Most surveys suggest the eurozone expanded further during the summer months and that the growth won't rely only on Germany, Europe's largest economy. Even Greece, mired in recession for the best part of six years as the global financial crisis morphed into a crippling sovereign debt crisis, is expected to start growing soon.
Hopes for an improvement in the eurozone economy were supported by a closely-watched manufacturing survey released Tuesday.
The purchasing managers' index for the manufacturing sector a gauge of business activity published by financial information company Markit was 51.1 points in September. Though down on August's 26-month high of 51.4, the survey points to continuing expansion anything above the 50 threshold indicates growth.
"This is good news for the eurozone but also for the global economy," said Chris Williamson, chief economist at Markit. "The downturn in demand caused by the region's recession and the uncertainty generated by its debt crisis had cast a shadow over economic recoveries across the globe. But we must not get too carried away."
Over the past three years, the eurozone, which has a population of around 330 million, has been the laggard of the world economy as it grappled with a debt crisis that at various times threatened the future of the euro currency itself.
Countries across the region, but mainly in the south, such as Greece, Portugal and Spain, have had to enact tough austerity measures to convince bond market investors that they could get a handle on their public finances. A combination of recession, poor management and expensive bank bailouts had caused public debt to swell in the region.
The problems afflicting the eurozone have weighed on sentiment around the world, putting a brake on the global economic recovery. Though the U.S. unemployment rate may have fallen steadily over the past two to three years to 7.3 percent in August, many economists think the decline would have been steeper were it not for Europe's problems.
The wider 28-country European Union, which includes non-euro countries such as Britain and Sweden and has a population of a little over 500 million, has also struggled in the wake of the eurozone's woes in recent years. Here, too, the unemployment rate appears to have steadied, staying unchanged in August at 10.9 percent for the fourth month running.
Olli Rehn, the EU's commissioner for economic affairs, warned that despite the indications of a rebound, the crisis in the eurozone is not yet over. He said governments should continue their economic reforms and debt cuts, lest they stymie the budding recovery.
He also lamented the shutdown of the U.S. government, but said that he thought the impact on other economies would be limited if it didn't last very long.
"But, of course, the recovery in the global economy, and also in the European economy, is so fragile that they do not need any new risks or any new elements of political instability," he told reporters in Paris.
Few economists think the eurozone's current economic growth is enough to significantly bring down unemployment, particularly among the young. The manufacturing PMI survey, for example, showed companies in the sector were still shedding jobs in September, though at a slower rate than before.
The Eurostat figures also mask huge divergences across the eurozone: While Germany has an unemployment rate of 5.2 percent, Spain's jobless rate stood at 26.2 percent. The situation in Greece is even worse, with 27.9 percent of people out of work in June Greek figures are compiled on a different timeframe.
The situation among the young that is, potential workers under the age of 25 is even more acute. Greece and Spain, for example, have over half their youth unemployed. In Greece, youth unemployment stood at a stunning 61.5 percent in June.
As well as being a burden to a country's coffers, sky-high levels of youth unemployment have an additional social cost of denying potential workers skills and experience that's a long-term cost to the region's economic potential and has also fueled an increase in social tensions.
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Sarah DiLorenzo in Paris contributed to this report.