Use of Restricted Residuals in SUR Systems: Some Finite Sample Results
- 1 March 1976
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 71 (353) , 183
- https://doi.org/10.2307/2285765
Abstract
Consider a system of two seemingly unrelated regression equations: , where X2 is a proper subset of X1, i.e., X1≡(X2: L2), and Σ = (σij) is the disturbance covariance matrix. Let be the -estimators based, respectively, on the restricted estimate of Σ and on the unrestricted estimate S of Σ. This paper derives finite sample variances of the , and examines their efficiency with respect to the are identical to the OLS estimator obtained directly from , and are efficient. On the other hand, is more (less) efficient at the lower (upper) end of the scale of . In practical applications, it may be preferable to use when | ρ | ≤ .5 (approximately) and df ≥ 5, and otherwise.Keywords
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