Investigating the two parameter analysis of Lipovetsky for simultaneous systems

Abstract

Two stage least squares regression analysis is the most practical statistical technique that is used in the analysis of structural equations. This study demonstrates the utility of some biased estimation methods when there is inherent multicollinearity among exogenous variables of a simultaneous system. Two stage ridge estimator is one of the biased estimators encountered in this model. In the light of the two parameter ridge estimator of Lipovetsky and Conklin (Appl Stoch Mod Bus Ind 21:525–540, 2005) in linear regression model, we propose two stage two parameter ridge estimator in the simultaneous equations model. Due to the fact that Lipovetsky and Conklin’s two parameter ridge estimator is superior to the ridge and ordinary least squares estimators, we expect the superiority of our new two stage two parameter ridge estimator to the two stage ridge estimator and the two stage least squares estimator. This superiority is proved theoretically. A data analysis involved with Klein Model I is examined to illustrate the mastery of the two stage two parameter ridge estimator in the sense of mean square error. In addition, an extensive Monte Carlo experiment is conducted. It is recommended that investigators who develop simultaneous equations models may perform the new estimator to eliminate the effect of multicollinearity on parameter estimates.