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How to fix Fed's 'huge' rate error: Ex-Fed advisor

Any public nod by the Federal Reserve to the recent market chaos, according to former Dallas Fed advisor Danielle DiMartino Booth, would be an admission that policymakers pulled the trigger too soon when increasing interest rates last month.

"I think the Fed has put themselves in a very tight spot because they need to have to find a way to communicate. I think beginning today, that they made a huge policy error," DiMartino Booth told CNBC'S "Worldwide Exchange" on Tuesday.

Strong jobs data at the end of 2015 were a vote of confidence for the first rate hike in almost a decade.

But DiMartino Booth said that only 3 percent of the jobs in the household survey went to people of prime working age between 25 and 55 years old, and many were part time.

"That's really indicative of the type of recovery we've seen these last few years," she said. "Labor is the most lagging of indicators, I think the Federal Reserve knew that. There were indications that it's going to continue to worsen and it has."

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DiMartino Booth, who was an advisor to Richard Fisher when he was president of the Dallas Fed, said she's not expecting a rate hike when central bankers conclude their two-day January meeting.

"I'm certainly not there yet, not with oil prices where they are," she said. "I'm going to have to wait and see whether or not December was an aberration." Nonfarm payrolls grew by 292,000 last month — much stronger than estimates for a 200,000 position advance.

By contrast, Torsten Slok, chief international economist at Deutsche Bank, said the Fed made the right decision at the time to raise rates because it was unambiguously clear the U.S. job picture was improving.

But with recent turmoil in the markets, the Fed is somewhat puzzled, Slok told "Worldwide Exchange" in a separate interview. "There's a huge discrepancy between what the market is thinking and what the economic data is actually showing."

"Maybe these problems in China could have some implications for the global economy later on," he said. "But up to this point the U.S. economic data, in particular the labor market data, the jobs data, nonfarm payrolls, all look pretty good."

DiMartino Booth's former boss, Fisher, recently wrote in a CNBC op-ed that some of the market sell-off in the new year was caused by too accommodative Fed policy. The third iteration of quantitative easing, DiMartino Booth said, was a bridge too far.

"That pushed financial markets to such extreme valuations that it put them in such a fragile state that any little thing was capable of setting the markets off and igniting what's called systemic risk," she contended. "I think that's what we're seeing today."

As for this week's meetings, DiMartino Booth said that the Fed might take a similar approach as it did in September 2015.

"They can nod in a nuanced way to turmoil in the financial markets. That will put a little bit of uncertainty as to whether or not they'll pull the trigger again come March," she said. "I don't think that they'll be too harsh in their communication."

If there's any hint of a rate hike coming, DiMartino Booth said, it'll be telegraphed by Fed Chair Janet Yellen in her testimony to Congress on Feb. 10.