How Important Is Health Inequality for Lifetime Earnings Inequality

Health and earnings are positively correlated and this is for several reasons. First, individuals who are in poor health are significantly less likely to work than healthy individuals. Second, conditional on working, individuals in poor health work fewer hours on average. Third, individuals in poor health earn lower wages on average. We document these facts using an objective measure of health called a frailty index which we construct for PSID respondents. The frailty index measures the fraction of observable health deficits an individual has. In previous work, we documented that health, as measured by the frailty index, deteriorates more rapidly and has a larger increase in dispersion with age than self-reported health. It is also more persistent over the life-cycle. These facts put together suggest that health inequality over the life cycle may be an important driver of lifetime earnings inequality. To assess this claim we develop a model of the joint dynamics of health and earnings over the life cycle. Individuals in the model face health, earnings and unemployment risk, and optimally choose labor supply on both the intensive and extensive margin. Agents are partially insured against these risks through government-run unemployment and disability insurance programs. We give agents in the model a dynamic process for frailty (health) that is estimated using the PSID data. Because of selection concerns, agents' productivity processes, including the contribution of frailty to productivity, are estimated using the model and a method of moments estimation. Targeted moments are constructed off distributions of wages, hours, and participation by frailty and age. These distributions are obtained from an auxiliary simulation model that is estimated using PSID data. We find that health inequality can account for a significant share of the variation in lifetime earnings among 70 year-olds. Most of this effect is due to the fact that unhealthy individuals exit the labor force at much younger ages than healthy ones. We find that health inequality has a larger impact on earnings inequality than previous literature for two reason. One, our model is the first in this literature that allows health to impact earnings through all three margins: participation, hours, and wages (productivity). Two, previous literature measured health using self-reported health status and thus understated the extent to with health deteriorates with age for some individuals.