We set up a search and matching model with a private and a public sector to understand the effects of employment and wage policies in the public sector on unemployment and education decisions. The effects on the educational composition of the labor force depend crucially on the structure of the labor market. An increase of skilled public-sector wages has a small positive impact on educational composition and larger negative impact on the private employment of skilled workers, if the two sectors are segmented. If there are movements across the two sectors, it has large positive impacts on education and on skilled private employment. We highlight the usefulness of the model for policymakers by calculating the value of public-sector job security for skilled and unskilled workers.