Advancing Medical Technology Aging Population

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Advancing Medical Technology Aging Population
Economic Growth

• Gilad Sorek
• 13 December 2005

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Background

• Remarkable advance of technology and science in
  the 20th century
• Medical technology innovations Implants, MRI,
  Catheterization etc.
• Prolong life but at significant costs
• Continuous increase of life expectancy, 2 years
  per decade since 50
• Decreasing fertility down to/below replacement
  levels

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• Health expenditures (share of income) tripled
  since 50 from 5 to 15 in the U.S
• Population is "two tailed" aging adults
  live longer and bare fewer children
• Dependency ratio increases -
• or better said
• Extensive analyze with respect to social
  security/pension systems. But very little
  considering health taxing.

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Objectives

• Unifying model of endogenous growth and TWO
  tailed aging population, in light of advancing
  medical technology
• Using the basic structure to analyze health tax
  policies

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Literature

• Exogenous mortality
• BlackburnCapriani(2002) and Soares (2005)
• Increasing adult's life expectancy/longevity
  longer streams of income in return to investment
  in education
• Increasing longevity through health tax can be
  optimized by the social planner, Cachunbary
  (2004)
• Increasing longevity stimulates investment in
  human capital and saving

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• Endogenous longevity - recent unpublished
  papers..
• Finlay(2005) focuses on the effect of donated to
  poor countries.
• - Donated health aid crowds out private local
  investment in health and education. Educational
  support is better.
• BhattacharyaQiau (2005) study the effect of
  mixed public and private investment in health.
• - Optimal Public health tax increases social
  welfare though might exposes the economoy to
  chaotic fluctuations.

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Potential contributions of this study

• Adults longevity and fertility choices are taken
  simultaneously, along with educational decisions
  
• Extending the life of elderly the retirement
  period
• Health sector and its technological progress, are
  modeled explicitly
• Medical technology progress in endogenous
• Health tax policy analysis

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The model

• Agents
• OLG of two (possibly) active periods adulthood
  and elderly
• Survival to elderly is probabilistic subject to
  increasing function of health services
  utilization
• Agents derive utility from consumption - and
  the quantity times quality of children

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• Felicity utility function is
• First period Adulthood
• Time allocation education, baring raring
  children (quantityquality) residual is
  labor time supply
• Income allocation health services at relative
  price
• and saving at the international interest rate
• Second period Elderly
• Retirement and consuming savings happily - if
  survived.. (perfect annuity markets)

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• Production
• Labor time supply
• e - Time devoted to education (professional
  training).
• n - Number of children
• F - fix time cost to bare each child.
• v - Variable time devoted to the rare each
  child
• Producing child's basic human capital - h,
• 
  Where
• The supply of effective labor units
  
• Where

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• Firms
• Small open economy
• Two perfectly competitive production sectors for
  C and Z
• Producing with neo-classic technologies (CRTS)
• L - Labor, C - Capital, -
  productivity factors
• Assume
• Technological progress in health sector is
  faster
• Health services are non tradable internationally
• And get relative price of heath services
  declines with educational level

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• After some manipulations
• w - laborer income, p(e)-relative price of health
  services
• To focus on Medical technology progress assume
  constant technology of consumption sector
• Health production measured by life expectancy -
  , Satisfies
• - Positive base survival rate.

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Maximization

• The agents optimization
• Inserting the constrains

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Four first order conditions

• 1. Differentiating with respect to we get
• 2. Differentiating with respect to we get

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• By dividing condition 1 by condition 2 we get
• Proposition 1 The number of children is
  decreasing in parent's educational, total time
  invest in each child, and in the fix cost of
  child bearing.

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• 3. Differentiating with respect to we get
• Combining conditions 2 and 3 we get
• Proposition 2 Time invested in each child is
  fixed by the parameters and .?
• " Indirect" quality/quantity trade
  off .

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• 4. Differentiating with respect to we get
• In terms of elasticity
• The ratio of expenditures is proportional to
  elasticity's ratio.

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• To get explicit demand for z , assume
• - survival function
• - utility function
• Plugging into the 4th F.O.C one can gets
• Proposition 3 Demand for health services and is
  non decreasing function of real income.

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• Minimum income level for positive demand for z
• Minimum income level increases with the base
  survival rate, and decreases with productivity of
  Z.
• Putting propositions 1 and 3 together we get a
  two tailed aging as education increases.

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Dynamics

• Using the results obtained from F.O.Cs we get
• Differentiating with respect to e we get
• Assume rational expectations equilibrium to
  impose

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• Analytical analysis didnt yield general results.
  
• We turn to simulation.
• Assume the price function (inverse to medical
  sector productivity)

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• Simulation results
• Converging increase of education, and all other
  derivatives c,z,u
• Convergence is FAST - around 5 periods
• For constant price convergence is slower with
  lower levels of e,c,z,u
• Health expenditures can increase but also
  decrease along the optimal path

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Health Expenditures and Optimal Taxation

• Countries have health tax as rate on income
• Optimal rate of health tax (by social planer)
  coincides with Agents optimization
• But the large variation makes it impossible
• Assumption concavity of W, we get proposition 4.
• Proposition 4 tax rates higher/lower than
  optimal, will increase/decrease educational level
  where is increasing in e. The opposite
  relations holds where is decreasing in e.

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Next step

• Intergenerational exchange
• In real world, old buy health services from
  young.
• Dynamic equilibrium requires perfect foresight
  (rational) expectations about next period
  technology.
• Assuming r0 it is easy to show that same steady
  states will hold
• Now define equilibrium..
• Next move to pay as you go system..

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