The abstract of a new NBER paper:

The province of Ontario has two publicly funded school systems: secular schools (known as public schools) that are open to all students, and separate schools that are open to children with Catholic backgrounds. The systems are administered independently and receive equal funding per student. In this paper we use detailed school and student-level data to assess whether competition between the systems leads to improved efficiency. Building on a simple model of school choice, we argue that incentives for effort will be greater in areas where there are more Catholic families, and where these families are less committed to a particular system. To measure the local determinants of cross-system competition we study the effects of school openings on enrollment growth at nearby elementary schools. We find significant cross-system responses to school openings, with a magnitude that is proportional to the fraction of Catholics in the area, and is higher in more rapidly growing areas. We then test whether schools that face greater cross-system competition have higher productivity, as measured by test score gains between 3rd and 6th grade. We estimate a statistically significant but modest-sized impact of potential competition on the growth rate of student achievement. The estimates suggest that extending competition to all students would raise average test scores in 6th grade by 6-8% of a standard deviation.