The quantity and quality of teachers: a dynamic trade-off

We study the dynamics of the quantity and quality of teachers in the framework of dynamic general equilibrium OLG model. The quantity and quality are jointly set by a government agency wishing to maximize the quality of basic education per student while being bound by teachers' collective bargaining agreement which equalizes teacher pay. Our model features two stages of education: basic and advanced (college), the latter being required of teachers. The cost of hiring teachers is influenced by the outside opportunities that college educated individuals have in the production sector. We show that this factor strengthens in the process of endogenous growth and moreover that it pushes the optimal trade-off between quantity and quality of teachers in the direction of the former. Namely, the number of teachers hired will grow over time while their relative quality (but not the absolute human capital attainment) will fall. This evolution of human capital accumulation is accompanied by increasing inequality, within the group of college educated workers in particular. Further, we consider the comparative dynamics effect of an exogenous skill biased technological change represented by a positive shock to productivity of the skilled workers, hence to the college premium. We show that this will exacerbate the negative trends in the quality of basic education in relation to GDP growth. Countering this trend would therefore require an increase in the share of GDP spent on basic education, assuming that the institutional setup of the school system remains unchanged.