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Cointegration and Error Correction Mechanisms for Singular Stochastic Vectors

Author

Listed:
  • Matteo Barigozzi

    () (Università di Bologna, Department of Economics, 40126 Bologna, Italy)

  • Marco Lippi

    () (Einaudi Institute for Economics and Finance, 00187 Roma, Italy)

  • Matteo Luciani

    () (Federal Reserve Board of Governors, Washington, DC 20551, USA)

Abstract

Large-dimensional dynamic factor models and dynamic stochastic general equilibrium models, both widely used in empirical macroeconomics, deal with singular stochastic vectors, i.e., vectors of dimension r which are driven by a q -dimensional white noise, with q < r . The present paper studies cointegration and error correction representations for an I ( 1 ) singular stochastic vector y t . It is easily seen that y t is necessarily cointegrated with cointegrating rank c ≥ r − q . Our contributions are: (i) we generalize Johansen’s proof of the Granger representation theorem to I ( 1 ) singular vectors under the assumption that y t has rational spectral density; (ii) using recent results on singular vectors by Anderson and Deistler, we prove that for generic values of the parameters the autoregressive representation of y t has a finite-degree polynomial. The relationship between the cointegration of the factors and the cointegration of the observable variables in a large-dimensional factor model is also discussed.

Suggested Citation

  • Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2020. "Cointegration and Error Correction Mechanisms for Singular Stochastic Vectors," Econometrics, MDPI, Open Access Journal, vol. 8(1), pages 1-1, February.
  • Handle: RePEc:gam:jecnmx:v:8:y:2020:i:1:p:3-:d:316273
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    References listed on IDEAS

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    Cited by:

    1. Tibor Szendrei & Katalin Varga, 2020. "FISS – A Factor-based Index of Systemic Stress in the Financial System," Russian Journal of Money and Finance, Bank of Russia, vol. 79(1), pages 3-34, March.

    More about this item

    Keywords

    singular stochastic vectors; cointegration for singular vectors; Granger representation theorem; large-dimensional dynamic factor models);

    JEL classification:

    • B23 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Econometrics; Quantitative and Mathematical Studies
    • C - Mathematical and Quantitative Methods
    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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