discounting future healthcare costs and benefits (part 2)

Catastrophic risks and the value of health projects

Mark Freeman

Centre for Health Economics, York7th 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. Highermoments matter

Low probability, but potentially catastrophic, economic outcomes cansignificantly influence valuations

Risk premiums can be negative, increasing healthcare projectvaluation

National or international perspective?


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 invaluation, as project benefits generally relate to the overallmacro-economy (non-zero ‘beta’).

Central ground

Some argue that risk premiums are too small to concern us. The USdiscounts at 7% and 3% (2.5%, 3% & 5% climate change, 3% health).


Stylistic example

Binomial process for consumption

Current aggregate consumption c0 = $1, 000. Consumption in 10 years ofcu (probability π) or cd (probability 1 − π).

Parameterizing

We set cu, cd and π so that future (10-year) consumption has anexpectation of $1,200 with a standard deviation of $300.

Vary π, let the mean and standard deviation determine cu and cd .


The consumption process

0

500

1,000

1,500

2,000

2,500

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Futu

re c

onsu

mpt

ion

Probability of being in the up state

Consumption in the up state

Consumption in the down state

Low probability of severe consumption catastrophe


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.


Cyclical benefits

-1

0

1

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0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Bene

fit


benefit in up state (pro-cyclical)

benefit in down state (pro-cyclical)


Counter-cyclical benefits - Mirror image

-1

0

1

2

3

4

5

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Bene

fit


benefit in up state (counter-cyclical)

benefit in down state (counter-cyclical)

Low probability of consumption catastrophe associated with high project benefits


Valuing the healthcare project

Equilibrium

Social planner gets time separable utility e−ρtU(ct) from aggregateconsumption. In equilibrium, the present value, p, of the project:

U(c0 − p) + e−ρtE [U(ct + b)] = U(c0) + e−ρtE [U(ct)]

The utility function

Power utility with relative risk aversion = 2, rate of pure time preferenceρ = 1%.


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%

Pres

ent v

alue

of t

he p

roje

ct


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)


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%

Pres

ent v

alue

of t

he p

roje

ct


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)


Present value of the counter-cyclical project

0.00

0.50

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1.50

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2.50

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3.50

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Pres

ent v

alue

of t

he p

roje

ct


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.


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 (lowprobability 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 veryhigh value.


What is the ‘beta’ of a healthcare project

National or international perspective

The probability of catastrophic economic outcomes, and the relationshipwith healthcare projects, within LMICs are greater/stronger on a nationalthan international perspective.

Proper international support would help mitigate national effects

Therefore, when undertaking these valuations, an assessment needs to bemade of the international policy response to a disaster


Risk of future pandemic

Uncertain future risk

The number of deaths (as % population), N, in a future pandemic isunknown. Both the policy maker and health expert think N is lognormallydistributed.

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.


How does the policy maker respond to the expert advice

Bayesian learning

The policy maker hears the opinion of the expert and rationally Bayesianupdates her beliefs (e.g., French 1985; Lindley 1985; Genest and Zidek1986).

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 closedform as functions of m,M, s,S (messy!)


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

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0.5

0 1 2 3 4 5 6 7 8 9 10

Prob

abili

ty D

ensi

ty F

unct

ion

N

Prior

Consensus

Posterior


Economic damages

Consumption drops from ct to (1 − D(N))ct at some future time t in theevent 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

Econ

omic

dam

ages

, D(N

)

Percentage of population killed, N


Main result

Expert opinion can result in decreasing WTP

After receiving expert opinion, a statistically and economically rationalpolicy maker with logarithmic utility will increase her expected value of N,but reduce her willingness to pay to avoid the potential pandemic if andonly 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.


Psychological evidence

Climate change communication reduces skepticism...

Expert communication is successful in reducing overall levels of climatechange 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 afterreceiving this communication (e.g. Deryugina & Shurchkov 2016; Kahan2016; Bolsen & Druckman 2016)


discounting future healthcare costs and benefits (part 2)

Health & Medicine