The gap in the middle: Luxembourg attracts low and high-skilled cross-border workers

We analyze the association between the probability of becoming a cross-border worker and a large set of predictors. In our data, we observe the yearly transitions to a cross-border job for individuals who, at the end of a given year, do not work in Luxembourg and live in Belgium. We rely on Belgian administrative data, namely the Belgian Crossroads Bank for Social Security, and analyze 142,765 yearly observations of Belgian residents living near the border with Luxembourg. To find the most important predictors of the transition to a cross-border job, we rely on supervised machine learning methods, such as the random forests algorithm. Our results show a U-shaped selection along with the past daily wages, level of education and household income, which suggests that Luxembourg attracts a highly polarized distribution of skills.