In arguing that Pennsylvania’s method of funding public education is so inadequate and inequitable as to be unconstitutional, the school districts, statewide groups, and parents suing the state have cited an expert’s calculations that districts are underfunded by $4.6 billion.

That figure is based on a study that is inherently flawed, an expert witness for Republican legislative leaders said Wednesday.

Testifying before a Commonwealth Court judge in Harrisburg, Eric Hanushek, a fellow at the Hoover Institution at Stanford University, said that the study commissioned by Pennsylvania lawmakers more than a decade ago was not a “reliable or trustworthy guide” and that he didn’t believe any studies trying to calculate what schools should be spending to achieve certain results were adequately grounded in evidence.

That’s in part because the relationship between school spending and student achievement is “currently unknown,” Hanushek said. “We have no empirical basis that allows us to take a given goal for achievement and translate that into some required dollar amount.”

Hanushek was the final witness called by Senate President Pro Tempore Jake Corman and House Speaker Bryan Cutler after 2½ weeks of defense testimony in the landmark trial, which began in mid-November. Hanushek is expected to finish testifying Thursday, and petitioners will be able to call rebuttal witnesses next week.

On cross-examination, Hanushek acknowledged that some studies have found that increases in school funding have improved student achievement — a case made by expert witnesses for petitioners who testified earlier in the trial that a growing body of research, using newer methods of tracking and comparing large numbers of students and their outcomes, has reached that conclusion.

“I believe that money can matter. It probably at times matters. The problem is that we don’t know when it’s going to matter,” Hanushek said. He said he’s held the position since the early 1980s that evidence is insufficient to show that more funding boosts achievement.

Hanushek wasn’t questioned by GOP lawyers about how he arrived at that position, but rather, how it colored his view of the study conducted by consultants for the Pennsylvania legislature, which produced spending targets for every district. The targets were adopted by the state in 2008 but abandoned amid the Great Recession a few years later, though the law requiring them wasn’t repealed.

That analysis — and similar “costing-out” studies — used problematic approaches, Hanushek said.

For instance, looking to successful school districts and what they spend as a model to help determine how others should be funded assumes that money is the reason for the district’s achievement, Hanushek said: “They choose a set of schools that are doing well without knowing why they’re doing well.”

He also took issue with the goals of the Pennsylvania study, which attempted to calculate the cost of achieving 100% proficiency in student reading and math — a target that was set by the federal No Child Left Behind law but that Hanushek called unrealistic.

The study formed the basis for part of a Pennsylvania State University professor’s expert opinion that Pennsylvania schools were underfunded by $4.6 billion. The professor, Matthew Kelly, said he updated the calculations using current data and found that not only were most districts not meeting the spending targets but also that the state’s poorest districts — which are disadvantaged by an education funding system that relies heavily on local taxes, petitioners argue — were owed the most.

Many states, including bipartisan legislatures, have commissioned costing-out studies to attempt to calculate what resources schools require — and courts have cited those studies when reaching decisions in school-funding lawsuits, Maura McInerney, a lawyer with the Education Law Center, noted while cross-examining Hanushek. Hanushek maintained that the studies provided “bad information.”

He agreed that disadvantaged students require additional funding but said that “every state in the nation already does that.” While Pennsylvania has a formula directing added money to districts based on the number of students living in poverty or learning English, among other factors, it currently doesn’t apply to most of the state aid going to schools.