On Necessary and Sufficient Conditions for Ordinary Least Squares Estimators to Be Best Linear Unbiased Estimators

Two comments are made concerning Anderson’s article (1978) on the identification and estimation of nonrecursive models. First, Anderson’s rule for identification is only a necessary but not sufficient condition. The necessary and sufficient conditions are presented using matrix notation and a modified version of Anderson’s rule is offered. Second, contrary to Anderson’s discussion, the choice of two-stage or ordinary least squares depends on the data results rather than the methodological properties of the estimators. A means for choosing between the estimates is provided.

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On the weighted least-squares, the ordinary least-squares and the best linear unbiased estimators under a restricted growth curve model

Statistical Papers ◽

10.1007/s00362-012-0483-9 ◽

2012 ◽

Vol 55 (2) ◽

pp. 375-392 ◽

Cited By ~ 4

Author(s):

Guang Jing Song ◽

Qing Wen Wang

Keyword(s):

Least Squares ◽

Growth Curve ◽

Weighted Least Squares ◽

Ordinary Least Squares ◽

Growth Curve Model ◽

Unbiased Estimators ◽

Curve Model ◽

Best Linear Unbiased ◽

Best Linear Unbiased Estimators

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REDUNDANCY OF MOMENT CONDITIONS AND THE EFFICIENCY OF OLS IN SUR MODELS

Econometric Theory ◽

10.1017/s0266466608080687 ◽

2008 ◽

Vol 24 (5) ◽

pp. 1456-1460 ◽

Cited By ~ 1

Author(s):

Hailong Qian

Keyword(s):

Least Squares ◽

Asymptotic Efficiency ◽

Generalized Method Of Moments ◽

Sufficient Conditions ◽

Generalized Least Squares ◽

Ordinary Least Squares ◽

American Statistical Association ◽

Orthogonality Condition ◽

Moment Conditions ◽

Necessary And Sufficient

In this note, based on the generalized method of moments (GMM) interpretation of the usual ordinary least squares (OLS) and feasible generalized least squares (FGLS) estimators of seemingly unrelated regressions (SUR) models, we show that the OLS estimator is asymptotically as efficient as the FGLS estimator if and only if the cross-equation orthogonality condition is redundant given the within-equation orthogonality condition. Using the condition for redundancy of moment conditions of Breusch, Qian, Schmidt, and Wyhowski (1999, Journal of Econometrics 99, 89–111), we then derive the necessary and sufficient condition for the equal asymptotic efficiency of the OLS and FGLS estimators of SUR models. We also provide several useful sufficient conditions for the equal asymptotic efficiency of OLS and FGLS estimators that can be interpreted as various mixings of the two famous sufficient conditions of Zellner (1962, Journal of the American Statistical Association 57, 348–368).

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Two Explicit Characterizations of the General Nonnegative-Definite Covariance Matrix Structure for Equality of BLUEs, WLSEs, and LSEs

International Journal of Statistics and Probability ◽

10.5539/ijsp.v9n6p108 ◽

2020 ◽

Vol 9 (6) ◽

pp. 108

Author(s):

Phil D. Young ◽

Joshua D. Patrick ◽

Dean M. Young

Keyword(s):

Least Squares ◽

Weighted Least Squares ◽

Sufficient Conditions ◽

Covariance Structure ◽

Least Squares Estimator ◽

Weighted Least Squares Estimator ◽

Best Linear Unbiased ◽

Necessary And Sufficient ◽

Nonnegative Definite

We provide a new, concise derivation of necessary and sufficient conditions for the explicit characterization of the general nonnegative-definite covariance structure V of a general Gauss-Markov model with E(y) and Var(y) such that the best linear unbiased estimator, the weighted least squares estimator, and the least squares estimator of Xβ are identical. In addition, we derive a representation of the general nonnegative-definite covariance structure V defined above in terms of its Moore-Penrose pseudo-inverse.

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