Unemployment claims fell from more than 850,000 the previous week to 790,000 last week, according to new data from the U.S. Department of Labor. Meanwhile, 659,000 people filed for Pandemic Unemployment Assistance, the government's relief program for freelancers, the self-employed and part-time workers, and the unemployment rate was at 8.6 percent. However, the economy is still on shaky ground—last week's numbers are still higher than those at the height of the Great Recession, the country's last economic downturn—and experts are warning of the risk of a "double-dip recession," particularly as Congress fails to compromise on passing a new economic stimulus package.

The largest increases in initial unemployment claims for the week ending Sept. 5 were in California (23,841), Texas (8,618), Louisiana (8,375), New Jersey (2,402) and Washington (2,173), while the largest decreases were in Kentucky (7,219), Florida (5,334), Pennsylvania (2,257), Kansas (1,915) and Michigan (994).