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Global Stochastic Properties of Dynamic Models and their Linear Approximations

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  • Ana Babus

    (University of Cambridge)

  • Casper G. de Vries

    (Erasmus University Rotterdam)

Abstract

The dynamic properties of micro based stochastic macro models are often analyzed through a linearization around the associated deterministic steady state. Recent literature has investigated the error made by such a deterministic approximation. Complementary to this literature we investigate how the linearization affects the stochastic properties of the original model. We consider a simple real business cycle model with noisy learning by doing. The solution has a stationary distribution that exhibits moment failure and has an unbounded support. The linear approximation, however, yields a stationary distribution with possibly a bounded support and all momentsfinite.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 10-081/2.

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Date of creation: 26 Aug 2010
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Handle: RePEc:dgr:uvatin:20100081

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Web page: http://www.tinbergen.nl

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Keywords: Linearization; ARCH process; Real business cycles model; Stochastic difference equation;

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  1. Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2004. "Estimating Dynamic Equilibrium Economies: Linear versus Nonlinear Likelihood," PIER Working Paper Archive 04-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
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  3. 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.
  4. Campbell, John Y., 1994. "Inspecting the mechanism: An analytical approach to the stochastic growth model," Journal of Monetary Economics, Elsevier, vol. 33(3), pages 463-506, June.
  5. Jinill Kim and Sunghyun Henry Kim, 2001. "Spurious Welfare Reversals in International Business Cycle Models," Computing in Economics and Finance 2001 3, Society for Computational Economics.
  6. de Haan, Laurens & Resnick, Sidney I. & Rootzén, Holger & de Vries, Casper G., 1989. "Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 213-224, August.
  7. Tesar, Linda L., 1995. "Evaluating the gains from international risksharing," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 42(1), pages 95-143, June.
  8. Sutherland, Alan, 2002. "A Simple Second-Order Solution Method For Dynamic General Equilibrium Models," CEPR Discussion Papers 3554, C.E.P.R. Discussion Papers.
  9. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  10. Dotsey, Michael & Mao, Ching Sheng, 1992. "How well do linear approximation methods work? : The production tax case," Journal of Monetary Economics, Elsevier, vol. 29(1), pages 25-58, February.
  11. Phornchanok Cumperayot & Casper G. de Vries, 2006. "Large Swings in Currencies driven by Fundamentals," Tinbergen Institute Discussion Papers 06-086/2, Tinbergen Institute.
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Cited by:
  1. Loretti I. Dobrescu & Mihaela Neamtu & Dumitru Opris, 2011. "A Discrete--Delay Dynamic Model for the Stock Market," Discussion Papers 2012-11, School of Economics, The University of New South Wales.

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