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An Augmented Steady-State Kalman Filter to Evaluate the Likelihood of Linear and Time-Invariant State-Space Models

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Abstract

We propose a modified version of the augmented Kalman filter (AKF) to evaluate the likelihood of linear and time-invariant state-space models (SSMs). Unlike the regular AKF, this augmented steady-state Kalman filter (ASKF), as we call it, is based on a steady-state Kalman filter (SKF). We show that to apply the ASKF, it is sufficient that the SSM at hand is stationary. We find that the ASKF can significantly reduce the computational burden to evaluate the likelihood of medium- to large-scale SSMs, making it particularly useful to estimate dynamic stochastic general equilibrium (DSGE) models and dynamic factor models. Tests using a medium-scale DSGE model, namely the 2007 version of the Smets and Wouters model, show that the ASKF is up to five times faster than the regular Kalman filter (KF). Other competing algorithms, such as the Chandrasekhar recursion (CR) or a univariate treatment of multivariate observation vectors (UKF), are also outperformed by the ASKF in terms of computational efficiency.

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  • Johannes Huber, 2022. "An Augmented Steady-State Kalman Filter to Evaluate the Likelihood of Linear and Time-Invariant State-Space Models," Discussion Paper Series 343, Universitaet Augsburg, Institute for Economics.
    • Handle: RePEc:aug:augsbe:0343
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    1. Leeper, Eric M. & Plante, Michael & Traum, Nora, 2010. "Dynamics of fiscal financing in the United States," Journal of Econometrics, Elsevier, vol. 156(2), pages 304-321, June.
    2. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
    3. Sanford V. Berg, 1973. "Annals of Economic and Social Measurement, Volume 2, number 4," NBER Books, National Bureau of Economic Research, Inc, number aesm73-4, March.
    4. Andrew C. Harvey, 1990. "The Econometric Analysis of Time Series, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026208189x, December.
    5. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 309-327, November.
    6. 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.
    7. Barr Rosenberg, 1973. "The Analysis of a Cross Section of Time Series by Stochastically Convergent Parameter Regression," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 2, number 4, pages 399-428, National Bureau of Economic Research, Inc.
    8. 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.
    9. Gadatsch, Niklas & Hauzenberger, Klemens & Stähler, Nikolai, 2016. "Fiscal policy during the crisis: A look on Germany and the Euro area with GEAR," Economic Modelling, Elsevier, vol. 52(PB), pages 997-1016.
    10. J. B. Taylor & Harald Uhlig (ed.), 2016. "Handbook of Macroeconomics," Handbook of Macroeconomics, Elsevier, edition 1, volume 2, number 2.
    11. Edward P. Herbst & Frank Schorfheide, 2016. "Bayesian Estimation of DSGE Models," Economics Books, Princeton University Press, edition 1, number 10612.
    12. V. V. Chari & Patrick J. Kehoe & Ellen R. McGrattan, 2007. "Business Cycle Accounting," Econometrica, Econometric Society, vol. 75(3), pages 781-836, May.
    13. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    14. Sanford V. Berg, 1973. "Annals of Economic and Social Measurement, Volume 2, number 2," NBER Books, National Bureau of Economic Research, Inc, number aesm73-2, March.
    15. Lars Peter Hansen & Thomas J. Sargent, 2013. "Recursive Models of Dynamic Linear Economies," Economics Books, Princeton University Press, edition 1, number 10141.
    16. S. J. Koopman & J. Durbin, 2000. "Fast Filtering and Smoothing for Multivariate State Space Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(3), pages 281-296, May.
    17. Ireland, Peter N., 2004. "A method for taking models to the data," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1205-1226, March.
    18. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    19. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    20. Chib, Siddhartha & Ramamurthy, Srikanth, 2010. "Tailored randomized block MCMC methods with application to DSGE models," Journal of Econometrics, Elsevier, vol. 155(1), pages 19-38, March.
    21. Frank Smets & Raf Wouters, 2003. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, September.
    22. David N. DeJong & Chetan Dave, 2011. "Structural Macroeconometrics Second Edition," Economics Books, Princeton University Press, edition 1, number 9622.
    23. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : I. The basic neoclassical model," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 195-232.
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    More about this item

    Keywords

    kalman filter; dsge; bayesian estimation; maximum-likelihood estimation; computational techniques;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)

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