Silvia Ascarelli/MarketWatch

The numbers: The rate of layoffs in the U.S. stuck near a 49-year low in early May, just more proof that an ultratight labor market shows no sign of softening.

Initial jobless claims were unchanged at 211,000 in the week ended May 5, the government said Thursday. Economists surveyed by MarketWatch had forecast a 215,000 reading.

The more stable monthly average of claims, meanwhile, fell by 5,500 to 216,000 to touch the lowest level since December 1969.

The number of people already collecting unemployment benefits, known as continuing claims, rose by 30,000 to 1.79 million.

What happened: Jobless claims are near the lowest levels ever recorded and probably cant drop much further. Companies are very reluctant to fire workers or see them leave for greener pastures since its so hard to fill open positions.

Big picture: The U.S. keeps churning out more than enough new jobs to absorb new entrants in the labor force, and companies might hire more aggressively if they could find suitably talented workers. Job openings hit another record in March, but a growing shortage of skilled labor means an unusually large number of positions are going unfilled.

As strong as the labor market is, though, worker wages still arent rising as rapidly as they normally would with an unemployment rate of just 3.9%.

Also Read: Consumer inflation soft in April, wont worry Fed

What they are saying?: In a tight job market, someone newly laid off is more likely to get a new job right away and therefore less likely to file a claim for unemployment benefits, said Scott Brown, chief economist at Raymond James. He said the monthly average has fallen to a level most economists had thought to be unachievable.

Market reaction: The Dow Jones Industrial Average DJIA, +0.92% and Standard & Poors SPX, +0.91% both rose in Thursday trades. The 10-year Treasury yield TMUBMUSD10Y, -0.61%   fell 4 basis points to 2.96%.