Subjective survival beliefs and the life-cycle model

Evidence from panel surveys of households, collected over several years and in different countries, shows that people's perception about their remaining lifetime deviates from actuarial data. This has consequences for consumption, savings and investment over an individual's financial life cycle, and in particular for retirement planning and the purchase of annuities. We use data from the U.S. Survey of Consumer Finances to estimate subjective survival probabilities at different ages. This relies on two different methods of adjusting survival probabilities from a suitable life table. We observe survival pessimism at younger ages and optimism at older ages, consistent with the literature. We optimize numerically for consumption, investment and annuitization in a life-cycle model where individuals receive stochastic labour income and invest in a risk-free asset and in stock whose returns are imperfectly correlated with wages, and where they can annuitize their wealth at retirement. We demonstrate that there is some under-saving before retirement, over-saving post-retirement, and under-annuitization when subjective survival beliefs are used, relative to objective survival expectations. These effects are fairly small, irrespective of the method employed to estimate subjective mortality. Subjective survival beliefs do not therefore fully explain household finance puzzles such as the "annuity puzzle", i.e. observed lower- than-optimal demand for annuities. This conclusion is robust to variations in risk preferences, in the labour income profile, and in the loading factored by insurers in annuity prices.