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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.

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Paper provided by Federal Reserve Bank of Dallas in its series Globalization and Monetary Policy Institute Working Paper with number 147.

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Date of creation: 2013
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Handle: RePEc:fip:feddgw:147

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Keywords: Simulation modeling ; Forecasting;

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  1. 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.
  2. 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.
  3. Giovanni Lombardo & Alan Sutherland, 2005. " Computing Second-Order-Accurate Solutions for Rational Expectation Models Using Linear Solution Methods," CDMA Conference Paper Series 0504, Centre for Dynamic Macroeconomic Analysis.
  4. An, Sungbae & Schorfheide, Frank, 2005. "Bayesian Analysis of DSGE Models," CEPR Discussion Papers 5207, C.E.P.R. Discussion Papers.
  5. 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.
  6. Martin M. Andreasen & Jesús Fernández-Villaverde & Juan Rubio-Ramírez, 2013. "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications," NBER Working Papers 18983, National Bureau of Economic Research, Inc.
  7. 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.
  8. Magnus, J.R., 1978. "The moments of products of quadratic forms in normal variables," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153205, Tilburg University.
  9. 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.
  10. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
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