Chicago’s open enrollment high schools were the driving force behind a steady rise in graduation rates citywide over the past 15 years.

In fact, new findings by the University of Chicago’s Consortium on Chicago School Research say graduation rates at schools that have to accept anyone have just about caught up to publicly funded, privately managed charter schools.

But it took a blend of policies rather than any single fix to bring about gains in graduation rates, which have risen yearly since 2006.

The good graduation news comes as Chicago Public Schools faces the possibilities of steep financial cuts to classrooms or possibly not opening on time in September without outside financial help. And it’s surely a boost for neighborhood high schools that have sorely wanted for help to survive as they lose enrollment to competition.

“Notably, we find significant growth in graduation rates at neighborhood high schools. It does not seem this progress has come at the expense of student achievement; in fact, graduates are more qualified than in the past,” said Elaine Allensworth, the lead author of the study on high school graduation rates.

“They are passing more classes in ninth grade; earning more credits while taking more difficult classes in high school; more students are taking the ACT, and average ACT scores have increased by almost two points from 16.7 to 18.6,” Allensworth said.

Measuring groups of ninth-graders until they turned 19, they found that overall graduation rates improved from 52.4 percent in 1999 to more than 74.8 percent in 2014, according to “High School Graduation Rates Through Two Decades of District Change,” which the Sun-Times obtained ahead of its release later this week.

There were some glitches. The consortium says that even if all students identified as transfers were dropouts — as CPS admitted to miscoding last fall — rates overall still would have improved. Study authors wrote that 2014’s “true graduation rate is most likely around 73 percent” or as low as 71 percent.

And success did not come at the same time for all students, with the graduation rates improving first among white children, then Hispanic students, and finally African-Americans.

The road to improvement showed mixed results.

While the report acknowledged that charter and selective-enrollment schools attracted some top students, researchers noted that even as charter schools gained students “the gap in graduation rates between charter and neighborhood schools has diminished.”

Requiring more courses for high-schoolers gave students more ways to pass, but rates improved only slightly because students also had to take more challenging college prep courses, they wrote.

CPS’ chief of college and career success, Alan Mather, said “That points out when you hold high standards up and you put in the supports necessary, then kids rise to it.”

A longtime principal at Lindblom Math and Science Academy High School, a test-in school in Englewood, Mather also pointed to CPS’ use of real-time reports on how many classes students passed and what they needed to do to make up credits — so-called “on track rates.”

The consortium has held up these freshman on-track rates as a student’s single greatest predictor of graduation success, saying ninth-graders who show up to school every day and pass all their classes are four times more likely to graduate.

“That whole idea of putting the focus on it allowed us to put things in place to make things better,” Mather said. And principals bought in because “there is that issue, certainly, for lack of a better term, of neighborhood schools seeing that they needed this for survival. There was a lot of competition going on” for students.