Market concentration and the relative demand for college-educated labour

If large firms employ relatively more educated workers, will an increase in market concentration increase income inequality by raising the relative demand for skill? I use Swedish employer-employee data from 1997-2016 and find a strong correlation between firm size and the share of college-educated ('skilled') workers. An increase in a sector's market concentration is correlated with a higher skilled wage premium and higher relative employment of skilled workers. This is due mainly to the reallocation of workers across firms. I demonstrate how these findings can be explained by a model of heterogeneous firms where productivity and skill intensity are positively correlated.