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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

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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 introduced 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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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 413.

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Date of creation: 2008
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Handle: RePEc:oxf:wpaper:413

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Related research
Keywords: Dynamic Stochastic General Equilibrium Models; Inference; Likelihood; MCMC; Metropolis-Hastings; Particle Filter; State Space Models; Stochastic Volatility;

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Find related papers by JEL classification:
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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