The public sector hires disproportionately more educated workers. To rationalize this finding, we propose a model with a perfectly competitive private sector, and non-Walrasian public sector. Our economy also features heterogeneity across individuals and jobs, and a simple sorting mechanism that generates underemployment - educated workers performing unskilled jobs. We find that the public-sector wage differential and excess underemployment account for 15 percent of the education bias, with the remaining accounted for by technology. In a counterintuitive fashion, we find that more compressed wages in the public sector raise inequality in the private sector.