Among teachers unions and their allies, an article of faith is that vouchers to allow attendance at private schools do nothing for students. All the more reason to look at two new studies tracking student performance in two states with voucher programs—Indiana and Louisiana.

Start with Louisiana. Today 7,100 students—nearly 90% of them African American—attend private or religious schools of their parents’ choice thanks to a statewide program that includes vouchers for private schools. In February 2016, Jonathan Mills of Tulane...