As European banks unwind, will the U.S. recovery come undone?

That’s what U.S. economists are trying to figure out as European banks, scrambling to strengthen their balance sheets, cut back on lending to American businesses and households.

Princeton University economist Hyun Song Shin said in a recent paper that European banks have played a much bigger role in the U.S. economy than has been generally thought — and could do a lot more damage than expected as they pull back.

Shin says European banks grew not only by making direct loans to U.S. businesses but also by sucking up vast U.S. money-market deposits and purchasing U.S. mortgage securities. During the previous decade, “European banks may have played a pivotal role in influencing credit conditions in the United States,” and that helped fuel the U.S. housing and financial bubble, Shin argued in a recent paper.

But now it could hurt the U.S. recovery as European banks shrink and bolster their capital reserves. “The European crisis of 2011 and the associated deleveraging of the European global banks will have far reaching implications not only for the eurozone, but also for credit supply conditions in the United States and capital flows to the emerging economies,” Shin wrote in a paper presented at an International Monetary Fund conference in November and which has been widely read among economists.

The vast extent of those European bank obligations to U.S. institutions, or counter-parties, helps explain U.S. policymakers’ anxiety as they watch European leaders try to head off a crisis like the one that followed the Lehman Brothers failure in the United States in 2008.

Shin’s paper “has orders of magnitude that I didn’t know,” said Kenneth Rogoff, a Harvard University economics professor and former chief economist at the International Monetary Fund.

Rogoff said it’s hard to calculate the impact that the unfolding European banking crisis could have on the United States. “If we saw a meltdown, it’s hard to be too hyperbolic about how grave the effects would be,” he said. More likely, he said, the European Central Bank would continue to give commercial banks large amounts of cheap credit to give them time to unwind investments in a more orderly fashion.

Quantifying what that means for the U.S. economy is difficult, Rogoff said. “It’s a very fluid situation because we don’t really know what the Europeans are going to do,” he said.

But quantifying such things is what private-sector economists are expected to do.

Goldman Sachs chief economist Jan Hatzius is among the pessimists. He says the slowdown in the euro-zone economy could shave 1 percentage point off of U.S. economic growth over the next year, with about half of that a direct result of a pullback by European banks.

Foreign banks’ branches account for about one-fifth of all commerical and industrial lending in the United States, Hatzius wrote in a recent Goldman Sachs report. While domestic banks are easing lending standards, a recent Federal Reserve study showed that those foreign banks are tightening standards in the United States. Hatzius wrote that “some pullback is indeed visible” already.

Moreover, Goldman Sachs’s note to investors highlights Shin’s recent study and its conclusion that European bank purchases of U.S. assets could be much more significant than realized. The Goldman report says that euro-area banks hold about $1.8 trillion, or 3.3 percent, of total U.S. debt outstanding. If those banks were to cut their lending to U.S. residents at the pace seen during the 2008-09 crisis, it would slice 0.4 percentage points off of U.S. growth, the report estimates.

Other U.S. economists are more sanguine.

Mark Zandi, chief economist of Moody’s, said there were signs that some European banks were tightening lending standards in the United States as well as abroad, but he said “the damage might be limited because the U.S. banks are filling the void.”

“They need loan growth, and my guess is they’re licking their chops at the prospect of taking market share,” Zandi said.

Another way the European banking crisis could hurt the U.S. economy is if European banks could not make payments owed to U.S. banks. But Zandi said that this week’s extension of credit by the ECB had eased worries about any disorderly winding down of a European bank’s holdings.

Finally, he added, a weak European economy would hurt U.S. exports and the earnings of European subsidiaries of U.S. companies.

“Add it all up, and it’s certainly not good,” said Zandi, “particularly given how fragile the global econoimic situation is.”But, he added, “I don’t think it’s one of those things that shaves half a point off GDP growth. Perhaps a tenth of a percent, something in that order of magnitude.”

Beth Ann Bovino, deputy chief economist at Standard & Poor’s, agrees. “A modest euro-zone recession is not going to derail a U.S. recovery,” she said, “and that is what our European economist is forecasting.” In the United States so far, she said, “it doesn’t look like businesses and consumers are being hit by the European crisis yet. You’ve seen some hit in terms of exports, but not too much.”

Bovino said, however, that a weaker euro and a stronger dollar could hurt U.S. exports, which would become more expensive relative to European goods. So far, she said, “exports have been one of the bright stars in the recovery.”