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Initial claims for unemployment–that’s the number of people filing claims for unemployment for the first time because they’ve just lost a job–fell by 33,000 from the previous week to just 521,000, according to data released this morning by the Department of Labor.

That’s the lowest number since January and below the 540,000 initial claims that economists had expected for the week.

The four-week moving average –which washes out some of the volatility in the weekly numbers–fell to 540,000 last week from 549,000 the week before.

So job loss is slowing. But progress is painfully slow.

 It will take a drop to the 400,000 level in weekly initial claims, economists estimate, before the economy starts to add net jobs. (Some people lose jobs even in a booming economy. But in a good economy those losses are more than balanced by new hiring. It’s the net number that determines if unemployment is rising or falling.)

 Last week the Department of Labor reported that the official unemployment rate had climbed to 9.8%, the highest level since 1983. The United States has now lost  7.2 million jobs since the recession began in December 2007.