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Non-linear DSGE Models, The Central Difference Kalman Filter, and The Mean Shifted Particle Filter

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  • Martin Møller Andreasen

    () (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

This paper shows how non-linear DSGE models with potential non-normal shocks can be estimated by Quasi-Maximum Likelihood based on the Central Difference Kalman Filter (CDKF). The advantage of this estimator is that evaluating the quasi log-likelihood function only takes a fraction of a second. The second contribution of this paper is to derive a new particle filter which we term the Mean Shifted Particle Filter (MSPFb). We show that the MSPFb outperforms the standard Particle Filter by delivering more precise state estimates, and in general the MSPFb has lower Monte Carlo variation in the reported log-likelihood function.

Suggested Citation

  • Martin Møller Andreasen, 2008. "Non-linear DSGE Models, The Central Difference Kalman Filter, and The Mean Shifted Particle Filter," CREATES Research Papers 2008-33, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2008-33
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    References listed on IDEAS

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    1. Geert Bekaert & Seonghoon Cho & Antonio Moreno, 2010. "New Keynesian Macroeconomics and the Term Structure," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(1), pages 33-62, February.
    2. Martin Andreasen, 2010. "How to Maximize the Likelihood Function for a DSGE Model," Computational Economics, Springer;Society for Computational Economics, vol. 35(2), pages 127-154, February.
    3. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-952, July.
    4. Godsill, Simon J. & Doucet, Arnaud & West, Mike, 2004. "Monte Carlo Smoothing for Nonlinear Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 156-168, January.
    5. David Altig & Lawrence Christiano & Martin Eichenbaum & Jesper Linde, 2011. "Firm-Specific Capital, Nominal Rigidities and the Business Cycle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 14(2), pages 225-247, April.
    6. 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.
    7. 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.
    8. Ingvar Strid, 2006. "Parallel particle filters for likelihood evaluation in DSGE models: An assessment," Computing in Economics and Finance 2006 395, Society for Computational Economics.
    9. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    10. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2005. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.
    11. Jinill Kim & Sunghyun Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and Using Second Order Accurate Solutions of Discrete Time," Levine's Bibliography 666156000000000284, UCLA Department of Economics.
    12. Martin Møller Andreasen, 2008. "Ensuring the Validity of the Micro Foundation in DSGE Models," CREATES Research Papers 2008-26, Department of Economics and Business Economics, Aarhus University.
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    Citations

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    Cited by:

    1. Sergey Ivashchenko, 2014. "DSGE Model Estimation on the Basis of Second-Order Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 43(1), pages 71-82, January.
    2. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "On the Stratonovich – Kalman - Bucy filtering algorithm application for accurate characterization of financial time series with use of state-space model by central banks," MPRA Paper 50235, University Library of Munich, Germany.
    3. Sergey Ivashchenko, 2014. "Forecasting in a Non-Linear DSGE Model," EUSP Department of Economics Working Paper Series Ec-02/14, European University at St. Petersburg, Department of Economics.
    4. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    5. 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.
    6. Martin Møller Andreasen, 2008. "Explaining Macroeconomic and Term Structure Dynamics Jointly in a Non-linear DSGE Model," CREATES Research Papers 2008-43, Department of Economics and Business Economics, Aarhus University.

    More about this item

    Keywords

    Multivariate Stirling interpolation; Particle filtering; Non-linear DSGE models; Non-normal shocks; Quasi-maximum likelihood;

    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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