  We propose and estimate a model of demand and supply of annuities. To this
end, we use rich data from Chile, where annuities are bought and sold in a
private market via a two-stage process: first-price auctions followed by
bargaining. We model firms with private information about costs and retirees
with different mortalities and preferences for bequests and firms' risk
ratings. We find substantial costs and preference heterogeneity, and because
there are many firms, the market performs well. Counterfactuals show that
simplifying the current mechanism with English auctions and "shutting down"
risk ratings increase pensions, but only for high-savers.
