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The maximum debt-GDP ratio and endogenous growth in the Diamond overlapping generations model: Three overlapping generations are better than two

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  • Mark Roberts

Abstract

While the public debt has an interior maximum in the Diamond OLG model, due to an inherent nonlinearity [Rankin and Roffia (2003)], this feature also extends to a linear, AK model when it is conjoined with a backward-looking adjustment process for public debt [Braeuninger (2005)]. We show that if the debt dynamics are forward-looking, the maximum will instead be at a degeneracy – another possibility considered by Rankin and Roffia. However, the main point of the present paper is to show that any debt maximum in a finite-horizon model will be of an implausibly low order of magnitude, unless households save over at least two periods. This is because it is the debt flow that crowds-out investment flows, while this is synonymous with the debt stock in a model with only two, non-altruistic, overlapping generations, thus leading to a low maximum stock by default. Removing this restriction produces plausible results, and causes a low rate of economic growth to be a cause as well as a consequence of a high public debt.

Suggested Citation

  • Mark Roberts, 2014. "The maximum debt-GDP ratio and endogenous growth in the Diamond overlapping generations model: Three overlapping generations are better than two," Discussion Papers 2013/01, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM).
  • Handle: RePEc:not:notcfc:14/01
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    File URL: https://www.nottingham.ac.uk/cfcm/documents/papers/cfcm-2014-01.pdf
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    References listed on IDEAS

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    1. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
    2. Barro, Robert J, 1974. "Are Government Bonds Net Wealth?," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1095-1117, Nov.-Dec..
    3. Chalk, Nigel A., 2000. "The sustainability of bond-financed deficits: An overlapping generations approach," Journal of Monetary Economics, Elsevier, vol. 45(2), pages 293-328, April.
    4. Alfred Greiner & Uwe Köller & Willi Semmler, 2007. "Debt sustainability in the European Monetary Union: Theory and empirical evidence for selected countries," Oxford Economic Papers, Oxford University Press, vol. 59(2), pages 194-218, April.
    5. Mark A Roberts, 2013. "Fiscal rules and the maximum sustainable size of the public debt in the Diamond overlapping generations model," Discussion Papers 2013/07, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM).
    6. Karl Farmer & Jacopo Zotti, 2010. "Sustainable government debt in a two-good, two-country overlapping generations model," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 57(3), pages 289-316, September.
    7. Bohn, Henning, 1995. "The Sustainability of Budget Deficits in a Stochastic Economy," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 27(1), pages 257-271, February.
    8. Mark Roberts, 2014. "A non-monotonic relationship between public debt and economic growth: the effect of financial monopsony," Discussion Papers 2014/02, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM).
    9. Michael Brauninger, 2005. "The Budget Deficit, Public Debt, and Endogenous Growth," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(5), pages 827-840, December.
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    Keywords

    Public debt; endogenous growth; primary deficit/surplus; dynamics; bifurcation; degeneracy; backward-looking; forward-looking;

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