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Finite State Markov-Chain Approximations to Highly Persistent Processes

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  • Kopecky, Karen A.
  • Suen, Richard M. H.

Abstract

This paper re-examines the Rouwenhorst method of approximating first-order autoregressive processes. This method is appealing because it can match the conditional and unconditional mean, the conditional and unconditional variance and the first-order autocorrelation of any AR(1) process. This paper provides the first formal proof of this and other results. When comparing to five other methods, the Rouwenhorst method has the best performance in approximating the business cycle moments generated by the stochastic growth model. In addition, when the Rouwenhorst method is used, moments computed directly off the stationary distribution are as accurate as those obtained using Monte Carlo simulations.

Suggested Citation

  • Kopecky, Karen A. & Suen, Richard M. H., 2009. "Finite State Markov-Chain Approximations to Highly Persistent Processes," MPRA Paper 17201, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:17201
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    References listed on IDEAS

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    1. 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.
    2. Tauchen, George, 1990. "Solving the Stochastic Growth Model by Using Quadrature Methods and Value-Function Iterations," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 49-51, January.
    3. Jerome Adda & Russell W. Cooper, 2003. "Dynamic Economics: Quantitative Methods and Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012014, January.
    4. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    5. King, Robert G. & Rebelo, Sergio T., 1999. "Resuscitating real business cycles," Handbook of Macroeconomics,in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 14, pages 927-1007 Elsevier.
    6. 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.
    7. 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.
    8. Flodén, Martin, 2008. "A note on the accuracy of Markov-chain approximations to highly persistent AR(1) processes," Economics Letters, Elsevier, vol. 99(3), pages 516-520, June.
    9. Craig Burnside, 1998. "Discrete State-Space Methods for the Study of Dynamic Economies," QM&RBC Codes 125, Quantitative Macroeconomics & Real Business Cycles.
    10. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    11. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
    12. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
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    More about this item

    Keywords

    Numerical Methods; Finite State Approximations; Optimal Growth Model;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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