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Computing 3SLS Solutions of Simultaneous Equation Models with a Possible Singular Variance-Convariance Matrix

KONTOGHIORGHES, ERRICOS ; DINENIS, ELIAS

In: Computational Economics, 1997, vol. 10, no. 3, p. 231-250

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    Titre
    • Computing 3SLS Solutions of Simultaneous Equation Models with a Possible Singular Variance-Convariance Matrix
    Auteur
    • KONTOGHIORGHES, ERRICOS. Institut d'Informatique, Université de Neuchâtel, Rue Emile-Argand 11, CH-2007, Neuchâtel, Switzerland e-mail
    • DINENIS, ELIAS. Centre for Mathematical Trading and Finance, City University Business School, Frobishcer, Crescent, Barbican Centre, London EC2Y 8HB, UK
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Computational Economics, 1997, vol. 10, no. 3, p. 231-250. Kluwer Academic Publishers
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:316315
    Summary
    Algorithms for computing the three-stage least squares (3SLS) estimator usually require the disturbance convariance matrix to be non-singular. However, the solution of a reformulated simultaneous equation model (SEM) results into the redundancy of this condition. Having as a basic tool the QR decomposition, the 3SLS estimator, its dispersion matrix and methods for estimating the singular disturbance covariance matrix and derived. Expressions revealing linear combinations between the observations which become redundant have also been presented. Algorithms for computing the 3SLS estimator after the SEM have been modified by deleting or adding new observations or variables are found not to be very efficient, due to the necessity of removing the endogeneity of the new data or by re-estimating the disturbance covariance matrix. Three methods have been described for solving SEMs subject to separable linear equalities constraints. The first method considers the constraints as additional precise observations while the other two methods reparameterized the constraints to solve reduced unconstrained SEMs. Method for computing the main matrix factorizations illustrate the basic principles to be adopted for solving SEMs on serial or parallel computers