One of the assumptions that should be provided to make parameter estimation with the Ordinary Least Squares (OLS) estimation method in the multiple linear regression model is that there is no relationship between independent variables. If this assumption is violated, the problem of “multicollinearity” arises. In this case, the parameter estimation values obtained from the OLS estimator deviates from the actual value of the parameter. A solution to avoid these negative consequences of multicollinearity is to use biased estimation methods. The most widely used of these estimation methods is the ridge regression estimator. The Liu estimator was then proposed as an alternative to the ridge regression estimator. Liu estimation methods have a single bias parameter. Numerous bias parameters have been proposed for biased estimators in the literature. Therefore, the selection of the optimum bias parameter is an important problem. In this study, in order to determine the optimum bias parameter for Ridge and Liu estimators, 20 popular bias parameters previously proposed in the literature were compared according to the Mean Square Error (MSE) and Variance Inflation Factor (VIF) criteria. For this, a simulation study was conducted using different dependency structures, different number of independent variables, different sample sizes and different standard errors. In the results obtained, it was observed that the parameter estimation values obtained using biased estimation methods had better MSE and VIF values than the parameter estimation values obtained with the OLS estimator. In addition, optimum bias parameter estimation values were determined for Ridge and Liu estimation methods.