The election of President Trump has raised speculation about an expansion of "voucher systems" for US schools.
These schemes give parents a "voucher", backed by public funding, to spend on a school place in either the state or private sector.
Andreas Schleicher, the OECD's director for education and skills, examines the possible impact.
Many education systems around the world are looking for ways to give parents more choice over where they send their children to school.
Proponents of school choice defend the rights of parents to send their children to their preferred school - which could be based on the quality of the school, the school ethos or a religious denomination.
For the system as a whole, expanding school choice can stimulate competition and encourage schools to innovate.
But opponents argue that this type of market-based system takes better-off students out of the state school system, with schools becoming increasingly socially and culturally segregated.
Critics also say voucher systems divert public resources to private providers, leaving state schools with a disproportionate number of disadvantaged students and reduced budgets to support them.
So what does the international evidence show about whether choice and competition are part of the solution to raising school standards, or whether they become part of the problem?
The first lesson is that successful choice-based systems, such as the Netherlands, Flanders or Hong Kong, do a lot to ensure that there is a level playing field, because markets alone don't do the trick.
If we think of schools in terms of markets, the amount of "elasticity" can be limited, both in terms of families looking for places and what schools can offer.
Across OECD countries, two thirds of parents of 15 year olds say they have some form of school choice. But what this means can vary widely in practice.
For example, for families in rural, poorer areas, distance might be a big factor in determining the extent of choice.
For other families, cost might be an important factor in how choice is exercised.
And in both these examples - where parental choice is limited by concerns about distance and cost - students are likely to underachieve, even after accounting for social background.
Voucher systems can allow families to seek a school place in either state or private schools.
But there is an important distinction between schools that are publicly run and those that are publicly funded.
Across the OECD, 84% of students are in publicly-run state schools, 12% attend schools which are private but government funded and 4% are in independently-funded private schools.
In countries like Sweden, Finland and the Netherlands there are private schools - but they receive essentially all of their resources from government, and they don't charge additional fees.
And in the Slovak Republic and Hong Kong, public funding for private schools is still over 90%.
But there are other countries where private schools are overwhelmingly privately funded. In Greece, Mexico, the United Kingdom and the United States the share of public funding for private schools is below 1%.
This matters - because in those countries where privately-managed schools receive higher proportions of public funding, there is less social segregation.
But there are some complicating factors. Publicly-funded private schools might charge additional fees - and this can give them an unfair advantage and undermine the principle of choice.
At some point, an extra tuition fee is going to be a deterrent for some lower-income families.
So public funding, such as from vouchers, may fail to widen access to private schools unless it is accompanied by rules on tuition fees.
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If private schools invest public resources to improve their quality - rather than to widen access - subsidies can exacerbate inequities.
This is one of the reasons why abolishing substantial add-on fees, in such a voucher system, can reduce attainment gaps between rich and poor students.
Vouchers can be an effective instrument to finance private education. But they can be targeted in different ways - sometimes for all families and in other cases, only for disadvantaged students.
This can make a big difference in their impact.
Vouchers that are available for all students can help to expand the choice of schools available to parents and promote competition among schools. School vouchers that target only disadvantaged students can help improve equity in access to schools.
For school systems with a similar share of public funding for private schools, the socio-economic gap between pupils in state and private schools is twice as large in education systems that use universal vouchers compared with systems that use targeted vouchers.
Regulating private school pricing and admissions criteria also seems to have a positive impact on the ability of voucher schemes to go hand in hand with limiting social inequity.
There are some other lessons too. Schools with selective admission tend to attract students with higher ability and socio-economic status, regardless of the school's educational quality.
Given that high-ability students are less costly to educate and can increase a school's attractiveness to parents, such a selective intake can provide schools with a competitive advantage.
Allowing private schools to select their students therefore provides them with an incentive to compete on the basis of exclusiveness, rather than the extra value they can add.
This can undermine the dynamics of competition, diminishing the positive effects it may otherwise have on quality.
The international evidence also points to selective admission as a source of increased inequality and stratification.
The social sorting of students occurs not only because of admissions rules and tests, but also because of parental self-selection and more subtle barriers to entry.
It also means there is no simple answer to whether private schools, with public voucher funding, get better results.
The over-riding conclusion is that it depends on the regulatory framework that is put in place. Governments and education authorities can intervene to change the impact of vouchers.
Vouchers work well in some systems and badly in others. The key message for the US is that it needs to ensure the right regulatory framework.