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The Value of Life Near Its End and Terminal Care

Old age health spending is highly skewed, about half of total ... Assume q denotes

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The Value of Life Near Its End and Terminal Care

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    1. The Value of Life Near Its End and Terminal Care 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.

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