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Bayesian Inference in High-Dimensional Time-varying Parameter Models using Integrated Rotated Gaussian Approximations

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Document pages: 20 pages

Abstract: Researchers increasingly wish to estimate time-varying parameter (TVP)regressions which involve a large number of explanatory variables. Includingprior information to mitigate over-parameterization concerns has led to manyusing Bayesian methods. However, Bayesian Markov Chain Monte Carlo (MCMC)methods can be very computationally demanding. In this paper, we developcomputationally efficient Bayesian methods for estimating TVP models using anintegrated rotated Gaussian approximation (IRGA). This exploits the fact thatwhereas constant coefficients on regressors are often important, most of theTVPs are often unimportant. Since Gaussian distributions are invariant torotations we can split the the posterior into two parts: one involving theconstant coefficients, the other involving the TVPs. Approximate methods areused on the latter and, conditional on these, the former are estimated withprecision using MCMC methods. In empirical exercises involving artificial dataand a large macroeconomic data set, we show the accuracy and computationalbenefits of IRGA methods.

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