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

We demonstrate how Bayesian shrinkage can address problems with utilizing large
information sets to calculate trend and cycle via a multivariate Beveridge-Nelson (BN)
decomposition. We illustrate our approach by estimating the U.S. output gap with large
Bayesian vector autoregressions that include up to 138 variables. Because the BN trend
and cycle are linear functions of historical forecast errors, we are also able to account for
the estimated output gap in terms of different sources of information, as well as particular
underlying structural shocks given identification restrictions. Our empirical analysis
suggests that, in addition to output growth, the unemployment rate, CPI inflation, and, to
a lesser extent, housing starts, consumption, stock prices, real M1, and the federal funds
rate are important conditioning variables for estimating the U.S. output gap, with
estimates largely robust to incorporating additional variables. Using standard
identification restrictions, we find that the role of monetary policy shocks in driving the
output gap is small, while oil price shocks explain about 10% of the variance over
different horizons.