This paper suggests that adverse selection problems in competitive annuity markets can generate quantity-constrained equilibria in which some agents, whose length of lifetime is uncertain, find it advantageous to accumulate capital privately. This occurs despite the higher rates of return on annuities. The welfare properties of these allocations are analyzed. It is shown that the level of capital accumulation is excessive in a Paretian sense. Policies that eliminate this inefficiency are discussed. Copyright 1987 by University of Chicago Press.