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
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.
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
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
- 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
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?
- 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.
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
- Infra-Marginal Value of Life from S to S’
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’
- 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
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
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
- Survival with possibility of future cure
- Valuing S’ alone undervalues gain in longevity
- FDA Regulatory Delays (Faster Cures of Milken Institute)
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
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
- Infra-marginal value of life as function of quality v(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
Evidence of Valuation Wedge
- Larger marginal costs of biologics
- Lower Elasticity of Demand
- However; the low elasticity revealed by high prices implies High Implicit Value of Life Year
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-post people are paying very large co-pays and are very inelastic compared to other drugs.
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
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
- 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.
- Current estimates of value of life may be inapplicable to value terminal care
- Low opportunity costs of care
- The Value of Hope and Option Value of Care
- The value of terminal care for frail people
- 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.