Evaluating Shrinkage Regression Techniques: a Comparative Analysis of Lasso, Ridge, Elastic Net and Best Subset Models in Forecasting Macroeconomic Variables

Student: Khadijat Idowu Adebeshin (Project, 2025)
Department of Mathematics and Statistics
Federal Polytechnic, Ilaro, Ogun State

Abstract

This study compares the performance of four regression models; Lasso, Ridge, Elastic Net, and Best Subset Model in forecasting macroeconomic variables, focusing on predictive accuracy, model stability, and generalizability. The evaluation metrics adopted include Mean Squared Error (MSE), R-Squared, Adjusted R-Squared, and Leave-One-Out Cross-
Validation (LOOCV) MSE. Lasso, known for feature selection, showed moderate accuracy with an MSE of 0.0347 and LOOCV MSE of 0.0039, but had low R-Squared due to excessive shrinkage. Ridge regression effectively managed multi-collinearity, achieving an MSE of
0.0034 and LOOCV MSE of 0.0037, showing consistent performance. Elastic Net balanced feature selection and multi-collinearity with an MSE of 0.0153 and LOOCV MSE of 0.0032.
The Best Subset Model excelled with the lowest MSE (0.0009888) and LOOCV MSE (0.0016), offering superior accuracy and stability. Therefore, the Best Subset Model emerged as the most reliable for forecasting, providing an optimal balance between model complexity and interpretability.

Keywords
evaluating shrinkage regression techniques comparative analysis lasso ridge elastic subset
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