Health, Longevity, and Welfare Inequality of the Elderly

We provide a framework to understand the distribution of individual well-being and its change over time with an application to the U.S. elderly population. We use data from the Health and Retirement Study to estimate life-cycle dynamics and simulate paths for consumption, leisure, health, and mortality starting at age sixty for every individual. We use an expected utility framework and the simulated profiles to construct measures of welfare distribution. Our analysis suggests substantial variation in welfare across individuals driven foremost by inequality in health and mortality followed by consumption. Not accounting for the effect of health on lifetime utility results in over-predicting the relative welfare for those in the bottom end of the distribution and under-predicting for those at the top. Elderly welfare inequality has increased over time due to growing gaps in consumption, health, and mortality. Cross-sectional income and consumption under-estimate aggregate welfare inequality and are only modestly correlated with elderly welfare at the individual level. Cross-sectional health is a better indicator of individual well-being rank than income or consumption.

Our findings can be summarized as follows:

1. There is substantial variation in the ex-ante welfare of individuals at age sixty. The Gini coefficient for consumption-equivalent welfare in our benchmark cohort is 0.66. Those at the ninetieth percentile of the distribution have 23 times higher welfare than those at the tenth percentile.

2.Health differences are crucial for understanding the overall distribution of elderly welfare. Excluding the utility cost of poor health and morbidities lowers the welfare Gini coefficient by 23%. This is driven by a positive correlation between health, consumption, and mortality.

3. The largest drivers of welfare inequality are health and mortality gaps followed by gaps in consumption. Differences in leisure play a comparatively minor role.

4. Welfare inequality among the elderly has increased over time due to growing gaps in consumption, health, and mortality. Compared to the cohort of individuals reaching age sixty between 1992-2001, the welfare Gini rose 9% for those reaching sixty between 2002-07 and 22% for those reaching between 2008-14.

5. Ignoring dynamic uncertainty and the persistence in outcomes over the life-cycle greatly underestimates welfare inequality. The Gini of age sixty flow utility is only 70% of that based on our dynamic welfare measure.

A key implication of our results is that cross-sectional distributions of income/consumption underestimate aggregate welfare inequality. This occurs for two primary reasons. First, cross-sectional measures ignore dynamic uncertainty and the persistence of inequality over life. Second, there is a positive correlation between health and consumption. However, even in cases where economic outcomes provide a reasonable approximation to aggregate welfare inequality, our results suggest they may still provide a poor ranking of individual well-being. For example, the rank correlation between consumption and welfare is a relatively modest 0.56 for our benchmark cohort. Moreover, we find cross-sectional health utility at age sixty to be a better predictor of remaining lifetime welfare rank, despite the fact that it drastically underestimates aggregate welfare inequality.