Paper: arXiv 2302.09218

Authors: Lin He, Zongxia Liang, Zhaojie Ren, Yilun Song

Abstract

In order to deal with the aging problem, pension system is actively transformed into the funded scheme. However, the funded scheme does not completely replace PAYGO (Pay as You Go) scheme and there exist heterogeneous mixes among PAYGO, EET (Exempt, Exempt, Taxed) and individual savings in different countries. In this paper, we establish the optimal mix by solving a Nash equilibrium between the pension participants and the government. Given the obligatory PAYGO and EET contribution rates, the participants choose the optimal asset allocation of the individual savings and the consumption policies to achieve the objective. The results extend the ``Samuelson-Aaron" criterion to age-dependent preference orderings. And we identify three critical ages to distinguish the multiple outcomes of preference orderings based on heterogeneous characteristic parameters. The government is fully aware of the optimal feedback of the participants. It chooses the optimal PAYGO and EET contribution rates to maximize the overall utility of the participants weighted by each cohort’s population. As such, the negative population growth rate leads to the decline of the PAYGO attractiveness as well as the increase of the older cohorts’ weight in the government decision-making. The optimal mix is the comprehensive result of the two effects.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated continuous-time life-cycle framework using Nash equilibrium and dynamic programming to model optimal pension schemes under demographic changes. While mathematically rigorous, it lacks empirical validation, backtesting, or real-world data calibration to back its theoretical insights.

Research Flowchart

  flowchart TD
    A[Research Goal: Determine Optimal Mix among PAYGO, EET, & Individual Savings] --> B[Inputs: Demographic Data, Age-Dependent Preferences, & Tax Schemes]
    B --> C[Step 1: Participants solve optimal asset allocation & consumption policies]
    C --> D[Identify 3 Critical Ages & Extend Samuelson-Aaron Criterion]
    D --> E[Step 2: Government sets PAYGO & EET rates to maximize cohort-weighted utility]
    E --> F[Establish Stackelberg/Nash Equilibrium between Participants & Government]
    F --> G[Key Outcome: Optimal pension mix balances declining PAYGO yield with aging voter weights]