ABSTRACT

In this paper, we study the optimal contribution rate of pay-as-you-go (PAYGO) pension under a Nash equilibrium between the participants and the government. Given the fixed contribution rate, the participants of different cohorts choose optimal consumption and asset allocation policies to achieve their objectives. Using the variational method, we derive the closed-form solution. The value function of the participants is monotonous with respect to the PAYGO contribution rate under constant population growth rate. As such, we modify the ‘Samuelson-Aaron’ criterion that the preference between PAYGO and fully funded pensions depends not only on the demography, investment and salary parameters but also on the age of the cohort. Moreover, we establish the critical age to separate the preference and the ex-post admissible scope for the contribution rate adjustment. As a central planner, the government is fully aware of the participants' optimal feedback functions. The objective of the government is to maximize the overall utility of the participants weighted by each cohort's population. For a shrinking population, the fully funded scheme is more preferable and only the elderly cohorts prefer PAYGO scheme. However, taking into account the larger political power of the elderly cohorts in the objective function, the optimal contribution rate raises slightly.

摘要

在本文中，我们研究了在参与者和政府之间的纳什均衡下现收现付 (PAYGO) 养老金的最优缴费率。给定缴费率，不同队列的参与者选择最优的消费和资产配置政策来实现他们的目标。使用变分方法，我们推导出封闭形式的解决方案。在人口增长率不变的情况下，参与者的价值函数相对于现收现付贡献率是单调的。因此，我们修改了“Samuelson-Aaron”标准，即现收现付和全额养老金之间的偏好不仅取决于人口统计、投资和工资参数，还取决于队列的年龄。而且，我们建立临界年龄来区分缴费率调整的优先和事后允许范围。作为中央计划者，政府充分意识到参与者的最优反馈功能。政府的目标是最大化每个队列人口加权的参与者的整体效用。对于萎缩的人口，全额资助计划更可取，只有年长者更喜欢现收现付计划。但考虑到目标函数中老年人群的政治权力较大，最优贡献率略有提高。政府的目标是最大化每个队列人口加权的参与者的整体效用。对于萎缩的人口，全额资助计划更可取，只有年长者更喜欢现收现付计划。但考虑到目标函数中老年人群的政治权力较大，最优贡献率略有提高。政府的目标是最大化每个队列人口加权的参与者的整体效用。对于萎缩的人口，全额资助计划更可取，只有年长者更喜欢现收现付计划。但考虑到目标函数中老年人群的政治权力较大，最优贡献率略有提高。