Despite the large welfare gains shown in life cycle models, few retirees voluntarily purchase private annuities. The stark contrast between the theoretical predictions and the empirical evidence is called the ‘Annuitization Puzzle’. The weak demand for annuities has been largely attributed to three factors: adverse selection in the private annuity market, the wealth preannuitized in social security system, and bequest motives. However, any one of them fails to explain the lack of interest in annuities. This prompt a search for explainations outside of rational choice framwork from behavioral considerations (Brown et al., 2008; Benartzi et al., 2011).

The first contribution of this paper is to combine the three factors and explain in a rational choice framwork why so many individuals, while holding a positive portfolio of assets, do not invest in annuities.

A second contribution is to show that other generic imperfections (marketing cost, administration cost, oligopoly profits, etc.) lowers the real return from the pooling annuity market and makes non-annuitization possible.

The paper is organised as follows. Section 2 presents the two-period model with bequest motives and lifetime uncertainty. Section 3 describes the role of adverse selection in the annuity market. Section 4 introduces the pay-as you-go social security system. Section 5 discusses other generic imperfections in the annuity market. Section 6 concludes.

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