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Finite State Markov-chain Approximations to Highly Persistent Processes

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  • Karen Kopecky

    (University of Western Ontario)

  • Richard Suen

    (University of California, Riverside)

Abstract

The Rouwenhorst method of approximating stationary AR(1) processes has been overlooked by much of the literature despite having many desirable properties unmatched by other methods. In particular, we prove that it can match the conditional and unconditional mean and variance, and the first-order autocorrelation of any stationary AR(1) process. These properties make the Rouwenhorst method more reliable than others in approximating highly persistent processes and generating accurate model solutions. To illustrate this, we compare the performances of the Rouwenhorst method and four others in solving the stochastic growth model and an income fluctuation problem. We find that (i) the choice of approximation method can have a large impact on the computed model solutions, and (ii) the Rouwenhorst method is more robust than others with respect to variation in the persistence of the process, the number of points used in the discrete approximation and the procedure used to generate model statistics. (Copyright: Elsevier)

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File URL: http://dx.doi.org/10.1016/j.red.2010.02.002
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Article provided by Elsevier for the Society for Economic Dynamics in its journal Review of Economic Dynamics.

Volume (Year): 13 (2010)
Issue (Month): 3 (July)
Pages: 701-714

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Handle: RePEc:red:issued:09-115

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Keywords: Numerical methods; Finite state approximations;

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  1. 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.
  2. S. B. Aruoba & Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2005. "Comparing Solution Methods for Dynamic Equilibrium Economies," Levine's Bibliography 122247000000000855, UCLA Department of Economics.
  3. Karen A. Kopecky & Richard M. H. Suen, 2009. "Finite State Markov-Chain Approximations to Highly Persistent Processes," Working Papers 200904, University of California at Riverside, Department of Economics, revised May 2009.
  4. John B. Taylor & Harald Uhlig, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," NBER Working Papers 3117, National Bureau of Economic Research, Inc.
  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. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  7. Craig Burnside, 1998. "Discrete State-Space Methods for the Study of Dynamic Economies," QM&RBC Codes 125, Quantitative Macroeconomics & Real Business Cycles.
  8. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
  9. 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.
  10. Jerome Adda & Russell W. Cooper, 2003. "Dynamic Economics: Quantitative Methods and Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012014, December.
  11. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-96, March.
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  1. MC Approximations for ARs
    by Agent Continuum in Agent Continuum on 2010-06-20 02:17:57
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