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Exact likelihood computation for nonlinear DSGE models with heteroskedastic innovations

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  • Tristani, Oreste
  • Amisano, Gianni

Abstract

Phenomena such as the Great Moderation have increased the attention of macro-economists towards models where shock processes are not (log-)normal. This paper studies a class of discrete-time rational expectations models where the variance of exogenous innovations is subject to stochastic regime shifts. We first show that, up to a second-order approximation using perturbation methods, regime switching in the variances has an impact only on the intercept coefficients of the decision rules. We then demonstrate how to derive the exact model likelihood for the second-order approximation of the solution when there are as many shocks as observable variables. We illustrate the applicability of the proposed solution and estimation methods in the case of a small DSGE model. JEL Classification: E0, C63

Suggested Citation

  • Tristani, Oreste & Amisano, Gianni, 2011. "Exact likelihood computation for nonlinear DSGE models with heteroskedastic innovations," Working Paper Series 1341, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:20111341
    Note: 24907
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    Cited by:

    1. 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.
    2. Amisano, Gianni & Tristani, Oreste, 2019. "Uncertainty shocks, monetary policy and long-term interest rates," Working Paper Series 2279, European Central Bank.
    3. Negro, Marco Del & Schorfheide, Frank, 2013. "DSGE Model-Based Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 57-140, Elsevier.
    4. Paolo Andreini & Cosimo Izzo & Giovanni Ricco, 2020. "Deep Dynamic Factor Models," Papers 2007.11887, arXiv.org, revised May 2023.
    5. Andrew Foerster & Juan F. Rubio‐Ramírez & Daniel F. Waggoner & Tao Zha, 2016. "Perturbation methods for Markov‐switching dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 7(2), pages 637-669, July.
    6. Maddalena Cavicchioli, 2020. "Invertibility and VAR Representations of Time-Varying Dynamic Stochastic General Equilibrium Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 61-86, January.
    7. Ajevskis, Viktors, 2019. "Nonlocal Solutions To Dynamic Equilibrium Models: The Approximate Stable Manifolds Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 23(6), pages 2544-2571, September.
    8. Hall, Jamie, 2012. "Rapid estimation of nonlinear DSGE models," MPRA Paper 41218, University Library of Munich, Germany.
    9. Raffaella Giacomini, 2013. "The relationship between DSGE and VAR models," CeMMAP working papers CWP21/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. 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.
    11. Luisa Corrado & Stefano Grassi & Aldo Paolillo, 2021. "Modelling and Estimating Large Macroeconomic Shocks During the Pandemic," National Institute of Economic and Social Research (NIESR) Discussion Papers 530, National Institute of Economic and Social Research.
    12. Gianni Amisano & Oreste Tristani, 2023. "Monetary policy and long‐term interest rates," Quantitative Economics, Econometric Society, vol. 14(2), pages 689-716, May.
    13. 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.
    14. Hall, Jamie, 2012. "Consumption dynamics in general equilibrium," MPRA Paper 43933, University Library of Munich, Germany.
    15. Raffaella Giacomini, 2013. "The relationship between DSGE and VAR models," CeMMAP working papers 21/13, Institute for Fiscal Studies.
    16. Horváth, Roman & Maršál, Aleš, 2014. "The term structure of interest rates in a small open economy DSGE model with Markov switching," FinMaP-Working Papers 22, Collaborative EU Project FinMaP - Financial Distortions and Macroeconomic Performance: Expectations, Constraints and Interaction of Agents.

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    More about this item

    Keywords

    DSGE models; regime switching; second-order approximation; time-varying volatility;
    All these keywords.

    JEL classification:

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

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