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Washington — U.S. productivity in the spring rose at the fastest pace since late 2013, while labor costs declined.

Worker productivity increased at an annual rate of 3.3 percent in the April-June quarter, the Labor Department reported Wednesday. That was a rebound from the first quarter when productivity had fallen at a 1.1 percent rate and a sizeable upward revision from the government’s first estimate of a 1.3 percent growth rate.

Labor costs fell at a 1.4 percent rate in the second quarter, indicating that wages are not rising even as unemployment declines.

Even with the strong gain in the second quarter, productivity over the past year has increased by just 0.7 percent, far below the long-run average of 2.2 percent. Productivity, the amount of output per hour of work, has been sluggish since the recession and economists have been at a loss to explain the reason for this weakness.

Faster productivity growth allows employers to boost pay without pushing up inflation. The Federal Reserve closes monitors both productivity and labor costs to determine whether inflation is starting to become a problem. However, the deep recession of 2007-2009 has left workers with less ability to demand higher wages.

The latest productivity figure reflects the revised estimate the government made for overall economic growth as measured by the gross domestic product. It revised GDP growth for the second quarter up to a 3.7 percent rate of gain, more than a percentage point higher than the initial estimate of 2.3 percent. This change triggered the higher estimate for productivity.

Productivity has risen an average of just 1.3 percent a year from 2007 through 2014. That is far below the strong 2.8 percent average annual growth that occurred from 1995 through 2004, gains that economists attributed to efficiency boosts the economy was getting from more widespread use of computers and the Internet.

Some experts believe that improvements in software and other high-tech products are not being accurately measured in the government’s statistics. But other economists argue that companies are failing to fully exploit the efficiency gains offered by smartphones, computer tablets and other recent innovations.

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