WASHINGTON — Unemployment rates have fallen to very low levels in a third of U.S. states, a trend that may push up wages in those areas.

The Labor Department said the unemployment rate is now significantly below the national figure of 4.7 percent in 16 states. It fell to 3.8 percent in Arkansas last month, the lowest on records dating back to 1976.

Pennsylvania’s unemployment rate was up two-tenths of a percentage point from April to 5.5 percent. Pennsylvania’s civilian labor force was up 15,000 in May to a record high of 6,541,000. Resident employment declined by 2,000 while the unemployment count increased by 17,000.

Steady hiring has lowered unemployment throughout the U.S. But rates have also fallen for a bad reason: many of those out of work have stopped searching for jobs. The government doesn’t count people as unemployed unless they are actively looking for work. That has pushed the rate lower than it would be otherwise.

Employers added a significant number of jobs in just three states last month, while four states lost jobs. Employment was essentially unchanged in 43 states. That reflects the tepid figures nationwide: Employers added just 38,000 jobs last month in the U.S. as a whole.

South Dakota had the nation’s lowest rate in May, at 2.5 percent, followed by New Hampshire, at 2.7 percent. Many states with very low unemployment rates are small.