Is a Scalar Health State Sufficient for Health Dynamics? Evidence from Health Deficit Accumulation

Can a scalar measure of current health provide a sufficiently rich state for modeling health dynamics? Using longitudinal data from the Health and Retirement Study, we represent health by a count of 31 deficits, yielding a scalar state with 32 ordered values. Building on a stochastic deficit-accumulation model, we study transitions among deficit states and death and test whether information outside the current state improves prediction. For morbidity among survivors, current deficit count is an approximately, but not strictly, sufficient predictive state. Chronological age and observed demographic and socioeconomic characteristics add little predictive information once current health is known, but recent health history retains a quantitatively meaningful contribution. Mortality reveals a different boundary: recent deficit-count history adds little, while chronological age, selected individual characteristics, and deficit composition remain informative.