On a freezing day in December 2010, Vince Cable, the Liberal Democrat business secretary, moved the government¡¯s motion to raise the cap on undergraduate tuition fees to ?9,000. He told MPs that the replacement of the government teaching grant with higher fees repaid by graduates was ¡°a central part of a policy that is designed to maintain high-quality universities in the long term, that tackles the fiscal deficit and that provides a more progressive system of graduate contributions based on people¡¯s ability to pay¡±.

After a five-hour debate, conducted as 50,000 protesters and 3,000 police officers massed outside the Houses of Parliament, MPs voted by 323 to 302 to support the motion.

But there is another debate still running: about the implications of that decision for the finances of the government, ÖйúAƬ and individual students.

Critics have been picking away at the government calculations behind the new loan system. Some argue that removing most of the teaching grant and replacing it with higher fees is akin to a ¡°dodgy private finance initiative¡± that hides the public borrowing still required, and that the government has dramatically overestimated the funds that it will receive from graduate repayments.

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To explore these arguments requires some rummaging in the details of government accounting practices and amid economics jargon such as ¡°RAB charges¡±. But the claims that the new student loans system is ¡°unsustainable¡± lead to some startling future scenarios - including the possibility that the government could introduce more funding cuts for universities or demand more money from graduate borrowers. The new system could even pave the way for the ¡°performance management¡± of universities according to their graduates¡¯ loan repayment profiles, some predict.

One of the experts in ÖйúAƬ policy to have been vocal about his concerns is Bahram Bekhradnia, director of the ÖйúAƬ Policy Institute. He calls the government¡¯s forecasts on future loan repayments ¡°terrifically over-optimistic¡±, and he warns of a ¡°huge hole¡± in government finances.

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For the purposes of public accounting, the cost of loans to the government is calculated differently from assessments of direct public spending. Loans and public spending have a different impact on the UK¡¯s national deficit (the annual difference between public expenditure and revenue). While public spending counts towards the national deficit, not all of the government¡¯s outlay on loans counts towards the deficit: only the portion of loans that the government estimates will never be paid back. On the face of it, this makes the shift to funding ÖйúAƬ predominantly through loans, rather than publicly funded grants, an attractive prospect for a government that has promised to drive the deficit down.

The portion of loans that will never be repaid by graduates - debt that will be ¡°written off¡± by the government - is known as the RAB charge, a reference to the resource accounting and budgeting system used for public expenditure planning and control. The new student loans system, with government loans covering university tuition fees of up to ?9,000 a year, drives the RAB charge higher than it was under the old system, under which fees were capped at ?3,375.

The new system not only increases the outlay on loans, it also increases the repayment threshold for loans: graduates will have to start repaying their loans only when they are earning an annual salary of ?21,000, rather than ?15,000 under the old system.

But other changes, such as introducing a ¡°real¡± (higher) interest rate on loans and extending the write-off period to 30 years from 25, lower the RAB charge.

While it sounds technical, the RAB charge has a significant impact on public finances. So what proportion of student loan debt will never be repaid?

In last summer¡¯s ÖйúAƬ White Paper, the government said the RAB charge, or write-off, on the new loans system would be between 30 and 32 per cent.

But Hepi, in an analysis of the White Paper written by John Thompson and Bekhradnia that was published last summer, pointed to two problems with this estimate. One was that the government posited an average undergraduate tuition fee, after fee waivers, of ?7,500 - Hepi predicted that it would be higher. (The actual average will not be known until a survey of student numbers in December.)

Hepi also claimed that the government had overestimated the future earnings of graduates and thus the repayments to the loans system. The government had not (and still has not) published full details of the modelling used in the White Paper estimates on loan repayments. So Hepi used the Department for Business, Innovation and Skills¡¯ ¡°ready reckoner¡± on fees and loans prepared for the Browne Review.

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According to Hepi, the government¡¯s 2011 calculations for the loans system assumed that in 30 years, male graduates will be earning a mean average of ?99,500.

