DAVOS, Switzerland — To listen to the talk here this past week, everyone is determined — really, really determined — to save the euro. But no one seems to know quite how.
One leader after another has marched before audiences at the World Economic Forum to declare an unshakeable will to overcome the euro area’s sovereign debt crisis and restore confidence in the common currency.
The euro ‘‘is more than a currency,’’ Chancellor Angela Merkel of Germany said in a speech in Davos on Friday. ‘‘It is Europe. If the euro fails, Europe fails.’’ Her speech came after an almost identical oath of allegiance to the euro in the past week by the President Nicolas Sarkozy of France.
But there still seem to be deep divisions among European leaders, as well as the big thinkers from economics and academia, about what policies will remove doubts about the euro’s future.
Buy back Greek bonds? Increase the size of the European rescue fund? Allow Greece to default? Or just keep muddling through?
‘‘If they’re not willing just to write blank checks to the peripheral countries, I don’t see what their strategy is,’’ said Kenneth Rogoff, an economics professor at Harvard University and former chief economist at the International Monetary Fund.
Even though many of the key figures in the debate are at Davos, no clear solutions have emerged. In fact, much of the rest of the world seems to have moved on. The most intense economic discussion seems to be about how to resolve the tensions created by the United States’ trade deficit and China’s surplus.
Timothy F. Geithner, the U.S. Treasury Secretary, told an audience Friday that the European sovereign debt crisis hurt the U.S. economy last year when it caused a plunge in stock prices, but that the effect was short-lived.
‘‘I think it had a significant effect on slowing the recovery at a delicate point,’’ Mr. Geithner said. ‘‘After a brief loss of momentum, the U.S. started to recover.’’
To be fair, there does seem to be some marginal progress on what to do about Greece. George A. Papandreou, the Greek prime minister, said in Davos on Friday that he expected the European Union and International Monetary Fund to grant the country more time to pay back the money it owed them.
‘‘This will be a major asset for calming markets,’’ he said.
Mr. Papandreou also said there was a discussion taking place behind the scenes on how to strengthen the European Financial Stability Facility, or E.F.S.F., which is administering a $604 billion, rescue fund.
One proposal is to give the E.F.S.F. the power to buy government bonds, or to buy Greek debt at depressed market values in a kind of stealth restructuring. The European Central Bank has been buying Greek, Irish and Portuguese bonds to stabilize markets but has made it clear that it wants political leaders to take over the heavy lifting.
‘‘There is a strong will to think about how the E.F.S.F. can be more robust,’’ Mr. Papandreou said.
But he continued to reject suggestions that Greece default on its debt or restructure its obligations so that it has more time to pay — measures that Mr. Rogoff and many other economists say are inevitable.
Instead, he and Finance Minister George Papaconstantinou insisted that Greece would modernize its tourism and agriculture to restore growth. In addition, they said, Greece will increase revenue by combating rampant tax evasion — seizing the yachts of wealthy deadbeats, going after assets hidden in foreign banks and other measures.
‘‘We sometimes underestimate the capabilities we have,’’ Mr. Papandreou said. Such measures helped Greece increase revenue 5.5 percent last year, according to government figures.
Mr. Rogoff, who has studied the history of sovereign defaults, said on the sidelines of the World Economic Forum that Greece might be able to get its debt under control someday, but that it would require years of sacrifice that few political systems can endure.
The only precedent for such long-term suffering in the service of debt repayment is Romania in the 1980s, Mr. Rogoff said. Then-dictator Nicolae Ceausescu imposed a draconian austerity program on his people, who later rose up and executed him.
Even among the rock stars of the economics world who have congregated at Davos, there is disagreement about if and when Greece should default.
Some advocate a restructuring as soon as possible. ‘‘The longer you delay it, the higher the stakes,’’ said Daniel Gros, director of the Center for European Policy Studies, a research organization in Brussels. ‘‘An orderly default of Greece is not such a bad thing. But do this now.’’
Others fear that a restructuring would heighten fears that Ireland, Portugal and even Spain will also default, alarming markets and risking a much bigger crisis.
‘‘To me the precedent of a default of a euro country is pretty bad,’’ said Robert J. Shiller, professor of economics at Yale.
There is one solution that everyone agrees would work, at least in the short term. Other European countries would simply give Greece and Ireland money to pay off their debts.
But that solution is considered politically unacceptable in Germany. Many economists agree that letting Greece off the hook would reward bad fiscal behavior, raise borrowing costs for other countries and eventually destabilize European monetary union.
‘‘It means that the incentive for Greeks to get their house in order is lowered,’’ said Dennis J. Snower, president of the Kiel Institute for the World Economy in Kiel, Germany. ‘‘Ultimately if any country misbehaves then the risk premium in other countries rises because they are among those who pay for the mess.’’
There was, at least, no shortage in Davos of moral support for the beleaguered euro area.
‘‘Britain has a real interest in the euro succeeding,’’ David Cameron, the prime minister of Britain, said at the forum Friday. Noting that euro members account for 44 percent of British exports, Mr. Cameron said, ‘‘A weak euro zone that doesn’t confront its difficulties is not good for us.’’ But he also sounded mighty glad that Britain still has its own currency.
‘‘There are times when different countries need different monetary policies,’’ he said, ‘‘and I want us to have a monetary policy that suits our needs.’’