Public versus Private Retirement Pensions: A Stackelberg Differential Game

This paper studies the dynamic interaction between a representative employer and the government, where both play roles in providing retirement pensions to a group of retirees with heterogenous wages. Public pension expenses drive the evolution of public debt, which can be positive or negative (a Social Security trust fund) in the long run. The relative sizes of public and private pensions affect income distribution. Social Security discriminates in favor of low‐paid employees, while the employer provided pension, which is assumed to be integrated with Social Security, counteracts this tilt by favoring highly‐paid employees. The Social optimum, understood as the central planner outcome or the government first best, can be attained in the decentralized scenario if the degree of Social Security integration is optimally chosen by the government. In addition, pensions obtained by retirees from a flat percentage private pension are compared to the pensions obtained by assuming a private plan that is optimally integrated with Social Security.