Competition in public school districts: Charter school entry, student sorting, and school input

I develop and estimate an equilibrium model of charter school entry, student sorting, and endogenous school inputs in public school markets using administrative student- and school-level data from North Carolina for 1998–2001. In the model, students differ by ability, and both charter and public schools make input decisions to test score production functions to affect the ability distribution of attendant students. The model successfully fits key endogenous outcomes as observed in the data: (1) charter schools enter larger markets and markets where they would have higher per-pupil resources, (2) charter schools and public schools in markets in which charter schools are present both choose higher input levels than public schools in markets where there are no charters, and (3) charter schools have the highest average test scores, followed by public schools in markets with charter school competition, followed by public schools in monopoly markets. I use the estimated model to simulate changes in the test score distribution for three counterfactual scenarios: (1) ban charter schools, (2) lift the currently binding statewide cap on the number of charter schools, and (3) equate charter and public school per-pupil resources. In the first and second counterfactuals, charter school entry increases test scores for students who would attend charters by one fifth of a standard deviation. Test scores for public school students in markets with charter schools increase marginally. Equating charter and public school capital triples the fraction of markets with charters and increases the test scores of students attending charters over the monopoly outcome by an even larger amount