"Bayesian inference based only on simulated likelihood: particle filter analysis of dynamic economic models"
Thomas Flury and Neil Shephard
Oxford-Man Institute, University of Oxford
Abstract
Suppose we wish to carry out likelihood based inference but we solely have an unbiased simula-
tion 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.
Keywords: Dynamic stochastic general equilibrium models, inference, likelihood, MCMC, Metropolis-
Hastings, particle filter, state space models, stochastic volatility
JEL codes: C11, C13, C15, C32, E32.