What a difference a few months make. Iraq was going to be Gordon Brown’s big prime ministerial headache but since the withdrawal of British troops from Basra it has slipped well down the political agenda. Brown took the poisoned chalice left by Tony Blair and quickly poured it down the drain. He has a sea of troubles, but Iraq, for now at least, is not high on the list of them.

In America, Iraq was going to dominate the presidential campaign, pundits predicted. If Barack Obama’s team have their way, it still will. They have been trying to generate some heat by reminding the electorate that John McCain and Hillary Clinton supported the war at first, unlike Obama, and have even been calling it the “Bush/McCain war”.

But, partly because of the success of the US troop surge in reducing casualty numbers in Iraq, and in particular the bodybag count for American forces, the issue is not as salient as it was. Polling in America shows that voters think the troop surge is working. They think the war was a mistake and are highly critical of George W Bush’s handling of it, but Bush is on his way out and Americans have something else to think about: the state of their economy. With main-stream forecasters talking about an election-year recession, even a foreign policy issue as explosive as Iraq has slipped into the background.

If Joe Stiglitz has anything to do with it, however, it will not remain there. He is the Nobel prizewinning economist who, unlike most who get to those dizzy intellectual heights, has refused to remain in an ivory tower.

Eight years ago he quit his position as chief economist at the World Bank, having launched an outspoken attack on its sister organisation, the International Monetary Fund. He said the fund was made up of “third-rate economists from first-rate universities”, peddling snake-oil remedies to poor countries desperate for economic development.

He wrote a book, Globalisation and Its Discontents, which made him a poster boy for the antiglobalisation movement. Another, Making Globalisation Work, tackled the question of how to make the world’s poor benefit from free trade. Having been an economic adviser to Bill Clinton in a decade he calls the Roaring Nineties, he has been keen to contrast the success of that era – in which a Democrat president slashed the budget deficit – with the troubles of the Bush era.

Stiglitz’s big passion now, however, is Iraq. In his new book, The Three Trillion Dollar War, written with Linda Bilmes (and published in Britain by Allen Lane), he argues that not only has the cost of the conflict been much greater than anybody close to the White House has admitted, but that the war is closely tied in to America’s present economic woes.

Three trillion dollars – or about £1.5 trillion – is a lot of money, particularly when contrasted with the White House’s initial estimates of $50-$60 billion. It dwarfs even official estimates of the cost of the war so far as about $645 billion.

Yet the book’s title, if you believe the figures, undersells it. Three trillion dollars is just the cost to America. The cost to the rest of the world, he suggests, is roughly the same again. Six trillion dollars, to put it in perspective, is nearly half America’s annual gross domestic product. Are these numbers plausible and why do they differ so much from the official figures?

It comes down, in the end, to what you choose to measure. The White House, which has an interest in playing down the financial impact, has focused on direct budgetary costs to America. Even these can be played in a number of ways. If you are maintaining a large regular army anyway, what is the additional cost of deploying it in the theatre of war?

Stiglitz and his co-author, in contrast, have looked at the wider costs of the war, not just the direct military costs but the social costs, the economic costs, even the effect on the world of higher oil prices, part of which he attributes to the war. Pretty well everything has gone in, including the kitchen sink, though he still claims that his numbers are almost certainly underestimates.

There is even a figure for Britain: more than £20 billion for direct military and social costs, not including some of the wider economic consequences. That, however, no longer looks such a big number when set against the £100 billion of Northern Rock debt the government has just taken onto its books.

When you talk to Stiglitz, it is hard to resist his enthusiasm, if not his precise figures. He has a way of putting things straightforwardly. Should US troops remain in Iraq, if only for another two years? His come-back is in the numbers. “Two years would cost us over half a trillion dollars,” he says. “Is that the best way to spend over half a trillion dollars?”

But do the big numbers really help the debate? Take the assumption that between $5 and $10 of the current near-$100 a barrel price of oil is due to the Iraq war. It may or may not be true: we are dealing here with what Donald Rumsfeld might have called “unknown unknowns”.

Even if it is true, costing it is by no means easy. The loss to oil consumers from paying more for crude is offset by the gain to oil producers. If things had followed the patterns of the past, when the global economy was brought to its knees by high oil prices, pointing the finger at Iraq would have been a powerful rhetorical device.

This time, however, high world oil prices appear to have been a reflection of the global economy’s strength, and the rise of China, rather than the fault of America’s Iraq blunders.

The fact that the $3 trillion figure has the imprimatur of a Nobel economist will give it weight, however. If that means Americans recognise what Stiglitz describes as the “terrible mistake” of the war and insist their government does not go down that road again he will say it has served its purpose.

It is hard to deny his compassion. Having dedicated the book to those who have died in both Iraq and Afghanistan but also the returning veterans, he gives an 18-point reform plan, a blueprint, ranging from giving Congress greater power to veto wars on financial grounds, to wide-ranging improvements in how America looks after its veterans.

One idea is that taxes should be raised explicitly to pay for wars, making voters immediately aware of the costs; another is that veterans should be given the automatic right to health-care. Britain’s treatment of its Iraq veterans has been much criticised. Compared with the conditions in America, where stressed and injured soldiers often have to fight for entitlement, it stands up pretty well.

Stiglitz, despite having worked for Bill Clinton, thinks Obama has the right answers on Iraq. Who knows, if Obama triumphs in November, he could find himself back in the White House, trying to put his blueprint into practice. That will be no easy task.

Andrew Sullivan is away

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