Estimating and Accounting for the Output Gap with Large Bayesian Vector Autoregressions

We consider how to estimate the trend and cycle of a time series, such as real GDP, given a large information set. Our approach makes use of the Beveridge-Nelson decom- position based on a vector autoregression, but with two practical considerations. First, we show how to determine which conditioning variables span the relevant information by directly accounting for the Beveridge-Nelson trend and cycle in terms of contributions from different forecast errors. Second, we employ Bayesian shrinkage to avoid over fitting in finite samples when estimating models that are large enough to include many possible sources of information. An empirical application with up to 138 variables covering vari- ous aspects of the U.S. economy reveals that the unemployment rate, inflation, and, to a lesser extent, housing starts, aggregate consumption, stock prices, real money balances, and the federal funds rate contain relevant information beyond that in output growth for estimating the output gap, with estimates largely robust to substituting some of these variables or incorporating additional variables.