"They don't have the advantage of having the next employment report. They'll have a little bit on the manufacturing sector…they'll have the ISM which could be important," said Deutsche Bank chief U.S. economist Jospeh LaVorgna. LaVorgna said next week's claims will be even more critical because next week is the survey week for the April jobs report, which will be released May 3.
The report also comes as the market debates just what is on the Fed's mind, after the Fed minutes revealed that several Fed officials were discussing tapering down the Fed's quantitative easing program sooner than expected. But the bad data, especially the March jobs report, has mitigated the concern in markets that the Fed would be able to end the $85 billion in monthly purchases of Treasurys and mortgage securities very soon.
The weekly claims data last week came in at an elevated 385,000, the worst level since November. That number was said to have been impacted by seasonal factors and the Easter holiday. Economists expect Thursday's report, released at 8:30 a.m. to show there were 360,000 new claims.
Last Thursday's disappointing claims report was followed by Friday's shockingly weak jobs report, with 88,000 nonfarm payrolls in March.
The four-week moving average for claims is 354,000, and LaVorgna expects the weekly number to return to that level. He also has a preliminary forecast for job growth of 190,000 nonfarm payrolls in the April employment report, which would push the three-month average to 182,000.
He also expects to see the Fed begin to taper QE during the third quarter and wind it down by year end. But other economists don't agree that the discussion in the minutes of the March 20 meeting was a precursor to an earlier than expected tapering of asset purchases.
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"A lot has happened since then. Since the meeting the economy is weaker. Since the meeting it's also become clear that people who are in the (Fed) core think it's worth going forward," said Diane Swonk, chief economist at Mesirow Financial. "They're not going to stop pulling the trigger. They still have their guns blazing."
Stocks raced to new highs Wednesday, as traders bet the Fed would not cut back on easing any time soon. The S&P 500 broke through its all-time high of 1575 to close at 1587, and the Dow went into record territory, gaining 128 to 14,802. The yield on the 10-year crept back above 1.8 percent.
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Daniel Greenhaus, global market strategist at BTIG, said the market is looking for a reversal of the decline in claims. "It's important in the sense, there was a spike. You want to see the spike reverse," he said.
"What really matters is Friday's retail sales number…nervousness about a spring swoon is certainly warranted right now," he said, adding a few more negative surprises could be the tipping point for stocks.
What Else to Watch
Besides jobless claims, import prices are released at 8:30 a.m. Earnings reports are expected form Commerce Bancshares, Pier 1 Imports, Rite Aid and JB Hunt Transport.
Chain stores release sales for March, an important look at the consumer ahead of Friday's retail sales report.
The House Ways and Means Committee holds a 10 a.m. hearing on President Obama's 2014 budget proposal. Treasury Secretary Jack Lew will testify.
St. Louis Fed President James Bullard speaks in Washington at 8:30 a.m. on resilience and rebuilding low income communities, while Philadelphia Fed President Charles Plosser is in Hong Kong, discussing monetary policy at 6 a.m. ET.
The CEOs of major banks will be in Washington meeting with President Obama. The meeting is part of the Financial Services Forum's quarterly meeting. Topics are expected to include job creation, immigration reform and cyber security.