If you had to choose a single measure to assess the return on billions of pounds of extra government funding for schools, it is fair to assume the following calculation would not be it.

It says: simply add up the money being spent, compare it with the number of pupils being taught, and you will get a figure for productivity, or how many pupils are being educated for each pound of taxpayers’ money.

The problems with this are manifold. Not least, it implies that if politicians want to create a more “productive” education system, all they have to do is to increase class sizes, as David Normington, education’s top civil servant pointed out to MPs in April.

By similar reasoning, you could come up with a gauge of police productivity which assessed the number of crimes the police deal with for each pound spend.

However, again there is one, rather fundamental, flaw: if crime fell with spending staying constant, “productivity” would fall because the police would be processing fewer crimes.

Yet, astonishingly, it is these calculations which are used in current official attempts to answer one of today’s most crucial political questions: is extra public spending delivering for voters?

They form the basis for public sector productivity calculations used in our national accounts. And, much more worryingly for ministers, they also lay behind a recent front-page article in a Sunday newspaper claiming, apparently without reservation about the underlying statistics, that Labour had “wasted pound;20 billion” since coming to power.

So, perhaps unsurprisingly given that Labour has staked its second term on being able to demonstrate public service improvements to justify tax rises, the Government is trying to devise a replacement measure.

But will it come up with anything more meaningful?

Ministers have entrusted this daunting task to Sir Tony Atkinson, from Nuffield College, Oxford, who is to produce a report for the Office for National Statistics on a possible new measure by next January.

An interim report is due next month, with a discussion of a productivity measure for education to be given prominence. In the first place, schools will be the focus, with productivity ratings for higher and further education left to a later date.

So, if the calculation attempts to measure inputs, for example government spending, against educational outputs, what will feature in the latter part of this equation?

Not surprisingly examination results will be a major element. It is likely that key stage 1, 2 and 3 results, GCSEs, A-level and vocational qualification performance will be included in a calculation of the “outputs” achieved in return for increasing investment.

A senior Department for Education and Skills source said it had not yet been decided whether the results included would be on a “raw score” or “value-added” basis.

According to DfES accounts, total education spending in England has risen from pound;30.7 billion in 1998-9 to pound;48.1bn in 2003-4. Although it is difficult to untangle the figures, schools funding appears to have increased from pound;21.2 to pound;34.2bn over the same period.

At its most basic, a productivity measure centred simply on exam results would seek to assess whether performance was improving at a rate faster or slower than this investment.

This, even the source conceded, is far from ideal. “Obviously, the education system is producing a whole lot more than just exam results,” he said.

Yes, many would argue, a good education is worth something in non-economic terms, insofar as it produces happier, more creative citizens.

But the proposition that education is about more than exams also appears to be an acknowledgement that a productivity measure centred on test performance alone does not even succeed in its own right, as there are wider benefits of education spending to the economy.

For example, it may be that as education spending increases, citizens’

health improves, lessening the burdens on the National Health Service.

Better educated people may also be less likely to commit crimes, the reasoning goes.

However, the source said it would be difficult to capture this relationship meaningfully. Although it might be possible to quantify the value of “outputs” such as improving health or falling crime rates, they would be “ballpark figures”.

It would be difficult, he said, to come up with a measure sufficiently precise to make meaningful year-on-year comparisons of increasing or falling productivity in this area, which is where interest is often focused.

Similar observations could be made about attempting to quantify the increased wages that individuals can be expected to earn as education levels improve.

But if these measures prove too tricky, it is likely that there will be one other important factor to consider besides exams - the monetary value of the childcare schools provide for younger children.

Officials will try to answer the question of how much money the state is saving parents by extending, for example, the provision of schooling for under-fives.

Again, the resulting figure will be a far-from-perfect measure, a fact the source acknowledged: “There’s more to this than a number to go into the national accounts,” he said. It is therefore possible that the productivity figure will be published alongside a brief written account, attempting to set out a qualitative guide to progress in the education system.

Critics say that any productivity index will prove problematic, and will underestimate the economic value of public-sector work. Whereas it is relatively easy to put a value on private-sector products for which people have to pay, for free public services this is problematic.

They also point to an issue raised in the Sixties by the American economist William Baurol. Whereas in the private sector, he said, productivity can rise as technology advances, there is less scope for this in the public sector.

Peter Robinson, senior economist at the Institute for Public Policy Research, a centre-left think tank, said that existing research was inconclusive even on relatively narrow questions of the benefits of increased spending on educational outcomes.

For example, he said, it had not been demonstrated beyond doubt that smaller class sizes led to improved exam results.

Given all these potential problems, it is tempting to ask why anyone should bother to attempt to introduce this new measurement at all.

The DfES source argued that it would at least provoke a debate about the relationship between education spending and results.

However, given the potential for more headlines about wasted billions, it may not be a debate that either ministers, or those working in the public sector, will find enjoyable.