We analyze the effect of health cost risk on optimal annuity demand and consumption/savings decisions.

Many retirees are exposed to sizeable out-of-pocket medical expenses, while annuities potentially impair the ability to get liquidity to cover these costs and smooth consumption. We find that if out-of-pocket medical expenses can already be very sizeable early in retirement, full annuitization is suboptimal.

In other cases, individuals take advantage of the mortality credit annuities provide and save out of the annuity income to build a buffer for health cost shocks at later ages. When comparing to empirically observed levels of annuitization, we find that sizeable health cost risk early in retirement may resolve the annuity puzzle.

Moreover, we explain the observed pattern of annuitization as a function of initial wealth at retirement.

For personal financial planning purposes, we develop a simple rule of thumb for annuity demand, based on expected health cost risk early in retirement, wealth at retirement, and subsistence consumption levels. We show that the welfare costs from using the rule compared to the life cycle model are small.