Effects of non-orthogonality on the efficiency of seemingly unrelated regression (SUR) models

by W. B. Yahya, S. B. Adebayo, E. T. Jolayemi, B. A. Oyejola and O. O. M. Sanni.

Abstract: This work examines the relative gain/loss in efficiency of Seemingly Unrelated Regression (SUR) estimators when one or more pair of the predictors in the system of equations are correlated (non-orthogonal). Literature has revealed that multicollinearity often affects the efficiency of SUR estimators. This paper, however, addresses such challenges by determining the ‘Tolerable Non-orthogonal Correlation Points’ (TNCP) among the predictors at which the efficiency of SUR estimators will still be preserved. Results from our simulation studies showed that SUR estimators are still efficient within the range of the TNCP values. By this result, the strict condition of purely uncorrelated covariates often advanced in the literature as a criteria for achieving efficient SUR estimators are relaxed up to the TNCP values proposed in this work. Comparisons of the SUR estimators with that of the equation-by-equation from the ordinary least squares (OLS) are also taken up to assess their respective performances in the presence of non-orthogonal explanatory variables. In all cases considered, SUR estimators are consistently more efficient than the OLS.

Key Words: Average Mean Square Error (AMSE), Contemporaneous correlation, Feasible Generalized Least Squares, Multicollinearity, Tolerable Non-orthogonal Correlation Point (TNCP), SUR

Waheed Babatunde Yahya, wb_yahya@daad-alumni.de
Samson Babatunde Adebayo
Emanuel Teju Jolayem
Benjamin Agboola Oyejola
Olusola Oladele Mohammed Sanni

Editor: Meintanis, Simos G.,simosmei@econ.uoa.gr

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