The article presents a method for calculating the cross-section internal rate of return on contributions to pension systems financed according to the pay-as-you-go principle. The method entails a procedure for valuing the contribution flow of pay-as-you-go financing, and identifies the complete set of factors that determine the cross-section internal rate of return. The procedure makes it possible to apply the algorithm of double-entry bookkeeping in analyzing and presenting the financial position and development of pay-as-you-go pension systems. JEL: classification: E62, E43, H55, J1, M41

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The aim of this paper is twofold: to show the usefulness of automatic balance mechanisms (ABMs) and to explore the issue of introducing an ABM into the Spanish state contributory retirement pension system. With this in mind, we define the concept of the ABM and carry out an analysis of that existing in Sweden, Canada, Germany, Japan and Finland. We also present an indicator of the Spanish system's solvency which emerges from the actuarial balance sheet, and simulates the effect that certain changes in the parameters of the present system would have on solvency, showing the direction that could be taken if the mechanism were to be introduced in Spain. A comparison between the official balance sheet for the Swedish notional account system and our balance sheet for the Spanish contributory pension system is also provided.

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Canada, Denmark, the Netherlands and Sweden have advanced multi‐pillar pension systems. Using micro‐simulations, this article presents a close examination of the interaction of pillars in these countries. The relative importance and the role of the different pension pillars vary from country to country, and according to age, income, gender and socio‐economic dimensions as well as between generations. A further area of investigation is the mitigation capacity of the four pension systems. On the one hand, adverse labour careers lead to lower life‐time earnings and lower private pension accruals. On the other hand, these effects are mitigated through the design of pillars and their interaction. Mitigation is important to income security and stability in retirement and to post‐retirement income distribution. However, mitigation mechanisms come at the cost of incentives. Moreover, in many countries, the generosity of public benefits is set to decrease – increasing the importance of private pensions. This will shift risk and uncertainty from employers and pension institutions to individuals. Thus, risks and uncertainties related to private pensions will become more important, raising questions about the division of responsibilities between public and private pensions, and about the potential of mitigating such risk through pillar interaction. These concerns are further reinforced by labour market changes. Although a pension system free of distortions is inconceivable, this article seeks to contribute to addressing how mitigation should be designed, and how mitigation and risk sharing should be balanced against incentives, challenges which are as much political as technical.