Estimating US Monetary Policy Shocks Using a Factor-Augmented Vector Autoregression: An EM Algorithm Approach

Abstract

Economy-wide effects of shocks to the US federal funds rate are estimated in a state space model with 120 US macroeconomic and financial time series driven by the dynamics of the federal funds rate and a few dynamic factors. This state space system is denoted a factor-augmented VAR (FAVAR) by Bernanke et al. (2005). I estimate the FAVAR by the fully parametric one-step EM algorithm as an alternative to the two-step principal component method and the one-step Bayesian method in Bernanke et al. (2005). The EM algorithm which is an iterative maximum likelihood method estimates all the parameters and the dynamic factors simultaneously and allows for classical inference. I demonstrate empirically that the same impulse responses but better fit emerge robustly from a low order FAVAR with eight correlated factors compared to a high order FAVAR with fewer correlated factors, for instance four factors. This empirical result accords with one of the theoretical results from Bai & Ng (2007) in which it is shown that the information in complicated factor dynamics may be substituted by panel information.