Some methods and solutions for estimating multiple regression model under ill conditioned and ill-posed problem

This study examines alternative methods to enhance the estimation performance of multiple regression models under ill-conditioned and ill-posed problems. The Classical Linear Regression Model (CLRM) often leads to instability in parameter estimates, especially in the presence of multicollinearity or insufficient observations. The study elaborates on the theoretical foundations of methods such as Ridge Regression and Generalized Maximum Entropy (GME) and evaluates their comparative performance through applied analyses. Applications based on agricultural input-output data and Gross Domestic Product (GDP) data from the United States from Ramanathan (1992) demonstrate that Ridge Regression improves stability through its penalty parameter, while GME outperforms in handling ill-posed problem. Consequently, both methods provide reliable and consistent alternatives to classical estimation techniques. This study contributes to the literature by offering solutions to improve estimation performance in econometric modeling. Keywords: Ill-conditioned, ill-posed, Ridge regression, Generalized maximum entropy, regression estimation.