Why a switch from payg to funded pension system has no link to demographic development?

The paper deals with a wide-spread myth that a switch from a PAYG to a funded pension system might solve adverse consequences of the population aging. It is shown, that under additional assumptions the pension debt (which is created during the process of the switch) is exactly equal to the value of assets that the pension funds accumulate. These additional assumptions are following: government imposes additional taxes, which are equal to the difference between the contributions to the former PAYG system and the contributions to the pension funds. Therefore workers contribute less to the pension funds but if the additional taxes are taken into account, they continue paying the same amount. It is shown, that if the additional taxes were permanently lower than what is supposed, the pension debt would grow beyond any limits. The other additional assumption made is that the interest rate paid by government from its pension debt is the same as the interest rate reached by the funds. If this assumption is relaxed, the qualitative conclusions do not change. Hence, demographic development cannot be used as an argument in favour of a switch of the pension system.