Forget the stage-managed rows, walkouts and last-minute reconciliations, today's G20 summit will end in agreement, amity and mutual congratulation. The summit's success is preordained in two and a half ways.

First, it is a matter of simple arithmetic that today's meeting will be essentially a rubber-stamping ceremony for deals already done between the sherpas, the senior civil servants who have spent the past three months clearing the way to the summit for the G20 leaders. This can be stated with certainty because genuine negotiations will be impossible in the summit's four hours of business sessions. With 24 political leaders not known for their self-effacement all determined to have a say, the time allotted averages barely 11 minutes per speaker - and this calculation makes no allowance for the central bankers, finance ministers and international officials also in attendance, or the long and ornate soliloquies delivered on such occasions by Italian, Spanish and Latin American politicians.

Second, it is a matter of political certainty that all the leaders genuinely want to save the world from the present crisis. And none has any reason to obstruct the four different roads to salvation on the summit agenda. Everyone agrees on the need for monetary, fiscal and trade stimulus, to save failing banks with government support, to save failing countries with support from international institutions and to save global capitalism with reforms that restore faith in the financial system.

Of course, different governments will have different priorities and there will be disagreements at the margin about the size of tax cuts and relative merits of public spending programmes, about the impact of trade policies or about precise techniques of monetary expansion. But all the leaders will be perfectly justified in boasting about the unprecedented stimulus already injected into the global economy since the Lehman bankruptcy on September 15 and about the extraordinary degree of monetary co-operation that has resulted in every big economy moving almost in lockstep to a regime of near-zero interest rates, which was unthinkable even a few months ago.

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This energetic response to the crisis has been as different as could be imagined from the suicidal fiscal retrenchments, currency misalignments and recriminations that helped to produce the Great Depression.

Which brings me to the half-reason for optimism about the London summit: there are tentative signs that the world economy is starting to respond to the epic policy efforts that the G20 leaders have already made.

In the past few weeks, home sales and mortgage financing figures have been improving in America and Britain, commodity prices and freight rates have rebounded, capital spending in China has risen sharply and the collapse in industrial activity has abated, especially in the US. Most importantly, the financial chaos that triggered the global recession appears to have calmed down, with fears of big bank collapses receding and the global credit system no longer completely paralysed. A return to growth looks possible for most of the world by the second half of this year.

Note the qualifiers in that last sentence: possible and most. To judge by the forecasts of the IMF, the World Bank and the OECD, a recovery this year is unlikely. All three predict the world economy will contract in 2009, for the first time since the Second World War. The OECD shows output continuing to fall in every leading economy, apart from Canada, until the end of this year - and predicts that output will remain lower, on average, in 2010 than in 2009. If these forecasts are taken seriously, then the world really is on the brink of a disaster, with unemployment in many countries rising to levels unseen since the 1930s.

It is just as well, then, that the forecasts produced by the OECD and others should not be taken seriously at all. The reason is obvious if we compare the OECD's latest forecasts with those it produced just four months ago. In November, the OECD believed that the GDP of its member countries would decline by a very moderate 0.4 per cent in 2009; today that has been revised to an unprecedented collapse of 4.3 per cent. In November the OECD and the IMF said that Britain would be the weakest of the leading economies; but today the OECD predicts that Britain will do better than any other major economy, apart from Canada and France. In November, the OECD believed that Japan and Germany would escape more or less unscathed from the recession, with declines of less than 1 per cent in GDP; today it predicts that Germany's GDP will plunge by 5.6 per cent and Japan's by 6.6 per cent.

Recessions and recoveries are impossible to predict, at least with the standard methods that economists employ. Indeed the IMF produced a study several years ago looking at 72 recessions in 68 countries over the previous 20 years. In only four of those 72 cases did econometric models predict these recessions even three months ahead.

The problem is that the forecasting models are all based on projecting past trends. That means, ipso facto, that when the world economy is subjected to unprecedented forces - the near-collapse of the financial system pulling in one direction and the unprecedented fiscal and monetary stimulus pulling the other way - computer models are bound to be completely useless.

But if forecasts are worthless at present, where does this leave the G20 leaders or indeed businessmen, investors and consumers who have to form some view about the future? The answer is that all we can rely on is careful observation of statistics and common sense. Common sense tells us that people in America, Britain, Australia, Canada and China who are offered tax cuts and virtually interest-free credit are likely to seize this opportunity and start investing and spending money. It is far less clear that Germans, Japanese, Italians and the French will react in the same way. As a result, it is likely that the Anglo-Saxon and Chinese economies will respond more quickly to the fiscal and monetary stimulus than the eurozone and Japan.

This is also the message conveyed by recent statistics. In the absence of another huge financial shock, a recovery in America, Britain and China looks quite probable in the second half of this year. In Germany and Japan, on the other hand, no such recovery is in prospect. Thus, a crisis supposedly caused by unsustainable housing booms and excessive consumer borrowing is likely to hit hardest the two countries that experienced neither. When Angela Merkel eventually submits to demands for more stimulus it will not be to please Gordon Brown or Barack Obama. It will be to save her own country from collapse.

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