Resolving the Annuity Puzzle: Estimating Lifecycle Models without (and with) Behavioral Data

Why do so few retirees purchase private annuities? Recent research suggests that bequest motives, precautionary savings motives, and actuarially-unfair pricing can explain the lack of demand for annuities. The degree to which these forces can explain the annuity puzzle depends crucially on retiree preferences, which can be challenging to properly identify. In this paper, we build an incomplete markets model of heterogeneous retirees, who save precautionarily when faced with health risks, the potential need for long term care, and an uncertain life span and who value consuming, leaving a bequest, and receiving long term care if they need it. Expenditures on long term care can be valued differently than typical consumption, depending on estimates of a health-state dependent utility function, and retirees can choose the amount to spend on LTC on the intensive margin, subject to a minimum cost of private LTC that captures the reality that this state is associated with large and lumpy costs. Additionally, since small, but important, changes in model specification can radically change preference parameter estimates, we develop Strategic Survey Questions (SSQs) that identify preference parameters using stated-preference methodology. The model is estimated using data from our newly created Vanguard Research Initiative Panel, allowing for heterogeneous preference parameter types, using moments from the wealth distribution alone, SSQs alone, and both wealth and SSQs. We explore retiree demand for different financial products, including annuities, and how these demand functions vary across the population and depend on prices and preferences.