Computational efficiency of Bayesian estimation techniques for “unfavorable” density

 
PIIS042473880014916-6-1
DOI10.31857/S042473880014916-6
Publication type Article
Status Published
Authors
Affiliation: The Institute of Regional Economy Studies Russian Academy of Sciences
Address: Saint-Petersburg , Russian Federation
Journal nameEkonomika i matematicheskie metody
EditionVolume 57 Issue 2
Pages121-134
Abstract

The Bayesian estimation of dynamic stochastic general equilibrium (DSGE) models implies usage of Monte Carlo Markov Chain (MCMC) algorithms. The analysis of MCMC algorithms is made for densities with unfavorable properties common in DSGE models (restricted density support, heavy tails, sharp peaks, non-convex log-density, and non-convex density). Three groups of algorithms are investigated: random walk (RW), MALA and suggested LTG (local truncated Gauss). Three versions of MALA and LTG are investigated: the version using local hessian and gradient of log-density, the version using only local gradient and the version that uses only information about the mode. Performance of MALA and LTG are close to each other. There is some advantage of LTG in average and in test with DSGE model. RW performance is worse than MALA or LTG (especially for small-scale cases). The computational costs are almost the similar for RW and approximation based versions of MALA or LTG. Existence of heavy tails leads to decrease of advantage of MALA and LTG algorithms. Acceptance rate (corresponding to the lowest inefficiency of sample) can be quite different from conventional values.

KeywordsMCMC; Markov chain Monte Carlo; Metropolis-Hastings algorithm; Bayesian econometrics techniques.
AcknowledgmentThe reported study was partly funded by RFBR according to the research (project 18-010-01185) «Structural changes in Russia: The role of human capital and investments». The author expresses personal ideas, which may not correlate with the official position of the Bank of Russia. The Bank of Russia carries no responsibility for the content of the article.
Received08.06.2021
Publication date25.06.2021
Number of characters36519
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