Aggregation of teachers within grades has different implications for the subsequent analyses. The initial variance decompositions focus on the amount of variation in student achievement that can be attributed to systematic differences of schools and teachers. For this, the aggregation across teachers in a grade leads to understating the systematic contribution of schools and teachers. The subsequent estimation of production functions is, however, affected quite differently. Average teacher characteristics by subject, grade and year are assigned to each student. Though students cannot be linked directly to their teachers (except in schools with one teacher per grade), this aggregation of regular classroom characteristics should not introduce any bias into the regression estimates. It will increase the standard errors by ignoring any systematic relationship between achievement and teacher characteristics within grades. On the other hand, it overcomes what is possibly the largest form of selection within schools-that which occurs when some parents maneuver their children toward specific, previously identified teachers. This within-grade teacher selection is circumvented by looking at overall grade differences, which is equivalent to an instrumental variable estimator based on grade rather than classroom assignment.
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The Importance of Schools and Teachers
What is the contribution of schools to student achievement? And, to what extent does any contribution represent factors common to a school building as opposed to specific teachers within the building? These questions are addressed by investigating the patterns of gains in student achievement within and across schools. We begin with a systematic decomposition of the variance of achievement gains and of correlations of school average gains across grades and time. The interpretation of these depends critically on the sources of underlying achievement variation including any nonrandom sorting of students and teachers across schools. While some past work has pursued portions of this, the limitations of previous data required the imposition of extremely strong assumptions to identify the various components of achievement gain. Separating the influences of schools, teachers, and families has been especially vexing – particularly when sorting by families and schools is acknowledged.