Optimal consumption and annuity equivalent wealth with mortality model uncertainty

Abstract

The classical Yaari (1965) lifecycle model (LCM) stands as a cornerstone in numerous modern retirement studies, especially in understanding the determinants of annuity demand. The LCM predicts a high annuity demand among individuals facing retirement, yet it is rarely the case in reality. This gap between economic theory and empirical reality, commonly referred to as the annuity puzzle, has spurred extensive research endeavors aimed at elucidating its economic and behavioral underpinnings.

In this paper, we examine the cause of low annuity demand through the angle of mortality model uncertainty. To this end, we advance Yaari's LCM via integrating a mortality perturbation analysis within a recursive utility framework. Through this approach, we derive the robust optimal consumption strategy and the corresponding annuity equivalent wealth. By utilizing stochastic dominance theory, we establish a series of monotonicity results about the annuity equivalent wealth with respect to ambiguity aversion parameter and other key parameters, such as interest, discount, and mortality rates. Our findings suggest that, among decision-makers with elasticity of intertemporal substitution less than unity, the economic value of an annuity is diminished for those who place greater confidence in their subjective mortality table. In other words, retirees may underestimate the additional utility gained from annuitization if they do not adequately consider the potential uncertainty surrounding their subjective mortality estimates.