Nonrandom Classroom Assignment Analysis

There is considerable anecdotal evidence that the assignment process of students to teachers in many schools is far from “random”. Many parents have had the experience of requesting a preferred teacher for their child. In many schools, teachers confer to decide on classroom assignments for the incoming students; in others, the decision is made by the principal (in both cases with input from parents). The process rarely appears on its face to resemble simple random assignment. Moreover, there are numerous reasons why it may be of interest to systematically sort weaker and stronger students to different classes. First, it may be helpful in allowing teachers to target their lessons (Duflo et al. (2011)). Allocating certain teachers to the lower-level

Assignment of students to schools is clearly not random, and represents another source of potential bias in value-added scores, but is not considered here. (Clotfelter et al. (2006)) I define two kinds of nonrandom classroom assignment practices, tracking and matching, that have often been lumped together in past work but that have different implications for value-added analysis. A school tracks if it assigns students to classrooms on the basis of prior test scores (or other characteristics correlated with them). A school matches if the same teachers tend to get the high-prior-score classrooms year after

At another 45%, classroom assignments appear to be purely random. As for other observables, I find that almost all schools balance their classrooms by gender, and probably due to desegregation efforts, little (though nonzero) sorting exists by race.

In a follow-up descriptive analysis, I show that larger schools, schools with and more heterogeneous student populations in terms of achievement and free- and reduced price lunch status, and higher teacher turnover are more likely to engage in tracking & matching. School district effects explain about 30% of the variation in school-level assignment policies, mainly due to the district-level socioeconomic environment.

This paper closely relates to three recent papers. Clotfelter et al. (2006) examine heterogeneity in school matching practices as they relate to teachers' observable characteristics. Kalogrides et al. (2013) estimate correlations between teacher observables and students' lagged scores, within school-grade-year cells. Both papers find evidence for some sorts of matching. Dieterle et al. (2013) distinguish between tracking and matching, as I do, and investigate the sensitivity of different value-added model specifications to these types of nonrandom classroom