Bekhradnia argues that the government should have used a median average of earnings. A mean, he claims, is ¡°meaningless¡±. Good modelling, he says, would take into account the fact that low-, middle- and high-earning graduates are likely to experience different rates of increase in their earnings over time.

If the forecast on earnings is too optimistic and the RAB charge turns out to be higher than the government has predicted, why does this matter? Because if the government spends too much on loans, it will need to recoup the money, Bekhradnia predicts. The government, or a future government, might choose to ¡°cut other parts of the ÖйúAƬ budget, which includes research and other ÖйúAƬ Funding Council for England funding¡± or it could ¡°reduce subsidies to students and make them pay even more¡±, he says.

London Economics was commissioned by BIS to carry out research for the White Paper. It estimated the RAB charge at 37 per cent, based on an average fee of ?7,500.

Writing in Times ÖйúAƬ this year, David Willetts, the universities and science minister, described the modelling used by Hepi and London Economics as ¡°relatively basic¡±.

He added: ¡°The independent Institute for Fiscal Studies, however, following a more sophisticated methodology, estimates the resource accounting and budgeting charge to be around 30 per cent.¡±

In reality, the figures published by the IFS are more complex than that. The IFS estimate, detailed in a paper published in May in the journal Fiscal Studies, is actually 33 per cent. And the appendix to the paper offers ¡°optimistic¡± and ¡°pessimistic¡± scenarios for long-run earnings growth (2.5 per cent and 1.5 per cent respectively), producing different estimates for taxpayer liabilities on loans under these scenarios. (Employment growth is zero per cent in both scenarios.)

¡°What we found is that under the optimistic scenario, the RAB charge is about 30 per cent,¡± says Haroon Chowdry, senior research economist at the IFS and one of the paper¡¯s authors. Under the pessimistic scenario, Chowdry adds, the RAB charge would be 37 per cent - in other words, significantly higher than BIS estimates.

While only a portion of the government borrowing needed to create loans counts towards the deficit, all the borrowing is counted in the public sector net debt. The Office for Budgetary Responsibility said in its Fiscal Sustainability Report for 2011 that student loans ¡°are projected to increase net debt by a maximum of 4.3 per cent of GDP (?63 billion in today¡¯s terms) around the early 2030s, falling to 3.3 per cent of GDP (?49 billion) by 2060-61 as the value of loan repayments rises relative to the value of new loans made¡±.

In the report, published in July this year, the OBR gave a different estimate. The impact of the student loans on net debt ¡°is projected to peak at 6.1 per cent of GDP (?94 billion in today¡¯s terms) around the early 2030s, falling to 4.4 per cent of GDP (?67 billion) by 2061-62¡±, it said. This year¡¯s figures include loans issued in the UK¡¯s devolved nations, the OBR added.

Andrew McGettigan, a researcher on ÖйúAƬ, looked at the effect of the new student loans system on the national deficit and debt in a report published for the Intergenerational Foundation earlier this year.

¡°There is an issue about a loan scheme which really only achieves operational maturity in 20 years¡¯ time, when the income from graduate repayments going in matches the annual outlay,¡± McGettigan says. The new loans system is ¡°unpredictable, volatile and potentially unsustainable in this current form¡±, he argues.

His report, titled False Accounting? Why the Government¡¯s ÖйúAƬ Reforms Don¡¯t Add Up, suggests that the annual block grant to universities will be cut by ?3 billion by 2014, and that the new funding system will reduce BIS¡¯ contribution to the deficit by around ?1 billion a year by 2014-15.

However, the rise in tuition fees will push up inflation in the fourth quarter of this year, as fees are among the basket of goods and services used in calculating the consumer price index of inflation. Therefore, fees will add ?2.2 billion to the cost of pensions and benefits by 2016, which are linked to the CPI, McGettigan argues. If these predictions are accurate, the rise in fees could potentially wipe out the savings to BIS from cutting the teaching grant, by increasing spending in the Department for Work and Pensions.

