Optimal mix among PAYGO, EET and individual savings

Abstract

In order to deal with the aging problem, the 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. Under the baseline model, 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's decision-making. The optimal mix is the comprehensive result of the two effects.

Keywords:

• Optimal mix
• PAYGO pension
• EET pension
• Nash equilibrium
• shrinking population

2010 Mathematics Subject Classifications:

• 91G05
• 91B05

JEL CLASSIFICATIONS:

• G22
• C61
• D81

Acknowledgments

The authors are particularly grateful to the two anonymous referees and the editor whose suggestions greatly improve the manuscript's quality. The authors also thank the members of the group of Actuarial Sciences and Mathematical Finance at the Department of Mathematical Sciences, Tsinghua University for their feedbacks and useful conversations.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors acknowledge the support from the National Natural Science Foundation of China [grant numbers 12271290, 11871036].