  In this paper, we write the time-varying parameter (TVP) regression model
involving K explanatory variables and T observations as a constant coefficient
regression model with KT explanatory variables. In contrast with much of the
existing literature which assumes coefficients to evolve according to a random
walk, a hierarchical mixture model on the TVPs is introduced. The resulting
model closely mimics a random coefficients specification which groups the TVPs
into several regimes. These flexible mixtures allow for TVPs that feature a
small, moderate or large number of structural breaks. We develop
computationally efficient Bayesian econometric methods based on the singular
value decomposition of the KT regressors. In artificial data, we find our
methods to be accurate and much faster than standard approaches in terms of
computation time. In an empirical exercise involving inflation forecasting
using a large number of predictors, we find our models to forecast better than
alternative approaches and document different patterns of parameter change than
are found with approaches which assume random walk evolution of parameters.
