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

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  • Barigozzi, Matteo
  • Lippi, Marco
  • Luciani, Matteo
Abstract
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.

Suggested Citation

  • Barigozzi, Matteo & Lippi, Marco & Luciani, Matteo, 2021. "Large-dimensional Dynamic Factor Models: Estimation of Impulse–Response Functions with I(1) cointegrated factors," Journal of Econometrics, Elsevier, vol. 221(2), pages 455-482.
    • Handle: RePEc:eee:econom:v:221:y:2021:i:2:p:455-482
    DOI: 10.1016/j.jeconom.2020.05.004
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    6. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    7. Mirela Sorina Miescu & Giorgio Motta & Dario Pontiggia & Raffaele Rossi, 2023. "The Expansionary Effects Of Housing Credit Supply Shocks," Working Papers 399832231, Lancaster University Management School, Economics Department.
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    9. Cantore, Cristiano & Ferroni, Filippo & Mumtaz, Hroon & Theophilopoulou, Angeliki, 2022. "A tail of labour supply and a tale of monetary policy," Bank of England working papers 989, Bank of England.
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    12. Takumah, Wisdom, 2023. "Fiscal Policy and Asset Prices in a Dynamic Factor Model with Cointegrated Factors," MPRA Paper 117897, University Library of Munich, Germany, revised 10 Jul 2023.
    13. Donato Ceci & Andrea Silvestrini, 2023. "Nowcasting the state of the Italian economy: The role of financial markets," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(7), pages 1569-1593, November.
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    15. Juho Koistinen & Bernd Funovits, 2022. "Estimation of Impulse-Response Functions with Dynamic Factor Models: A New Parametrization," Papers 2202.00310, arXiv.org, revised Feb 2022.

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    More about this item

    Keywords

    Dynamic Factor Models; Unit root processes; Cointegration; Impulse–Response Functions;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • E0 - Macroeconomics and Monetary Economics - - General

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