  This paper proposes a variational Bayes algorithm for computationally
efficient posterior and predictive inference in time-varying parameter (TVP)
models. Within this context we specify a new dynamic variable/model selection
strategy for TVP dynamic regression models in the presence of a large number of
predictors. This strategy allows for assessing in individual time periods which
predictors are relevant (or not) for forecasting the dependent variable. The
new algorithm is evaluated numerically using synthetic data and its
computational advantages are established. Using macroeconomic data for the US
we find that regression models that combine time-varying parameters with the
information in many predictors have the potential to improve forecasts of price
inflation over a number of alternative forecasting models.
