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Parallel Tempering for DSGE Estimation

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  • Joshua Brault

Abstract

In this paper, I develop a population-based Markov chain Monte Carlo (MCMC) algorithm known as parallel tempering to estimate dynamic stochastic general equilibrium (DSGE) models. Parallel tempering approximates the posterior distribution of interest using a family of Markov chains with tempered posteriors. At each iteration, two randomly selected chains in the ensemble are proposed to swap parameter vectors, after which each chain mutates via Metropolis-Hastings. The algorithm results in a fast-mixing MCMC, particularly well suited for problems with irregular posterior distributions. Also, due to its global nature, the algorithm can be initialized directly from the prior distributions. I provide two empirical examples with complex posteriors: a New Keynesian model with equilibrium indeterminacy and the Smets-Wouters model with more diffuse prior distributions. In both examples, parallel tempering overcomes the inherent estimation challenge, providing extremely consistent estimates across different runs of the algorithm with large effective sample sizes. I provide code compatible with Dynare mod files, making this routine straightforward for DSGE practitioners to implement.

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  • Joshua Brault, 2024. "Parallel Tempering for DSGE Estimation," Staff Working Papers 24-13, Bank of Canada.
  • Handle: RePEc:bca:bocawp:24-13
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    References listed on IDEAS

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    More about this item

    Keywords

    Econometric and statistical methods; Economic models;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General

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