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Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation and Pruning

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  • Robert Kollmann

Abstract

This paper develops a novel approach for estimating latent state variables of Dynamic Stochastic General Equilibrium (DSGE) models that are solved using a second-order accurate approximation. I apply the Kalman filter to a state-space representation of the second-order solution based on the ‘pruning’ scheme of Kim et al. (J Econ Dyn Control 32:3397–3414, 2008). By contrast to particle filters, no stochastic simulations are needed for the deterministic filter here; the present method is thus much faster; in terms of estimation accuracy for latent states it is competitive with the standard particle filter. Use of the pruning scheme distinguishes the filter here from the deterministic Quadratic Kalman filter presented by Ivashchenko (Comput Econ, 43:71–82, 2014). The filter here performs well even in models with big shocks and high curvature.

Suggested Citation

  • Robert Kollmann, 2014. "Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation and Pruning," ULB Institutional Repository 2013/250061, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/250061
    Note: SCOPUS: ar.j
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    Cited by:

    1. Benchimol, Jonathan & Ivashchenko, Sergey, 2021. "Switching volatility in a nonlinear open economy," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 110, pages 1-31.
    2. Kollmann, Robert, 2015. "Risk Sharing in a World Economy with Uncertainty Shocks," CEPR Discussion Papers 10940, C.E.P.R. Discussion Papers.
    3. Andrew Binning & Junior Maih, 2015. "Sigma point filters for dynamic nonlinear regime switching models," Working Paper 2015/10, Norges Bank.
    4. Kollmann, Robert, 2016. "International business cycles and risk sharing with uncertainty shocks and recursive preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 72(C), pages 115-124.
    5. 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.
    6. Pablo Cuba‐Borda & Luca Guerrieri & Matteo Iacoviello & Molin Zhong, 2019. "Likelihood evaluation of models with occasionally binding constraints," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(7), pages 1073-1085, November.
    7. Kollmann, Robert, 2017. "Tractable likelihood-based estimation of non-linear DSGE models," Economics Letters, Elsevier, vol. 161(C), pages 90-92.
    8. Herbst, Edward & Schorfheide, Frank, 2019. "Tempered particle filtering," Journal of Econometrics, Elsevier, vol. 210(1), pages 26-44.
    9. 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.
    10. Robert Kollmann, 2016. "Tractable Likelihood-Based Estimation of Non-Linear DSGE Models Using Higher-Order Approximations," Working Papers ECARES ECARES 2016-15, ULB -- Universite Libre de Bruxelles.
    11. Luisa Corrado & Stefano Grassi & Aldo Paolillo, 2021. "Modelling and Estimating Large Macroeconomic Shocks During the Pandemic," CREATES Research Papers 2021-08, Department of Economics and Business Economics, Aarhus University.
    12. Sergey Ivashchenko, 2014. "Forecasting in a Non-Linear DSGE Model," EUSP Department of Economics Working Paper Series 2014/02, European University at St. Petersburg, Department of Economics.
    13. 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.
    14. Robert Kollmann, 2016. "Risk Sharing, the Exchange Rate and Net Foreign Assets in a World Economy with Uncertainty Shocks," 2016 Meeting Papers 721, Society for Economic Dynamics.
    15. Luisa Corrado & Stefano Grassi & Aldo Paolillo, 2021. "Identifying Economic Shocks in a Rare Disaster Environment," CEIS Research Paper 517, Tor Vergata University, CEIS, revised 18 Jul 2024.

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    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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