Although not surprised, I am quite disappointed with the Browne report. I haven’t read it in detail, but at first glance it reads as something in which the outcome was essentially known from the beginning. There appears to be very little discussion of the fundamental reasons for the existence of a higher education (HE) sector, and it appears to assume that the current funding model has to change. The basic idea from the report is that tuition fees would be uncapped and that students would be lent the money to cover the tuition fees, and to help cover the cost of living. It seems unlikely that fees will actually be uncapped, but will probably rise to about £6250 per year with an additional £3750 per year for living expenses. Students will therefore accrue debts of about £10000 per year. If this does end up being the case, Universities will supposedly actually gain nothing, in that the government is likely to cut the HE budget by an amount equivalent to the extra amount that the HE sector will get through tuition fees. The main thrust of the Browne report is that the money lent to a student will only be paid back once the student earns more than £21000 per year and would be written off 30 years after the person has finished their degree.

Fundamentally I think it is wrong and I believe that a free market Higher Education (HE) sector will not be as effective as one that is primarily funded by the public and that is largely free to pursue excellence. However, rather than going into a long discourse about why I think this is the case, I thought I would present some basic consequences of the Browne report – assuming that it is accepted as the new model for funding the HE sector.

A little while ago I was playing around with distribution functions and managed to produce one that largely matches the income distribution in the UK. It’s shown in the figure below. It’s not perfect but it has approximately the correct mean (£25000), the correct median (£19000) and the 10th, 25th, 50th, 75th and 90th percentile incomes are very close to the actual values for 2007/2008.

The table below is taken from the Browne report and it shows the amount of money that someone will pay per month to repay the loan they were given to cover tuition fees and cost of living expenses.

At first glance it doesn’t seem unreasonable; the highest earners pay more per month than the lower earners. There are, however, a couple of things one can do straight away. The payment as a percentage of total income is straightforward. It is also likely that there will be interest, at about 2.2%, that will accrue once someone crosses the £21000 threshold. One can therefore calculate how long it will take for someone to repay the loan. These are both shown in the figure below. The solid line is the payment as a percentage of income, while the dashed line is the number of years it will take for someone to repay the loan, capped at 30 years after which the remainder is written off. Included in this calculation is the assumption that people’s salaries will rise with inflation at a rate of 2.2 % per year (for simplicity, the same as the loan interest rate).

What the above figure shows is that everyone earning, today, between £21000 and £32000 per year will repay for the full 30 years. Those earning close to £32000 per year will be paying almost 3% of their income for the entire 30 years. If we go back to the income distribution figure that I showed at the beginning of this post, one can calculate that about 45% of those in employment (about 15 million people) earn £21000 per year or more. Since slightly more than 40% of school leavers go to university, we can assume that almost everyone earning £21000 per year or more will have gone to university and will therefore be repaying a student loan. If this is the case, almost 5 million people will have their income reduced by between 1% and 3% for 30 years. If one considers those who will pay for 10 years or more it amounts to almost 9 million people. Someone earning £50000 per year will pay almost 5% of their income for 10 years in order to pay back their student loan. Almost half of all those earning £21000 per year or more will therefore effectively have their tax raised by 1% or more for 30 years, while 2/3 will have an effective increase of 1% or more for at least 10 years. Of course, inflation could be higher than I assumed and so the repayment period may reduce slightly, but it is unlikely to change things significantly.

One can also determine how much each person will pay. This is shown in the figure below. The full amount will only be repaid by those earning £32000 per year or more. Someone earning £32000 per year will end up paying more than £40000 over a period of 30 years, while someone earning £100000 per year will pay £32000 over a period of about 4 years. This illustrates that the middle income group will pay much more than the highest earners who will be able to repay the loan very quickly.

We can also use the distribution function that I showed at the beginning of the post to determine how much money the government can recover every year. It’s not necessarily exact, but here is what I assumed. Everyone earning over £21000 per year went to university and has to repay a student loan of £30000 pounds. Everyone works for 40 years after graduating, but the loan is only repaid for the first 30 years (any remaining parts of the loan are written off after 30 years). The fraction of people in a given income bracket who will be repaying at any given time is therefore the number of years those people have to repay for, divided by 40. It turns out that if this was already in place and people today were repaying a student loan, the government would recover about 8 billion pounds. Here’s where I have a problem. There are currently 1.2 million people at British universities today. If the government is lending them £10000 each, they are then lending £12 billion and recovering £8 billion. Unless I’m mistaken, this ratio will always remain the same. The government will only ever recover 2/3 of the money because at least 1/3 of those who go to university will not finish paying within 30 years and quite a lot of those are only paying back interest.

If I’ve got this right (which maybe I haven’t as I’ve been trying to do this while my son keeps clambering all over me) the government is about to cut the HE budget by about 4.2 billion and will recover this money by increasing tuition fees. The money for the increased tuition fees will be loaned to students, resulting in an increase in the effective taxation of about 2/3 of those earning above £21000 by at least 1% for at least 10 years after they graduate. Ultimately, however, the government will only recover 2/3 of the money lent which, in today’s terms, will amount to a loss of about £4 billion. Furthermore if they simply increased the level of taxation for those earning above £21000 by 1.5%, revenues would increase by £9 billion. I don’t know about everyone else, but I would rather pay 1.5% more in tax and have a publically funded HE sector, than pay something like 4% for 10 years after graduating (or 1% for 30 years) and end up with a supposedly free market HE sector. I’m of course ignoring that this is still £3 billion less than the £12 billion required for all the 1.2 million students so students would still need to borrow something to cover cost of living expenses and to pay some top-up fees.

Maybe I’ve made some kind of silly mistake or maybe my assumptions are too simplistic but it seems quite possible that – to reduce direct funding to the HE sector by £4.2 billion – the government is going to introduce a graduate tax that could result in some paying 4% more in tax for a decade after they graduate, and after all that the government will still end up paying £4 billion per year to the HE sector. Effectively the government will introduce a very complicated taxation system for middle earners who will lose significant amounts of money just when they’re trying to have families and buy houses and as a result of this, the government will effectively save £200 million. Am I stupid or are they?

I was a little concerned that my calculation about how much money the government would recover was maybe a little simplistic, so I’ve considered a slightly different approach. If we assume graduates typically start at about £21000 we can calculate how much they would repay within 30 years for a given annual increase in salary. If the threshold for payment rises with inflation, then only those who reach the top 10% of earners within 30 years will repay the loan in full. This suggests that only 20% of graduates would repay in full. Overall, the government would eventually recover about 2/3 of the money paid – similar to the result I obtained earlier. The only way that the government would be able to recover everything is if it kept the threshold constant over the next 30 years, but this seems somewhat unlikely – although I wouldn’t put it past the government to try this.

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There is a report on the BBC website