Seemingly unrelated regression models.

*(English)*Zbl 1274.62451Seemingly unrelated regressions (SUR) proposed by A. Zellner [J. Am. Stat. Assoc. 57, 348–368 (1962; Zbl 0113.34902)] are systems of equations that can be estimated one-by-one, but, due to a correlation among the error terms of the equations, efficient estimation is performed by generalized least squares applied to the whole system of equations. The estimation of SUR has been extensively studied by many authors and the presented work provides some explicit expressions for the special case of two regression equations with both univariate or multivariate responses.

In particular, the formulas for the best linear unbiased estimator of the regression coefficients and estimates of the covariance structure (under homoscedasticity) are presented. Furthermore, the tests of equality of the coefficients in the two regression equations are derived. As the paper strictly concentrates on the statement and derivation of the results in the univariate and multivariate cases without more extensive discussion of more recent contributions to and developments of this stream of literature, an interested reader might complement the paper by reading, for example D.G. Fiebig [Seemingly unrelated regression. B.H. Baltagi, A companion to theoretical econometrics. Blackwell Publishing Ltd, Malden, MA, USA (2007)].

In particular, the formulas for the best linear unbiased estimator of the regression coefficients and estimates of the covariance structure (under homoscedasticity) are presented. Furthermore, the tests of equality of the coefficients in the two regression equations are derived. As the paper strictly concentrates on the statement and derivation of the results in the univariate and multivariate cases without more extensive discussion of more recent contributions to and developments of this stream of literature, an interested reader might complement the paper by reading, for example D.G. Fiebig [Seemingly unrelated regression. B.H. Baltagi, A companion to theoretical econometrics. Blackwell Publishing Ltd, Malden, MA, USA (2007)].

Reviewer: Pavel Čížek (Tilburg)

##### MSC:

62J05 | Linear regression; mixed models |

62P20 | Applications of statistics to economics |

62F10 | Point estimation |

62H12 | Estimation in multivariate analysis |

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DOI

##### References:

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