  Researchers increasingly wish to estimate time-varying parameter (TVP)
regressions which involve a large number of explanatory variables. Including
prior information to mitigate over-parameterization concerns has led to many
using Bayesian methods. However, Bayesian Markov Chain Monte Carlo (MCMC)
methods can be very computationally demanding. In this paper, we develop
computationally efficient Bayesian methods for estimating TVP models using an
integrated rotated Gaussian approximation (IRGA). This exploits the fact that
whereas constant coefficients on regressors are often important, most of the
TVPs are often unimportant. Since Gaussian distributions are invariant to
rotations we can split the the posterior into two parts: one involving the
constant coefficients, the other involving the TVPs. Approximate methods are
used on the latter and, conditional on these, the former are estimated with
precision using MCMC methods. In empirical exercises involving artificial data
and a large macroeconomic data set, we show the accuracy and computational
benefits of IRGA methods.
