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BAYESIAN INFERENCE BASED ONLY ON SIMULATED LIKELIHOOD: PARTICLE FILTER ANALYSIS OF DYNAMIC ECONOMIC MODELS

Published online by Cambridge University Press:  17 May 2011

Thomas Flury  and
Neil Shephard
Thomas Flury*
Affiliation:
University of Oxford
Neil Shephard
Affiliation:
University of Oxford
*
*Address correspondence to Thomas Flury, Oxford-Man Institute, University of Oxford, Eagle House, Walton Well Road, Oxford OX2 6EE, United Kingdom; e-mail: thomas.flury@oxford-man.ox.ac.uk.
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Abstract

We note that likelihood inference can be based on an unbiased simulation-based estimator of the likelihood when it is used inside a Metropolis–Hastings algorithm. This result has recently been introduced in statistics literature by Andrieu, Doucet, and Holenstein (2010, Journal of the Royal Statistical Society, Series B, 72, 269–342) and is perhaps surprising given the 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 through a particle filter. We illustrate these methods on four problems, 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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Type
ARTICLES
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Econometric Theory , Volume 27 , Issue 5: SPECIAL ISSUE ON BOOTSTRAP AND NUMERICAL METHODS IN TIME SERIES , October 2011 , pp. 933 - 956
Copyright
Copyright © Cambridge University Press 2011

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