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A Note on the Accuracy of Markov-Chain Approximations to Highly Persistent AR(1)-Processes

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This note examines the accuracy of methods that are commonly used to approximate AR(1)-processes with discrete Markov chains. The quadrature-based method suggested by Tauchen and Hussey (1991) generates excellent approximations with a small number of nodes when the autocorrelation is low or modest. This method however has problems when the autocorrelation is high, as it typically is found to be in recent empirical studies of income processes. I suggest an alternative weighting function for the Tauchen-Hussey method, and I also note that the older method suggested by Tauchen (1986) is relatively robust to high autocorrelation.

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  • Floden, Martin, 2007. "A Note on the Accuracy of Markov-Chain Approximations to Highly Persistent AR(1)-Processes," SSE/EFI Working Paper Series in Economics and Finance 656, Stockholm School of Economics.
  • Handle: RePEc:hhs:hastef:0656
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    1. Hubbard, R Glenn & Skinner, Jonathan & Zeldes, Stephen P, 1995. "Precautionary Saving and Social Insurance," Journal of Political Economy, University of Chicago Press, vol. 103(2), pages 360-399, April.
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    5. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, Oxford University Press, vol. 109(3), pages 659-684.
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    2. Martin Floden, 2008. "Aggregate Savings When Individual Income Varies," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(1), pages 70-82, January.
    3. Karen Kopecky & Richard Suen, 2010. "Finite State Markov-chain Approximations to Highly Persistent Processes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(3), pages 701-714, July.
    4. José Cao-Alvira, 2012. "Velocity Volatility Assessment of Monetary Shocks on Cash-in-Advance Economies," Computational Economics, Springer;Society for Computational Economics, vol. 40(3), pages 293-311, October.
    5. Zhiyang Jia & Weizhen Zhu, 2012. "The effect of pension wealth on private savings. Results from an extended life cycle model," Discussion Papers 697, Statistics Norway, Research Department.
    6. Luca Fornaro, 2012. "International debt deleveraging," Economics Working Papers 1401, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 2016.
    7. Jonas D. M. Fisher & Martin Gervais, 2007. "First-time home buyers and residential investment volatility," Working Paper Series WP-07-15, Federal Reserve Bank of Chicago.
    8. Gianluca Benigno & Huigang Chen & Christopher Otrok & Alessandro Rebucci & Eric R. Young, 2011. "Revisiting Overborrowing and its Policy Implications," Central Banking, Analysis, and Economic Policies Book Series,in: Luis Felipe Céspedes & Roberto Chang & Diego Saravia (ed.), Monetary Policy under Financial Turbulence, edition 1, volume 16, chapter 6, pages 145-184 Central Bank of Chile.
    9. Fernando M. Martin, 2013. "Government Policy In Monetary Economies," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(1), pages 185-217, February.
    10. Jess Benhabib & Alberto Bisin & Shenghao Zhu, 2011. "The Distribution of Wealth and Fiscal Policy in Economies With Finitely Lived Agents," Econometrica, Econometric Society, vol. 79(1), pages 123-157, January.
    11. Pashchenko, Svetlana & Porapakkarm, Ponpoje, 2010. "Quantitative Analysis of Health Insurance Reform: Separating Community Rating from Income Redistribution," MPRA Paper 26158, University Library of Munich, Germany.
    12. Galindev, Ragchaasuren & Lkhagvasuren, Damba, 2010. "Discretization of highly persistent correlated AR(1) shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 34(7), pages 1260-1276, July.
    13. Svetlana Pashchenko & Ponpoje Porapakkarm, 2013. "Quantitative Analysis of Health Insurance Reform: Separating Regulation from Redistribution," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 16(3), pages 383-404, July.
    14. Gospodinov, Nikolay & Lkhagvasuren, Damba, 2011. "A new method for approximating vector autoregressive processes by finite-state Markov chains," MPRA Paper 33827, University Library of Munich, Germany.
    15. Svetlana Pashchenko & Ponpoje Porapakkarm, 2013. "Quantitative Analysis of Health Insurance Reform: Separating Regulation from Redistribution," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 16(3), pages 383-404, July.
    16. Pashchenko, Svetlana & Porapakkarm, Ponpoje, 2013. "Work Incentives of Medicaid Beneficiaries and The Role of Asset Testing," MPRA Paper 49730, University Library of Munich, Germany.
    17. Kartik B. Athreya & Xuan S. Tam & Eric R. Young, 2009. "Are harsh penalties for default really better?," Working Paper 09-11, Federal Reserve Bank of Richmond.
    18. Jonen, Benjamin & Scheuring, Simon, 2014. "Time-varying international diversification and the forward premium," Journal of International Money and Finance, Elsevier, vol. 40(C), pages 128-148.
    19. Nikolay Gospodinov & Damba Lkhagvasuren, 2014. "A Moment‐Matching Method For Approximating Vector Autoregressive Processes By Finite‐State Markov Chains," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 843-859, August.
    20. Gust, Christopher & López-Salido, J David, 2009. "Monetary Policy, Velocity, and the Equity Premium," CEPR Discussion Papers 7388, C.E.P.R. Discussion Papers.
    21. Ponpoje (Poe) Porapakkarm & Svetlana Pashchenko, 2013. "Labor Supply Incentives of Medicaid," 2013 Meeting Papers 1082, Society for Economic Dynamics.
    22. Bommier, Antoine & Harenberg, Daniel & Le Grand, François, 2017. "Household Finance and the Value of Life," Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168189, Verein für Socialpolitik / German Economic Association.
    23. Ole Wilms & Karl Schmedders & Walt Pohl, 2016. "Higher-Order Effects in Asset-Pricing Models with Long-Run Risks," 2016 Meeting Papers 306, Society for Economic Dynamics.

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    Keywords

    numerical methods; income processes; autoregressive process;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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