The number of people filing new claims for unemployment benefits fell to its lowest level in more than five years last week, the U.S. government reported Thursday, signaling steady labor-market improvement despite fiscal austerity in Washington. The Labor Department said jobless claims fell 4,000 to 323,000 last week, the lowest level since January 2008. The four-week moving average of claims, a less volatile figure, fell 6,250 to 336,750, the lowest level since November 2007, before the Great Recession began. The third consecutive weekly decline in claims pushed them further below the 350,000 level that economists normally associate with an improving labor market. Jobless claims, a proxy for layoffs, have fallen about 9 percent since November and now are at a level consistent with a healthy economy. They are showing no signs of increasing, even as other parts of the economy, like manufacturing, begin to show strains from tighter fiscal policy.