Health-State Transitions and the Lifetime Cost of Aging: A Multi- State Actuarial Model of Medicare Spending and Household Out-of- Pocket Tail Risk

Abstract

Medicare’s Hospital Insurance trust fund is projected to be depleted in 2033, but aggregate projections say little about how
the cost of aging falls on households. We build a six-state continuous-time Markov model of later life (healthy, chronic
illness, disability, severe disability at home, nursing home, dead) from 197,258 intervals between Health and Retirement
Study interviews, 1998 to 2022, with deaths dated to the month, a linear spline in age, and standard errors clustered on the
household. Medicare costs by state come from the Medicare Current Beneficiary Survey with the concentration of spending
in the last year of life imposed; out-of-pocket costs are drawn from HRS core and exit interviews by state, age, sex, Medicaid
status and income tertile, with persistence modeled as a permanent component plus an AR(1); Medicaid eligibility is reached
by asset spend-down inside the simulation. Mortality is calibrated to the 2023 US life table. For a 65-year-old drawn from
the population, the present value at 3% of lifetime Medicare spending is $154,423 for men and $171,804 for women, and
of household out-of-pocket spending on care $35,329 and $43,666, with Part B and Part D premiums adding $32,195 and
$33,977. The distribution is heavily skewed: the mean of the worst 5% of outcomes is $188,368 for men and $235,495 for
women, 5.3 and 5.4 times the mean, and 71.8% and 85.7% of the lives in that tail pass through long-term care against 44.2%
and 57.9% of all lives. 15.3% of men and 23.2% of women reach Medicaid, and among the lowest income tertile 37% and
45% do. Passing half of the post-2033 Part A shortfall to beneficiaries raises expected out-of-pocket cost by about $2,000; real
cost growth at the Trustees’ rate raises the worst-5% mean by $52,211 and $77,837. Code and a public calculator are released.