An estimated 631,000 people applied for unemployment benefits last week, the Labor Department just reported. That was down 12,000 from the number of first-time claims filed the previous week.

Also down slightly: The four-week moving average. It stood at 628,500 last week, vs. 632,000 the week before.

Still, the total number of people collecting the benefits remains high. Labor said 6.7 million people were getting checks from state programs in the week ended May 9, up by 75,000 from the previous week.

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