The analysis in this paper was motivated by the apparent puzzle that, despite substantial uncertainty about future inflation rates, private pensions are almost universally unindexed. Moreover, although a variable annuity invested in short-term money market instruments provides a good inflation hedge, almost all private pensions provide a fixed annuity. The results of the analysis indicate that the existence of unindexed pensions and fixed annuities is not at all surprising. Even without Social Security, it may be optimal to have a completely unindexed private pension and it is generally not optimal to have a completely indexed pension. The availability of an optimal (or greater than optimal) amount of Social Security generally reduces the desired degree of indexing and, under a variety of conditions, makes it optimal to have no indexing at all in the private pension. Because unexpected changes in the price level do not alter the value of Social Security pensions, the existence of inflation uncertainty makes a Social Security pension optimal when it would not otherwise be and an increase in inflation uncertainty is likely to increase the optimal reliance on Social Security. But despite these conclusions, the analysis shows that including some Social Security in an overall pension program is necessarily optimal only when both money market instruments and Social Security have rates of return that are known with certainty. When the real yield on money market instruments is uncertain, the optimal pension arrangement may be a partially indexed private pension even though Social Security is risk-free and has a return that is higher than the expected rate on the money market instruments. Similarly, when Social Security is risky, the optimal arrangement my be to exclude Social Security and to use a partially indexed private pension. In all cases, an individual who has a low enough degree of risk aversion will prefer no Social Security and a completely unindexed private pension.
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