And McGettigan emphasises that because loans count towards public sector net debt, the new loans system will actually add to the UK¡¯s public sector debt.

While the coalition¡¯s narrative, as he sees it, is that ¡°we are reducing the deficit, that slows down the growth of the debt and we pay off some of the debt¡±, McGettigan says ¡°the opposite is happening in ÖйúAƬ¡±.

Turning to the RAB charge, McGettigan believes that the government might have gone as high as a 40 per cent estimate for future non-repayment if it had wanted to accommodate uncertainty.

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As the size of the loan book swells, and if the government decides that it wants to recoup money faster, borrowers could look like a relatively easy target. This is a concern that has been raised by McGettigan and the National Union of Students. The terms and conditions of student loans can be changed without primary legislation, McGettigan explains.

He suggests another scenario that could arise from the switch to loans from teaching grant. The ONS¡¯ Labour Force Survey now collects information on graduate earnings by university. What if it were possible to calculate RAB charges and repayment rates by institution and by course? Writing in THE last year, Willetts said: ¡°I expect that, in the future, as the data accrue, the policy debate will be about the RAB charge for individual institutions.¡±

This would have the ¡°potential to be a rather unpleasant performance metric¡± for universities, McGettigan suggests. ¡°You can imagine a situation in which the RAB charge (for a particular course) is as high as 80 or 90 per cent, and someone is saying ¡®why are we subsidising these graduates? We are not getting any of the money back¡¯.¡±

This links to another loans issue on the horizon: the government¡¯s plans to sell the student loan book to private buyers, most likely banks. The coalition government commissioned the investment bank Rothschild to undertake a feasibility study of such a sale, following the Labour government¡¯s passing of the Sale of Student Loans Act in 2008.

The volatility of the new loans scheme makes a sale difficult, McGettigan argues. The loans would be ¡°extremely difficult to price¡± for a bank in terms of risk, as ¡°income-contingent loans don¡¯t look like the kind of loans banks are familiar with¡±.

But McGettigan suggests that with individual RAB charges for universities or courses, the government could ¡°create an appetite, create an initial market by putting out the most secure, vanilla product you could¡­Russell Group or medical students, even better¡±.

What does Nick Barr, professor of public economics at the London School of Economics and a key player in the design of the previous top-up-fee loans system, think? Barr looks at the new loans system in a forthcoming paper, to be published in the journal Social Policy and Administration. The paper is titled ¡°The ÖйúAƬ White Paper: The Good, the Bad, the Unspeakable - and the Next White Paper¡±. The last part of the title, Barr says, is a reference to his belief that a 2016 White Paper is inevitable ¡°because the current system is unsustainable¡±.

In the paper, Barr criticises the government for abolishing the teaching grant in arts, humanities and social sciences subjects, given the economic and social benefits arising from ÖйúAƬ. Highlighting the way in which the bulk of student loans are not classed as expenditure in government accounts, he writes that ¡°the changes look like a dodgy [Private] Finance Initiative: with optimistic assumptions, the numbers look good in the short run but are likely to have a high long-run cost¡±.

In an interview, Barr is blunt about the government¡¯s switch to loans from grants. ¡°It is crap policy. Why did they do it? Answer: because of this accounting wheeze.¡±

He adds: ¡°The problem with the loan system is not that it adds to the public sector net debt but that of all the money shipped out, so much will never come back. That is why it is unsustainable and why it will have to be fixed in the 2016 White Paper.¡±

For Barr, the Blair government made progress in widening participation in ÖйúAƬ because of a 0-to-18 approach that included the education maintenance allowance for poorer pupils in further education as well as the Aimhigher outreach scheme. ¡°Abolishing EMA and Aimhigher is truly horrible, unspeakable,¡± he says.

The next White Paper, Barr argues, should ¡°resurrect those policies and put more welly into them¡­ That would give you the political position to do the second thing, which is fix the design flaws in the student loan system. A good loan system should be designed so that graduates with reasonable earnings repay their loan in full.¡±

And the government should ¡°lower the threshold at which loan repayments start, back towards ?15,000¡±.

