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A Cohort Framework for Describing Medicare Expenditure Growth

Written By: Jason Shafrin - Feb• 22•11

Medicare spending changes over time for multiple reasons.  First, for any cohort of individuals, these individuals the age as time passes.  As their age increases, expected medical expenditure will also rise.   Second, the individual will likely received different medical services as the standards of care change over time.  The standards of care can change due to improved technology, policy, cultural factors, medical education, and other causes.

On the other hand, one could examine trends in Medicare spending for a certain age group over time.  For instance, how much did Medicare spend on care for 70 year-olds in 1970, 1990 and 2010?  In this case, medical expenditure change as the standards of care change over time.  In addition, certain cohorts may be more or less healthy than others when the reach a certain age, or the cohort may have difference preferences over medical treatment.

The post today review a method for describing differential growth rates in Medicare Expenditures.  For cohort c at age α, the following equation describes medical expenditures y.

  • y(c,α) = g(c,α) + uc,α

To identify the effects of the different components of this equation is not trivial.  In fact, there is an “…inherent identification problem, which is well known in the literature (e.g., Heckman and Robb, 1985), that prevents one from being able to distinguish among age, period, and cohort effects.”  In the MaCurdy and Geppert chapter, the authors use the follow specification to estimate the combined how aging affects medical expenditures for different birth cohorts.

  • g(c,α) = Σj βj(c) * φj(α)

The quantities βj(c) determine the shape of a cohort’s lifetime profile with respect to age, and the function φj(α) captures cross-cohort variation in lifecycle profiles.  In the paper, the authors assume that there there are 3 separate cohorts. They parameterize the function g as follow:

  • g(c,α) = β0(c) + β1(c)α + β2(c)α2


  • βj(c) = β0j + β1j*c + β2j*c2,       j=1, 2, 3

In addition, the authors assume that the error distribmances can be decomposed as follows:

  • uc,α = ūt + ūt,α

Here, ūt are the common time effects and the errors ūt,α are the idiosyncratic deviations from trends for cohorts c at age α after the removal of common year components.  One can then use a simple OLS specification to estimate the vector parameters β and fixed time deviations ūt.

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