Before we get onto the budget and what Rachel Reeves might do to fiddle her fiscal rules and give herself a little more room to spend, I want you to ponder, for a moment, a recent report from the Office for Budget Responsibility (OBR).

This wasn’t one of those big OBR reports that get lots of attention – such as the documents and numbers it produces alongside each budget, full of the forecasts and analyses on the state of the economy and the public finances.

Instead, it was a chin-scratchy working paper that asked the question: if the government invests in something – say, a road or a railway, or a new school building – how long does it generally take for that investment to come good?

The answer, according to the report, was: actually quite a long time. Imagine the government spends a chunk of money – 1% of national income – on investment this year. In five years’ time that investment will only have created 0.4 per cent of GDP. In other words, in net terms, it’s costed us 0.6% of GDP.

But, and this is the important thing, look a little further off. A high-speed rail network is designed to last decades, and as those decades go on, it gradually improves people’s lives – think of the time saved by each commuter each day – small amounts each day, but they gradually mount up. So while the investment costs money in the short run, in the longer run, the benefits gradually mount.

The OBR’s calculation was that while a 1% of GDP public investment would only deliver 0.4% of GDP in five years, by the time 10 or 12 years had passed, the investment would be responsible for approaching 1% of GDP. In other words, it would have broken even. The money put in at the start would be fully earned back in benefits.

And by the time that investment was 50 years old, it would have delivered a whopping 2.5% of GDP in economic benefits. Future generations would benefit enormously – or so said the OBR’s sums.

Having laid that out, I want you now to ponder the fiscal rules Rachel Reeves is confronted with at this, her first budget. Most pressingly, ponder the so-called debt rule, which insists that the chancellor must have the national debt – well, technically it’s “public sector net debt excluding Bank of England interventions” – falling within five years.

There is, it’s worth underlining at this point, nothing fundamental about this rule. Reeves inherited it from the Conservative Party, who only dreamed it up a few years ago, after COVID. Back before then, there have been countless rules that were supposed to prevent the national debt falling and, frankly, rarely ever succeeded.

But since Reeves wanted everyone to know, ahead of the election, just how serious Labour was about managing the public finances, she decided she would keep those Tory rules. One can understand the politics of this; the economics, less so – then again, I confess I’ve always been a bit sceptical about all these rules.

The upshot is, to meet this rule, she needs the national debt to be falling between the fourth and fifth year of the OBR’s five-year forecast. And according to the last OBR forecasts, which date back to Jeremy Hunt‘s last budget, it is. But not by much: only by £8.9bn. If that number rings a bell, it is because this is the much-vaunted, but not much understood, “headroom” figure a lot of people in Westminster like to drone on about.

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And – if you’re taking these rules very literally, which everyone in Westminster seems to be doing – then the takeaway is that the chancellor really doesn’t have much room left to spend in the coming budget. She only has £8.9bn extra leeway to borrow!

Every spending decision – whether on investment, on the NHS, on benefits or indeed on anything else, happens in the shadow of this terrifying £8.9bn headroom figure. And since the chancellor has already explained, in her “black hole” event earlier this year, that the Conservatives promised a lot of extra spending they hadn’t budgeted for – not, perhaps, the entire £22bn figure she likes to cite but still a fair chunk – then it stands to reason there’s really “no money left”.

Or is there? So far we’ve been taking the fiscal rules quite literally but at this stage it’s worth asking the question: why? First off, there’s nothing gospel about these rules. There’s no tablet of stone that says the national debt needs to be falling in five years’ time.

Second, remember what we learned from that OBR paper. Sometimes investments in things can actually generate more money than they cost. Yet fixating on a debt rule means the money you borrow to fund those investments is always counted as a negative – not a positive. And since the debt rule only looks five years into the future, you only ever see the cost and not the breakeven point.

Third, the debt rule used by this government actually focuses on a measure of the national debt which might not necessarily be the right one. That might sound odd until you realise there are actually quite a few different ways of expressing the scale of UK national debt.

The measure we currently use excludes the Bank of England, which seemed, a few years ago, to be a sensible thing to do. The Bank has been engaged in a policy called quantitative easing which involves buying and selling lots of government debt – which distorts the national debt. Perhaps it’s best to exclude it.

Except that recently those Bank of England interventions have actually been serving to drive up losses for the state. I won’t go into it in depth here for risk of causing a headache, but the upshot is most economists think focusing on a debt measure which is mostly being affected right now not by government decisions but by the central bank reversing a monetary policy exercise seems pretty perverse.

In other words, there’s a very strong argument that instead of focusing on the ex-BoE measure of net debt, the fiscal rules should instead be focusing on the overall measure of net debt. And here’s the thing: when you look at that measure of net debt, lo and behold it’s falling more between year four and five. In other words, there’s considerably more headroom: just under £25bn rather than just under £9bn based on that other Bank-excluding measure of debt.

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Might Reeves declare, at the budget or in the run-up, that it makes far more sense to focus on overall PSND from now on? Quite plausibly. And while in one respect it’s a fiddle, in her defence it’s a fiddle from one silly rule to an ever so slightly less silly rule.

It would also mean she has more room to borrow to invest – if that’s what she chooses to do. But it doesn’t resolve the deeper issue: that both of these measures fixate on the short-term cost of debt without taking into account the long-term benefits of investment – back to that OBR paper.

If Reeves is determined to stick to the, some would say arbitrary, five-year deadline to get debt falling but wants to incorporate some measure of the benefits of investment, she could always choose one of two other measures for this rule.

She could focus on something called “public sector net financial liabilities” or “public sector net worth”. Both of these measures include some of the assets owned by the state as well as its debts – the upshot being that hopefully they reflect a little more of the benefits of investing more money.

The problem with these measures is they are subject to quite a lot of revision when, say, accountants change their opinion about the value of the national road or rail network. So some would argue these measures are prone to more volatility and fiddling than simple net debt.

Even so, these measures would dramatically transform the “headroom” picture. All of a sudden, Reeves would have over £60bn of headroom to play with. More than enough to splurge on loads of investments without breaking her fiscal rule.

There’s one other change to the rule that would probably make more sense than any of the above: changing that five-year deadline to a 10 or even 15-year deadline. At that kind of horizon, a pound spent on a decent investment would suddenly look net positive for the economy rather than a drain.

Whether Reeves wants to do any of the above depends, ultimately, on how she wants to begin her term in office. Does she want to establish herself as a tough, fiscally conservative Chancellor – with a view, perhaps, to relaxing in later years? Or does she feel it’s more important to begin investing early, so some of the potential benefits might be obvious within a decade or so?

Really, there’s nothing in the economics to stop her choosing either path. Certainly not a set of fiscal rules which are riddled with flaws.