Effect of Multicollinearity on Power Rates of the Ordinary Least Squares Estimators
O.O. Alabi, Kayode Ayinde and T.O. Olatayo
DOI : 10.3844/jmssp.2008.75.80
Journal of Mathematics and Statistics
Volume 4, Issue 2
Inferences on the parameter estimates of Ordinary Least Square (OLS) estimator in regression model when regressors exhibit multicollinearity is a problem in that large standard errors of the regression coefficients which cause low t-statistic value often result into the acceptance of the null hypothesis. This paper, therefore, makes efforts to investigate the effect of multicollinearity on the power rates of the OLS estimator. A regression model with constant term (β0) and two independent variables (with (β1 and (β2 as their respective regression coefficients) that exhibit multicollinearity was considered. A Monte Carlo study of 1000 trials was conducted at eight levels of multicollinearity (0, 0.25, 0.5, 0.7, 0.75, 0.8, 0.9 and 0.99) and sample sizes (10, 20, 40, 80, 100, 150, 250 and 500). At each specification, the true regression coefficients were set at unity while 1.5, 2.0 and 2.5 were taken as their hypothesized values. Results show that at each hypothesized value of β0 the power rate is the same at all the levels of multicollinearity at a specified sample size and that the error rate decreases asymptotically. Furthermore as the hypothesized value increases, results do not only show that the power rate increases but tends faster to one asymptotically. The pattern of effect of power rate of β1 and β2 is the same as that of β0 except that at each hypothesized value the power rate decreases as level of multicollinearity increases at a specified sample size. Consequently, increasing the sample size increase the power rate of the OLS estimator in all the levels of multicollinearity.
© 2008 O.O. Alabi, Kayode Ayinde and T.O. Olatayo. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.