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Resolving Aaron's Social Insurance Paradox

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  • Martin Drees

Abstract

This paper resolves Aaron's social insurance paradox, which suggests that introducing a pay-as-you-go (PAYG) pension system increases welfare when population growth plus average wage growth exceeds interest rates. Using a simplified overlapping generations model, we demonstrate this apparent advantage stems from asset reduction rather than inherent superiority. We analyze three pension systems - traditional PAYG, capital-funded, and capital-funded with bonus payments - and establish an equivalence between PAYG and the bonus-payment system. This equivalence reveals that systems with identical contributions and benefits differ only in accounting frameworks and asset positions, challenging the notion of PAYG superiority. Our analysis exposes a fundamental conceptual inconsistency in how sustainability is assessed across equivalent pension systems. As an alternative, we propose $\alpha$-stability, a framework using index shares to evaluate pension systems relative to economic indicators. These findings suggest that perceived advantages between pension systems often result from their formulation rather than substantive economic differences.

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  • Martin Drees, 2025. "Resolving Aaron's Social Insurance Paradox," Papers 2504.00909, arXiv.org.
  • Handle: RePEc:arx:papers:2504.00909
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    References listed on IDEAS

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    1. Robert Holzmann, 2017. "The ABCs of nonfinancial defined contribution (NDC) schemes," International Social Security Review, John Wiley & Sons, vol. 70(3), pages 53-77, July.
    2. Jose Enrique Devesa-Carpio & Mar Devesa-Carpio, 2010. "The cost and actuarial imbalance of pay-as-you-go systems: the case of Spain," Journal of Economic Policy Reform, Taylor & Francis Journals, vol. 13(3), pages 259-276.
    3. Assar Lindbeck & Mats Persson, 2003. "The Gains from Pension Reform," Journal of Economic Literature, American Economic Association, vol. 41(1), pages 74-112, March.
    4. José Enrique Devesa‐Carpio & Mar Devesa‐Carpio, 2010. "The cost and actuarial imbalance of pay‐as‐you‐go systems: the case of Spain," Journal of Economic Policy Reform, Taylor and Francis Journals, vol. 13(3), pages 259-276.
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