Large Bayesian vector auto regressions

Abstract

SUMMARYThis paper shows that vector auto regression (VAR) with Bayesian shrinkage is an appropriate tool for large dynamic models. We build on the results of De Mol and co-workers (2008) and show that, when the degree of shrinkage is set in relation to the cross-sectional dimension, the forecasting performance of small monetary VARs can be improved by adding additional macroeconomic variables and sectoral information. In addition, we show that large VARs with shrinkage produce credible impulse responses and are suitable for structural analysis.

Financial Nowcasts and Their Usefulness in Macroeconomic Forecasting

“…Our benchmark quarterly empirical models are VARs given their general popularity as forecasting tools, which reflects both their simplicity to use and the accurate forecasts they produce (see Bańbura et al 2010 andCarriero et al 2015 . In this n dimensional VAR, each equation has k=np+1 regressors, and with n equations, there are n×k parameters to be estimated.…”

“…11 models with Bayesian methods and equip the models with Minnesota and sum of coefficient priors; Bańbura et al (2010), Beauchemin andZaman (2011), andKoop (2013), among others, document substantial gains in forecasting accuracy from equipping these types of models with these priors. We allow the model specifications to differ along the following dimensions: in the number of financial variables included; in whether financial variables are included in the regressions in levels or transformed into spreads (e.g., we construct the risk spread as the Baa corporate bond yield less the 10-year Treasury yield); and in the estimation period (i.e., we begin the estimation in either 1985 or 1959).…”

“…High-dimensional VARs are susceptible to overfitting, and so to deal with this curse of dimensionality we estimate them using Bayesian methods as discussed in Bańbura et al (2010), Beauchemin and Zaman (2011), Koop (2013), and Carriero et al (2015. Specifically, coefficient estimates in 1 ,..., p AA and  are shrunk to their prior means.…”

“…The estimation of this BFAVAR model closely follows Bernanke et al (2005), Bańbura et al (2010), and Berg and Henzel (2015). Specifically, parameters are estimated using a two-step approach.…”

Hierarchical Shrinkage in Time-Varying Parameter Models

“…This has led many papers (including De Mol, Giannone andReichlin 2008, andBanbura, Giannone andReichlin 2010) to use Bayesian methods which use shrinkage to reduce over-fitting problems and improve forecast performance. Closely related to the idea of shrinkage is the idea of variable selection (which can be thought of as shrinking the coefficient on a predictor to zero).…”