What's gone wrong in the design of PAYG systems?

In order to face the population ageing problem, most countries with PAYG systems introduced pension reforms during the last twenty years. However, in many cases these reforms are considered as insufficient to guarantee the pension sustainability; in other cases, the pension sustainability is achieved through the introduction of drastic reforms and, thus, at the expense of a dramatic reduction in the well-being of current and future generations. The objective of this article is to show that the non-sustainability of PAYG systems and, consequently, the necessity to introduce drastic pension reforms, is explained by the fact that in countries with PAYG systems pensions have not been computed according to appropriate rules. In particular, we show that the sustainability of the pension system is guaranteed if (i) pension benefits are computed using actuarial principles, (ii) the implicit rate of return on contributions is the same for each retiree and equal to the average wage bill growth rate, and (iii) pension reserves are remunerated at a risk-free interest rate equal to the average wage bill growth rate. These conditions allow a PAYG system to face any demographic shock, such as an increase in life expectancy and a transitory increase in fertility rates (baby boom) followed by a transitory reduction in fertility rates (baby boost)