Italian bank analysts combed through years of data and applied advanced mathematics to try to understand the country’s rising interest rates. But what sparked a breakthrough this summer was a blunter tool: a look at the number of Google searches for phrases such as “euro breakup” and “end of euro.”

The finding was stark. Such searches peaked at the same time that the rates on Italian government bonds were spiking. This suggested that there was a link between investors’ concern about putting their money in Italy and their more general anxiety about whether the euro zone as a whole might break apart.

This observation by analysts with the Italian central bank added to other evidence that Italy’s borrowing costs were no longer solely related to economic conditions inside the country or the health of its government finances. These costs were also being driven higher by events beyond Italy’s control — in particular, the fear that it and other countries could be forced out of the currency union.

“Concerns about the fragility of the euro are increasingly and widely mentioned by a number of market observers and have apparently caught the attention of the public at large,” a Bank of Italy report said in September. The analysts pointed to the “Google-based indicator” as proof Italy was being punished with higher rates for something over which it had little influence.

Initially, it was politicians from cash-strapped countries and a handful of economists who maintained that a few individual European countries such as Italy and Spain were being unfairly burdened because global investors were fearful about the euro zone’s fate as a whole.

But that argument has found a wider audience in recent months and provided the European Central Bank with a justification for its dramatic shift in how it approaches the euro zone’s problems. After years of reluctance, ECB officials say they will spend as much money as necessary to control runaway interest rates and stabilize conditions in euro-zone countries. The announcement by ECB President Mario Draghi last month that the central bank would buy the bonds of ailing governments in unlimited amounts helped bring some bond rates down from dangerous levels and gave global markets a boost.

Draghi said at a London speech in July that interest rates in Italy and Spain were being forced up by something called “convertibility risk” — essentially a premium demanded by investors who think a country might be forced to leave the euro zone and revert to a different currency, say the Italian lira or Spanish peseta, undercutting the value of government bonds.

By linking the surge in Italian and Spanish interest rates to causes outside the control of local officials, the ECB could justify an initiative that might otherwise have been impossible in a continent divided between struggling countries in southern Europe and more successful ones to the north. Draghi argued that the ECB needed to assert itself so interest rates and other conditions could be brought into line for all euro members.

“Until May or June of this year, the perception was prevailing that if you have high interest rates in the marketplace, that is just the real measure of your degree of sin,” Italian Prime Minister Mario Monti recently said at the Council on Foreign Relations in New York. Since then, “the Germans, the Dutch, the Finns have come to recognize there was a component linked to skepticism about the integrity of the euro over time.”

But even economists who accept that countries such as Italy and Spain are paying a euro-zone risk premium say it is hard, if not impossible, to measure this effect and determine how much of the interest rate reflects Europe-wide concerns and how much reflects the country’s economic conditions and financial health.

The ECB has not published any studies estimating the impact of convertibility risk on European government borrowing costs. Google searches aside, the Bank of Italy study said that several other factors could be at work, including changes in how investors analyze risks.

The components of a government bond rate “are almost impossible to separate,” said Jean Pisani-Ferry, head of the Brussels-based think tank Bruegel.

Arguments over the behavior of interest rates — and what it means for the ECB’s proper role — have been underway since the region’s debt crisis began three years ago. Economists and analysts familiar with the discussions say Jean-Claude Trichet, the ECB’s chief at the time, drew a hard line when it came to policies that strayed too far from the central bank’s mandate of controlling inflation. And he balked at suggestions that the euro zone was vulnerable to a breakup.

The debate began to change after Draghi, a former Italian central banker and Goldman Sachs executive, took over a year ago.

Europe’s economy began to slip into a recession. Meanwhile, studies by the International Monetary Fund showed that the euro zone was disintegrating with the flight of hundreds of billions of dollars out of struggling countries. This dynamic meant that countries such as Italy and Spain, as well as Greece, Portugal and Ireland, were having to pay vastly higher interest rates to attract investors than were economically solid countries such as Germany.

The IMF now considers the euro zone to be in the midst of a full-blown balance-of-payments crisis — terminology usually reserved for developing nations that are abandoned by international investors and left without access to the currency they need to keep their economies working.

“The system was collapsing. . . . The euro itself had the potential to drive countries into a bad equilibrium” of rising interest rates and evaporating capital, said Belgian economist Paul De Grauwe, an early advocate of the idea that the euro crisis would subside only when the ECB took a more active role.

De Grauwe said his arguments were often rejected by European officials, central bankers and other economists, but he sensed matters were changing when he was invited in June to present his research to top ECB staff.

The change in direction at the ECB, embodied in a Draghi pledge this summer to do “whatever it takes” to preserve the currency union, raises a host of questions about what might have been if the central bank had acted earlier. Had the ECB’s bond-buying programs been available for Spain a year ago, for instance, the country might have saved billions of dollars in higher interest costs — money that could have been spent fighting a recession or a 25 percent unemployment rate instead of being paid to bondholders.

The ECB is still developing the details of its new program. It has offered unlimited purchases of government bonds, but only once the country issuing the bonds agrees to abide by economic policies that the central bank finds credible. That “conditionality” has been one reason Spain, for instance, has so far held off asking for help.

Draghi, meanwhile, has not detailed exactly when the ECB will embark on bond buying, only that he and others will monitor a broad set of indicators and act when they need to do so.