Consumption value of health & its evolution over time James K. - - PowerPoint PPT Presentation

Consumption value of health & its evolution over time

James K. Hammitt

Harvard ard Center er for Risk Analysi ysis

Outline

• Conceptual issues
• Evidence (relevant, available)
• Reasonable assessment

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Value per statistical case

• Individual’s rate of substitution between own:

― wealth ― probability of avoiding/preventing specified health outcome

• within defined time period
• Most research on small changes in probability of death

― Value per statistical life (VSL) ― Marginal rate of substitution ― Model can be applied to non-fatal health effects

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VSL = slope (local)

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Indifference curve Wealth Survival probability ( = 1 - risk) 1

VSL x

Standard model of VSL

• maximize 𝐹𝑉 = 𝑡𝑣𝑏 + 1 − 𝑡 𝑣𝑒

― s = probability of surviving time period ― ua = utility conditional on surviving period ― ud = utility of leaving wealth as a bequest ― ua, ud are functions of

• wealth
• future conditions given survival

– life expectancy – health – earnings, expenses – other factors that influence wellbeing

• future conditions given death

– number dependents – preferences for leaving wealth to others

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Standard model of VSL

• 𝑊𝑇𝑀 = −

𝑒𝑥 𝑒𝑡 = 𝑣𝑏−𝑣𝑒 𝑡𝑣𝑏

′ + 1−𝑡 𝑣𝑒 ′ =

∆𝑣 𝐹𝑣′ = 𝑣𝑢𝑗𝑚𝑗𝑢𝑧 𝑤𝑏𝑚𝑣𝑓 𝑝𝑔 𝑡𝑣𝑠𝑤𝑗𝑤𝑏𝑚 𝐹 (𝑝𝑞𝑞𝑝𝑠𝑢𝑣𝑜𝑗𝑢𝑧 𝑑𝑝𝑡𝑢 𝑝𝑔 𝑡𝑞𝑓𝑜𝑒𝑗𝑜𝑕)

• Assume

ua > ud survival preferred to death ua' > ud' ≥ 0 marginal utility of wealth larger given survival marginal utility of bequest non-negative ua", ud" ≤ 0 (weak) aversion to financial risk

• Conclude

𝜖𝑊𝑇𝑀 𝜖𝑥 > 0 𝜖𝑊𝑇𝑀 𝜖𝑦 ⪋ 0?

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― Increase in x (health, life expectancy):

• Increases numerator
• May increase denominator

― Increase in w:

• Increases numerator
• Decreases denominator

What would constitute relevant evidence for evolution of value of health?

• Value of health is ratio of

― Utility gain from better health (numerator) ― Expected opportunity cost of spending (denominator)

• Value of health does not change autonomously
• May change in response to changes in factors that affect

numerator and/or denominator

― To forecast change in value of health, must forecast changes in values of factors that influence it

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t t t i i i

dv v v x w dt w t x t          



What would constitute relevant evidence for evolution of value of health?

• Numerator & denominator depend on multiple factors

that may change over time

― Wealth, real income

• Increase value of health
• Note: utility value of consumption depends on

– Available goods & services, which change over time – Risks to wealth & consumption – Risks to health that affect utility of consumption

― Effects of health, life expectancy, other factors?

• For VSL, health & life expectancy increase numerator, may

increase denominator

• Value of avoiding nonfatal health state

― Technology, social support decrease numerator, decrease value?

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Available evidence: empirical estimates

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• Revealed preference (compensating wage differentials)

― Cannot estimate wealth dependence directly

• wage is dependent variable

― Compare VSL with income & other factors between samples

• Meta-analysis, cross sections at different dates
• Stated preference

― Estimate effects of income & individual characteristics on WTP within sample ― Compare VSL with income & other factors between samples

• Wealth v. other factors

― Within-sample comparisons can isolate effect of wealth ― Between-sample comparisons include effects of other factors

• Little research on

― effects of factors other than income (some on age) ― effect of income & other factors on value of nonfatal risk

Empirical estimates (mostly US)

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Referen rence ce Method hod Income

• me elasticity

ticity Kniesner, Viscusi, & Ziliak 2010 Wage differential, quantile regression 1.2 – 2.2 (highest to lowest quintile) Viscusi 2015 Wage differential, meta-analysis 0.8 – 1.1 Viscusi & Masterman 2017 Wage differential, meta-analysis 0.5 (US) 1.1 (international) Corso, Hammitt, & Graham 2001 Stated preference, traffic risk 0.4 Hammitt & Haninger 2010 Stated preference, pesticides 0.1 Cameron & DeShazo 2003 Stated preference, multiple 0.7 Costa & Kahn 2004 Wage differential 1940-1980 v. GNI pc 1.5 – 1.7 Hammitt, Liu, & Liu 2017 Wage differential 1982-1997 Taiwan v. HH income, risk, workers 0.6 – 0.9

In preparation

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• SP study in Chengdu, China, 2005 & 2016

― VSL increased 20x ($25,000 → $500,000) ― Household income increased 4x ($3,000 → $12,000)

• Meta-analysis of VSL estimates in LMICs

― General population, data collected in last 20 years

• 34 SP studies (17 countries)
• 9 RP studies (8 countries)

― Regress VSL/GNI pc on GNI pc

• SP: income elasticity ≈ 0.7
• RP: income elasticity ≈ 0.1

Stated preference

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Revealed preference

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A reasonable assessment?

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• Project change in value as (change in wealth) x

(response to wealth)

― Project change in wealth/income ― Use a central-value wealth elasticity of about 1

• Conduct sensitivity analysis

― Could changes in factors other than wealth be important?

• Be very humble