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

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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, Kim, Schaumburg and Sims (2008). By contrast to particle filters, no stochastic simulations are needed for the filter here--the present method is thus much faster. In Monte Carlo experiments, the filter here generates more accurate estimates of latent state variables than the standard particle filter. The present filter is also more accurate than a conventional Kalman filter that treats the linearized model as the true data generating process. Due to its high speed, the filter presented here is suited for the estimation of model parameters; a quasi-maximum likelihood procedure can be used for that purpose.

Suggested Citation

  • Robert Kollmann, 2013. "Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation," Working Papers ECARES ECARES 2013-24, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/143755
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    References listed on IDEAS

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    1. Lombardo, Giovanni & Sutherland, Alan, 2007. "Computing second-order-accurate solutions for rational expectation models using linear solution methods," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 515-530, February.
    2. Magnus, J.R., 1978. "The moments of products of quadratic forms in normal variables," Other publications TiSEM 17c77a44-1789-4cf4-a382-a, Tilburg University, School of Economics and Management.
    3. Kollmann, Robert & Maliar, Serguei & Malin, Benjamin A. & Pichler, Paul, 2011. "Comparison of solutions to the multi-country Real Business Cycle model," Journal of Economic Dynamics and Control, Elsevier, pages 186-202.
    4. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
    5. Kollmann, Robert & Kim, Jinill & Kim, Sunghyun H., 2011. "Solving the multi-country Real Business Cycle model using a perturbation method," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 203-206, February.
    6. 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.
    7. Jinill Kim & Sunghyun Henry Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and using second order accurate solutions of discrete time dynamic equilibrium models," Finance and Economics Discussion Series 2003-61, Board of Governors of the Federal Reserve System (U.S.).
    8. Martin M. Andreasen & Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez, 2013. "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications," CREATES Research Papers 2013-12, Department of Economics and Business Economics, Aarhus University.
    9. Kollmann, Robert, 1996. "Incomplete asset markets and the cross-country consumption correlation puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 20(5), pages 945-961, May.
    10. Kollmann, Robert, 2002. "Monetary policy rules in the open economy: effects on welfare and business cycles," Journal of Monetary Economics, Elsevier, vol. 49(5), pages 989-1015, July.
    11. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
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    Cited by:

    1. Michael K. Johnston & Robert G. King & Denny Lie, 2014. "Straightforward approximate stochastic equilibria for nonlinear rational expectations models," CAMA Working Papers 2014-59, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    2. Robert Kollmann, 2015. "Exchange Rates Dynamics with Long-Run Risk and Recursive Preferences," Open Economies Review, Springer, pages 175-196.
    3. repec:eee:macchp:v2-527 is not listed on IDEAS
    4. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, Elsevier.
    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. Badel, Alejandro & Huggett, Mark, 2017. "The sufficient statistic approach: Predicting the top of the Laffer curve," Journal of Monetary Economics, Elsevier, pages 1-12.
    7. 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.

    More about this item

    Keywords

    latent state filtering; estimation of DSGE models; second-order approximation; pruning; Kalman filter; particle filter; quasi-maximum likelihood;

    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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