This might sound ¡°like a right-wing bastard being cruel to students. Not so at all,¡± Barr says. The new loans system was designed as ¡°a sop to the Lib Dems¡± after they backtracked on their pledge not to raise fees, allowing them to claim the new system was ¡°more progressive¡±, he argues. But the new system ¡°actually harms access for the most disadvantaged¡± because the cost of the loans system means that the government has to cap student numbers: as the most disadvantaged tend to have lower academic grades, they are the most likely to be excluded from university owing to a shortage of places.

In addition, Barr says, the cap on numbers creates excess demand for places, which means it is still ¡°a seller¡¯s market for universities¡±. Thus competition ¡°doesn¡¯t have the effect on quality it should have¡±.

So what does BIS say about these concerns? A spokeswoman for the department says: ¡°Our estimate of the RAB charge is 32 per cent. Some people take a more pessimistic view than we do about the amount that will be repaid to government because they disagree with things like our future earnings assumptions. However, many other experts claim our RAB charge estimate is far too high because it doesn¡¯t actually reflect the current low cost of borrowing. So our figures are actually somewhere in the middle of the debate.¡±

The spokeswoman says the OBR¡¯s estimate on ?94 billion being added to the public sector net debt is ¡°reasonable¡±, adding: ¡°Because the majority of money that is loaned out is repaid - don¡¯t forget student loans are contractual obligations - then the beneficial impact on the deficit scores very differently to the medium-term impact on the debt.¡±

What about McGettigan¡¯s warning that higher tuition fees will push up the CPI and benefit payments?

¡°This idea is based on a rather narrow view of how inflation arises - for example, it assumes a static policy position whereby inflation is not influenced by other decisions around base rates and quantitative easing,¡± the spokeswoman claims.

In response to Hepi¡¯s criticisms of its graduate earnings forecasts, she says: ¡°On graduate earnings, we assume past graduate earnings are indicative of future graduate earnings and we assume OBR forecasts of future earnings growth are applicable to the entire graduate population. Both of these assumptions are important and uncertain but they are not unreasonable for central forecasts.¡±

BIS has just released a ¡°simplified¡± version of the model it has used most recently to estimate the RAB charge for student loans.

Guidance accompanying this shows that the department has not changed its official estimate of the proportion of loans that will never be repaid - this remains 32 per cent.

Hepi is now working on a new analysis using the information released by BIS. According to the thinktank, it appears that the department has changed its assumptions on long-term average earnings, using the most recent projections from the OBR. These assume lower growth in earnings than previous predictions, and thus lower repayments from graduates.

We do not yet know whether the government¡¯s assumptions will turn out to be correct. The new generation of ¡°9K students¡± is only just starting university, so actual rates of repayment will not begin to be known for some years. But it appears that questions about its calculations are being asked at the highest levels in the sector. Sir Alan Langlands, chief executive of Hefce, singled out three main resources risks to the sector in his presentation at the funding council¡¯s annual conference in April. One of these risks was ¡°the robustness of government calculations on the repayment profiles for the student loan book¡±.

And some key tests for the government¡¯s calculations are approaching. Its estimates are based on an 85 per cent take-up rate from students for tuition-fee loans, and on an average fee of ?7,500. We will soon know how those estimates match up against the real results for the 2012-13 academic year.

But Bekhradnia remains unhappy that Hepi¡¯s requests to BIS for full modelling to be released have been refused, including one request under the Freedom of Information Act.

Bekhradnia sums up the new funding systems as ¡°ill-thought-through and rushed¡±. ¡°The implications weren¡¯t properly thought through and the calculations weren¡¯t done properly. As it has become apparent that the costs have been underestimated and the budget is going to be broken, the government is probably anxious that the debate should not focus on all that.¡±

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The case can be made that it is ¡°extremely irresponsible to pass this level of debt on to future governments against highly doubtful assumptions that it will be repaid¡±, he adds.