The stock market's bullishness has been penned in by the Fed's tapering plans, which Bernanke said would be dependent on improvement in the economy. The S&P 500 Wednesday rose 15 to 1603, the center of what had been a supportive range before the market fell through it last week. The 10-year Treasury yield, meanwhile, fell to 2.54 percent from 2.61 percent, as investors stepped in to buy bonds
"People are still looking at GDP which is very much yesterday's data. That kind of revision makes people say that it makes it harder for Bernanke to taper," said Art Cashin, UBS director of floor operations at the NYSE. On Tuesday, stocks went higher but that was after better-than-expected economic data on housing and durable goods. Tuesday's move was also driven by comments from the People's Bank of China that helped soothe global market concerns about a credit crunch in China.
Dudley speaks at 10 a.m. ET on the regional economy and the labor market for college graduates, and while those topics are not about Fed policy, traders have been speculating his speech would be worth watching.
"That will be a real focus. People will be watching. They think if anybody's a spokesman for Bernanke, it's him," said Cashin.
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Dudley is a key member of the Fed's core, and no one other than Bernanke, or Fed Vice Chair Janet Yellen, possible successor to Bernanke, has as much credibility when it comes to conveying what direction the Fed might take.
"That will be an important speech. He is in the center of the committee, or one of those towards the center for the committee and aligned with Chairman Bernanke, so it will be interesting to hear how he discusses the outlook, what he says about tapering and how he's interpreting the recent data," said Dean Maki, chief U.S. economist at Barclays. Traders also want to hear what he says about the violent reaction in markets since the Fed meeting last week.
Maki said the markets may have become confused when Bernanke signaled during his press conference that the unemployment rate would be the most important variable to determine when the Fed will taper its bond buying. Bernanke said the Fed would reduce its purchases in "measured steps" and that it would be done with purchases by the middle of next year, when the unemployment rate should be about 7 percent.
"We think that's (7 percent) going to be achieved by the first quarter, so that's why even though growth will be sluggish, we think the Fed will be tapering," said Maki. Maki said he expects the Fed to begin cutting back on its purchases in September.
He said the Fed confused the markets by pinning a 7 percent unemployment rate target on the quantitative easing program, while it has also said a trigger to raise short-term rates could be when unemployment reaches 6.5 percent.
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"I think the problem is by tying tapering and the first rate hike to the unemployment rate when the Fed moves up the timing on tapering, it seems reasonable to many market participants that the Fed may be also raising rates sooner than it otherwise might have," said Maki. The Fed forecasts hiking the Fed funds rate, now zero, in 2015 but some traders see it happening sooner.
"It's an odd time for the Fed to be talking about tapering when GDP growth is slowing, job growth is slow…and inflation is about half the rate they expect it to be," said Maki. He expects 1.5 percent growth in the second quarter, and 2 percent growth for the balance of the year, while the Fed sees growth picking up to 3 percent later this year.
Other Fed speakers Thursday include Fed Gov. Jerome Powell, who speaks at 10:30 a.m. on non-conventional monetary policy, and Atlanta Fed President Dennis Lockhart, a non-voting member, speaks at 12:30 on the economic outlook.
Minneapolis Fed President Narayana Kocherlakota told CNBC's senior economic correspondent Steve Liesman, in an interview Wednesday on "Squawk Box" that the Fed needs to be clearer in its communication on the Fed funds target rate, and the market reaction to Fed tapering has been "out-sized."
"There continues to be a great deal of uncertainty about what the Fed is going to do with the Fed Funds rate, our main policy instrument, as the economy recovers more," he said. The Fed did repeat that it would not raise rates until unemployment falls to 6.5 percent or lower, providing the outlook for inflation stays under 2.5 percent.
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"We sort of take for granted that people understand that we're going to be in the business of [rate] accommodation for long after asset purchases end," Kocherlakota said. "We're in the business of accommodation as the economic recovery strengthens."
Besides the Fed, traders will be focused on data, including weekly jobless claims and personal income and spending at 8:30 a.m. ET, and pending home sales at 10 a.m. The Treasury auctions $29 billion in 7-year notes at 1 p.m.
The auction follows a $35 billion 5-year auction Wednesday and a $35 billion 2-year auction Tuesday, both with weakish results. "The results for the 2- and 5-year do not bode well for the 7-year tomorrow," said Ian Lyngen, senior Treasury strategist at CRT Capital. "There's limited risk appetite ahead of the end of the quarter. "