The results of the stress tests were a big step along the road the administration is taking. They impose enough pain to appear credible, but not enough to be disruptive. The 10 affected banks will easily raise the needed money: a total of $75bn (€55bn, ￡59bn). Their market valuations duly soared.

Douglas Elliott of the Brookings Institution has provided a comparative analysis of how the US regulators reached their conclusions.* He contrasts their numbers with those of the International Monetary Fund, in its latest Global Financial Stability Report, and Nouriel Roubini of RGE Monitor and New York University. He also allows for the fact that the IMF and Mr Roubini look at all losses in US banking, while the tests apply to 19 institutions that hold some 70 per cent of US banking assets.

Estimated losses for 2009 and 2010 by the US regulators, the IMF and Mr Roubini are $535bn, $321bn and $811bn, respectively. So regulators were noticeably more risk-aware than the IMF, albeit less so than Mr Roubini. Against these losses are set the expected earnings (after dividends) over these years, plus a provision for 2011 losses. Here the regulators estimate earnings at $363bn, against an assumed $210bn for the IMF and Mr Roubini. This means the reduction in capital is estimated at $172bn by the regulators, $111bn by the IMF and $601bn by Mr Roubini. But, after allowing for planned capital-raising and excess earnings in the first quarter of 2009, the final reduction in capital is just $62bn for the regulators and a mere $1bn for the IMF, but as much as $491bn for Mr Roubini.

There are two important numbers in the above analysis: possible losses, and the buoyancy of earnings. Yet there is a final number of no less significance: how much capital does a bank need? The answer is: how long is a piece of string? Since many of these banks are deemed too big to fail, taxpayers are risk-bearers of last resort. The capital requirement depends partly on how well the government wants to be cushioned against possible losses and partly on how well bond-holders want to be insured against the possibility that government might refuse a rescue.

At the end of 2008, the ratio of total common equity to US banking assets was 3.7 per cent. Without the explicit and implicit insurance provided by government, it would surely have been higher. As the IMF notes, in the mid-1990s, before the leverage boom, the ratio was 6 per cent. In the 19th century, before deposit insurance, it was much higher still.

The conclusions are three: first, the government's exercise is more conservative on losses than that of the IMF, albeit far less so than Mr Roubini's; second, most of the capital to be raised will come from the earnings of a banking system able to borrow on the favourable terms arranged by the central bank and then to lend more expensively to its customers; and third, the target capital ratios – Tier 1 risk-weighted capital of 6 per cent of assets and Tier 1 common equity capital of 4 per cent – are not especially onerous.

The purpose of the exercise was indeed conservative: to make it credible, though not certain, that the existing banking system and assets can survive the likely battering. This has been done well enough to satisfy the markets. But these banks will also be unable to expand their balance sheet significantly in the near future.

The biggest question is how far this exercise will help restore the economy. Commercial banks provide only a quarter of financial sector credit in the US, down from close to 40 per cent in the mid-1990s (see chart). Much of the rest came from various forms of securitisation. Unless and until the latter markets reopen fully, private sector credit is likely to be constrained. How far that constraint is binding depends on how far highly leveraged borrowers are willing to borrow, particularly when the collateral against which they borrow has lost value. For this reason, it is the huge stimulus – the least conservative parts of the economic package – that will deliver the recovery. These are also the least upsetting to the interests of powerful lobbies, particularly in finance.

More radical approaches – allowing more banks to default, for example – would have increased uncertainty in the short run and so undermined the return to stability Mr Obama craves. But here the president must reckon on a longer-term danger: that the rescued financial system will, in time, start to lay the foundations for another and possibly still bigger financial crisis in the years ahead.

Ensuring the rescue of a financial system packed even more than before with complex and “too-big-to-fail” institutions may well be the cautious response to this crisis. But it leaves the government with the even more onerous task of imposing effective regulation in future. Unhappily, the record of regulation of generously insured financial systems is extremely poor. The mobilised self-interest of highly rewarded players easily overwhelms the constraints imposed by far less well-rewarded and almost certainly less able regulators.

The more the crisis unfolds, the more evident it is that incentives in the financial system were (and are) badly distorted. I sympathise with the conservative approach to crises, but not if it leaves in place the plethora of perverse incentives that created them. At the end of this, then, there will be one big test: will the number of institutions thought “too big to fail” be as large as now and, if so, how will they be controlled? If the answers are still not clear, there will need to be yet more change.

*Implications of the Stress Tests, May 11 2009, www.brookings.edu