Regression Estimators under Joint Multicollinearity and Autocorrelation Conditions: The Two-Stage Kibria-Lukman Estimator as an Enhanced Approach

Abstract

Multicollinearity among predictors and autocorrelation in residuals present significant challenges to the reliability and accuracy of linear regression models. These issues cause traditional Ordinary Least Squares (OLS) estimators to yield inflated variances and biased parameter estimates, ultimately leading to unreliable statistical inferences. To address these limitations, various biased estimators have been developed. This paper investigates the performance of several such estimators, including the Ridge, Liu, Kibria-Lukman (KL), and the newly proposed Two-Stage Kibria-Lukman (Two-Stage KL) estimator. The Two-Stage KL estimator integrates the Prais-Winsten transformation, which corrects for autocorrelation, with the KL estimator’s biasing mechanism to reduce the inflated variances caused by multicollinearity. Using extensive Monte Carlo simulations, we evaluate the performance of these estimators in settings characterized by varying levels of multicollinearity (predictor correlation values, ρX , of 0.8, 0.9, and 0.99) and autocorrelation (residual autocorrelation values, ρ, of 0.6, 0.8, and 0.9), across sample sizes ranging from 25 to 500. The simulations reveal that OLS is highly sensitive to these conditions, with Mean Squared Error (MSE) values reaching as high as 738.6690 in extreme multicollinearity (ρX=0.99) and autocorrelation (ρ=0.9) at a sample size of 50. In contrast, the Two-Stage KL estimator consistently achieves the lowest MSE values, reducing the error to 265.3667 under the same conditions. For moderate multicollinearity (ρX=0.8) and autocorrelation (ρ=0.8), and a sample size of 50, OLS yields an MSE of 1.254, while the Two-Stage KL estimator reduces this to 0.764, outperforming both Ridge and Liu estimators, which record MSEs of 0.953 and 0.902, respectively. In empirical testing using the Portland cement dataset, which is known for its multicollinearity, the Two-Stage KL estimator provides the lowest MSE of 0.0486, compared to OLS (0.0638), Ridge (0.0581), Liu (0.0554), and KL (0.0522). These results demonstrate that the Two-Stage KL estimator effectively mitigates the effects of both multicollinearity and autocorrelation, offering a robust solution for regression models where these conditions co-occur. The integration of the Prais-Winsten transformation with the KL biasing approach allows the Two-Stage KL to maintain low error rates, even in high-dimensional and high-correlation settings.