Optimal onset and exhaustion of retirement savings in a life-cycle model

Abstract

Abstract This paper facilitates the exploration of optimal individual retirement savings strategies within a life-cycle framework by providing a convenient tool to implement a model suggested by Yaari (1965) with an uncertain lifetime and borrowing constraints. The solution is given both for the general case and for cases leading to closed-form equations such as power utility and Gompertz mortality. Illustrations for a wide range of parameters indicate that starting to save for retirement in the first phase of one's career is rarely optimal. Of course, this is not to say that young workers should not save for other motives – a limitation of this model is that risks besides mortality are not considered. The conclusion should also be interpreted cautiously as it is difficult to represent every possible individual circumstance and saving incentive in a single model. The intuition behind the result is that an efficient strategy allocates the burden of financing retirement first to periods with higher income (i.e. lower opportunity costs), creating the potential for an initial period without savings when income grows.

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