WASHINGTON — The productivity of U.S. workers rose at an annual rate of 2.3% in the third quarter as output and hours worked increased, the Labor Department reported Wednesday.

The productivity gain was revised upward from the 1.09% increase initially reported for the third quarter. Productivity has been volatile this year, falling 1.8% in the second quarter after expanding 3.9% in the first quarter.

Unit labor costs, a ratio of hourly compensation to productivity, were unchanged from initial estimates at a 0.1% dip. They rose 4.9% in the second quarter. Economists expected a 2.3% gain in productivity and a 0.4% drop in unit labor costs.

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