So it comes as a surprise, not least to Mr. Sims and Mr. Sargent, that these two now find themselves thrust into an uncomfortable spotlight. Conservative voices, like the editorial page of The Wall Street Journal, have claimed them as their own. The men’s work on economic cause and effect and the theory of rational expectations — which maintains that people use all the information available in making economic decisions — proves that Keynes had it wrong, these commentators say.

It would be a provocative thesis — if it were true. But Mr. Sims and Mr. Sargent say their work is being misread. Both, in fact, are longtime Democrats who maintain that government can, and should, play a role in economic affairs. They stand behind many recent policies of the Obama administration and the Federal Reserve. They even have some ideas about how European governments might defuse the running crisis on the Continent.

They won their Nobel for “their empirical research on cause and effect in the macroeconomy,” in the academy’s words. What that means, in part, is that they have done some serious math. Today, ideas they largely formed in the 1970s and ’80s help shape the thinking inside the Fed and on Wall Street.

Their work goes beyond old labels like Keynesianism and the monetarism of Milton Friedman. They have shown that fiscal and monetary policy are inextricably linked, and their research reflects the broad shift in economics from words to numbers — toward a level of empirical analysis that few outside the profession can readily grasp. But it contains a kernel of skepticism appropriate for these troubled times. In a world of uncertainty and constraint, cause and effect may not be what they seem. As a result, we must test and retest our assumptions — and try to prepare for the unexpected.

“The most impressive thing about them as scholars,” says David Easley, an economist at Cornell University, “is that in recent years they have questioned the assumptions of the models they helped to create, and they have been at the vanguard of the efforts to go beyond them.”

Mr. Sargent says his most important work is spoken “in the beautiful language of math.” He knows it’s not widely understood.

“The kind of work we do, that real economists do, will never catch on with the public,” he says.

THOMAS SARGENT, in a draft of his Nobel acceptance speech, refers to himself as an “American provincial.” On a recent afternoon, over a bowl of noodles at an Asian restaurant near N.Y.U. in Greenwich Village, he used football metaphors to discuss economics. He compared fiscal policymakers to coaches, with X’s and O’s. He often wears T-shirts, sweatshirts and baseball caps, gear as appropriate in Montana, where he keeps a cabin, as it is in Washington Square.