Ridge and Liu-Type Estimators for Tobit SUR Model: Application to Air pollution Data

Abstract

This study extends the seemingly unrelated regression (SUR) model through introducing the ridge (RTSUR) and Liu-Type (LTSUR) estimators as biased estimation techniques to address the problem of multicollinearity in the SUR Tobit (SURT) model. This study theoretically evaluates the superiority of the proposed estimators based on the mean square error (MSE) criterion. The results for the theoretically study showing that, the Liu-Type estimator outperforms other estimators under many conditions. A simulation study was conducted to compare the estimators under various factors. The results of simulation show that, the maximum likelihood (MLE) estimator is the worst estimator at all factors and the LTSUR and RTSUR estimators perform better at high levels of multicollinearity and censoring. The LTSUR still achieved a significant superiority over the RTSUR. In addition, when the number of observations in the equations increases, the performance of the LTSUR and RTSUR estimators improves. Moreover, the simulation mean squared errors (SMSE) values for LTSUR estimator converge as number of observation and censored level increase. To study the behavior of the proposed estimators on real data, we used weather data from Cairo city to examine their influence on pollution levels of carbon monoxide (CO), sulfur dioxide (SO2), and nitrogen dioxide (NO2). The results from the real data were consistent with the findings from the simulation study.