Grossman’s Health Threshold and Retirement

We formulate a stylized structural model of health, wealth accumulation and retirement decisions building on the human capital framework of health provided by Grossman. We explicitly assume a functional form of the utility function and carefully account for initial conditions, which allow us to derive analytic solutions for the time paths of consumption, health, health investment, savings and retirement. We argue that the Grossman literature has been unnecessarily restrictive in assuming that health is always at Grossman’s “optimal” health level. Exploring the properties of corner solutions we find that advances in population health (health capital) can explain the paradox that while population health and mortality have continued to improve in the developed world, retirement ages have continued to fall with retirees pointing to deteriorating health as an important reason for early retirement. We find that improvements in population health decrease the retirement age, while at the same time individuals retire when their health has deteriorated. In our model, workers with higher human capital (say white collar workers) invest more in health and because they stay healthier retire later than those with lower human capital (say blue collar workers) whose health deteriorates faster. Plausibly, most individuals are endowed with an initial stock of health that is substantially greater than the level required to be economically productive.