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This post is part of CGD’s work looking at the UK’s role in delivering shared prosperity beyond Brexit. We’ll be looking into further ideas in the coming weeks.

Whatever you think about Brexit, it doesn’t make sense to secure Britain’s economic future by adding red tape. Theresa May’s government wants to tamp down net migration. That’s has opened space for some new self-defeating proposals. During the UK’s recent Conservative Party conference, Home Secretary Amber Rudd outlined a plan to tackle immigration by enforcing a new visa system for international students.

Clamping down on international students threatens a surprisingly important export sector. It damages Britain’s brand and limits an important instrument of soft power. And it would needlessly constrain opportunities for intellectual and professional achievement for foreign-born students, undermining a valuable and often-unrecognised contribution that the UK makes to shared, global prosperity. Migration is a contentious topic, but on this issue the numbers are clear: most voters don’t think of short-term students as immigrants.

A simple, one-line change avoids this false dilemma: redefine the way the Office of National Statistics calculates Long Term International Migration to exclude short-term and temporary non-EU students.

These students arrive in the UK to study and then leave. There are already strict rules in place requiring those who want to stay to re-apply to transition to other visa classes. And according to a year’s worth of data from exit checks, only around 1 percent of foreign students actually overstay. Whether or not you think net migration is a problem, it's bad policy to target the softest part of a badly-defined indicator—rather like “losing weight” by taking off a heavy coat before getting on the scale.

We don’t think of teaching as an export, but it is. In the jargon, education sold to foreign students is a ‘mode 2’ services export. That shows up as a credit in the UK’s balance of trade. International students contribute directly to University finances and the cities and towns in which they study. Figures collected by accountancy firm Grant Thornton for the non-partisan Times Higher Education indicate that international students paid UK universities more than £4 billion in fees in 2014-15.

They also contribute a further multiple to local economies—£3.5 billion a year in 2011-12 according to analysis by Universities UK, an education industry group. (The British Beer & Pub Association, another industry that also profits handsomely from students, has been curiously silent.) And non-EU students subsidise their peers by paying much more for the same courses, much as the pinstriped bankers who instinctively turn left when boarding the plane help pay for those of us at the back. British undergraduates at Oxford next year, for example, will pay £9,250. Their non-EU peers pay up to £23,190.

Giving international students access to the hallowed halls of British institutions is also an important instrument of the UK’s soft power. A remarkable paper published in the American Economic Review—our field’s most prestigious and competitive journal—shows that being educated in democratic countries catalyses the promotion of democracy at home. Students, in short, bring Britain home with them.

And there’s the well-established fact that studying abroad is good for the students themselves. It increases earnings by upgrading skills. It improves employment by conferring a recognised qualification. It expands their social and professional networks. And it enables them to work in a globalised world. Research shows that English-language skills can create a wage premium of up to 20 percent. Surprisingly, most of these important benefits flow to relatively poorer countries– data from the OECD show that in 2012 (the most recent year for which figures are available) more than half the foreign students in the UK were from countries that receive foreign aid.

As for the politics of this problem, most people inherently recognise that students are not migrants at all. Polling from 2014 commissioned by Universities UK found that nearly 6 in 10 respondents would not reduce the number of international students even if that made it harder to reduce immigration numbers.

Students can’t just transition to the labour market: non-EU students who want to remain in the UK to work still need to apply under other visa categories; permanent settlement still requires a successful application for Indefinite Leave to Remain (ILR). And there are already policies in place targeting institutions that might facilitate visas for people to work under the guise of studying. If the Home Office rejects just 1 in 10 or more visa applications associated a particular institution, it loses its designation as a trusted sponsor and faces a higher compliance burden, making it much harder to accept international students in the future.

Early last year, we (along with our colleague Michael Clemens) introduced a list of 13 shovel-ready improvements that would support British employers, grow the economy, provide better services to British consumes, and support development overseas. Revising the definition of migration to exclude international students was on our list then. Now it seems this one-line fix is more urgent and important than ever.