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Markov-chain approximations of vector autoregressions: application of general multivariate-normal integration techniques

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  • Edward S. Knotek
  • Stephen J. Terry

Abstract

Discrete Markov chains can be useful to approximate vector autoregressive processes for economists doing computational work. One such approximation method first presented by Tauchen (1986) operates under the general theoretical assumption of a transformed VAR with diagonal covariance structure for the process error term. We demonstrate one simple method of more conveniently treating this approximation problem in practice using readily available multivariate-normal integration techniques to allow for arbitrary positive-semidefinite covariance structures. Examples are provided using processes with non-diagonal and singular non-diagonal error covariances.

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  • Edward S. Knotek & Stephen J. Terry, 2008. "Markov-chain approximations of vector autoregressions: application of general multivariate-normal integration techniques," Research Working Paper RWP 08-02, Federal Reserve Bank of Kansas City.
    • Handle: RePEc:fip:fedkrw:rwp08-02
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    1. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    2. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-396, March.
    3. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
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    2. Max Groneck & Johanna Wallenius, 2021. "It Sucks to Be Single! Marital Status and Redistribution of Social Security [Female labor supply as insurance against idiosyncratic risk]," The Economic Journal, Royal Economic Society, vol. 131(633), pages 327-371.
    3. 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.
    4. Damba Lkhagvasuren & Erdenebat Bataa, 2023. "Finite-State Markov Chains with Flexible Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 611-644, February.
    5. Carlos Hatchondo, Juan & Martinez, Leonardo & Sánchez, Juan M., 2015. "Mortgage defaults," Journal of Monetary Economics, Elsevier, vol. 76(C), pages 173-190.
      • Juan Carlos Hatchondo & Leonardo Martinez & Juan M. Sanchez, 2011. "Mortgage defaults," Working Paper 11-05, Federal Reserve Bank of Richmond.
      • Mr. Leonardo Martinez & Juan Carlos Hatchondo & Mr. Juan M. Sanchez, 2012. "Mortgage Defaults," IMF Working Papers 2012/026, International Monetary Fund.
      • Juan Carlos Hatchondo & Leonardo Martinez & Juan M. Sanchez, 2011. "Mortgage defaults," Working Papers 2011-019, Federal Reserve Bank of St. Louis.
      • Juan Carlos Hatchondo & Leonardo Martinez & Juan M. Sanchez, 2015. "Mortgage Defaults," CAEPR Working Papers 2015-011, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    6. Samer Shousha, 2017. "International Reserves, Credit Constraints, and Systemic Sudden Stops," International Finance Discussion Papers 1205, Board of Governors of the Federal Reserve System (U.S.).
    7. Sergio J. Rey & Wei Kang & Levi Wolf, 2016. "The properties of tests for spatial effects in discrete Markov chain models of regional income distribution dynamics," Journal of Geographical Systems, Springer, vol. 18(4), pages 377-398, October.
    8. Leland E. Farmer & Alexis Akira Toda, 2017. "Discretizing nonlinear, non‐Gaussian Markov processes with exact conditional moments," Quantitative Economics, Econometric Society, vol. 8(2), pages 651-683, July.
    9. Edward S. Knotek & Stephen J. Terry, 2008. "Alternative methods of solving state-dependent pricing models," Research Working Paper RWP 08-10, Federal Reserve Bank of Kansas City.
    10. 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.
    11. Gordon, Grey, 2021. "Efficient VAR discretization," Economics Letters, Elsevier, vol. 204(C).
    12. Mitsuru Katagiri, 2018. "Equilibrium Yield Curve, the Phillips Curve, and Monetary Policy," IMF Working Papers 2018/242, International Monetary Fund.
    13. 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.
    14. Reyes-Heroles, Ricardo & Tenorio, Gabriel, 2020. "Macroprudential policy in the presence of external risks," Journal of International Economics, Elsevier, vol. 126(C).
    15. Gete, Pedro & Porchia, Paolo, 2010. "Fertility and Consumption when Having a Child is a Risky Investment," MPRA Paper 27885, University Library of Munich, Germany.
    16. Gonzalez-Aguado, Eugenia, 2022. "Interest Rate Shocks and the Composition of Sovereign Debt," TSE Working Papers 22-1379, Toulouse School of Economics (TSE).
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    18. Andrea Gamba & Alexander J. Triantis, 2014. "Corporate Risk Management: Integrating Liquidity, Hedging, and Operating Policies," Management Science, INFORMS, vol. 60(1), pages 246-264, January.

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