The efficiency of unfunded pension schemes

Public pension schemes can be designed either as capital reserve systems or as unfunded (or pay-as-you-go) schemes. In the literature it has been alleged that unfunded schemes are intergenerationally efficient in Pareto's sense. Here we show that this holds only if contributions to the system are levied as lump-sum taxes. But in reality, flat-rate income taxes are normally used instead  and then, an unfunded scheme induced distortions and can completely be abolished in finite time without inflicting damage upon any generation.