Welfare-enhancing annuity divisor for notional defined contribution design

In this study, we investigate the optimal annuity divisor for a Notional Defined Contribution (NDC) pension scheme. Our analysis reveals that both the constant and actuarially fair annuity divisors, commonly used in practice, disproportionately benefit high-income individuals, resulting in an unintended wealth transfer from low-income to high-income groups. To address this issue, we employ an optimization framework based on a weighted social welfare function and derive the optimal annuity divisor using optimal control techniques. We present the explicit solution when the income distribution follows either Pareto or Pareto-lognormal and when the S-Gini function is adopted in prioritizing different income classes. Our findings suggest that excluding the low-income class from the NDC plan, as practiced in China, renders the NDC plan unnecessary unless the society is nearly inequality-neutral. By calibrating our model with Chinese data, we propose a progressive annuity divisor formula that adjusts for income inequality and mortality differentials, demonstrating its potential to enhance social welfare and achieve a more equitable pension system.