One could make the argument that children whose parents enroll them in public charters are fundamentally different from those whose parents enroll them in their local TPS. Those differences, they argue, could explain the funding inequities and the different returns on investments across sectors. Perhaps the children of parents choosing charter schools would end up with larger lifetime earnings on average no matter which type of school they were enrolled in. Further, TPS enroll more special needs children than charters, on average, and this may explain the bulk of the funding disparities and may negatively impact their average standardized test scores for TPS.[*] This is a plausible theory and we conducted a linear regression analysis that controls for average student demographics, including special education status, at the city level. The regression equation used is:

Υι = β0 + β1Charterι + β2Femaleι + β3ELLι + β4SPEDι
+ β5Disadvantagedι + β6Minorityι = ει

Where Y is the outcome of interest for a given city and sector, i. The outcomes we examine are per-pupil expenditures, cost effectiveness and ROI for each city. The coefficient of interest, β1, shows the average differences in charter school funding, cost effectiveness and ROI relative to TPS after controlling for these student demographic factors.

We gather city-level controls for each sector using the 2014-15 “Student Count” data file from the website.[18] We control for the percent of female students, percent of English language learners, percent of students requiring special services, percent of economically disadvantaged students and the percent of minority students in each city and sector.

[*] It is important to note that the Michigan Department of Education allows schools to use a wide variety of appropriate tools, supports and accommodations to administer the state's standardized assessments to students with recognized learning disabilities. For more information, see: “M-STEP, MI-Access, SAT, ACT WorkKeys and WIDA Student Supports and Accommodations Table” (Michigan Department of Education, Feb. 13, 2017),