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Title: Computing 3sls solutions of simultaneous equation models with a possible singular variance-covariance matrix
Authors: Dinenis, Elias 
Kontoghiorghes, Erricos John 
Keywords: Parallel algorithms;Algorithms;Least squares;Analysis of covariance
Issue Date: 1997
Publisher: Springer Link
Source: Computational Economics, 1997, Volume 10, Issue 3, Pages 231-250
Abstract: Algorithms for computing the three-stage least squares (3SLS) estimator usually require the disturbance covariance 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 are derived. Expressions revealing linear combinations between the observations which become redundant have also been presented. Algorithms for computing the 3SLS estimator after the SEM has 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. Methods for computing the main matrix factorizations illustrate the basic principles to be adopted for solving SEMs on serial or parallel computers.
ISSN: 0927-7099 (print)
1572-9974 (online)
DOI: 10.1023/A:1008617207791
Rights: © 1997 Kluwer Academic Publishers. Printed in the Netherlands.
Type: Article
Appears in Collections:Άρθρα/Articles

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