Does class size matter? How, and at what cost?

Using Greek high quality administrative data we show that class size has a hump shaped effect on achievement whereas most of the literature assumes linearity. We then embed our estimates for this relationship in a dynamic structural model with costs of hiring and firing. We find that class sizes around 19 maximize the attainment, and the existing costs result in an average class size of 22-23 being chosen. Firing costs are about the same size as hiring costs consistent with the presence of unions. Reducing firing costs to zero raises class size by 4-6 students and reduces achievement by 0.8 to 1.2 GPA points. Reducing hiring costs to zero reduces class size by 3-5 students and increases GPA by 0.3 GPA points. Raising wages by 50%, class size increases by 2 students and GPA falls by 0.3 GPA points suggesting that unions (which raise salaries and firing costs) do raise class size, but have a small effect on achievement. We show that class size caps are costly, and more so for small schools, even when they are set at levels well above the average class size. (C) 2021 Elsevier B.V. All rights reserved.