Optimal contribution rate of PAYGO pension

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.