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

  • Robert Kollmann

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.

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Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number ECARES 2013-24.

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Length: 19 p.
Date of creation: May 2013
Date of revision:
Publication status: Published by:
Handle: RePEc:eca:wpaper:2013/143755
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  1. Robert Kollmann & Jinill Kim & Sunghyun H. Kim, 2010. "Solving the multi-country real business cycle model using a perturbation method," Post-Print hal-00765826, HAL.
  2. Christopher A. Sims & Jinill Kim & Sunghyun Kim, 2003. "Calculating and Using Second Order Accurate Solution of Discrete Time Dynamic Equilibrium Models," Computing in Economics and Finance 2003 162, Society for Computational Economics.
  3. Andreasen, Martin M. & Fernández-Villaverde, Jesús & Rubio-Ramírez, Juan Francisco, 2013. "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications," CEPR Discussion Papers 9442, C.E.P.R. Discussion Papers.
  4. Sungbae An & Frank Schorfheide, 2006. "Bayesian analysis of DSGE models," Working Papers 06-5, Federal Reserve Bank of Philadelphia.
  5. Stephanie Schmitt-Grohe & Martin Uribe, 2002. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," NBER Technical Working Papers 0282, National Bureau of Economic Research, Inc.
  6. Kollmann, Robert, 2002. "Monetary Policy Rules in the Open Economy: Effects on Welfare and Business Cycles," CEPR Discussion Papers 3279, C.E.P.R. Discussion Papers.
  7. 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.
  8. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
  9. Robert Kollmann, 1996. "Incomplete asset markets and the cross-country consumption correlation puzzle," ULB Institutional Repository 2013/7640, ULB -- Universite Libre de Bruxelles.
  10. 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.
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