Education Secretary Betsy DeVos is pushing to expand school-choice programs, including private-school vouchers. (Andrew Harnik/Associated Press)

Students who received publicly funded vouchers in Indiana and Louisiana appeared to lose significant academic ground in the first two years after switching to private schools but then caught up to their public-school counterparts in subsequent years, according to two studies made public Monday.

The studies do not show that vouchers led to significantly stronger math and reading performance overall, even as President Trump and Education Secretary Betsy DeVos promise to pour billions of dollars into expanding vouchers nationwide.

Vouchers are direct government payments that families use as scholarships to attend private schools, and they are bitterly contested.

Both sides could claim a measure of validation from the new research: advocates of school choice who say it isn’t fair to judge voucher programs based on test results from a student’s first year in private school, and critics who say vouchers drain funding from public schools without improving achievement.

Douglas Harris, a Tulane University professor of economics and director of the Education Research Alliance for New Orleans, which released the Louisiana study, said the new research underlines that the immediate effects of big education policy changes are likely to change over time.

“But the experience in Louisiana has to give pause to anyone pushing broad federal or statewide programs,” he said, adding that there are no examples of any statewide program producing overall positive academic results.

Louisiana’s program is meant for children from low- and moderate-income families who attend low-performing public schools. Started as a pilot program in 2008, it expanded statewide in 2012 and now helps more than 7,000 students pay for private education.

Previous studies found that students in the Louisiana Scholarship Program performed significantly worse on math and reading tests than their public-school counterparts in the first year after receiving a voucher. Their performance also was weaker in the second year, although less so.

But by their third year in the voucher program, students were performing no differently from their peers in math and reading, according to the new research conducted by professors Jonathan Mills and Patrick Wolf of the University of Arkansas and released Monday by the Education Research Alliance for New Orleans.

The study examined the performance of a small subset of voucher recipients: those who were in grades three through five in 2012 and whose first-choice schools had fewer open seats than applicants. Students who won lottery admission to those schools were tracked over time and compared to those who did not.

The researchers acknowledge that because of that methodology, their findings may make the voucher program look better than it actually is, because they examined student performance only at schools that are strong enough to attract many applicants.

They also cautioned that their results apply only to the narrow band of students they studied and not to students who applied to the voucher program at a younger age. Those students had no test-score record before applying and therefore couldn’t be as directly compared to public-school students, but they appeared to lose significant ground in math.

Nevertheless, the results heartened John White, Louisiana’s superintendent of education, who said improving performance over time shows that his state’s approach to vouchers is working.

“We don’t take this study as evidence that vouchers work or don’t work,” White said. “We take it as a promising sign that the way that Louisiana has chosen to regulate private school choice can really work.”

Louisiana’s voucher program is one of the most highly regulated in the country. Unlike in most other programs, participating private schools may not exercise selective admissions. They must agree to administer state standardized tests to voucher students, and schools with weak test scores may not enroll more voucher students.

Free-market purists on the political right had argued that Louisiana’s rules discouraged many strong private schools from taking part in the state’s voucher program, leading to weak academic results early on. White said he thinks the new results show the opposite: When schools face consequences for failure, it pushes them to improve.

Researchers wrote that they could not say how much the threat of sanctions contributed to the improvement over time, but that they thought other factors played a larger role. Three years gave students time to adjust to their new schools, for example, and gave private schools time to adjust to preparing for standardized tests that had long been used to measure achievement in public schools.

Indiana’s voucher program is, like Louisiana’s, relatively heavily regulated. But it is far larger, helping more than 34,000 students pay private-school tuition in the 2016-2017 school year.

Initially meant to help poor children escape lower-performing public schools, its eligibility criteria later expanded to include middle-class children and those who have never attended public schools, leading to criticism that taxpayers are subsidizing tuition for families that would have chosen private schools anyway.

R. Joseph Waddington of the University of Kentucky and Mark Berends of the University of Notre Dame chose to focus on only those students who used the vouchers to transfer from public to private school, comparing them to students with similar characteristics who remained in public school.

The researchers, whose study has not yet been released in an academic journal, examined students who were in grades three through eight, and therefore required to take standardized math and reading tests, between 2011 and 2012, the first year of the program, and 2014 and 2015.

On average, voucher recipients’ math performance declined compared with that of their public-school counterparts, while there was no difference between the two groups in reading.

As in Louisiana, voucher recipients’ achievement changed significantly over time: They underperformed public-school students in math during their first two years in private school, according to the study, but then improved, with no dis­cern­ible difference between the two groups by the fourth year. Losses in reading were erased by the third year, and voucher students even appeared to surpass their public-school peers in the fourth year.

But many students returned to public school before they reached years three and four, and researchers wrote that the improvement in later years among voucher recipients could be because the weakest students were no longer counted among them. Those students who returned to public school experienced what the researchers described as “modest-to-substantial achievement losses during their time in private schools.”