For a large set of countries, we document how the labor earnings inequality varies with GDP per capita. As countries get richer, the mean-to-median ratio and the Gini coefficient decline. Yet, this decline masks divergent patterns: while inequality at the top of the earnings distribution falls, inequality at the bottom increases. We interpret these facts within a model economy with heterogeneous workers and firms, featuring industry dynamics, search and matching frictions, and skill accumulation of workers through learning-by-doing and on-the-job training. The benchmark economy is calibrated to the UK. We then study how the earnings distribution changes with distortions that penalize high-productivity firms and frictions that reduce match formation. Distortions and frictions reduce employment, average firm size, and GDP per capita. They also affect how much firms are willing to pay workers, how well high-skill workers are matched with high-productivity firms, and how much training workers receive. The model generates the observed cross-country relation between GDP per capita and earnings inequality, as well as a host of cross-country facts on firm size distribution, firms' training decisions, and workers' life-cycle and job tenure earnings profiles.