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Using the "Chandrasekhar Recursions" for likelihood evaluation of DSGE models

  • Edward Herbst

In likelihood-based estimation of linearized Dynamic Stochastic General Equilibrium (DSGE) models, the evaluation of the Kalman Filter dominates the running time of the entire algorithm. In this paper, we revisit a set of simple recursions known as the "Chandrasekhar Recursions" developed by Morf (1974) and Morf, Sidhu, and Kalaith (1974) for evaluating the likelihood of a Linear Gaussian State Space System. We show that DSGE models are ideally suited for the use of these recursions, which work best when the number of states is much greater than the number of observables. In several examples, we show that there are substantial benefits to using the recursions, with likelihood evaluation up to five times faster. This gain is especially pronounced in light of the trivial implementation costs--no model modification is required. Moreover, the algorithm is complementary with other approaches.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2012-35.

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Date of creation: 2012
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Handle: RePEc:fip:fedgfe:2012-35
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  1. Edward P. Herbst & Frank Schorfheide, 2013. "Sequential Monte Carlo Sampling for DSGE Models," NBER Working Papers 19152, National Bureau of Economic Research, Inc.
  2. Schmitt-Grohé, Stephanie & Uribe, Martín, 2012. "What's News in Business Cycles," CEPR Discussion Papers 8984, C.E.P.R. Discussion Papers.
  3. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
  4. Nir Jaimovich & Sergio Rebelo, 2006. "Can News About the Future Drive the Business Cycle?," NBER Working Papers 12537, National Bureau of Economic Research, Inc.
  5. Smets, Frank & Wouters, Raf, 2007. "Shocks and frictions in US business cycles: a Bayesian DSGE approach," Working Paper Series 0722, European Central Bank.
  6. Ingvar Strid & Karl Walentin, 2009. "Block Kalman Filtering for Large-Scale DSGE Models," Computational Economics, Society for Computational Economics, vol. 33(3), pages 277-304, April.
  7. Chib, Siddhartha & Ramamurthy, Srikanth, 2010. "Tailored randomized block MCMC methods with application to DSGE models," Journal of Econometrics, Elsevier, vol. 155(1), pages 19-38, March.
  8. Stephanie Schmitt‐Grohé & Martín Uribe, 2012. "What's News in Business Cycles," Econometrica, Econometric Society, vol. 80(6), pages 2733-2764, November.
  9. André Klein & Guy Melard & Toufik Zahaf, 1998. "Computation of the exact information matrix of Gaussian dynamic regression time series models," ULB Institutional Repository 2013/13738, ULB -- Universite Libre de Bruxelles.
  10. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
  11. Sungbae An & Frank Schorfheide, 2006. "Bayesian analysis of DSGE models," Working Papers 06-5, Federal Reserve Bank of Philadelphia.
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