Mandated annuitization, gender-neutral pricing, and the possibility of negative correlation between risk type and purchase level

Mandated annuitization is often proposed to eliminate the inefficiency caused by the positive correlation between risk type and purchase level in insurance markets. We revisit this solution in a mandatory annuity program with partial waiver, which is empirically relevant. With the standard assumptions of positive health-wealth correlation as well as gender gaps in health and wealth, we obtain two main results. First, when annuity purchases are mandatory under gender-based pricing, risk type and purchase level are still positively correlated. Second, based on decomposing the severity of distortion due to mandated annuitization into the within-group and between-group effects under gender-neutral pricing, it is shown that risk type and purchase level may be negatively correlated if the between-group effect is stronger than the within-group effect.