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 F-t is 1(1) and driven by a number of shocks that is smaller than the dimension of F-t; and, (ii) the idiosyncratic components are either I(1) or I(0). Under (i), the factors F-t 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 F-t, 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. Published by Elsevier B.V.

Automated summary

This study examines a large-dimensional Dynamic Factor Model, providing consistent estimators for factors, loadings, shocks, coefficients of the VECM, and Impulse-Response Functions as both cross-sectional size n and time dimension T approach infinity. The study also explores the finite-sample properties of the estimators through MonteCarlo exercises, overturning some results from previous literature by modeling the long-run dynamics of factors. Specifically, it finds that oil price shocks have only a temporary effect on US real activity, and a positive news shock leads to a significant boom followed by a milder recession.