I guess it is time to talk about discount rates.
In the world’s least engaging game show I – as host – present you with a simple decision: should I give you a bag of money now or a different bag of money in ten years time. Your role is to tell me (before you learn what amount of money is in each bag) how you would make your decision.
There’s various considerations that might come into play. The first is, on the face of it, straightforward – the time preference rate. If you have a bag of money now you can spend it straight away. That immediacy is of value. You could buy yourself a good lunch, or a new car, or whatever it is you want, this very afternoon – and start using it as soon as you unwrap it. Maybe it is a purchase that will help you make money – or save money – straight away, so that opportunity cost needs to be factored in too.
How much do you want to have new stuff right now? If you are very keen, you might set a high time preference rate: the money is much more valuable to you now than later, so you will almost certainly choose the “now” bag unless the “later” bag is significantly more valuable. Likewise – do you honestly believe that I am trustworthy enough to give you the bag of money in ten years time? If you don’t I suggest you take the cash straight away.
If you are thinking about investing the money in the bag there is a different rate to think of; the expected rate of return. If you know that you could stick the money in the “now” bag into (for example) a cash ISA to get 4 per cent interest every year, the money in the “later” bag would need to be worth more than what you end up with after 10 years at 4 percent for it to be worth considering. If you are playing with the stock market the rates of return may be higher, if less predictable – you could use a projection based on the past performance of the funds or other vehicles you are investing in, or an expectation of GDP growth.
And finally we need to think about spending power. Inflation is a measure of the average growth of a key set of prices – it tells you how much one pound could buy now compared to what it could buy ten years ago, and a projection of inflation could give you information on what you might expect to be able to buy ten years in the future. So in comparing the two bags, you need to be talking that into account too.
This – it turns out – is why all my proposed game show formats fail. Too much maths.
I’m from the government
Let’s imagine you are not a person, but a nation state. Instead of the two bags you have, on the one hand, £28,605. And on the other hand, in three years time, a university graduate.
Broadly speaking, the same three considerations – time preference, rate of return, inflation – apply. As a nation, you could spend that £28,605 on all kinds of things right now: just about every part of the public sphere needs investment.
For this reason another part of the equation has to significantly outweigh the immediate need – and that is the rate of return. Graduates earn more (even when you take inflation into account) , they pay more direct tax, they interact with the economy that generates indirect returns to the government. And there’s a bunch of less easily quantifiable returns: improved health, civic participation.
To be clear, the economy has other skills and capability needs that are not met by graduates even in the longer term – we also need builders, care workers, drivers, technicians, and so on. That’s another opportunity cost.
Green
Rather than participating in poorly designed thought experiments, the government has already set out its methodology for making decisions like this. You’ll find it in a supplement to the Treasury Green Book.
For the first thirty years – the formula for the social time preference rate (STPR) looks like this:
STPR = ⍴ + μg
where ⍴ = δ + L
The ⍴ represents time preference. The Treasury splits this into two components – pure time preference (δ) which represents an “impatience” to have benefits from public spending now rather than later; and an allowance for catastrophic risk (L).
And μg is the wealth effect, two parameters multiplied together. Here, μ is the “elasticity of marginal utility of consumption” – how a person (and indeed society as a whole) will see their wellbeing change as their consumption of resources changes . And g is the expected annual growth rate of future real (so, unaffected by changes to inflation) per capita consumption of goods and services. The whole STPR calculation ignores inflation entirely and focuses on the “real” values.
Astute readers will have spotted that none of these things are externally derived measures – all of the parameters here are based on estimates or projections. The Treasury assigns values for use as follows:
- δ (pure time preference) is 0.5 per cent
- L (catastrophic risk) is 1.0 per cent
- So ⍴ is 1.5 per cent
- μ (elasticity of marginal utility of consumption) is 1.0 per cent
- g (expected annual growth rate of future real per capita consumption) is 2.0 per cent
- So μg is 2.0 per cent
- And therefore STPR is 3.5 per cent
How Treasury decisions are made
Applying the discount rate helps us compare a present value (the money now) with a future value (the money, or the thing we are buying with the money). So £100 now, or goods/services/benefits to the real value of £120 in three years time? Take the money, or open the box?
We apply the discount rate once for each year. So the £120 worth of stuff in three years time comes to:
- Year 1: £120 – (£120*3.5%) is £115.80
- Year 2: £115.80 – (£115.80*3.5%) is £111.75
- Year 3: £111.75 – (£111.75*3.5%) is £107.84
You get a £7.84 real terms value benefit (according to government rules) if you wait. Therefore, the policy gets the green light. And that’s how Treasury decisions are made.
