Extending the Aaron Condition for Alternative Pay-as-You-Go Pension Systems

Welfare comparisons between funded and pay-as-you-go (PAYG) pension systems are often made using the Aaron condition. However, the Aaron condition as usually stated is not precise enough about the exact form of the PAYG pension system. PAYG pension systems can be either of the defined-benefit or defined-contribution variety. They can also differ with regard to intra-generational redistribution. For example, pension benefits can be flat or earnings related. Here, four alternative PAYG pension systems are considered. It is shown that each system generates its own Aaron condition. In addition, the standard Aaron condition assumes that the wage rate and labor participation rate does not vary across individuals and that the rate of population growth is constant and exogenous. These assumptions are also relaxed. Using US data covering the period 1933-2001, I then show that the results of comparisons between PAYG and funded systems depend critically on exactly which variety of PAYG system is being compared, and that PAYG systems are becoming less attractive over time as fertility rates decline.