The Quantity and Quality of Teachers: Dynamics of the Trade-Off

Abstract

The paper addresses the two-fold rise in teacher-student ratio in the American K-12 school system in the post-World War II period accompanied by the evidence of a decline in the relative quality of teachers. We develop a dynamic general equilibrium framework for analyzing the teacher quantity-quality trade-off and offer an explanation to the observed trends. Our OLG model features two stages of education: basic and advanced (college), the latter required of teachers. The cost of hiring teachers is influenced by the outside opportunities for college graduates in the production sector. We show that the latter factor strengthens in the process of endogenous growth and that it affects the optimal trade-off between quantity and quality of teachers such that the number of teachers hired will grow over time while their relative, but not the absolute, human capital attainment will fall. This is accompanied by increasing inequality, among the group of college educated workers in particular. We show that this effect, which we call the rising talent premium, applies whether teacher salaries are determined based on merit pay or, alternatively, by collective bargaining. Moreover, the salary compression characterizing the collective bargaining regime has an additional effect exacerbating the loss of the more talented workers by the teaching profession. Further, we analyze a comparative dynamics effect of exogenous skill-biased technological change which raises the college premium. We show that the effect is detrimental to the aggregate quality of teachers and to the quality of basic education. An important insight from this analysis is that in the process of human capital driven economic growth the rise in premium for high ability outpaces that for the average, whereby this effect is accelerated by technological change. This puts a downward pressure on the “real” quality of education inputs and therefore can create a negative feedback effect on human capital development as a factor of economic growth.