Effect of Multicollinearity on Power Rates of the Ordinary Least Squares Estimators

Kayode Ayinde,O.O Alabi,T.O Olatayo

doi:10.3844/jmssp.2008.75.80

Abstract

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.

Highlights

In classical linear regression model, regressors are assumed to be independent
Multicollinearity is found in business and economics
Interpretation given to the regression coefficients may no longer be valid because the assumption under which the regression model is built has been violated[4]

Summary

Introduction

In classical linear regression model, regressors are assumed to be independent. When this assumption fails, the problem of multicollinearity arises. The estimates of the regression coefficients provided by the OLS estimator is still unbiased as long as multicollinearity is not perfect[5], the regression coefficients may have large sampling errors which affect both the inference and forecasting that is based on the model[4]. Pointed out that multicollinearity is less serious when attention is on prediction or forecasting of values for the dependent variable than when interest is on estimates of the parameters of the model. With high standard errors of the regression coefficients, the value of the t-statistic of each of the regression coefficients is low causing the null hypothesis to be often accepted. With generated collinear data, this paper attempts to investigate the power rate (1-β) of the OLS estimators at different levels of multicollinearity and sample size through Monte Carlo studies

Methods

Results

Conclusion