Developing Ridge Parameters for SUR Model

Abstract

Abstract This paper proposes a number of procedures for developing new biased estimators of the seemingly unrelated regression (SUR) parameters, when the explanatory variables are affected by multicollinearity. Several ridge parameters are proposed and then compared in terms of the trace mean squared error (TMSE) and (PR) criteria. The PR criterion is the proportion of replication (out of 1,000) for which the SUR version of the generalized least squares (SGLS) estimator has a smaller TMSE than others. The study was performed using Monte Carlo simulations where the number of equations in the system, the number of observations, the correlation among equations, and the correlation between explanatory variables have been varied. For each model, we performed 1,000 replications. Our results show that under certain conditions some of the proposed SUR ridge parameters, (R Sgeom , R Skmed , R Sqarith , and R Sqmax ), performed well when compared, in terms of TMSE and PR criteria, with other proposed and popular existing ridge parameters. In large samples and when the collinearity between the explanatory variables is not high, the unbiased SUR estimator (SGLS), performed better than the other ridge parameters. Keywords: Biased estimatorsGeneralized least squaresMonte Carlo simulationsMulticollinearitySUR ridge regressionMathematics Subject Classification: 62J07 Acknowledgments The authors are grateful to the editor and the anonymous referee(s) for useful comments that improved an earlier draft of this article. Notes The PR values (in percentage) are placed in parentheses below the values of the corresponding estimators. The PR values (in percentage) are placed in parentheses below the values of the corresponding estimators. The PR values (in percentage) are placed in parentheses below the values of the corresponding estimators. The PR values (in percentage) are placed in parentheses below the values of the corresponding estimators. The PR values (in percentage) are placed in parentheses below the values of the corresponding estimators. The PR values (in percentage) are placed in parentheses below the values of the corresponding estimators. The PR values (in percentage) are placed in parentheses below the values of the corresponding estimators The PR values (in percentage) are placed in parentheses below the values of the corresponding estimators. The PR values (in percentage) are placed in parentheses below the values of the corresponding estimators. The PR values (in percentage) are placed in parentheses below the values of the corresponding estimators.