Modified Ridge Parameters for Seemingly Unrelated Regression Model

Abstract

In this article, we modify a number of new biased estimators of seemingly unrelated regression (SUR) parameters which are developed by Alkhamisi and Shukur (2008), AS, when the explanatory variables are affected by multicollinearity. Nine estimators of the ridge parameters have been modified and compared in terms of the trace mean squared error (TMSE) and (PR) criterion. The results from this extended study are the also compared with those founded by AS. A simulation study has been conducted to compare the performance of the modified estimators of the ridge parameters. The results showed that under certain conditions the performance of the multivariate ridge regression estimators based on SUR ridge R _MSmax is superior to other estimators in terms of TMSE and PR criterion. In large samples and when the collinearity between the explanatory variables is not high, the unbiased SUR, estimator produces a smaller TMSEs.

Keywords:

• Modified SUR ridge regression
• Monte Carlo simulations
• Multicollinearity
• TMSE

Mathematics Subject Classification:

• 62J07

Notes

X represents the exogenous variables excluding the constant term and E represents the matrix consisting merely of ones.