third time in a year the European Union is going through the same ritual, bailing out another insolvent country. Portugal now follows Greece and Ireland to the European welfare office to ask for new loans on the condition of ever more drastic spending cuts.

For the third time in a year the European Union is going through the same ritual, bailing out another insolvent country. Portugal now follows Greece and Ireland to the European welfare office to ask for new loans on the condition of ever more drastic spending cuts.

So far the markets have taken Europe’s third successive sovereign financial crisis in stride. But many economists are a good deal more alarmed, most notably because the bailout formula European leaders keep applying to their most indebted member nations shows no signs of working.

Greece, Ireland and now almost certainly Portugal have access to hundreds of billions of dollars in emergency European aid to help them avoid defaulting on their debt. But the aid is really just more loans, and the interest rates the countries are paying, if a little lower than what the private market would charge, are still crushingly high. Their pile of debt gets bigger with every passing day.

Moreover, the price of these loans has been a commitment to slash government spending far more drastically than domestic leaders would have the desire or the political power to accomplish on their own. And for countries that depend a good deal on government spending to generate growth, rapid decreases in spending have meant sustained economic stagnation or outright recession, making every dollar of debt that much harder to pay back.

Economists call this “the debt trap.” Escape from the trap generally requires devaluation of the currency, which cannot happen among countries that use the euro as their common currency, or strong economic growth, which none of the three have, or some kind of bankruptcy process, which all three forswear. Add to that the likelihood that all three countries will continue to have unstable governments until they figure a way out, and Europe’s financial crisis has no end in sight.

“What has been missing, in the debate about how countries can restore their finances to some kind of sustainability, is the limit of how much they can cut in a period of austerity,” said Simon Tilford, chief economist for the Center for European Reform in London. “There is a limit of how much any government can cut back spending and survive politically unless there is a light at the end of the tunnel, a route back to economic growth.”

The problems of the weaker countries are not just sovereign debt, but also lack of competitiveness, both in Europe and the larger world. Without the nations’ restoring competitiveness and selling more goods abroad, which can come only through a longer-term process of reducing wages and taxes to spur private sector investment, economists are not optimistic about prospects for new growth soon.

The crisis in Portugal also raises new questions about whether the European Union will come to grips with the other side of its crisis: the banks. Banks in well-off countries like Germany, France and the Netherlands, as well as Britain, hold a lot of Greek, Portuguese and Irish debt. And if these countries cannot pay their debts, they would have to reschedule them, reduce them or default, causing a major banking crisis in the rest of Europe.

That reckoning would require governments to ask their taxpayers to recapitalize the banks, which is exactly what political leaders are afraid to do.

“We have a banking crisis interwoven with a sovereign debt crisis,” Mr. Tilford said. “Europe needs to address both, and it needs to acknowledge that the banking sectors of creditor countries — especially Germany — are not now in a position to handle restructuring and default, and that governments will have to pump money into the banks to recapitalize them.”

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