This paper discusses the challenges faced by the empirical macroeconomist and methods for surmounting them. These challenges arise due to the fact that macroeconometric models potentially include a large number of variables and allow for time variation in parameters. These considerations lead to models which have a large number of parameters to estimate relative to the number of observations. A wide range of approaches are surveyed which aim to overcome the resulting problems. We stress the related themes of prior shrinkage, model averaging and model selection. Subsequently, we consider a particular modelling approach in detail. This involves the use of dynamic model selection methods with large TVP-VARs. A forecasting exercise involving a large US macroeconomic data set illustrates the practicality and empirical success of our approach.
Bayesian VAR (BVAR) models offer a practical solution to the parameter proliferation concerns as they allow to introduce a priori information on seasonality and persistence of inflation in a multivariate framework. We investigate alternative prior specifications in the case of time series with a clear seasonal pattern. In the empirical part we forecast the monthly headline inflation in the Polish economy over the period 2011‒2014 employing two popular BVAR frameworks: a steady-state reduced-form BVAR and just-identified structural BVAR model. To evaluate the forecast performance we use the pseudo real-time vintages of timely information from consumer and financial markets. We compare different models in terms of both point and density forecasts. Using formal testing procedure for density-based scores we provide the empirical evidence of superiority of the steady-state BVAR specifications with tight seasonal priors.