic if and
only if
M4
M2 + S2
− s2
< m2
<
M4
M2 + S2
The example
In the example, m = 2.46% > m = 2%, yet the WTP drops from 5.13%
to 4.86% of current income.
Mark Freeman (University of York) Risk & Valuation December 2017 19 / 20
Psychological evidence
Climate change communication reduces skepticism...
Expert communication is successful in reducing overall levels of climate
change skepticism through knowledge transfer (e.g. Lewandowsky, Gignac
& Vaughan 2013, van der Linden et al. 2015; Ramney & Clark 2016)
... but not WTP
... but people become no more willing to pay for preventative action after
receiving this communication (e.g. Deryugina & Shurchkov 2016; Kahan
2016; Bolsen & Druckman 2016)
Mark Freeman (University of York) Risk & Valuation December 2017 20 / 20

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Discounting future healthcare costs and benefits (part 2)

  • 1. Catastrophic risks and the value of health projects Mark Freeman Centre for Health Economics, York 7th December 2017 Mark Freeman (University of York) Risk & Valuation December 2017 1 / 20
  • 2. What is appropriate for valuing healthcare in LMICs? Risk matters Macroeconomic risk has a different valuation implication (precautionary saving) than project uncertainty (risk premium) Risk should not be measured by standard deviation alone. Higher moments matter Low probability, but potentially catastrophic, economic outcomes can significantly influence valuations Risk premiums can be negative, increasing healthcare project valuation National or international perspective? Mark Freeman (University of York) Risk & Valuation December 2017 2 / 20
  • 3. Risk-free or risk-adjusted discounting? Risk-free discounting Many governments value all social projects using the simple Ramsey rule (e.g. UK for horizons < 30 years). Based on the Arrow-Lind theorem Risk-adjusted discounting Others (e.g. French, Dutch and Norwegian), explicitly allow for risk in valuation, as project benefits generally relate to the overall macro-economy (non-zero ‘beta’). Central ground Some argue that risk premiums are too small to concern us. The US discounts at 7% and 3% (2.5%, 3% & 5% climate change, 3% health). Mark Freeman (University of York) Risk & Valuation December 2017 3 / 20
  • 4. Stylistic example Binomial process for consumption Current aggregate consumption c0 = $1, 000. Consumption in 10 years of cu (probability π) or cd (probability 1 − π). Parameterizing We set cu, cd and π so that future (10-year) consumption has an expectation of $1,200 with a standard deviation of $300. Vary π, let the mean and standard deviation determine cu and cd . Mark Freeman (University of York) Risk & Valuation December 2017 4 / 20
  • 5. The consumption process 0 500 1,000 1,500 2,000 2,500 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Futureconsumption Probability of being in the up state Consumption in the up state Consumption in the down state Low probability of severe consumption catastrophe Mark Freeman (University of York) Risk & Valuation December 2017 5 / 20
  • 6. An LMIC healthcare project Another binomial process Healthcare project with monetized benefit of bu or bd in ten years: Pro-cyclical: bu occurs iff cu occurs; probability π Counter-cyclical: bu occurs iff cd occurs; probability 1 − π Also look at risk-free and acyclical projects. Parameterizing bu and bd set so the expected benefit is $2, with standard deviation to $1. They depend on π. Mark Freeman (University of York) Risk & Valuation December 2017 6 / 20
  • 7. Cyclical benefits -1 0 1 2 3 4 5 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Benefit Probability of being in the up state benefit in up state (pro-cyclical) benefit in down state (pro-cyclical) Mark Freeman (University of York) Risk & Valuation December 2017 7 / 20
  • 8. Counter-cyclical benefits - Mirror image -1 0 1 2 3 4 5 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Benefit Probability of being in the up state benefit in up state (counter-cyclical) benefit in down state (counter-cyclical) Low probability of consumption catastrophe associated with high project benefits Mark Freeman (University of York) Risk & Valuation December 2017 8 / 20
  • 9. Valuing the healthcare project Equilibrium Social planner gets time separable utility e−ρtU(ct) from aggregate consumption. In equilibrium, the present value, p, of the project: U(c0 − p) + e−ρt E[U(ct + b)] = U(c0) + e−ρt E[U(ct)] The utility function Power utility with relative risk aversion = 2, rate of pure time preference ρ = 1%. Mark Freeman (University of York) Risk & Valuation December 2017 9 / 20
  • 10. Present value of the risk-free project 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Presentvalueoftheproject Probability of being in the up state PV (risk-free) PV (risk-free, certain consumption) Precautionary effect increases price of risk-free projects (extended Ramsey Rule) Precautionary effect gets stronger with catastrophic consumption outcomes (Rietz 1988, Barro 2006 & 2009, Gabaix 2012) Mark Freeman (University of York) Risk & Valuation December 2017 10 / 20
