Structural analysis with multivariate autoregressive index models

We address the issue of parameter dimensionality reduction in Vector Autoregressive models (VARs) for many variables by imposing specific reduced rank restrictions on the coefficient matrices that simplify the VARs into Multivariate Autoregressive Index (MAI) models. We derive the Wold representation implied by the MAIs and show that it is closely related to that associated with dynamic factor models. Then, the theoretical analysis is extended to the case of general rank restrictions on the VAR coefficients. Next, we describe classical and Bayesian estimation of large MAIs, and discuss methods for rank determination. Finally, the performance of the MAIs is compared with that of large Bayesian VARs in the context of Monte Carlo simulations and two empirical applications, on the transmission mechanism of monetary policy and on the propagation of demand and supply shocks.