New claims for unemployment benefits fell again last week to 348,000, a new four-year low as the economic recovery continues to accelerate. There were 5,000 fewer people filing jobless claims last week than in the previous week, the Labor Department said Thursday. The moving four-week average, a more reliable gauge than the weekly figures, also decreased, to 355,000. The number of claims last week was the lowest since March 2008, when the effects of the just-beginning deep recession began hitting the labor market. By early 2009, more than 600,000 people were filing for benefits each week. New York and California showed the biggest improvements last week. Jobless claims dropped by 14,222 in New York and 4,696 in California because of fewer layoffs, the Labor Department said. Economists say that weekly unemployment claims below 350,000 indicate that the economy is adding jobs at a significant pace, and Thursday’s data adds to recent signs that the recovery is picking up steam.