By Yaodi Yong, Jinggong Zhang & Xiaobai Zhu

In response to demographic shifts such as declining fertility rates and increasing life expectancy, many countries are raising the full retirement age (FRA). This paper develops a novel optimization framework for designing FRA increase schedules, explicitly balancing the minimization of aggregate welfare loss across affected generations with intergenerational fairness considerations. Within a continuous-time framework, we model welfare loss through disutility functions applied to actuarial losses generated by pension reforms, while incorporating smoothness penalties on the reform schedule to prevent abrupt intergenerational changes. We derive analytical characterizations of the optimal schedules under linear, exponential, and power disutility, with closed-form expressions available in certain special cases. Moreover, we construct efficient frontiers that visualize the inherent trade-off between welfare loss and intergenerational inequality. Robustness checks using alternative inequality measures, alternative disutility specifications, and binding deficit recovery constraints confirm the qualitative validity of our findings. The deficit-constrained case yields a novel triphasic reform structure, with sharp increases for older workers, a slowdown for middle-aged cohorts, and renewed acceleration for the youngest, which aligns with the structure observed in the U.S. Social Security reform of 1983. Our framework provides policymakers with a transparent toolkit to evaluate the critical trade-offs between efficiency and fairness.

Source SSRN