Entropy based solutions for detecting and treating multicollinearity in econometrics

Multicollinearity significantly compromises the reliability of econometric estimations by inflating standard errors and distorting inferential conclusions, often forcing a trade-off between model interpretability and statistical robustness. This paper introduces a novel entropy-based framework for both the detection and treatment of multicollinearity, addressing limitations of conventional methods like the Variance Inflation Factor (VIF), ridge regression, and principal component regression (PCR). We define the Entropy-Based Multicollinearity Index (EMI) as a diagnostic tool, capable of identifying both linear and non-linear dependencies by quantifying the discrepancy between aggregate marginal entropy and joint entropy. For treatment, we propose Entropy-Guided Variable Reconstruction (EGVR), a method that leverages mutual information to transform the regressor matrix, maximizing information preservation while effectively eliminating multicollinearity. Extensive Monte Carlo simulations demonstrate that EGVR consistently outperforms Ordinary Least Squares (OLS), ridge regression, and PCR in reducing Mean Squared Error (MSE) and stabilizing estimates. Furthermore, an empirical application to a real-world wage regression dataset shows EMI's superior ability to detect hidden collinearities missed by VIF, and EGVR's success in improving model fit while maintaining interpretability. This framework offers a significant advancement in econometric modeling by providing robust, interpretable solutions to the pervasive problem of multicollinearity.