* New unemployment benefit claims fall 20,000 last week * Trade deficit widens to $38.7 billion in December * Exports fall 1.8 percent, imports tick up 0.3 percent * Productivity strong in Q4 but trend still weak By Lucia Mutikani WASHINGTON, Feb 6 (Reuters) - The number of Americans filing new claims for unemployment benefits fell more than expected last week, in a boost to the labor market outlook and the broader economy. The upbeat news, however, was undermined somewhat by other data on Thursday showing a slump in U.S. exports in December. Economists said that suggested trade likely contributed a bit less to fourth-quarter economic growth than previously believed and it augurs poorly for the first three months of 2014. Even so, investors were heartened that the labor market recovery appeared on track after some recent data had raised concerns about the economy's health. Economists said a government report on January hiring on Friday should send a similar signal. "The underlying momentum in the labor market remains positive and it is very likely that this is the narrative that we get from tomorrow's employment report," said Millan Mulraine, deputy chief economist at TD Securities in New York. Initial claims for state unemployment benefits declined 20,000 last week to a seasonally adjusted 331,000, the Labor Department said. While the data has no direct bearing on January's employment report, as it falls outside the survey period, it bodes well for the jobs market. Hiring is expected to have accelerated in January after being held down by unseasonably cold weather the prior month. That would offer confirmation that the economy continued to expand after robust growth in the second half of 2013 that was driven by consumer spending, inventory accumulation and trade. So far, data for January have been mixed. Cold weather caused a sharp slowdown in factory activity and held back automobile sales, and retailers on Thursday complained of reduced traffic volumes because of the freezing temperatures. Kohl's Corp reported that sales last month were "significantly" lower than expected. While some chains managed to register sales gains, those came either at the expense of rivals or profit margins. On the other hand, reports on Wednesday showed relatively strong hiring by private companies and an acceleration in services sector activity after two months of slower growth. Stocks on Wall Street were trading higher on the claims data, while U.S. Treasury debt prices fell. The dollar fell against the euro after European Central Bank President Mario Draghi said there is no euro zone deflation problem and left interest rates unchanged. WEAK EXPORTS TO SHAVE FOURTH-QUARTER GROWTH The largest decline in exports since October 2012 helped widen the trade deficit by 12 percent in December to $38.7 billion, the Commerce Department said. When adjusted for inflation, the trade gap rose to $49.5 billion. In its first estimate of fourth-quarter GDP last week, the government said trade accounted for 1.33 percentage points of the economy's 3.2 percent annual growth pace during the period. However, the deficit in December was bigger than the government had assumed, and economists said fourth-quarter GDP growth would likely be lowered when a revision is published later this month. "The net contribution from trade will be much smaller than the first estimate and could dial back the pace of fourth-quarter growth by as much as half a percentage point," said Tim Quinlan, an economist at Wells Fargo Securities in Charlotte, North Carolina. The deficit last year was the smallest since 2009, helped by record exports and the first drop in imported goods in four years. In December, however, exports dropped 1.8 percent, even as petroleum and food exports hit a record high, and imports edged up 0.3 percent. Imports of consumer goods hit an all-time high, but the impact was muted by a fall in the price of imported crude oil, which hit its lowest level since February 2011. A separate report showed U.S. productivity rose at a strong 3.2 percent rate in the fourth quarter after an even brisker 3.6 percent pace in the third quarter as businesses managed to step up output sharply while keeping a lid on hiring and hours worked. Still, the underlying trend remained soft. For all of 2013, productivity rose just 0.6 percent, the smallest gain since 2011. The rise in fourth-quarter productivity helped keep down unit labor costs - a gauge of the labor-related cost for any given unit of output. They fell at a 1.6 percent rate, showing no wage inflation pressures in the economy. For the year as a whole, unit labor costs were up just 1.0 percent, the weakest reading since 2010. "Declining labor costs combined with faster growth in worker productivity suggests little pressure to add workers," said Jay Morelock, an economist at FTN Financial in New York.