EFFECT OF MULTICOLLINEARITY ON HETEROSCEDASTICITY CORRECTION MEASURES FOR PARAMETER ESTIMATION OF LINEAR REGRESSION MODEL

Abstract

Weighted Least Square (WLS) regression estimator (using various Heteroscedasticity Correction Measures (HCMs) to generate weights) have been identified to be more efficient than the Ordinary Least Square (OLS) estimator in the presence of heteroscedasticity. Nonetheless, much is left to be known about the effect of multicollinearity on these HCMs when using the Weighted Least Square estimator. This study was aimed at understanding the effect of multicollinearity on measures of heteroscedasticity correction in the presence of heteroscedasticity for parameter estimation of a linear regression model. In this study, the concept of using different functional forms of residuals, unique regressor combinations and non-parametric estimator (kernel regression) in the auxiliary regression model resulted in the proposition of 123 HCMs. Three (3) residual functional forms were adopted for use in this study (i.e. residual squares, absolute residuals and log of residual squares) while One residual functional form was proposed, namely log of absolute residuals. Investigation of the proposed and existing HCMs was done using ten (10) heteroscedasticity structures. The simulation study was done using a Monte Carlo experiment with a multiple linear regression of three (3) explanatory variables. This experiment was conducted with 1000 replications using the following linear model parameters: 𝛽0 = 4, 𝛽1 = 0.4, 𝛽2 = 1.5 and 𝛽3 = 3.6, at several levels of multicollinearity (i.e. 𝜌 = 0.8, 0.9, 0.95, 0.99 and 0.999) and sample sizes (n= 15, 20, 30, 40, 50, 100 and 250) while adopting the procedure used by McDonald and Galarneau (1975), Wichern and Churchill (1978), Gibbons (1981), Kibria (2003), and Lukman and Ayinde (2015) to generate the explanatory variables. The HCMs were compared using Mean Square Error (MSE) criterion. The major finding of this study shows that different levels of multicollinearity have varying effects on HCMs. Nonetheless, HCM fits obtained from using the kernel approach appears to consistently produce highest counts of minimum MSE amongst various other HCMs considered in this study irrespective of the degree of multicollinearity present in the model. It was also observed that the results obtained from using log of absolute residual and log of residual square as dependent variables in the auxiliary regression of various HCMs are exactly the same. This study also reveals that HCM by real weight produces the most efficient parameter estimates only in the absence of severe multicollinearity problem. Several highly performing HCMs have been identified and recommended for use, to obtain efficient parameter estimates in a linear regression model in the presence of heteroscedasticity when the real weight is unknown.