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On approximating DSGE models by series expansions

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  • Lombardo, Giovanni

Abstract

We show how to use a simple perturbation method to solve non-linear rational expectation models. Drawing from the applied mathematics literature we propose a method consisting of series expansions of the non-linear system around a known solution. The variables are represented in terms of their orders of approximation with respect to a perturbation parameter. The final solution, therefore, is the sum of the different orders. This approach links to formal arguments the idea that each order of approximation is solved recursively taking as given the lower order of approximation. Therefore, this method is not subject to the ambiguity concerning the order of the variables in the resulting state-space representation as, for example, has been discussed by Kim et al. (2008). Provided that the model is locally stable, the approximation technique discussed in this paper delivers stable solutions at any order of approximation. JEL Classification: C63, E0

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Bibliographic Info

Paper provided by European Central Bank in its series Working Paper Series with number 1264.

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Date of creation: Nov 2010
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Handle: RePEc:ecb:ecbwps:20101264

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Related research

Keywords: Non-linear difference equations; Perturbation methods; Series expansions; Solving dynamic stochastic general equilibrium models;

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Cited by:
  1. Lan, Hong & Meyer-Gohde, Alexander, 2013. "Solving DSGE models with a nonlinear moving average," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2643-2667.
  2. Jaroslav Borovicka & Lars Hansen, 2012. "Examining macroeconomic models through the lens of asset pricing," Working Paper Series WP-2012-01, Federal Reserve Bank of Chicago.
  3. RUGE-MURCIA, Francisco J., 2010. "Estimating Nonlinear DSGE Models by the Simulated Method of Moments," Cahiers de recherche 2010-10, Universite de Montreal, Departement de sciences economiques.
  4. Den Haan, Wouter J. & De Wind, Joris, 2012. "Nonlinear and stable perturbation-based approximations," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1477-1497.
  5. Viktor Tsyrennikov & Serhiy Stepanchuk & Katrin Rabitsch, 2013. "International Portfolios: A Comparison of Solution Methods," 2013 Meeting Papers 1146, Society for Economic Dynamics.
  6. Hong Lan & Alexander Meyer-Gohde, 2012. "Existence and Uniqueness of Perturbation Solutions to DSGE Models," SFB 649 Discussion Papers SFB649DP2012-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  7. Caterina Mendicino, 2012. "Collateral Requirements: Macroeconomic Fluctuations and Macro-Prudential Policy," Working Papers w201211, Banco de Portugal, Economics and Research Department.
  8. Lars Hansen & Jaroslav Borovicka, 2013. "Robust preference expansions," 2013 Meeting Papers 1199, Society for Economic Dynamics.
  9. Katrin Rabitsch & Serhiy Stepanchuk & Viktor Tsyrennikov, 2014. "International Portfolios: A Comparison of Solution Methods," Department of Economics Working Papers wuwp159, Vienna University of Economics, Department of Economics.
  10. Ruge-Murcia, Francisco, 2012. "Estimating nonlinear DSGE models by the simulated method of moments: With an application to business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 36(6), pages 914-938.

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