Title: Spike and slab priors on variable orderings in VARs
Authors: Ping Wu - University of Strathclyde (United Kingdom) [presenting]
Gary Koop - University of Strathclyde (United Kingdom)
Abstract: It is increasingly common to estimate Bayesian Vector Autoregressions (VARs) in a structural form involving the Cholesky decomposition of the reduced form error covariance matrix. The resulting structural form has an error covariance matrix which is diagonal, allowing for equation-by-equation estimation of the VAR, leading to a huge reduction in the computational burden. However, this leads to order dependence. Posterior and predictive results differ depending on the way the variables are ordered in the VAR. We propose the use of spike and slab priors over different variable orderings and allow the data to select the optimal ordering. We develop two models and Markov Chain Monte Carlo (MCMC) methods for posterior sampling over orderings based on the Plackett-Luce and Bradley-Terry models. In a macroeconomic exercise involving VARs with 20 variables, we demonstrate the effectiveness of our two approaches in choosing the optimal ordering and find substantive forecasting improvements relative to a strategy of subjectively selecting a single ordering.