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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 quasimaximum likelihood procedure can be used for that purpose.

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File URL: http://cama.crawford.anu.edu.au/pdf/working-papers/2013/292013.pdf
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Bibliographic Info

Paper provided by Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University in its series CAMA Working Papers with number 2013-29.

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Length: 21 pages
Date of creation: May 2013
Date of revision:
Handle: RePEc:een:camaaa:2013-29

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Keywords: Latent state filtering; estimation of DSGE models; second-order approximation; pruning; Kalman filter; particle filter; quasi-maximum likelihood.;

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  1. 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, Society for Computational Economics 162, Society for Computational Economics.
  2. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
  3. Robert Kollmann, 2002. "Monetary policy rules in the open economy: effects of welfare and business cycles," ULB Institutional Repository, ULB -- Universite Libre de Bruxelles 2013/7628, ULB -- Universite Libre de Bruxelles.
  4. Stephanie Schmitt-Grohe & Martin Uribe, 2002. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0282, National Bureau of Economic Research, Inc.
  5. Magnus, J.R., 1978. "The moments of products of quadratic forms in normal variables," Open Access publications from Tilburg University, Tilburg University urn:nbn:nl:ui:12-153205, Tilburg University.
  6. Lombardo, Giovanni & Sutherland, Alan, 2005. "Computing second-order-accurate solutions for rational expectation models using linear solution methods," Working Paper Series, European Central Bank 0487, European Central Bank.
  7. An, Sungbae & Schorfheide, Frank, 2005. "Bayesian Analysis of DSGE Models," CEPR Discussion Papers, C.E.P.R. Discussion Papers 5207, C.E.P.R. Discussion Papers.
  8. 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, C.E.P.R. Discussion Papers 9442, C.E.P.R. Discussion Papers.
  9. Robert Kollmann, 1996. "Incomplete asset markets and the cross-country consumption correlation puzzle," ULB Institutional Repository, ULB -- Universite Libre de Bruxelles 2013/7640, ULB -- Universite Libre de Bruxelles.
  10. 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, Elsevier, vol. 35(2), pages 203-206, February.
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