In this article, we are interested in the statistical methods that can be used to test for the wage differential between local workers and cross-border commuters at the low end of the pay scale. This article uses numerical simulations and recently developed tests for Cumulative Distribution Function (CDF) crossing. The present study applies the model to data for Geneva. Numerical simulations suggest that recently developed tests for distribution crossing are powerful, even when the two distributions studied are fairly similar and that these tests can be usefully combined with more typical quantile tests to characterize the wages of unskilled workers at the bottom of the income distribution. Although the present analyses demonstrated no obvious cross point between native and cross-border wages, future studies should explore the extent to which volunteer samples are, in general, representative of the larger population of local workers.