Large-dimensional Dynamic Factor Models: Estimation of Impulse–Response Functions with I(1) cointegrated factors

We study a large-dimensional Dynamic Factor Model where: (i) the vector of factors Ft is I(1) and driven by a number of shocks that is smaller than the dimension of Ft; and, (ii) the idiosyncratic components are either I(1) or I(0). Under (i), the factors Ft are cointegrated and can be modeled as a Vector Error Correction Model (VECM). Under (i) and (ii), we provide consistent estimators, as both the cross-sectional size n and the time dimension T go to infinity, for the factors, the loadings, the shocks, the coefficients of the VECM and therefore the Impulse–Response Functions (IRF) of the observed variables to the shocks. Furthermore, possible deterministic linear trends are fully accounted for, and the case of an unrestricted VAR in the levels Ft, instead of a VECM, is also studied. The finite-sample properties the proposed estimators are explored by means of a MonteCarlo exercise. Finally, we revisit two distinct and widely studied empirical applications. By correctly modeling the long-run dynamics of the factors, our results partly overturn those obtained by recent literature. Specifically, we find that: (i) oil price shocks have just a temporary effect on US real activity; and, (ii) in response to a positive news shock, the economy first experiences a significant boom, and then a milder recession.