Here's the Fed's real problem: Ex-Fed Gov Mishkin

The Federal Reserve 's biggest problem is not the timing of its initial rate hike, but rather its communication strategy, Frederic Mishkin said Monday.

"In September, they said they were not going to raise and that there are reasons to not raise; there was a lot of uncertainty in the economy … and now we're in a situation where in fact the data is coming in quite weak," the former Fed governor told CNBC's " Squawk on the Street ."

The Labor Department said Friday the U.S. economy added 142,000 jobs in September, below the expected 203,000. The unemployment rate remained at 5.1 percent, but labor participation dropped to 62.4 percent, its lowest since October 1977 .

"However, speeches that both [Fed Chair Janet Yellen ] made and also [New York Fed President] Bill Dudley shortly after the FOMC meeting kept on saying they would be likely to raise by the end of the year, and that's really not consistent with the statement and possibly not consistent with what the data is saying," said Mishkin, a professor at Columbia Business School.

Last Monday, Dudley said the central bank would "probably raise rates later this year," echoing Yellen's Sept. 24 remarks when she said a hike would be appropriate "sometime later this year."

Mishkin added that the combination of the weak data and the Fed's statements have painted it into a corner where it can't raise rates.

"They've put themselves in a box that they didn't need to put themselves into," he said. "Unless the data is much stronger, there is not going to be a case for tightening, and when they don't tighten, people are going to say 'Yeah, but, you said that you were going by the end of the year.'"

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