Felix Reichling and Kent Smetters write (gated–ungated version here),

But the presence of stochastic mortality probabilities also introduces a correlated risk. After a negative shock to health that reduces a household’s life expectancy, the present value of the annuity stream falls. At the same time, a negative health shock produces potential losses, including lost wage income not replaced by disability insurance, out-of-pocket medical costs, and uninsured nursing care expenses, that may increase a household’s marginal utility. Since the value of non-annuitized wealth is not affected by one’s health state, the optimal level of annuitization falls below 100 percent.

I once wrote,

An annuity is risk-reducing if the only risk you face is additional longevity. In fact, other risks may be more serious. You could easily find yourself needing to take out a loan if your savings are tied up in an annuity and your spouse requires a home health aide.

Economists have been preaching for 50 years that the low usage of annuities illustrates a market failure. In fact, what it may illustrate is that economists who relied on a mathematical model left out some important considerations. We need a term for this. I propose model failure.