Critics have questioned some of the authors' estimates, since these were first rehearsed in an academic paper in 2006. The head of the non-partisan Congressional Budget Office, for example, thinks that paper overestimated the burden of brain injuries, overstated the cost of replacing munitions and equipment, and misattributed other military expenses. But the authors have taken pains to answer those quibbles, and they disclose their sources so that readers can add or subtract as they see fit.

They go on to pursue the war's trail through every twist and turn of the macroeconomic labyrinth. Here, their reasoning is a bit too ingenious. They argue, for example, that the government's spending abroad prevented it from giving America a needed fiscal boost at home. Even if you believe America has suffered from a shortfall of demand in the past five years, surely the blame cannot be pinned on the Iraq war. It must lie instead with the Federal Reserve, which is supposed to maintain full employment as best it can.

Indeed, what is remarkable is how small a macroeconomic price America has paid for its adventure. Not only has the war been financed by borrowing rather than taxes, but also the borrowing has been dirt cheap. Neo-imperialists worry that America has the responsibilities of a global superpower, but an electorate unwilling to shoulder them. For better or worse, though, the combination of volunteer soldiers, hired guns and Asian creditors has lightened the load.

Unlike some other economists, Mr Stiglitz and Ms Bilmes do not weigh the cost of the war against the obvious counterfactual: the cost of containing Saddam Hussein. (They do subtract the cost of enforcing the no-fly zones over the country). Keeping a big force in the region—big enough to cow the dictator into letting weapons inspectors do their job—would not have been cheap, although with hindsight the strategy looks like a bargain. Nor do they pay much attention to the benefits of the invasion, however meagre. For example, the world now knows for sure that Saddam will never lay his hands on weapons of mass destruction. That knowledge may not be worth $3 trillion. But it is surely worth something.

The book mixes the patience of an auditor with the passion of a polemicist; it combines forensic intelligence with prosecutorial zeal. This reviewer responded more to its quieter virtues. As the authors say, the book is not just about the big number on the cover. More importantly, “by examining the costs, we come to understand better the implications of the war.”

Great powers almost never pay for their wars up front. Even in America's war of independence, the revolutionaries printed money to finance their campaign. But a government contemplating war should surely provide a credible advance estimate of the final bill, akin to what Mr Stiglitz and Ms Bilmes have done. If they cannot, it is a good sign they have not fully weighed the implications of their venture. If so, perhaps they should not undertake it at all.