I. Empirical framework
The starting point for our analysis is the observation that education is a cumulative
process. In the context of a very simple model in which the only component of education
that matters is teacher quality and in which all other determinants of achievement such as
student background, ability, and motivation are set aside, we can write
Ait = f(TQit, TQi t-1,….) + error
where A refers to student achievement and TQ refers to teacher quality. This equation
expresses student i’s achievement in year t as a function of the q