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The Optimum Quantity of Debt: Technical Appendix


  • S. Rao Aiyagari

    (Research Department, Federal Reserve Bank of Minneapolis)

  • Ellen R. McGrattan

    (Research Department, Federal Reserve Bank of Minneapolis)


We describe the numerical method used to compute equilibria in the economies studied by Aiyagari and McGrattan, The Optimum Quantity of Debt (Journal of Monetary Economics 1998). These economies have a large number of infinitely lived households whose saving behavior is influenced by precautionary saving motives and borrowing constraints. We apply the finite element method to compute households¡¯ saving decisions and to compute the distribution of asset holdings. To verify that the method works well for our problems, we apply them to some related test problems with known solutions.

Suggested Citation

  • S. Rao Aiyagari & Ellen R. McGrattan, 2003. "The Optimum Quantity of Debt: Technical Appendix," Annals of Economics and Finance, Society for AEF, vol. 4(1), pages 193-217, May.
  • Handle: RePEc:cuf:journl:y:2003:v:4:i:1:p:193-217

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    References listed on IDEAS

    1. Barro, Robert J, 1979. "On the Determination of the Public Debt," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 940-971, October.
    2. Mehrling, Perry, 1995. "A note on the optimum quantity of money," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 249-258.
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    4. Varian, Hal R., 1980. "Redistributive taxation as social insurance," Journal of Public Economics, Elsevier, vol. 14(1), pages 49-68, August.
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    6. Chamley, Christophe, 1986. "Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives," Econometrica, Econometric Society, vol. 54(3), pages 607-622, May.
    7. McGrattan, Ellen R., 1996. "Solving the stochastic growth model with a finite element method," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 19-42.
    8. Imrohoroglu, Ayse, 1992. "The welfare cost of inflation under imperfect insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 16(1), pages 79-91, January.
    9. Aiyagari, S. Rao & McGrattan, Ellen R., 1998. "The optimum quantity of debt," Journal of Monetary Economics, Elsevier, vol. 42(3), pages 447-469, October.
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    11. Lucas, Robert E, Jr, 1990. "Supply-Side Economics: An Analytical Review," Oxford Economic Papers, Oxford University Press, vol. 42(2), pages 293-316, April.
    12. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, Oxford University Press, vol. 109(3), pages 659-684.
    13. Partha Dasgupta & Douglas Gale & Oliver Hart & Eric Maskin (ed.), 1992. "Economic Analysis of Markets and Games: Essays in Honor of Frank Hahn," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262541599, January.
    14. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    15. Laitner, John P, 1979. "Bequests, Golden-age Capital Accumulation and Government Debt," Economica, London School of Economics and Political Science, vol. 46(184), pages 403-414, November.
    16. Timothy J. Kehoe & David K. Levine & Michael Woodford, 1990. "The optimum quantity of money revisited," Working Papers 404, Federal Reserve Bank of Minneapolis.
    17. Fernando Alvarez & Terry J. Fitzgerald, 1992. "Banking in computable general equilibrium economies: technical appendices I and II," Staff Report 155, Federal Reserve Bank of Minneapolis.
    18. Woodford, Michael, 1990. "Public Debt as Private Liquidity," American Economic Review, American Economic Association, vol. 80(2), pages 382-388, May.
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    Cited by:

    1. Miguel Viegas & Ana Paula Ribeiro, 2011. "Welfare-improving Government Behaviour and Inequality - Inspection Using a Heterogeneous-agent Model," CEF.UP Working Papers 1103, Universidade do Porto, Faculdade de Economia do Porto.
    2. Wang, Gaowang, 2011. "Time Preference and Interest Rate in a dynamic general Equilibrium Model," MPRA Paper 34063, University Library of Munich, Germany.
    3. Viegas, Miguel & Ribeiro, Ana Paula, 2013. "Welfare-improving government behavior and inequality in a heterogeneous agents model," Journal of Macroeconomics, Elsevier, vol. 37(C), pages 146-160.
    4. Wang, Gaowang & Zou, Heng-fu, 2011. "Mercantilism, Foreign Asset Accumulation and Macroeconomic Policy," MPRA Paper 34519, University Library of Munich, Germany.

    More about this item


    Finite element method; Optimal debt;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy


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