Retirement income, bequests, and insurance : implications of mortality risk in a stochastic life cycle model

Abstract

This thesis is composed of four studies on the role of annuities and life insurance in the portfolios of elderly households. It has long been known in the economics literature that annuities should be of substantial value in the portfolios of retired individuals. However, outside of private pension plans. the purchase of private annuity contracts is relatively rare. This paper explores the issues associated with this "Annuity Puzzle" using the framework of a life cycle model of consumption, extended to account for mortality uncertainty. Chapter 1 empirically examines household decisions about whether or not to annuitize balances 111 defined contribution pension plans upon retirement. This study calculates a utility based measure of annuity valuation for households nearing retirement, and allows for variation across households to result from variation in mortality rates, risk aversion. marital status, and the presence of pre-existing annuities such as Social Security. It finds that a one percentage point increase in the calculated gain from annuitization is associated with a one percentage point increase in the ex ante probability of annuitizing one's retirement resources. It also finds that the presence of bequest motives has no effect on the disposition of definer.'. contribution plan assets. The finding that bequest motives do not affect marginal annuity decisions is in contrast to some of the previous literature. In particular, previous research has argued that a significant fraction of the elderly are over-annuitized by Social Security, as evidenced by their decision to held life insurance. Chapter 2 re-examines this finding using new and better data on the age 70+ population, and finds little support for the existence of strong bequest motives. One important source of variation in the decision of whether or not to annuitizc is marital status. Chapter 3 explores the demand for joint-life annuity products among marrind couples, and finds that couples should value annuitization less than single individuals. This is because couples have Opportunities to share risk between them, and as such, marriage is a partial substitute for perfect annuity markets. This may help to explain the relative scarcity of private annuity contracts in the U.S. Chapter 4 extends the analysis of annuities to account for inflation risk. It explores the relative value of real versus nominal annuities, and also explores the gains to purchasing annuities that arc linked to an underlying portfolio of risky assets.