After Friday’s shock US jobless figures, there was rather better economic news yesterday, which helped to steady the stock market’s nerves. The UK services sector grew at its fastest rate for two years in September, according to the monthly purchasing managers’ index.

The figures for manufacturing and construction were weaker, but the services reading makes it all but certain that the economy did start to grow again in the third quarter.

Services companies were also relatively optimistic about the future, with a majority saying that they expected growth to be sustained over the next year.

The news helped the FTSE 100 up above the 5,000 mark, after the wobble at the end of last week.

Yet the continued strength of the stock market appears dramatically at odds with the gloomy noises coming from many business leaders.

Michael Geoghegan, chief executive of HSBC, this week joined the ranks of those predicting a W-shaped recovery. And, in a round of interviews yesterday, Steve Ballmer, chief executive of Microsoft, was almost as gloomy.

Of course, one should not set too much store by the predictions of even the most successful chief executives. Their record is no better than economists and they have no interest in talking up the recovery — they would much rather under-promise and over-deliver. In private, some confess they are deliberately cautious in public to keep their staff on their toes.

Nevertheless, there is no denying that the mood in the boardroom is very downbeat, with many business leaders sharing the same concern — unemployment.

One of the most striking characteristics of this recession has been the relatively slow increase in unemployment. The rise has still been very grim, but much less than would have been expected when comparing the present downturn with those of the 1980s and 1990s.

But the fact that unemployment has been sticky on the way up prompts many economists and business leaders to fear that it will be sticky on the way down, too. The purchasing managers’ survey yesterday added to those concerns, with services companies reporting that they planned to axe staff at a faster rate despite the increase in activity.

Job losses have been minimised partly because of the efforts by companies and unions to cut pay or hours instead. This means that when demand turns up there will be plenty of slack in the system to be used up before new hiring takes place.

The Bank of England has warned that pay moderation and increased flexible working may only have delayed the fall in employment. Moreover, a recovery in employment may be dampened by the increased burden of red tape and tax, including the hike in National Insurance.

Yesterday’s proposal from the Tories to exempt new companies from paying National Insurance on their first ten employees looks a sensible use of resources, which was welcomed by the CBI.

But what really worries some business leaders is that even assuming that private sector unemployment peaks in the middle of next year, we might then be hit with the threat of widespread job losses in the public sector as the new government seeks to control the ballooning deficit.

That could easily knock the wind out of consumer confidence, propelling us down the third leg of the W.

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