This paper seeks to explain why annuity purchases are postponed to a later age. We consider an overlapping generations model with uncertain lifetime and two types of annuities. It is shown that, if the economy is dynamically inefficient, individuals demand annuities without delay. However, if it is efficient, annuity purchases are postponed. We also show that these results are robust to several extensions. (c) 2021 Elsevier B.V. All rights reserved.