Recent research on statewide voucher programs in Louisiana and Indiana has found that public school students that received vouchers to attend private schools subsequently scored lower on reading and math tests compared to similar students that remained in public schools. The magnitudes of the negative impacts were large. These studies used rigorous research designs that allow for strong causal conclusions. And they showed that the results were not explained by the particular tests that were used or the possibility that students receiving vouchers transferred out of above-average public schools.I think it's worth adding that — where accountability has been lacking for charter schools, particularly on-line charters — the same kinds of results are being seen. Most charter schools are generally privately operated schools using public tax dollars. And some of them aren't very public in admissions. See New Orleans, where top charter schools have devised admissions processes aimed at further skimming the best cream of the student pool.
Another explanation is that our historical understanding of the superior performance of private schools is no longer accurate. Since the nineties, public schools have been under heavy pressure to improve test scores. Private schools were exempt from these accountability requirements. A recent study showed that public schools closed the score gap with private schools. That study did not look specifically at Louisiana and Indiana, but trends in scores on the National Assessment of Educational Progress for public school students in those states are similar to national trends.