At the end of 2012, the Fed announced that it would keep short-term interest rates low so long as the unemployment rate remained above 6.5 percent — the first time the central bank had ever declared so precise an economic objective. (The Fed has a dual mandate, to maximize employment while at the same time keeping inflation below 2 percent.)

For the last decade I’ve studied the behavior of policy makers at the Fed, the European Central Bank and the central banks of England, Germany, New Zealand and Sweden. Their leaders have for decades searched for a new conceptual anchor for monetary affairs — no longer gold or fixed exchange rates, but an evolving relationship with the public. Communication has become a fulcrum of policy. Policy makers shape expectations and, thus, economic behavior.

By the late 1990s a vast majority of the central banks had begun to incorporate elements of inflation targeting. The aim is to shape the expectations around the most fundamental dynamic of market economies: the evolution of prices. The experiments relied on theories going back decades. As far back as the 1930s, the economists Knut Wicksell, Irving Fisher and John Maynard Keynes proposed that price behavior was based in large part on expectations.

The pronouncements by central banks, through statements, testimony and news conferences, endow the future with discernible features that we can reflect and act upon, animating or curtailing our propensities to produce, consume, borrow, lend and so on. Markets are, after all, a function of language.

Ms. Yellen faces immense challenges: The most immediate is the gradual slowing of the policy of “quantitative easing” that the Fed has used to hold down interest rates, through large-scale purchase of bonds. Ms. Yellen has to continue to articulate the Fed’s dual mandate — maximum employment and stable prices — to the markets, to consumers and to government officials. She will have to orchestrate and communicate decision making within the Fed, so that disagreements can enhance rather than diminish confidence in monetary policy. She also has the added burden, which the Fed has shouldered since the financial crisis, of ensuring the stability of the American financial system.

A senior official of the European Central Bank, Benoît Coeuré, said in a speech last year that monetary stability was “a cornerstone of the social contract.” Fed officials who remember the high inflation of the 1970s, brought under control by Mr. Greenspan’s predecessor, Paul A. Volcker, pretty much agree.

Ms. Yellen is likely to continue the policies of Mr. Bernanke, who helped make Fed policy much more transparent. Like him, she will have to communicate to multiple audiences — members of Congress, the financial markets and consumers — who have come to expect clear and precise messages from the central bank.

The incremental experiments with language and explanation pursued by the Fed over the last decade are setting a new relationship with the public, one in which ordinary people’s predicaments are recognized and have come to serve as a fulcrum of policy. The days in which the leader of the Fed could mumble incoherently, obscuring his true intentions behind a cloud of verbiage, are gone.