“International headwinds affecting the U.S. economy have been widely discussed in global financial markets during the last several years,” he said. “Recent negative international influences on the U.S. economy appear to be waning.”

He looked at two factors that have been widely cited in the international headwinds discussion: global financial stress and the negative impact of a stronger dollar on U.S. gross domestic product (GDP) growth.

“Measures of U.S. financial stress indicate that stress has fallen off its peak earlier this year,” he said. Regarding the second headwind, Bullard noted that the dollar appreciated mostly during the second half of 2014, coinciding with the run-up to the European Central Bank’s quantitative easing program. “This appeared to have had a substantial effect on the net exports contribution to U.S. GDP growth during the winter of 2014-2015,” he said. “Since then, however, the effects of a stronger dollar appear to be waning.”

There are factors slowing global growth, and they’re very real. But to some extent, the attention has distorted their size and scope, and it’s important to separate the facts from the chatter. The data don’t show that the song is over. Europe may be under something of a gray cloud, but the death of European growth, to paraphrase Mark Twain, is greatly exaggerated. I don’t want to evince a stereotypical American overoptimism—and as a native Californian, I will admit to being an optimist in general—but I don’t see a looming global crisis. Growth expectations may be slightly tempered, but that’s a far cry from the triage bay we were in eight years ago. My view is essentially, let’s just stay on track. Let’s not get sidelined by the noise and distraction commentary can sometimes cause.

The world’s largest economy is doing "quite well," Williams said Monday in an interview on CNBC, citing stable inflation and strong employment growth. The U.S. economy grew at a faster pace than expected in the fourth quarter, with a 1.4 percent increase. That compared with a prior Commerce Department estimate of 1 percent, figures issued Friday show.

"The real issue is the global financial and economic developments. There’s uncertainty about what’s happening around the world and how that feeds back to the dollar and the U.S. economy," Williams, who doesn’t vote on monetary policy this year, told CNBC. "We understand that we’re in a global economy so what happens in Brazil or China has a huge impact on the U.S. in terms of our inflation and employment goals."

"We've been missing our 2 percent inflation goal for three and a half years or so, global disinflationary factors are still holding inflation down...The data to me isn't so much about the labor market continuing to improve, I'm very positive on that, it's more about inflation moving back to 2 percent in the context of very strong headwinds," he explained, citing the strong dollar and low commodity prices.

[Brainard’s] concern is that stresses in emerging markets including China and slow growth in developed economies could spill over to the U.S. “This translates into weaker exports, business investment and manufacturing in the United States, slower progress on hitting the inflation target, and financial tightening through the exchange rate and rising risk spreads on financial assets,” Ms. Brainard said Monday in response to questions from The Wall Street Journal.

“Recent developments reinforce the case for watchful waiting,” she said.

"This is a time for patience and analysis, and really assessing data, because there has been some slowing," Robert Kaplan told reporters after speaking before the Real Estate Council in Dallas. "Certainly financial conditions have tightened, and we know that non-U.S. growth is weakening, and I have got to take that into account as a policymaker."

Increased concern about the global outlook, particularly the ongoing structural adjustments in China and the effects of the declines in the prices of oil and other commodities on commodity exporting nations, appeared early this year to have triggered volatility in global asset markets. At this point, it is difficult to judge the likely implications of this volatility. If these developments lead to a persistent tightening of financial conditions, they could signal a slowing in the global economy that could affect growth and inflation in the United States. But we have seen similar periods of volatility in recent years that have left little permanent imprint on the economy.

“Global growth has slowed” and China’s economy is moving to a slower pace, he said in a panel discussion in San Francisco. “We have a strong domestic economy and we can basically offset that. If it weren’t for these headwinds, the economy would easily be growing at 3 percent a year.”

“If you were to ask me what keeps me up at night, or what are the shocks that could cause a recession, I would say almost all of them are outside the U.S. borders,” Williams said Friday on a panel discussion in San Francisco. “I’m actually feeling a little bit more positive around Europe,” he said, but “China’s the wild card.”

“Policy makers should take seriously the potential downside risks to their economic forecasts and manage those risks as we think about the appropriate path for monetary policy,” said Rosengren, a voting member of the FOMC this year.

“These downside risks reflect continued headwinds from weakness within countries that represent many of our major trading partners, and only limited data to support the projected path of inflation,” he said.

Last week we saw a global selloff in stock markets apparently triggered by data from China that fell short of expectations. The bearish environment was compounded by tensions between Iran and Saudi Arabia, the bomb test claimed by North Korea, and lower oil prices. When such volatility develops, I think it's helpful to look at the real economy of the United States (as opposed to the financial economy) and ask if something is fundamentally wrong. Are there serious imbalances that make the broad economy vulnerable to foreign shocks? I don't see that kind of connection in current circumstances.

Richmond Fed President Jeffrey Lacker said the Asian financial crisis of the late 1990s, which helped prompt interest rate cuts by the U.S. central bank, was a "great analogy" for viewing the current situation.

"People overestimated the implication of the Asian market volatility for U.S. growth and we overreacted," Lacker told reporters after a speech in Baltimore. "And I think we have to be careful not to overreact without evidence of significant effects on U.S. fundamentals."

My general view is that many emerging markets are in the stronger position than they would have been in the 1990s. For example, that they have stronger macroeconomic policies. They have taken steps to strengthen their financial systems and are better positioned to deal with this. On the other hand, there are vulnerabilities there and there are countries that have been badly affected by declining commodity prices, so we will monitor this very carefully, but we have taken care to avoid unnecessary negative spillovers.

This greater degree of monetary accommodation seems appropriate given the adverse effects on U.S. aggregate demand coming from the rise in the dollar, an associated weakening of foreign economic prospects, and other developments that have restrained spending and kept inflation undesirably low.

At [the October 27-28] meeting, the Fed removed language it had inserted in its September statement expressing concern that global weakness could hinder U.S. growth and further depress inflation. Until China's surprise devaluation of its currency on Aug. 11 sent financial markets into a tailspin, the Fed had been expected to begin raising rates in September.

In his interview with the AP, Williams said the Fed had been correct to note these developments in its September statement. But since then, he said, markets have stabilized.

"What has happened in the last six weeks is that volatility has come down," Williams said. "I think the uncertainties, risks, seem to have ebbed."