The curious case of the missing graduates

The latest figures from the OECD on graduation rates across the developed world show that, relatively, the UK’s position is deteriorating.
In 2000, the proportion of young people getting a degree put the UK third, behind only Finland and New Zealand. In that year, 37 per cent of the relevant age group in the UK were graduating, against an OECD average of 28 per cent. By 2008, the latest edition of the OECD publication Education at a Glance shows, the UK’s figure had fallen to 35 per cent, while the OECD average had risen to 38 per cent.
There’s something very strange about this, as official UK figures on participation in higher education in the UK do not show a decline, but a slowly rising trend. In 2007-08, statistics from the Department for Innovation, Universities and Skills showed, 43 per cent of the age group between 17 and 30 began  a course of higher education.
But the OECD report (Table A3.2, Trends in Tertiary Graduation Rates) shows the UK figure for graduates falling from 39 per cent in 2007 to 35 per cent in 2008. Such an abrupt change is impossible.
A note explains that there is a break in the time series for the UK following a methodological change in 2008, but does not elaborate. Annex 3 to the tables, which contains notes, provides no further explanation of what the methodological change may have been, but it has certainly had a dramatic effect on the UK’s relative position.
In fact, to draw any conclusions on the basis of this table would be unwarranted, though that did not prevent the OECD, Universities UK, the National Union of Students, and the University and College Union from doing so.
On the presumption that the revised methodology is correct, then the UK’s previous figures ought to be modified also, which implies that the position was never as strong as the comparisons made by all these people suggest. If the revised methodology is incorrect, then we have not fallen as far behind as everyone is assuming. (If anybody can shed light on what the methodological change was, I’d be delighted to know. The Higher Education Statistics Agency was unable to help.)
There is a further puzzle, however, for those who only follow higher education from a distance. Universities appear to have been expanding fairly rapidly in the past decade, yet the OECD figures show a declining proportion of UK-born students graduating from them.
Data from HESA confirm that there has been an expansion of around 310,000 students in higher education since 2001-02 (14.9 per cent).
But, as often happens, there has been a change in the methods of measurement and  a consistent time series exists only since 2004-05 (see Fig 1). Over that period, the numbers of full- and part-time students on higher education courses in the UK has grown from 2,236,270 to 2,396,055 – an increase of almost 160,000.  But as Fig 1 shows,  almost half that increase (72,070) has actually been due to foreign students, either from other EU countries or from outside the EU.

The reason, of course, is that universities can earn more in tuition fees from foreign students than they can from home–grown ones, so have made every effort to recruit them. Plenty of the non-EU contingent will take the opportunity to turn their stay into a permanent one, if given a chance, although this is unlikely to be true of Chinese students who form the largest group. HESA gives the following breakdown (Fig 2) by nationality for the top ten non-EU countries of domicile, somewhat oddly treating China and Hong Kong as distinct countries. Please don't tell the Chinese.