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This is a blight on our economy: Pimco's McCulley

The May jobs report shows an economy in full-blown healing, but also highlights the "dirty little secret" that the Federal Reserve's monetary policy has exacerbated income inequality in the U.S., Pimco chief economist Paul McCulley said Friday.

"One of the blights on our economy right now and our society is income inequity. And I wouldn't say the Fed is responsible for it, but it is a consequence of the fact that we had to rely heavily on monetary policy to get out of the liquidity trap," McCulley said on an interview on "Closing Bell."

The May jobs report showed a gain of 217,000 jobs—bringing the number up to a pre-recession level. Unemployment held steady at 6.3 percent and wages rose modestly.

Read MoreSteady as she goes: Job creation keeps up pace

"We're not seeing really robust, even modest, increases in real wages for those who only have labor to bring to the party," McCulley said.

Paul McCulley
Andrew Harrer | Bloomberg | Getty Images
Paul McCulley

Overall, he said, the jobs report is "indicating an economy that's in full-blowing healing. I think we're on the cusp of escaping from the liquidity trap of the last five years."

McCulley believes the economy will continue to do well, with the Federal Reserve hiking interest rates "in our lifetime"—although not as much as it would have historically.

Read MoreWhat's the real unemployment rate?

He thinks bonds will ultimately price off of 2 percent normalized Fed funds rates, which will bring 10-year Treasury yields to the 3 percent range. "I think we're at the bottom of the end of the range for the years ahead."

Although he smells some exuberance in the marketplace, he does not think we're setting up for a calamitous event.

"The overall market, looking at broad-based valuations, is not artificial and is not out of line with reality. And the reality is that we have a permanently lowered neutral fed funds rate," he said.

Read MoreWe 'had rough patch,' says Bill Gross about Pimco outflows

—By CNBC's Michelle Fox

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