For completeness I should note the exceptions. First up, if you are investing in something that will have an impact on people’s health or stops them from being alive, you ignore the “wealth” component – thus setting STPR at 1.5 per cent. Why? The Green Book supplement says:
The diminishing marginal utility associated with higher incomes does not apply, as the welfare or utility from additional years of life will not decline as real incomes rise
If you are doing overseas development, a different discount rate will apply: the growth rates and risks in other countries will be different in other parts of the world. The Foreign Office is in charge of those rates.
And what about long term benefits – over 30 years away. Uncertainty over the future values of our parameters mean we use lower discount rates: 3 per cent for year 31 to year 75, and 2.5 per cent for years 76 to 125.
For proposals that will provide benefits more than 50 years out, you need an additional sensitivity analysis to think about the way time preference is used. There are ethical concerns about “irreversible wealth transfers” from the future to the present, so in making a case for any policy this needs to be set out very carefully.
Discount rates and student finance
Before I continue, I just want to be very clear about the difference between discounting (which is used to assess the value of investment decisions for the government) and the graduate repayment system. You’d imagine that in a sane world the graduate repayment system would only need to cover any difference between the cost of educating a graduate and the likely benefit to the public purse (as discounted). That’s not, for various reasons, quite how things work – and I’m not proposing to say much about the repayment rate here (see Jim’s piece for that).
But it is instructive to apply the discounting rate to student funding. A male undergraduate student in England can borrow a maximum of £14,135 (living in London, away from home) in maintenance loans, and £28,605 in fee loans – the Institute for Fiscal Studies suggests that the gross (undiscounted) exchequer return would be £400,000, and it even applies the appropriate Green Book discounting to give us a lifetime exchequer return premium of just under £110,000.
For this average male graduate, our investment decision is a go. Even accounting for time preference and all the rest, the rise in discounted government income dwarfs (by just over £68k) the outlay. That’s including loan repayments – if we exclude these, we’re looking at approaching £136k of additional tax intake over a lifetime. The picture is less optimistic for women, purely because of lower lifetime earnings (largely driven by career gaps and part-time working to support family – something that any sensible system of accounting would take account of), but even so the average female graduate covers their initial outlay with room to spare, even before repayments are taken into account.
So why bother with repayments at all?
Arguably, discount rates are not a sensible way to address the lifetime returns from a large population of graduates. We know, that while the discount rates make having graduates in 40 years time look less valuable, this is the point at which graduates are generally paying most in tax. Sure, there might be an unexpected event (why do I keep thinking about Liz Truss here?) that could change that, but generally – the longer you have graduates in the workforce, the more they earn, and the more tax you take.
I feel duty bound to add that everyone else pays tax too. It would be very helpful to know the difference between the projected lifetime tax take for graduates and non-graduates: we know that mean earnings at 30 (just under ten years after graduation) are around 40 per cent higher (£42k) for graduates than non-graduate men (for women the figure is about £35k, though there is a plateau during peak childbearing years).
It would be a fascinating exercise for the IFS (with their access to all the LEO data) to run: what is the additional tax take for graduates compared to non-graduates, and what would the figure be if we disregarded loan repayments (which are levied on pre-tax income). Maybe I’ll drop that Jack Britton a line.
In thinking about student finance, the powerful inertia generated by the current model means that we are obsessed with whether fee and maintenance “loans” (they are not loans, surely we can all admit that now) are covered by the additional “repayments” (it’s a tax it’s a tax it’s a tax) made via the SLC.
Considerations of the wider Treasury benefit (or indeed the economic indicators for a wider societal benefit) from a growing population of graduate are few and far between. If the sector washes its face via the tax system (as I feel like it may) the argument for such onerous repayments becomes moot. John Blake made a linked but distinct argument for the Post 18 Project, I would go further and say even the case for a distinct “graduate tax” is overstated.
And the wider issue of discounting, to me, overstates society’s preference for short term benefits from spending at a time where the majority of problems the UK faces are very long term in nature. There is a need to think over a longer period of time for any infrastructure investment – I would argue that higher education is critical national infrastructure with a long-term pay off, and judging it against short term return (even 10 year LEO data is short term!) is wrong.
In Wales, the Future Generations Commissioner highlights one way forward. What kind of world do we want our grandchildren to grow up in? What kind of skills and tax based does that world need? What role will people with higher level skills play?
The higher education funding model in England is focused far too much on the short term. And the first step towards fixing the hole we are in is to look at the outcomes over a lifetime.
