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Identification conditions in simultaneous systems of cointegrating equations with integrated variables of higher order

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  • Mosconi, Rocco
  • Paruolo, Paolo

Abstract

This paper discusses identification of systems of simultaneous cointegrating equations with integrated variables of order two or higher, under constraints on the cointegration parameters. Rank and order conditions for identification are provided for general linear constraints, covering both cross-equation and equation-by-equation restrictions.

Suggested Citation

  • Mosconi, Rocco & Paruolo, Paolo, 2017. "Identification conditions in simultaneous systems of cointegrating equations with integrated variables of higher order," Journal of Econometrics, Elsevier, vol. 198(2), pages 271-276.
    • Handle: RePEc:eee:econom:v:198:y:2017:i:2:p:271-276
    DOI: 10.1016/j.jeconom.2017.01.007
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    References listed on IDEAS

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    1. Saikkonen, Pentti, 1993. "Estimation of Cointegration Vectors with Linear Restrictions," Econometric Theory, Cambridge University Press, vol. 9(1), pages 19-35, January.
    2. Granger, C W J & Lee, T H, 1989. "Investigation of Production, Sales and Inventory Relationships Using Multicointegration and Non-symmetric Error Correction Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages 145-159, Supplemen.
    3. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
    4. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    5. Boswijk, H. Peter, 2000. "Mixed Normality And Ancillarity In I(2) Systems," Econometric Theory, Cambridge University Press, vol. 16(6), pages 878-904, December.
    6. Davidson, James, 1994. "Identifying Cointegrating Regressions by the Rank Condition," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 56(1), pages 105-110, February.
    7. H. Peter Boswijk & Jurgen A. Doornik, 2004. "Identifying, estimating and testing restricted cointegrated systems: An overview," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 440-465, November.
    8. Johansen, Søren & Juselius, Katarina & Frydman, Roman & Goldberg, Michael, 2010. "Testing hypotheses in an I(2) model with piecewise linear trends. An analysis of the persistent long swings in the Dmk/$ rate," Journal of Econometrics, Elsevier, vol. 158(1), pages 117-129, September.
    9. Johansen, Soren, 1995. "Identifying restrictions of linear equations with applications to simultaneous equations and cointegration," Journal of Econometrics, Elsevier, vol. 69(1), pages 111-132, September.
    10. Johansen, Søren, 1992. "A Representation of Vector Autoregressive Processes Integrated of Order 2," Econometric Theory, Cambridge University Press, vol. 8(2), pages 188-202, June.
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    Cited by:

    1. Massimo Franchi & Paolo Paruolo, 2021. "Cointegration, Root Functions and Minimal Bases," Econometrics, MDPI, vol. 9(3), pages 1-27, August.
    2. Jurgen A. Doornik & Rocco Mosconi & Paolo Paruolo, 2017. "Formula I(1) and I(2): Race Tracks for Likelihood Maximization Algorithms of I(1) and I(2) Cointegrated VAR Models," Econometrics, MDPI, vol. 5(4), pages 1-30, November.
    3. Andreas Hetland & Simon Hetland, 2017. "Short-Term Expectation Formation Versus Long-Term Equilibrium Conditions: The Danish Housing Market," Econometrics, MDPI, vol. 5(3), pages 1-21, September.
    4. Amogh Ghimire & Feiting Lin & Peifen Zhuang, 2021. "The Impacts of Agricultural Trade on Economic Growth and Environmental Pollution: Evidence from Bangladesh Using ARDL in the Presence of Structural Breaks," Sustainability, MDPI, vol. 13(15), pages 1-15, July.
    5. Yuanyuan Li & Dietmar Bauer, 2020. "Modeling I(2) Processes Using Vector Autoregressions Where the Lag Length Increases with the Sample Size," Econometrics, MDPI, vol. 8(3), pages 1-28, September.

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    More about this item

    Keywords

    Identification; (Multi-)Cointegration; I(d); Stocks and flows; Inventory models;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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