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Author(s): Okeke Ngozi Christy, Olanrewaju Samuel Olayemi, Zubair Mohammed Anono.

Volume/Issue: Volume 9, Issue 2 (2026)

Page No: 1-10

Journal: African Journal of Mathematics and Statistics Studies (AJMSS)

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Abstract:

Multicollinearity, a situation where explanatory variables in a regression model are highly correlated, remains a fundamental challenge in statistical analysis, particularly when dealing with complex datasets. When multicollinearity occurs, it becomes difficult to isolate the individual effects of predictor variables, often leading to inflated standard errors, unstable parameter estimates, and reduced statistical power. Numerous authors have contributed significantly to the body of literature surrounding the detection, consequences, and mitigation of multicollinearity across various regression models, and in recent years, innovative approaches have emerged that aim to address this issue directly. This section provides an overview of these advancements, highlighting the progress made in linear regression modeling and emphasizing the need for similar innovations in the context of simultaneous equation models (SEMs). Another significant challenge in estimating Linear Regression Model is the presence of heteroscedasticity, where the variance of the error terms is not constant across observations (Chen & Wang, 2018). Heteroscedasticity violates one of the key assumptions of the OLS method, leading to inefficient and biased estimates of the regression parameters. To address this issue, heteroscedasticity-consistent estimators, such as Whites robust standard errors and the Generalized Method of Moments (GMM), have been developed (Pérez-Sánchez et al., 2021). These methods provide more reliable estimates in the presence of heteroscedasticity by accounting for the varying error variances. In SEMs, heteroscedasticity is particularly problematic because the error terms in different equations may have different variances, and these variances may be correlated with the explanatory variables. There is need to address this issue within SEMs framework

Keywords:

Simultaneous Equation Models, Multicollinearity, Heteroscedasticity, Elastic-net, GMM.

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