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The U.S. economy added 2.5 million jobs in May, the Labor Department reported today. The official rate of unemployment fell to 13.3% from 14.7%. In April the economy had shed 20.5 million jobs.

Economists were surprised by the gains, to put it mildly. The consensus projection among economists surveyed by Bloomberg had called for the economy to lose another 6 million jobs in May.

According to the Labor Department’s figures 21 million Americans remain unemployed.

I think there are problems with this month’s numbers and that the gains in jobs aren’t nearly as great as expected and the drop in the unemployment rate is overstated. I’m going to devote the rest of this post to laying out the official numbers and then devote two more posts to the problems with this data and the unfortunate timing of the job in jobs according to the official numbers.

One of the things that the Labor Department report showed this morning is that the return to work, even according to the official numbers, is extremely uneven. The unemployment rate among African Americans rose to 16.8%.

The U6 unemployment rate was a staggering 20.6% in May. The U6 rate counts all those unemployed people that the the official rate doesn’t. That includes workers who are so discouraged that they have stopped looking for work and part-time workers who would like to have full-time positions.

The service sector added 2.43 million jobs in May after losing 17.35 million jobs in April.  Retail trade, wholesale trade, financial activities, and professional and business services also added jobs for the month. The goods-producing sector also added jobs, rising by 669,000 after declining by 2.373 million in April. Manufacturing payrolls rose by 225,000, recovering some of the 1.324 million jobs lost in April.

Government payrolls, however, extended declines, with jobs in this sector falling by 585,000 In May after a drop of 963,000 in April.

Stocks rocketed higher on the news, which seems to confirm the market’s hopes for a V-shaped economic recovery. As of 2 p.m. New York time the Standard & Poor’s 500 was up 2.90% and the Dow Jones Industrial Average had gained 3.63%. The NASDAQ Composite was ahead 2.26% and the Russell 2000 small cap index was higher by 4.67%. The iShares MSCI Emerging Markets ETF (EEM) climbed 2.85%.