In high-dimensional datasets, it is a subject of investigation whether robust regression methods have high prediction and variable selection performance when vertical outliers and leverage points change from light-tailed errors to heavy-tailed errors. In this paper, we study the performance of six types of high-dimensional robust regression models (LAD-Lasso, Q-Lasso applied at the 0.25 and 0.75 quantile levels, Huber-Lasso, MTE-Lasso, RLARS, and Sparse-LTS) by creating both uncontaminated and contaminated control groups with different distributions of error terms. The methods are validated by comparing the estimation metrics at different scenarios through object-oriented simulations. Additionally, in this study, real data sets are examined and the performance of robust regression methods is evaluated to select the factors determining the CO2 emissions per capita of OECD countries under the EKC (Environmental Kuznets Curve) hypothesis. The results prove that, although simulations show that different methods perform well on different datasets with different contaminations, Spars LTS is superior to other methods. In addition, sparse LTS also performs better in terms of variable selection and prediction success in real OECD dataset with outliers and leverage points.