The Value of Life Near Its End and Terminal Care NBER Working Paper 13333 [www.nber.org]  Gary Becker Kevin Murphy Tomas J...
High Spending Levels on Terminal Care <ul><li>Often estimated that one-quarter or more of lifetime medical costs accrue in...
Excessive Terminal Care  <ul><li>Common estimates of the value of a life year in range $50-100 K  </li></ul><ul><ul><li>La...
Terminal Care Wasteful <ul><li>Spending on people who die anyways  </li></ul><ul><li>“ Cost of dying” estimated to be larg...
Two Views <ul><li>World is crazy and need to be changed despite the fact that we don’t understand the behavior </li></ul><...
Rational Terminal Care <ul><li>Incentives involved poorly understood </li></ul><ul><li>Lack of theory that explains </li><...
Main Argument  <ul><li>There are important incentives that imply that the value of terminal care differs from that implied...
The Canonical Determination of The Value of Life <ul><li>Indirect utility over wealth and survival V(Y,S) </li></ul><ul><u...
Difference #1: Infra-marginal versus marginal valuation <ul><li>Infra-marginal value of terminal care may be entire wealth...
Difference #2: The Value of Hope <ul><li>Define hope as current consumption of future survival </li></ul><ul><ul><li>Ex: 6...
Hope, Part 2: Technological Change Raises Value of Life <ul><li>The “Michael Milken, Christopher Reeve, or Michael J Fox E...
Difference #3: The Social versus Private Value of a Life <ul><li>Spending Excessive even with Public Subsidies (RAND: 70% ...
Difference # 4: The Value of Life As High for Frail as Healthy <ul><li>Assume q denotes “quality” of life ore level of hea...
Evidence of Valuation Wedge  <ul><li>Demand for Biologics </li></ul><ul><li>Why High Prices? </li></ul><ul><ul><li>Larger ...
Existing Work Directly Estimating Inelastic Demand For Cancer Biologics <ul><li>Goldman et al,  Health Affairs , 2006.  </...
Future Analysis:  Implications for Valuing New Technologies  <ul><li>Linear valuation methods (QALY, DALY etc) will lead t...
Future Work: R&D  “Denial Aversion” in Altruism and Technological Change <ul><li>Altruist averse to denying technology if ...
Conclusion <ul><li>Current estimates of value of life may be inapplicable to value terminal care </li></ul><ul><ul><li>Low...
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Test 1

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

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