In empirical studies often the values of some variables for some observations are much larger or smaller than the values for the other observations in the sample. These extreme observations, or outliers, often have a large impact on the results of statistical analyses. Conclusions based on a sample with and without these units may differ drastically. While applied researchers are usually aware of this the detection of outliers and their appropriate treatment is often dealt with in a rather sloppy manner. One reason for this habit seems to be the lack of availability of appropriate canned programs for robust methods that can be used in the presence of outliers. Our paper intents to improve on this situation by presenting a highly robust method for estimation of the popular linear fixed effects panel data model and to supply Stata code for it. In an application from the field of the micro-econometrics of international firm activities we demonstrate that outliers can indeed drive results.