The Value of Life Near Its End and Terminal Care NBER Working Paper 13333 www'nber'org

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The Value of Life Near Its End and Terminal
CareNBER Working Paper 13333www.nber.org

• Gary Becker
• Kevin Murphy
• Tomas J. Philipson
• The University of Chicago
• IHEA July 10, 2007

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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.

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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

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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

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Two Views

• World is crazy and need to be changed despite the
  fact that we dont understand the behavior
• We dont understand the behavior and would like
  to
• Here latter approach adopted

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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?

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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.

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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)

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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

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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) HAu(S) Au(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

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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) gt S
• Valuing S alone undervalues gain in longevity
• Factors affecting W
• Prevalence induced RD a
• FDA Regulatory Delays (Faster Cures of Milken
  Institute)

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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 gt 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

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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)
• AU(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

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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

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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.

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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

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Future Work RD Denial Aversion in Altruism
and Technological Change

• Altruist averse to denying technology if
• U(No Use, No Technology) gt U(No Use, Technology)
• RD may be excessive even though
• Social WTP gt 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.

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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.