The number of Americans initially applying for unemployment aid fell for a third consecutive week, but remained well above the pre-shutdown level, the Labor Department reported Thursday. In the week ending Oct. 26, the advance figure of seasonally adjusted initial claims for jobless benefits edged down by 10,000 to 340,000 from the previous week's revised figure of 350,000. Meanwhile, the four-week moving average, which helps smooth out week-to-week volatility, rose by 8,000 to 356,250, the highest since early July. The advance figure of seasonally adjusted insured unemployment during the week ending Oct. 19 stood at 2.881 million, up 31,000 from the previous week. An update of computer systems in California, combined with the 16-day partial federal shutdown at the beginning of this month, led to a spike in claims in recent weeks. With both now over, claims may gradually go back to a normal level. Before the shutdown, claims were slightly more than 300,000. In September, the U.S. unemployment rate edged down to 7.2 percent, with only 148,000 jobs added to the economy. And private companies added 130,000 workers this month, the fewest in six months. Jason Furman, chairman of the White House Council of Economic Advisers, said the government shutdown had cut 0.25 of a percentage point off fourth-quarter economic growth and cost 120,000 jobs in October.