Endogenous time variation in vector autoregressions

Bayesian Vector Autoregressions

This article provides an introduction to the burgeoning academic literature on Bayesian Vector Autoregressions, benchmark models for applied macroeconomic research. We first explain Bayes’ theorem and the derivation of the closed-form solution for the posterior distribution of the parameters of the model given data. We further consider parameter shrinkage, a distinguishing feature of the prior ...

Vector Autoregressions and Cointegration*

Prior Selection for Vector Autoregressions∗

Vector autoregressions (VARs) are flexible time series models that can capture complex dynamic interrelationships among macroeconomic variables. However, their dense parameterization leads to unstable inference and inaccurate out-ofsample forecasts, particularly for models with many variables. A potential solution to this problem is to use informative priors, in order to shrink the richly param...

Time-Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum

This note corrects a mistake in the estimation algorithm of the time-varying structural vector autoregression model of Primiceri (2005) and proposes a new algorithm that correctly applies the procedure proposed by Kim, Shephard, and Chib (1998) to the estimation of VAR or DSGE models with stochastic volatility. Relative to Primiceri (2005), the correct algorithm involves a different ordering of...

Priors about Observables in Vector Autoregressions

Standard practice in Bayesian VARs is to formulate priors on the autoregressive parameters, but economists and policy makers actually have priors about the behavior of observable variables. We show how this kind of prior can be used in a VAR under strict probability theory principles. We state the inverse problem to be solved and we propose a numerical algorithm that works well in practical sit...