The evidence presented thus far has concerned the saving behavior and wealth profiles of consumers during the working period of life. The Life Cycle model has another set of testable implications for behavior in the latter stages of life, after retirement. In particular, according to the standard Life Cycle model, even patient consumers want to spend all of their wealth before they die. Of course, an uncertain date of death makes this difficult to achieve on one’s own. However, there is a financial instrument which accomplishes exactly the goal implied by the model: annuities. One test of the rough accuracy of the basic Life Cycle model is therefore whether the wealth of retired households is largely annuitized.
Carrying out such a test requires some methodology for calculating annuity wealth. I assume that the annuity is fixed in real terms (primarily because the largest form of annuity income, Social Security, is inflation-adjusted). I assume a real interest rate, and use the mortality tables from HSZ to construct the expected present discounted value of a one-dollar per year annuity as:
where A * is the probability of surviving from year i 1 to year i and R — 1 + r is the gross interest rate (I assume R = 1.03 but results would be similar for other plausible interest rates). The wealth value of the observed annuity income YANN at age a is then Га YANNa.
Using this method, and including home equity among annuitized wealth, the mean household over age 65 has approximately 55 percent of their wealth in annuitized form. However, among the richest 1 percent of households, the mean annuitization rate is only 10 percent.
This evidence on annuitization is suggestive, but hardly conclusive. Annuity markets are likely far from perfect; as in other insurance markets, adverse selection may distort the market sufficiently to make inference hazardous. Furthermore, annuities are the perfect financial vehicle to counter only one kind of risk, mortality risk. If other kinds of risk are important, it is no longer obvious that even selfish Life Cycle consumers should annuitize most or all of their wealth. For example, if there is a small probability of a very expensive medical problem, it may be important to have access to a large chunk of nonannuitized wealth in order to pay the bills (assuming that no health insurance will fully cover every possible medical catastrophe or every potentially desirable experimental treatment).