Countries that have relatively fewer workers with a secondary education have smaller firms. The shortage of skilled workers limits the growth of more productive firms. Two factors influence the availability of skilled workers: i) the education level of the workforce and ii) large public sectors that predominantly hire individuals with a better education. We set up a model economy with a government and private firm formation where production requires unskilled and skilled jobs. Workers with a secondary education are pivotal as they can perform both types of jobs. We find that level of education and public sector employment account for 40-45% of the differences between the United States and Mexico in terms of average firm size, GDP per capita, and GDP per hour worked. We also show that the impact of public employment on skill premiums and productivity measures depends on the skill bias in public hiring.