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Solving Portfolio Problems with the Smolyak-Parameterized Expectations Algorithm

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  • Ángel Gavilán

    ()
    (Banco de España)

  • Juan A. Rojas

    ()
    (Banco de España)

Abstract

We propose a new numerical method to solve stochastic models that combines the parameterized expectations (PEA) and the Smolyak algorithms. This method is especially convenient to address problems with occasionally binding constraints (a feature inherited from PEA) and/or a large number of state variables (a feature inherited from Smolyak), i.e. DSGE models that incorporate portfolio problems and incomplete markets. We describe the proposed Smolyak-PEA algorithm in the context of a one-country stochastic neoclassical growth model and compare its accuracy with that of a standard PEA collocation algorithm. Despite estimating fewer parameters, the former is able to reach the high accuracy levels of the latter. We further illustrate the working of this algorithm in a two-country neoclassical model with incomplete markets and portfolio choice. Again, the Smolyak-PEA algorithm approximates the solution of the problem with a high degree of accuracy. Finally, we show how this algorithm can efficiently incorporate both occasionally binding constraints and a partial information approach.

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File URL: http://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/08/Fic/dt0838e.pdf
File Function: First version, February 2009
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Bibliographic Info

Paper provided by Banco de Espa�a in its series Banco de Espa�a Working Papers with number 0838.

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Length: 30 pages
Date of creation: Feb 2009
Date of revision:
Handle: RePEc:bde:wpaper:0838

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Keywords: Portfolio Choice; Dynamic Macroeconomics; Computational Methods;

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  1. Michael B. Devereux & Alan Sutherland, 2011. "Country Portfolios In Open Economy Macro‐Models," Journal of the European Economic Association, European Economic Association, European Economic Association, vol. 9(2), pages 337-369, 04.
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  4. Martin D. D. Evans (Georgetown University) and Viktoria Hnatkovska (Georgetown University), 2005. "Solving General Equilibrium Models with Incomplete Markets and Many Assets," Working Papers, Georgetown University, Department of Economics gueconwpa~05-05-18, Georgetown University, Department of Economics.
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  6. Lawrence J. Christiano & Jonas D. M. Fisher, 1994. "Algorithms for solving dynamic models with occasionally binding constraints," Staff Report, Federal Reserve Bank of Minneapolis 171, Federal Reserve Bank of Minneapolis.
  7. Maliar, Lilia & Maliar, Serguei, 2003. "Parameterized Expectations Algorithm and the Moving Bounds," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 21(1), pages 88-92, January.
  8. Martin Floden & David Domeij, 2004. "Population Aging and International Capital Flows," 2004 Meeting Papers, Society for Economic Dynamics 490, Society for Economic Dynamics.
  9. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, Elsevier, vol. 58(2), pages 410-452, December.
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  11. Stephanie Schmitt-Grohe & Martin Uribe, 2001. "Closing Small Open Economy Models," Departmental Working Papers, Rutgers University, Department of Economics 200115, Rutgers University, Department of Economics.
  12. Benjamin Malin & Dirk Krueger & Felix Kubler, 2007. "Computing Stochastic Dynamic Economic Models with a Large Number of State Variables: A Description and Application of a Smolyak-Collocation Method," NBER Working Papers 13517, National Bureau of Economic Research, Inc.
  13. den Haan, Wouter J & Marcet, Albert, 1990. "Solving the Stochastic Growth Model by Parameterizing Expectations," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 8(1), pages 31-34, January.
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Cited by:
  1. Kenneth L. Judd & Lilia Maliar & Serguei Maliar & Rafael Valero, 2013. "Smolyak Method for Solving Dynamic Economic Models: Lagrange Interpolation, Anisotropic Grid and Adaptive Domain," NBER Working Papers 19326, National Bureau of Economic Research, Inc.

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