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Bayesian inference based only on simulated likelihood: particle filter analysis of dynamic economic models

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  • Thomas Flury

    ()

  • Neil Shephard

    ()

Abstract

Suppose we wish to carry out likelihood based inference but we solely have an unbiased simulation based estimator of the likelihood. We note that unbiasedness is enough when the estimated likelihood is used inside a Metropolis-Hastings algorithm. This result has recently been intro- duced in statistics literature by Andrieu, Doucet, and Holenstein (2007) and is perhaps surprising given the celebrated results on maximum simulated likelihood estimation. Bayesian inference based on simulated likelihood can be widely applied in microeconomics, macroeconomics and financial econometrics. One way of generating unbiased estimates of the likelihood is by the use of a particle filter. We illustrate these methods on four problems in econometrics, producing rather generic methods. Taken together, these methods imply that if we can simulate from an economic model we can carry out likelihood based inference using its simulations.

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Bibliographic Info

Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2008fe32.

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Length: 28
Date of creation: 2008
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Handle: RePEc:sbs:wpsefe:2008fe32

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Keywords: Dynamic stochastic general equilibrium models; inference; likelihood; MCMC; Metropolis-Hastings; particle filter; state space models; stochastic volatility;

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References

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Cited by:
  1. Nima Nonejad, 2013. "Particle Markov Chain Monte Carlo Techniques of Unobserved Component Time Series Models Using Ox," CREATES Research Papers 2013-27, School of Economics and Management, University of Aarhus.
  2. Luc Bauwens & Arnaud Dufays & Jeroen V.K. Rombouts, 2011. "Marginal Likelihood for Markov-Switching and Change-Point GARCH Models," Cahiers de recherche 1138, CIRPEE.
  3. Nonejad, Nima, 2014. "Particle Markov Chain Monte Carlo Techniques of Unobserved Component Time Series Models Using Ox," MPRA Paper 55662, University Library of Munich, Germany.
  4. Arnaud Doucet & Neil Shephard, 2012. "Robust inference on parameters via particle filters and sandwich covariance matrices," Economics Papers 2012-W05, Economics Group, Nuffield College, University of Oxford.
  5. Angelo Marsiglia Fasolo, 2012. "A Note on Particle Filters Applied to DSGE Models," Working Papers Series 281, Central Bank of Brazil, Research Department.
  6. Andreasen, Martin & Meldrum, Andrew, 2013. "Likelihood inference in non-linear term structure models: the importance of the lower bound," Bank of England working papers 481, Bank of England.
  7. Neil Shephard, 2013. "Martingale unobserved component models," Economics Series Working Papers 644, University of Oxford, Department of Economics.
  8. Creal, D., 2009. "A survey of sequential Monte Carlo methods for economics and finance," Serie Research Memoranda 0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  9. Rhys Bidder & Matthew E. Smith, 2013. "Doubts and variability: a robust perspective on exotic consumption series," Working Paper Series 2013-28, Federal Reserve Bank of San Francisco.
  10. Pitt, Michael K. & Silva, Ralph dos Santos & Giordani, Paolo & Kohn, Robert, 2012. "On some properties of Markov chain Monte Carlo simulation methods based on the particle filter," Journal of Econometrics, Elsevier, vol. 171(2), pages 134-151.
  11. Gallant, A. Ronald & Giacomini, Raffaella & Ragusa, Giuseppe, 2013. "Generalized Method of Moments with Latent Variables," CEPR Discussion Papers 9692, C.E.P.R. Discussion Papers.
  12. Celik, Nurcin & Son, Young-Jun, 2011. "State estimation of a shop floor using improved resampling rules for particle filtering," International Journal of Production Economics, Elsevier, vol. 134(1), pages 224-237, November.
  13. Martin M. Andreasen, 2010. "Non-linear DSGE Models and The Optimized Particle Filter," CREATES Research Papers 2010-05, School of Economics and Management, University of Aarhus.
  14. Laurini, Márcio Poletti & Hotta, Luiz Koodi, 2013. "Indirect Inference in fractional short-term interest rate diffusions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 109-126.
  15. Joshua Chan & Rodney Strachan, 2012. "Estimation in Non-Linear Non-Gaussian State Space Models with Precision-Based Methods," CAMA Working Papers 2012-13, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  16. Hall, Jamie & Pitt, Michael K. & Kohn, Robert, 2014. "Bayesian inference for nonlinear structural time series models," Journal of Econometrics, Elsevier, vol. 179(2), pages 99-111.

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