As a voucher program in Milwaukee has expanded, taking money and pupils out of public schools, the schools have responded by ramping up their own performance, a forthcoming study in the Journal of Public Economics argues.

The paper offers one of the most positive conclusions yet drawn in the heated debate over the effects of the 17-year-old Milwaukee program, which in 2007 sent more than 17,000 low-income Milwaukee students to private schools via publicly funded scholarships. It is the nation’s largest publicly funded voucher experiment, having grown from seven participating private schools in 1990 to 121 in 2007.

At issue is whether the program has appreciably helped the students who are given places in private schools, as well whether it has hurt the students who stay in public schools.

The soon-to-be-published paper, by a Harvard University-trained economist who is now at the New York Federal Reserve Bank, Rajashri Chakrabarti, answers the second question with a solid no. Ms. Chakrabarti argues that two major changes in the program pushed public schools to improve after 1999.

The first was a court ruling that allowed religious schools — which in Milwaukee are primarily Catholic and Lutheran — to join the voucher program, giving students many more options to choose from. The second was a funding change that raised the amount of money public schools lost when a student left the school via a voucher.

Ms. Chakrabarti’s analysis compares Milwaukee schools from which students left via vouchers to public schools outside the city with similar demographics that did not participate in the program. She found only small relative improvements in the Milwaukee schools’ reading, language arts, and math scores prior to the two changes, but describes “a different picture” after they took effect, with affected public schools showing bigger improvements. She also found improvements in science and social studies, which were not tested until the late 1990s.

A political science professor at the University of Wisconsin at Madison who has studied the Milwaukee program for years, John Witte, said any conclusion linking big effects directly to the rise of vouchers should be met with suspicion. Several factors make drawing a direct link to vouchers difficult, he said.

“Changes of superintendents, changes of school boards, changes of curriculum — the list of other things that could have an effect is as long as your arm,” Mr. Witte said.

His own recent study of the program, undertaken with a professor at Stanford University, Martin Carnoy, who has been critical of vouchers in the past, studied the effects of the vouchers alongside the effects of other alternatives to public school in Milwaukee, such as charter schools and a program that allows inner-city students to transfer to schools in the suburbs, Mr. Witte said.

According to that analysis, only charter schools spurred a competitive improvement in public schools, and that effect was small, Mr. Witte said.

Messrs. Carnoy and Witte have quibbled with previous positive voucher studies, including one by a Stanford economist, Caroline Hoxby, whose results Mr. Witte said he could not replicate in a follow-up study. In comments published on the Talking Points Memo Web site this summer, Mr. Carnoy, who did not respond to a request for comment yesterday, argued that evidence of positive effects from voucher programs is so sparse that future programs should be tabled.

But an education professor at the University of Arkansas, Jay Greene, praised Ms. Chakrabarti’s design, saying it appeared to control for outside variables carefully. He characterized previous studies by Ms. Chakrabarti as having been fair, drawing both favorable and unfavorable conclusions about vouchers.

“She does honestly call them as she sees them,” Mr. Greene said. Ms. Chakrabarti told The New York Sun that her paper’s policy indications are clear. Though the early version of the Milwaukee program “did not have much of a bite,” her paper argues, the changes in the late 1990s “led to significant improvement in performance of the treated public schools.”

“Design matters,” she said, summarizing her paper’s implications.