Comment on S. Valdés‐Prieto, “The Financial Stability of Notional Account Pensions”

Abstract

In an important contribution to this Journal, Valdes-Prieto (2000) has shown that the recently popular concept of accounts cannot guarantee short-run financial stability of pay-as-you-go financed public pension schemes in the sense of automatic budget equality for any given time path of the contribution rate. In Result 2 (p. 406), he states that notional accounts do not provide automatic financial balance in the short run when the interest rate is the growth rate of contribution revenue except for the steady-state growth case. In the proof he uses a table (p. 408, Table 1) in which the maximum value of the ratio of expenditures to revenues of the pension plan is calculated for the case of a rising growth rate of contribution revenue. This maximum ratio is always above 1. The author explains his finding as follows. When the growth rate of contribution revenue is used as the interest rate which is credited to the stock of capital of those members reaching age 65, the rise in expenditure is greater than the rise in revenue, generating a deficit (ibid.). The following simple example confirms Result 2 but shows that the ratio of expenditures to revenues behaves in the opposite way to that asserted by Valdes-Prieto. A rise in the growth rate of revenues leads to a temporary surplus of the plan, whereas a fall in the growth rate implies a temporary deficit. The example is based on a discrete-time 3-OLG model in which individuals work the first two periods of their three-period life, earning 1 dollar each, and the contribution rate 0 is fixed at 20 percent. Contributions are to the account in the period in which they are paid and earn an interest equal to the growth rate of contribution revenue, which is to the account at the beginning of the next period. At the beginning of the third period, the account balance is paid out as a one-shot retirement benefit. In panel (a) of Table 1 it is assumed that there are 100 workers in each of the cohorts entering the labor market in period t <2 and that this number