The variable selection is a challenging task in statistical analysis. In many real situations, a large number of potential predictors are available and a selection among them is recommended. For dealing with this problem, the automated procedures are the most commonly used methods, without taking into account their drawbacks and disadvantages. To overcome them, the shrinkage methods are a good alternative. Our aim is to investigate the performance of some variable selection methods, focusing on a statistical procedure suitable for the competing risks model. In this theoretical setting, the same variables might have different degrees of influence on the risks due to multiple causes and this has to be taken into account in the choice of the ”best” subset. The proposed procedure, based on shrinkage techniques, is evaluated by means of empirical analysis on a data-set of financial indicators computed from a sample of industrial firms annual reports.