Ridge regression in the context of a system of seemingly unrelated regression equations

Abstract

This paper discusses the use of Ridge Regression in the context of a system of Seemingly Unrelatged Regression Equations, when the explanatory variables are affected by multi-collineaarity.

The properties of Ridge Regression estimators are derived assuming the shrinkage parameters are nonstochastic. The optimal values of the parameters are found to be dependent on the unknown parameters of the model.

Some operational Ridge Regression estimators are proposed and then compared, in a Monte Carlo study, with an operational Generalized Least Squares estimator. It is found that the Ridge Regression estimators can outperform the Operational Generalized Least Squares estimator, when the data are multicollinear and the signal to noise ratio of the equations is not too large.

Keywords:

• Ridge regression
• seemingly unrelated regressions
• collinearity
• simulation