Abstract
This paper studies how the rates of deduction for early retirement have to be determined in pay-as-you-go (PAYG) systems in order to keep their budget stable. The derivation of these deductions requires the use of a multiperiod intertemporal budget constraint that involves assumptions about the retirement behavior of past, present, and future cohorts. In general, it is not possible to calculate budget-neutral deductions from the budget constraint of a single individual who retires before the target retirement age—an approach that dominates the related literature. Only for specific cases one can use this second approach but then one has to adjust the discount rate to the assumption about collective retirement. If there is only one deviating individual, then the right choice is the market interest rate while for a stationary retirement distribution it is the internal rate of return of the PAYG system. In this case, the necessary deductions are lower than under the standard approach. This is also true for retirement ages that fluctuate randomly around a stationary distribution. Various long-run developments (e.g., increases in life expectancy or permanent changes in the average retirement age) might cause challenges for the sustainability of the pension system. These developments, however, can only be dealt with by adequate adjustments to the basic pension formulas and not by the use of deduction rates.
Actuarial deductions for early retirement