Banning gender-based pricing in a mandatory annuity program with partial waiver may unintentionally lead to advantageous selection

A standard solution to adverse selection in insurance markets is to mandate all buyers to purchase insurance. This paper revisits this solution in a mandatory annuity program with partial waiver, which is empirically relevant. With the assumptions of positive health-wealth correlation and gender gaps in health and wealth, we obtain two main results. First, under gender-based pricing, adverse selection is not eliminated when annuity purchases are mandatory. Second, based on decomposing the severity of adverse selection into the within-group and between-group effects under gender-neutral pricing, advantageous selection may be present if the between-group effect is stronger than the within-group effect.