Competition in Public School Districts: Charter School Entry, Student Sorting, and School Input Determination

I develop a model of competition between charter schools and traditional public schools and estimate the model using administrative data from North Carolina. The model allows peers to affect the production of student achievement. I use the model to quantify how existing charter schools have affected test scores for both charter and public school students and to simulate how lifting binding caps on charters would affect charter school entry and student test scores. The structural model renders a comprehensive and internally consistent picture of treatment effects, and highlights heterogeneity that studies based on subsets of schools or students may not be able to recover. In particular, I find that i) contextual peer effects are large at public schools but do not significantly affect test scores for students at charters, ii) the mean effect of charter schools on attendant students (direct effect) is 11% of a standard deviation, iii) there is substantial heterogeneity in the mean direct effect by market, including many markets where the mean direct effect is negative, iv) the mean spillover effect on public school students is positive, but marginal, v) lifting caps on charter schools would more than double entry and cause much smaller increases in mean test scores for attendant students.