If 2012 was the year when a sense of calm returned to euro-zone financial markets, 2013 will be when Europe needs to show that its recipe of austerity and reforms can work. Strong evidence for that would be if a bailed-out country could finance itself again. Hence the hopes invested in Ireland, which entered its rescue program in 2010 and is scheduled to make a full return to the bond markets at the end of 2013.

The markets seem to be signaling that it can be done. Yields on Irish government bonds maturing in 2020 fell from 8.5 percent at the start of 2012 to 4.5 percent by the end of the year. Renewed appetite for Irish debt allowed the government to regain partial access to bond markets in 2012. Ireland's debt-management agency plans to raise $13.2 billion by issuing bonds in 2013. That will leave it with $24.9 billion of cash reserves, sufficient to cover the government's needs for 2014.

There are stirrings of life in the battered Irish economy. Although GDP is thought by the IMF to have grown by only 0.4 percent in 2012, that compares well with deep recessions in Italy and Spain and followed a 1.4 percent rise in 2011. The current account has been in surplus since 2010. Underlying competitiveness has improved sharply, judging by unit labor costs.

Helped by a low corporate tax rate of 12.5 percent, Ireland continues to attract foreign investment, especially from U.S. firms and particularly in pharmaceuticals, information technology and financial services. The number of new projects in 2012 has been similar to that in 2011, itself the highest for a decade, said Barry O'Leary, the boss of Ireland's inward-investment agency.

The foreign presence is now a towering one, so much so that Irish exports actually exceed the value of GDP. The contribution from net trade -- exports less imports -- has more than offset falls in domestic demand, which remains traumatized by excessive debt, continuing austerity and a financial squeeze as the now well-capitalized but unprofitable Irish banks limp along.

But this brightening picture is not all that it appears. Take Ireland's reliance on foreign firms, which gears the Irish economy to global growth so that it suffers when world trade falters, says Simon Hayes of Barclays. Exports have been growing at only 2 percent a year since last spring, the slowest since they started to recover in early 2010.

It also makes the economy vulnerable to shocks affecting specific sectors. Ireland's success in attracting global drug firms -- pharmaceuticals made up half of exported goods in 2011 -- means that it is being affected by the expiration of patents on many popular drugs.

Another concern is that Irish progress, both economic and fiscal, is typically measured using GDP, the output generated within Ireland. But for an economy where foreign firms are so dominant, GNP, or the income that goes to residents, is more relevant. Irish GNP is lower than GDP because of the big profits made by foreign firms. The gap between the two has been widening, from 14 percent in 2007 to 20 percent in 2011.

That widening shortfall reflects the fact that the Irish people have fared much worse than the Irish economy. National output measured by GDP was 7 percent smaller in 2011 than in 2007, whereas national income measured by GNP was 11 percent smaller. This matters not just for living standards but also for Ireland's fiscal situation: it is GNP that does the heavy lifting on the public finances, since multinational profits are taxed so lightly.

Ireland's vulnerabilities explain why the IMF wants Ireland's European creditors to give it more help. In particular it advocates lightening the debt-servicing charges on promissory notes, a sort of IOU, which the Irish government issued in 2010 mainly to prop up the collapsed Anglo Irish Bank.

A lot has gone right for Ireland. But it wouldn't take much for the eurozone's model pupil to fail to graduate from its rescue program.