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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. P r sterholm 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.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 22 (2006)
Issue (Month): 02 (April)
Pages: 235-257

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Handle: RePEc:cup:etheor:v:22:y:2006:i:02:p:235-257_06

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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. Par Osterholm, 2008. "A structural Bayesian VAR for model-based fan charts," Applied Economics, Taylor & Francis Journals, vol. 40(12), pages 1557-1569.
  2. 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.
  3. Meredith Beechey & P�R �Sterholm, 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.
  4. 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.
  5. 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.
  6. Caporin Massimiliano & Paruolo Paolo, 2005. "Spatial effects in multivariate ARCH," Economics and Quantitative Methods qf0501, Department of Economics, University of Insubria.
  7. 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.
  8. 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.

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