The authors said the findings should lead to a national discussion over restructuring school funding, and prompt governments to make the non-government sector abide by the same rules as public schools. "They have no obligations to serve a wide variety of students," said Mr Bonnor. Since the Gonski reforms, funding increases to private schools have outstripped those to public schools because the federal government, which provides most public funding to private schools, has met its targets faster than the states. States have a bigger cost because they are the majority funders of state schools, and there are two public schools for each private school. By 2017 differences in per-student funding had narrowed to $13,300 in the public system, $11,500 for Catholic school students and $9600 in the independent sector on average, according to the most recent data from the My School website. But the researchers argued those figures masked the fact that students in the public system were the most expensive to educate, because they had higher numbers of disadvantaged, Indigenous and disabled students. When the authors - who also included the former principal of St Paul's Grammar, academic Paul Kidson - compared per-student spending on schools with similar students, the gap became much narrower.

Among disadvantaged schools, the median amount of per-student taxpayer money spent on Catholic students was highest at $14,350, followed by $13,850 in the independent sector and $13,450 in the government system. When the researchers calculated the cost of funding all students at the same per-student cost of government students across all bands of disadvantage, they found the cost would be between $800 million and $1.1 billion. "Advocates for school systems need to keep up to date with the changing financial situation," Mr Bonnor said. "Because non government schools charge fees, they are de facto selective schools on a socio-educational basis. In equivalent countries overseas, that doesn't happen." Dr Wilson said there was increasing evidence that segregation eroded the quality of school systems. "Now is the time for a full, national discussion on this," she said. "There's a creeping awareness that across education we need some really bold reform. "And these school funding arrangements would have to be central to how that would occur."

The chief executive of the Association of Independent Schools NSW, Geoff Newcombe, said one in three students attended private schools, and parents paid a third of the recurrent cost and 90 per cent of building costs. "It is clear parents enrolling their children in non-government schools save taxpayers billions of dollars each year in recurrent and capital funding," he said. "Savings estimates will vary based on methodology. Non-government schools are already required by governments to meet significant compliance obligations as part of their registration requirements. We welcome transparency and accountability." A spokeswoman for the National Catholic Education Committee, said 2017 figures showed the Catholic system saved taxpayers $2.3 billion in savings from the amount deducted from the base level of government funding. They also saved $1.3 billion in building costs. "Catholic schools funded 89 per cent of capital works with state and federal governments contributing only $152 million combined," she said. Private and public schools had different reporting requirements because they were different entities.