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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

Suggested Citation

  • Lombardo, Giovanni, 2010. "On approximating DSGE models by series expansions," Working Paper Series 1264, European Central Bank.
  • Handle: RePEc:ecb:ecbwps:20101264
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    Cited by:

    1. Brzoza-Brzezina, Michał & Kolasa, Marcin & Makarski, Krzysztof, 2015. "A penalty function approach to occasionally binding credit constraints," Economic Modelling, Elsevier, vol. 51(C), pages 315-327.
    2. Tao Zha & Juan F. Rubio-Ramirez & Daniel F. Waggoner & Andrew T. Foerster, 2010. "Perturbation Methods for Markov-Switching Models," 2010 Meeting Papers 239, Society for Economic Dynamics.
    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. Anmol Bhandari & Jaroslav Borovička & Paul Ho, 2016. "Identifying Ambiguity Shocks in Business Cycle Models Using Survey Data," NBER Working Papers 22225, National Bureau of Economic Research, Inc.
    5. Aruoba, S. Borağan & Bocola, Luigi & Schorfheide, Frank, 2017. "Assessing DSGE model nonlinearities," Journal of Economic Dynamics and Control, Elsevier, vol. 83(C), pages 34-54.
    6. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    7. 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.
    8. Rabitsch, Katrin & Stepanchuk, Serhiy & Tsyrennikov, Viktor, 2015. "International portfolios: A comparison of solution methods," Journal of International Economics, Elsevier, vol. 97(2), pages 404-422.
    9. Lee, Junghoon, 2016. "The impact of idiosyncratic uncertainty when investment opportunities are endogenous," Journal of Economic Dynamics and Control, Elsevier, vol. 65(C), pages 105-124.
    10. Caterina Mendicino, 2012. "Collateral Requirements: Macroeconomic Fluctuations and Macro-Prudential Policy," Working Papers w201211, Banco de Portugal, Economics and Research Department.
    11. Lombardo, Giovanni & Uhlig, Harald, 2014. "A theory of pruning," Working Paper Series 1696, European Central Bank.
    12. 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.
    13. Lars Hansen & Jaroslav Borovicka, 2013. "Robust preference expansions," 2013 Meeting Papers 1199, Society for Economic Dynamics.
    14. 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.

    More about this item

    Keywords

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

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E0 - Macroeconomics and Monetary Economics - - General

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