Cognitive Decline and Dynamic Selection
Understanding cognitive health, its decline, and the investments that shape its age profile in later life are important in an aging society, and yet, estimating the cognitive health production function is complicated by non-random mortality and sample attrition. I study this dynamic selection problem in the context of education, race, and cigarette smoking, characteristics thought to affect the level, but not slope, of cognitive decline. I develop a general framework that involves estimation of a system of dynamic equations consistent with the Grossman (1972) model. Exploiting exciting longitudinal data from the National Health and Aging Trends Study (NHATS), I find substantially wider gaps in cognitive health by these characteristics relative to cross-sectional comparisons, in some cases by 100%. Furthermore, these gaps grow in age, which suggests that the bias generated by dynamic selection is not constant. The implication of these results is that theories of cognitive decline need to accommodate differential rates of change -- rather than just differences in levels -- in cognitive health by education and race. Connecting theory and empirical work offers an important tool for economists studying health investment and health in older populations.