Factor-Augmented VARs with Noisy Factor Proxies

In factor-augmented vector autoregression (FAVAR) models, some of the factors are treated as observable while the remaining factors are latent and need to be estimated from a large cross-section of time series. Given that economic concepts such as inflation or output can often be proxied by different variables and that macroeconomic time series are commonly subject to substantial data revisions, the assumption that some factors are perfectly observable appears unnecessarily strong. In this paper we relax the assumption and treat observable factor proxies as noisy measures of true underlying factors. We show that when there are more observable proxies than true underlying factors, the standard FAVAR models reduce to a dynamic factor model (DFM) with a rank constraint. We propose an iterative estimation procedure that alternates between principal components estimation and solving a reducedrank regression model. We further discuss a modification of the method with group-lasso sparsity constraints to incorporate regularization and variable selection at the same time. We use Monte Carlo simulations to demonstrate the effectiveness of the proposed method for factor estimation and forecasting in a DFM with weak factors and its usefulness for estimating structural impulse responses to oil supply and demand shocks using a FAVAR model.