Large-dimensional Dynamic Factor Models: Estimation of Impulse–Response Functions with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e5147" altimg="si902.svg"><mml:mrow><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> cointegrated factors

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