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Identification Of Covariance Structures


  • Lucchetti, Riccardo


The issue of identification of covariance structures, which arises in a number of different contexts, has been so far linked to conditions on the true parameters to be estimated. In this paper, this limitation is removed. As done by Johansen (1995) in the context of linear models, the present paper provides necessary and sufficient conditions for the identification of a covariance structure that depend only on the constraints, and can therefore be checked independently of estimated parameters. A sufficient condition is developed, which only depends on the structure of the constraints. It is shown that this structure condition, if coupled with the familiar order condition, provides a sufficient condition for identification. In practice, since the structure condition holds if and only if a certain matrix, constructed from the constraint matrices, is invertible, automatic software checking for identification is feasible even for large-scale systems.
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Suggested Citation

  • Lucchetti, Riccardo, 2006. "Identification Of Covariance Structures," Econometric Theory, Cambridge University Press, vol. 22(02), pages 235-257, April.
  • Handle: RePEc:cup:etheor:v:22:y:2006:i:02:p:235-257_06

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    References listed on IDEAS

    1. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    2. 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.
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    Cited by:

    1. Lisandro Abrego & Pär Österholm, 2010. "External Linkages and Economic Growth in Colombia: Insights from a Bayesian VAR Model," The World Economy, Wiley Blackwell, vol. 33(12), pages 1788-1810, December.
    2. Meredith Beechey & Pär Österholm, 2008. "A Bayesian Vector Autoregressive Model with Informative Steady-state Priors for the Australian Economy," The Economic Record, The Economic Society of Australia, vol. 84(267), pages 449-465, December.
    3. Gustafsson, Peter & Stockhammar, Pär & Österholm, Pär, 2016. "Macroeconomic effects of a decline in housing prices in Sweden," Journal of Policy Modeling, Elsevier, vol. 38(2), pages 242-255.
    4. Emanuele BACCHIOCCHI & Luca FANELLI, 2012. "Identification in structural vector autoregressive models with structural changes," Departmental Working Papers 2012-16, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    5. Roberto ESPOSTI & Pierpaolo PIERANI, 2005. "Price, Private Demand and Optimal Provision of Public R&D in Italian Agriculture," Working Papers 238, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    6. Renato BALDUCCI, 2005. "Public Expenditure and Economic Growth. A critical extension of Barro's (1990) model," Working Papers 240, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    7. Caporin Massimiliano & Paruolo Paolo, 2005. "Spatial effects in multivariate ARCH," Economics and Quantitative Methods qf0501, Department of Economics, University of Insubria.
    8. Roberto ESPOSTI, 2007. "On the Decline of Agriculture. Evidence from Italian Regions in the Post-WWII Period," Working Papers 300, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    9. Stefania BUSSOLETTI & Roberto ESPOSTI, 2004. "Regional Convergence, Structural Funds and the Role of Agricolture in the EU. A Panel-Data Approach," Working Papers 220, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    10. Par Osterholm, 2008. "A structural Bayesian VAR for model-based fan charts," Applied Economics, Taylor & Francis Journals, vol. 40(12), pages 1557-1569.
    11. Esposti, Roberto, 2014. "On why and how agriculture declines," Structural Change and Economic Dynamics, Elsevier, vol. 31(C), pages 73-88.

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General


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