  • 11. Present value of the pro-cyclical & acyclical projects 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Presentvalueoftheproject Probability of being in the up state PV (pro-cyclical) PV (independent) PV (risk-free) Positive (zero) risk premium for positive (zero) beta healthcare project (CCAPM) Risk premium high in the presence of catastrophic risk (Rietz, 1988; Barro 2006 & 2009; Gabaix 2012) High sensitivity of valuation to precise likelihood and outcome of catastrophe (Martin, 2013; Gollier, 2016) Mark Freeman (University of York) Risk & Valuation December 2017 11 / 20
  • 12. Present value of the counter-cyclical project 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Presentvalueoftheproject Probability of being in the up state PV (counter-cyclical) PV (risk-free) Counter-cyclical projects more highly priced than risk-free assets (CCAPM) Projects with strong payoffs in catastrophic states are very highly valued (e.g. Weitzman 2007 & 2009, Dietz 2011, Barro 2013, Pindyck 2013). Discount rate here negative. Mark Freeman (University of York) Risk & Valuation December 2017 12 / 20
  • 13. A counter-cyclical healthcare project Healthcare projects in LMICs to protect against economic collapse Consider an LMIC that, in the event of an economic collapse (low probability event), expects a healthcare crisis (famine, malaria outbreak, etc.). Project to protect against this outcome Since this project’s benefits are greatest in catastrophic states, it has very high value. Mark Freeman (University of York) Risk & Valuation December 2017 13 / 20
  • 14. What is the ‘beta’ of a healthcare project National or international perspective The probability of catastrophic economic outcomes, and the relationship with healthcare projects, within LMICs are greater/stronger on a national than international perspective. Proper international support would help mitigate national effects Therefore, when undertaking these valuations, an assessment needs to be made of the international policy response to a disaster Mark Freeman (University of York) Risk & Valuation December 2017 14 / 20
  • 15. Risk of future pandemic Uncertain future risk The number of deaths (as % population), N, in a future pandemic is unknown. Both the policy maker and health expert think N is lognormally distributed. Different parameter values E[N] = m for the policy maker and E[N] = M > m for the expert. Var[N] = s2 for the policy maker and Var[N] = S2 for the expert. Mark Freeman (University of York) Risk & Valuation December 2017 15 / 20
  • 16. How does the policy maker respond to the expert advice Bayesian learning The policy maker hears the opinion of the expert and rationally Bayesian updates her beliefs (e.g., French 1985; Lindley 1985; Genest and Zidek 1986). Bayesian posterior The Bayesian posterior of the expert is also lognormally distributed in N. The mean and variance of this distribution, m , s 2 are known in closed form as functions of m, M, s, S (messy!) Mark Freeman (University of York) Risk & Valuation December 2017 16 / 20
  • 17. Example m = 2%, s = 2%, M = 3.2%, S = 2%. Then m = 2.46% and s = 1.23% 0 0.1 0.2 0.3 0.4 0.5 0 1 2 3 4 5 6 7 8 9 10 ProbabilityDensityFunction N Prior Consensus Posterior Mark Freeman (University of York) Risk & Valuation December 2017 17 / 20
  • 18. Economic damages Consumption drops from ct to (1 − D(N))ct at some future time t in the event of a pandemic. D(N) = 1 − exp(−θN2) for θ = 0.006585 0% 10% 20% 30% 40% 50% 60% 0 1 2 3 4 5 6 7 8 9 10 Economicdamages,D(N) Percentage of population killed, N Mark Freeman (University of York) Risk & Valuation December 2017 18 / 20
  • 19. Main result Expert opinion can result in decreasing WTP After receiving expert opinion, a statistically and economically rational policy maker with logarithmic utility will increase her expected value of N, but reduce her willingness to pay to avoid the potential pandemic if and only if M4 M2 + S2 − s2 < m2 < M4 M2 + S2 The example In the example, m = 2.46% > m = 2%, yet the WTP drops from 5.13% to 4.86% of current income. Mark Freeman (University of York) Risk & Valuation December 2017 19 / 20
  • 20. Psychological evidence Climate change communication reduces skepticism... Expert communication is successful in reducing overall levels of climate change skepticism through knowledge transfer (e.g. Lewandowsky, Gignac & Vaughan 2013, van der Linden et al. 2015; Ramney & Clark 2016) ... but not WTP ... but people become no more willing to pay for preventative action after receiving this communication (e.g. Deryugina & Shurchkov 2016; Kahan 2016; Bolsen & Druckman 2016) Mark Freeman (University of York) Risk & Valuation December 2017 20 / 20