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Identification Of Covariance Structures

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  • Lucchetti, Riccardo

Abstract

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, Journal of Econometrics 69, 112–132) in the context of linear models, the present paper provides necessary and sufficient conditions for the identification of a covariance structure that depends only on the constraints and can therefore be checked independently of estimated parameters.A structure condition is developed, which only depends on the structure of the constraints. It is shown that this condition, if coupled with the familiar order condition, provides a sufficient condition for identification. In practice, because 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.Most of the paper focuses on structural vector autoregressions, but extensions to other statistical models are also briefly discussed.I thank all the participants at the meeting held in Pavia on June 11, 2004, in honor of Carlo Giannini for their comments; it goes without saying that Carlo himself provided not only acute observations on the day but also the main inspiration for this piece of work. Sadly, Carlo passed away on September 11, 2004, and this paper is dedicated to his memory. Pär Österholm spotted several mistakes in an earlier version and helped me clarify some implementation details. Thanks are also due to Gianni Amisano, Bruce Hansen, Giulio Palomba, Paolo Paruolo, and two anonymous referees. The usual disclaimer obviously applies.

Suggested Citation

  • Lucchetti, Riccardo, 2006. "Identification Of Covariance Structures," Econometric Theory, Cambridge University Press, vol. 22(2), 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

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    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. 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.
    2. 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.
    3. Hassan B. Ghassan & Hassan R. Alhajhoj & Faruk Balli, 2022. "Bi-demographic and current account dynamics using SVAR model: evidence from Saudi Arabia," Economic Change and Restructuring, Springer, vol. 55(3), pages 1327-1363, August.
    4. 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.
    5. Caporin Massimiliano & Paruolo Paolo, 2005. "Spatial effects in multivariate ARCH," Economics and Quantitative Methods qf0501, Department of Economics, University of Insubria.
    6. 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.
    7. 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.
    8. 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.
    9. Ghassan, Hassan & Alhajhoj, Hassan R. & Balli, Faruk, 2018. "Bi-Demographic Changes and Current Account using SVAR Modeling: Evidence from Saudi Arabia," MPRA Paper 93013, University Library of Munich, Germany, revised 01 Feb 2019.
    10. 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.
    11. Hassan Belkacem Ghassan & Hassan Rafdan Al-Hajhoj & Faruk Balli, 2019. "Bi-Demographic Changes and Current Account using SVAR Modeling: Evidence from Saudi Economy," Working Papers hal-01742574, HAL.
    12. Emanuele Bacchiocchi & Toru Kitagawa, 2020. "Locally- but not globally-identified SVARs," CeMMAP working papers CWP40/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. 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.
    14. Par Osterholm, 2008. "A structural Bayesian VAR for model-based fan charts," Applied Economics, Taylor & Francis Journals, vol. 40(12), pages 1557-1569.
    15. Hassan B. Ghassan & Hassan R. Al-Hajhoj & Faruk Balli, 2018. "Bi-Demographic Changes and Current Account using SVAR Modeling," Papers 1803.11161, arXiv.org, revised Mar 2019.
    16. 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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    More about this item

    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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