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  • 1. The Value of Life Near Its End and Terminal Care NBER Working Paper 13333 [www.nber.org] Gary Becker Kevin Murphy Tomas J. Philipson The University of Chicago IHEA July 10, 2007
  • 2. High Spending Levels on Terminal Care
    • Often estimated that one-quarter or more of lifetime medical costs accrue in the last year of life
    • Old age health spending is highly skewed, about half of total spending comes from top 5 percent which often involves tail-spending of terminal care.
  • 3. Excessive Terminal Care
    • Common estimates of the value of a life year in range $50-100 K
      • Labor-market studies (e.g. compensating differentials)
      • Product Demand Studies (e.g. seat belts)
      • Public Regulation Studies (e.g. speed limits)
    • Terminal care spending often far greater than those estimates
      • Substantially higher costs to extend life by a few months
  • 4. Terminal Care Wasteful
    • Spending on people who die anyways
    • “ Cost of dying” estimated to be large and not changing, in some countries growing
    • Exceeds [survival gains] x [value of survival gains]
    • Seem as vastly miss-allocated resources
  • 5. Two Views
    • World is crazy and need to be changed despite the fact that we don’t understand the behavior
    • We don’t understand the behavior and would like to
    • Here: latter approach adopted
  • 6. Rational Terminal Care
    • Incentives involved poorly understood
    • Lack of theory that explains
      • Observed spending levels above existing estimates of the value of life
      • Rationalizes the high values of terminal care in co-existence with lower existing estimates
        • Are both right and if so why?
  • 7. Main Argument
    • There are important incentives that imply that the value of terminal care differs from that implied by existing estimates of the value of a statistical life year.
  • 8. The Canonical Determination of The Value of Life
    • Indirect utility over wealth and survival V(Y,S)
      • Ex: Standard Consumption Smoothing V(Y,S)=A(S)U(Y/A(S)), A(S)=Annuity Value
    • Marginal Value of Life
      • dY/dS=-(dV/dS)/(dV/dY)
    • Infra-Marginal Value of Life from S to S’
      • V(Y-v,S’) = V(Y,S)
  • 9. Difference #1: Infra-marginal versus marginal valuation
    • Infra-marginal value of terminal care may be entire wealth
      • V(Y-v,S’)=V(Y,0) implies v = Y for all S’
      • Regardless of S’ !
    • Empirical estimates of value of life are marginal
      • Ex: Hedonic wage regressions
    • Terminal care often involves infra-marginal
      • “ Gun to head” comparison is correct!
    • Non-linearity in value of life
      • Diminishing marginal value with level as for other goods?
      • Non-linearity inconsistent with linear valuation methods (QALY,DALY, etc).
      • Constant elasticity U implies Cobb-Douglas preferences over (Y,T)  MRS falls with level
      • Existing Estimates for lower marginal values when have more of life compared to terminal care when have less
  • 10. Difference #2: The Value of Hope
    • Define hope as current consumption of future survival
      • Ex: 6 months to live enjoyed more if future living possible, e.g. fear of death.
    • Value of Hope: U(S,c)=Hu(S) + U(c)
      • Infra-Marginal value of life as function of hope v(H) increasing
        • V(Y-v(H),S’)-V(Y,S) = H[Au(S) –A’u(S’)]
    • Survival is “double-counted” in its value
      • Both current and future consumption value
    • However: Empirical estimates of value of life for healthy individuals with longer life spans does not include value of hope
  • 11. Hope, Part 2: Technological Change Raises Value of Life
    • The “Michael Milken, Christopher Reeve, or Michael J Fox Effect”: using existing technology while hoping for new
      • Ex: HIV Drugs in 1996 only 15 years after discovery
    • W(t) survival function of “cure” arrival time
    • Probability of dying before cure arrives
      • P=∑ [S’(t)-S’(t-1)]W(t)
    • Survival with possibility of future cure
      • PS’ +(1-P)S(Cure) > S’
    • Valuing S’ alone undervalues gain in longevity
    • Factors affecting W:
      • Prevalence induced R&D a
      • FDA Regulatory Delays (Faster Cures of Milken Institute)
  • 12. Difference #3: The Social versus Private Value of a Life
    • Spending Excessive even with Public Subsidies (RAND: 70% of spending if fully paid  still high)
    • Non-Private Values in Terminal Care
      • Within Family: Others Value of life > Bequest Motives (Age Effect)
      • Across Families: PAYG Financing and Average Child vs Own Child
      • Producer Benefits from Public Provision
        • Efficiency versus Transfers
    • However: Empirical value of life estimates for private valuations
  • 13. Difference # 4: The Value of Life As High for Frail as Healthy
    • Assume q denotes “quality” of life ore level of health and utility U(c,q) increasing in both c and q
    • Consider case of perfect consumption smoothing
      • V(Y,S)=AU(Y/A,q)
    • Infra-marginal value of life as function of quality v(q)
      • A’U([Y-v(q)]/A’,q)=AU(Y/A,q)
    • Quality affects both sides  q unclear effect on v(q)
      • RHS: The value of living longer rises with quality
      • LHS: The value of foregone consumption rises with quality
  • 14. Evidence of Valuation Wedge
    • Demand for Biologics
    • Why High Prices?
      • Larger marginal costs of biologics
      • Lower Elasticity of Demand
    • However; the low elasticity revealed by high prices implies High Implicit Value of Life Year
  • 15. Existing Work Directly Estimating Inelastic Demand For Cancer Biologics
    • Goldman et al, Health Affairs , 2006.
    • Goldman et al, JAMA , 2007
    • Important question; what valuation of life is implicit in these demand curves?
      • Ex-ante
      • Ex-post people are paying very large co-pays and are very inelastic compared to other drugs.
  • 16. Future Analysis: Implications for Valuing New Technologies
    • Linear valuation methods (QALY, DALY etc) will lead to inefficiency in adoption
    • Common valuation methods often calculate value of new technology as its monetized clinical benefit:
        • [survival gain in years ] x [value of life year]
    • E.g., a drug that extends life by one month is worth $100K/12 = $8,333
    • Linear methods undervalues terminal care technologies
  • 17. Future Work: R&D “Denial Aversion” in Altruism and Technological Change
    • Altruist averse to denying technology if
      • U(No Use, No Technology) > U(No Use, Technology )
    • R&D may be excessive even though
      • Social WTP > Costs
    • Denial aversion & technological change  rising health care spending
    • Standard welfare analysis of new inventions (as price reductions) biased.
      • Shift in social demand curve with new technology, not only reduction in price.
  • 18. Conclusion
    • Current estimates of value of life may be inapplicable to value terminal care
      • Low opportunity costs of care
      • Social vs Private value
      • The Value of Hope and Option Value of Care
      • The value of terminal care for frail people
    • Future Research
      • Empirically assessing relative importance of incentives that drive wedge between value of terminal and non-terminal care
      • Test Implications for major life-threatening illnesses; does the ex-post demand for biologics reveal higher value of life than existing estimates ?
      • Develop implications for rational adoption of new technologies for terminal care based on non-linear rather than linear (QALY-type) valuation.