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Specification Bias in Seemingly Unrelated Regressions

  • Potluri Rao

Abstract

Multiple regression analysis specifies a linear relation between a dependent variable and a set of independent variables. When the independent variables are non-stochastic, and the error terms are homoscedastic and serially independent, the ordinary least squares estimation of the parameters yields the best linear unbiased estimates. But when there is a set of linear regression equations whose error terms are contemporaneously correlated, then the ordinary least squares estimation of each of the equations separately is not the ‘best’ estimation procedure. When the parameters of contemporaneous correlation are known then it is possible to obtain unbiased estimates with smaller variance than the corresponding ordinary least squares estimates by estimating all the regression equations jointly using the Aitken’s generalised least squares.1 In the absence of information on these parameters Professor Zellner [5] suggested the use of estimates of these parameters from residuals of the ordinary least squares. This procedure is called the ‘seemingly unrelated regression equations’ (SURE) procedure.

Keywords

Estimation Procedure Linear Regression Equation American Statistical Association Unrelated Regression Asymptotic Bias 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Kmenta, Jan and Gilbert, R., Small Sample Properties of Alternative Estimators of Seemingly Unrelated Regressions, Journal of the American Statistical Association, LXIII (December 1968) 1180–1200.CrossRefGoogle Scholar
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    Rao, Potluri, Some Notes on Misspecification in Multiple Regressions, The American Statistician, XXV (December 1971) 37–9.Google Scholar
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    Rao, Potluri and Miller, R. L., Applied Econometrics, Belmont: Wadsworth Publishing Co., 1971.Google Scholar
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    Telser, Lester G., Iterative Estimation of a Set of Linear Regression Equations, Journal of the American Statistical Association, LIX (September 1964) 845–62.CrossRefGoogle Scholar
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    Zellner, Arnold, An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias, Journal of the American Statistical Association, LVII (June 1962) 348–68.CrossRefGoogle Scholar
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    Zellner, Arnold, Estimators for Seemingly Unrelated Regression Equations: Some Exact Finite Sample Results, Journal of the American Statistical Association, LVIII (December 1963) 977–92.CrossRefGoogle Scholar

Copyright information

© Potluri Rao 1974

Authors and Affiliations

  • Potluri Rao
    • 1
  1. 1.University of WashingtonSeattleUSA

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