The logic underlying how school choice programs can bring about district-wide improvement relies on the idea that choice will spur competition as students migrate to better performing schools. While much empirical research in choice estimates the performance consequences that emerge from this process (such as the association between market concentration and student achievement, or the treatment effect of attending a choice school), much less work quantitatively analyzes the student migration patterns that are the precursor to potential improvements. In this paper, we directly examine the extent to which student flows in one of the largest public choice systems in the country match the ones required to bring about competition.

The data come from 9 cohorts of 8th grade students in the Chicago Public Schools from 1995-2004, and include student-level standardized test scores, the high school to which the student was assigned, and the high school in which the student actually enrolled. We use this data to create a network of student flows between schools for any given year y, where each school i is connected to school j by an arc if there are students that were assigned to i but instead enrolled in j. 

To characterize the extent to which students move from low to high performing schools in this network, we define a new measure -- school achievement differential (SAD). For each student, SAD is defined as the difference between the mean Prairie State Achievement Examination (PSAE) of their attended school j and their assigned school i. We then calculate the mean SAD:  1) over all students in the district who did not enroll in their assigned school, 2) disaggregated by the 8^thgrade achievement of the students, and 3) disaggregated by emergent “sub-districts” within CPS, as defined by a custom algorithm that groups together schools with similar student sending and receiving patterns in the network. In all cases, a positive mean SAD implies a movement consistent with the movement required to spur competition; a zero or negative mean SAD, the opposite.  Note that while our approach enables us to characterize a logical precursor to competition – directed student flows – an important limitation is that we cannot determine whether those flows actually resulted in competitive school responses.

We find that the SAD for the entire district is 14.12 points (p < 0.0001), implying students flow from lower to higher achieving schools. However, we also find significant differences between the flows of high and low achievers. The difference in mean SAD between the highest achievement quartile of 8^th grades test scores, and an equivalent number of moving students from lowest end of the 8^th grade test score distribution is 20.36 (p < 0.0001); and low achievers are much more likely to stay within their existing sub-district (55.52%), when compared to high achievers (34.63%). From a policy perspective, our results are consistent with the idea that student mobility can spur competition beneficial to all in the district district, but the differences in mobility across subgroups may potentially widen existing achievement gaps.