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Non-linear DSGE Models and The Central Difference Kalman Filter

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  • Martin M. Andreasen

    (Bank of England and CREATES)

Abstract

This paper introduces a Quasi Maximum Likelihood (QML) approach based on the Central Difference Kalman Filter (CDKF) to estimate non-linear DSGE models with potentially non-Gaussian shocks. We argue that this estimator can be expected to be consistent and asymptotically normal for DSGE models solved up to third order. A Monte Carlo study shows that this QML estimator is basically unbiased and normally distributed infi?nite samples for DSGE models solved using a second order or a third order approximation. These results hold even when structural shocks are Gaussian, Laplace distributed, or display stochastic volatility.

Suggested Citation

  • Martin M. Andreasen, 2010. "Non-linear DSGE Models and The Central Difference Kalman Filter," CREATES Research Papers 2010-30, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2010-30
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    File URL: https://repec.econ.au.dk/repec/creates/rp/10/rp10_30.pdf
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    References listed on IDEAS

    as
    1. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Manuel S. Santos, 2006. "Convergence Properties of the Likelihood of Computed Dynamic Models," Econometrica, Econometric Society, vol. 74(1), pages 93-119, January.
    2. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
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    Cited by:

    1. Robert Kollmann, 2015. "Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation and Pruning," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 239-260, February.
    2. Andrew Binning & Junior Maih, 2015. "Sigma Point Filters For Dynamic Nonlinear Regime Switching Models," Working Papers No 4/2015, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    3. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    4. Andreasen, Martin M., 2011. "Non-linear DSGE models and the optimized central difference particle filter," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1671-1695, October.
    5. Mutschler, Willi, 2015. "Identification of DSGE models—The effect of higher-order approximation and pruning," Journal of Economic Dynamics and Control, Elsevier, vol. 56(C), pages 34-54.
    6. Martin M. Andreasen & Andrew Meldrum, 2014. "Dynamic term structure models: The best way to enforce the zero lower bound," CREATES Research Papers 2014-47, Department of Economics and Business Economics, Aarhus University.
    7. Andreasen, Martin, 2011. "An estimated DSGE model: explaining variation in term premia," Bank of England working papers 441, Bank of England.

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    More about this item

    Keywords

    Non-linear filtering; Non-Gaussian shocks; Quasi Maximum Likelihood; Stochastic volatility; Third order perturbation.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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