1986 Volume 13 Issue 19 Pages 103-120
For the multiple linear regression problem, a number of alternative estimators to ordinary least squares (OLS) have been proposed for situations in which multicollinearity is present among the explanatory variables. Multicollinearity may have several adverse effects on estimated coefficients in a multiple regression analysis.
This paper investigates the relative efficiency of these 12 alternative estimators from the point of view of mean squared error (MSE) by the Monte Carlo simulation, and discusses the practical implication of the use of such estimators. The results of this study are that OLS, Ridges, BYS and ITR estimators are more efficient than the others, when multicollinearity is not present. However, when multicollinearity is present, Ridges, GRB, BYS, ITR and PCA estimators are more efficient than OLS for almost all values of σ. Ridges have uniformly smaller MSEs than OLS. Relative efficiencies of these estimators vary with the value of σ. In the interval of small σ, Ridges are more efficient than the others, but, for large σ, each of GRB, BYS, ITR, PCA and LAT is more efficient.
From our experiment in which these 12 estimators are applied to the economic data of France, we find that, while OLS has the negative coefficient, some of these alternative have positive appropriate values, where regression coefficient must have the positive sign from the point of view of Economics. Therefore, we can conclude that these alternative estimators are effective for the practical regression problem with multicollinearity.