Retirees face a major uncertainty when they have to decide how much to spend from their assets: how long they are going to live. You do not want to spend too much in case you end up centenarian, but it would also be a waste to live thriftily when one ends up dying early. Luckily, the market provides a solution and has done so for centuries: annuities, which provide a constant stream of income as long as one is alive. This represents substantial welfare gains. Yet, very few people take advantage of this.
The literature has been puzzling over this for a while, see Jeffrey Brown. For one, public pension plans already provide some constant income. But this still leaves a lot of gain from annuities. Inflation risk is not a problem as annuity products are offered that are indexed, even even some that provide long-term care benefits. Bequest motives have been ruled out as well, as is risk-sharing within families.
Note also that in a lot of the life-cycle modeling with uncertain lifetimes, researchers use annuities to represent the dynamics of assets during retirement and death, because it is simple to model and because it is plain rational to buy annuities. The fact that this is not borne by facts is worrisome for some results coming out of this research.
In a recent NBER paper, Brown, Kling, Mullainathan and Wrobel may have found a solution to the annuity puzzle: it is all about how annuities are sold. If it is clearly labeled as a consumption insurance, then people are willing to buy it, as consumption risk is minimal. If it is sold as an investment, people realize it is very risky (as an investment): one may lose a lot if one dies early. This does not look like a rational reasoning, but the authors have conducted experiments that confirm that how annuities are framed matters crucially.
Then why would companies selling annuities frame it as an investment product? The authors conjecture that this is simply what they are used to. Maybe this research will show them how to change their marketing.