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The central bank's goals to control prices are evident, especially after Chairman Jerome Powell's hawkish speech at Jackson Hole last month, he told CNBC on Friday, noting that "failure is not an option."

What’s not clear now is how high rates will soar and for how long they will stay there, said Clarida, who is now managing director and global economic advisor at bond giant PIMCO.

"I think they're going to 4% hell or high water, if I had to put it into two boxes," he said. "They are data dependent, but that's why they're going to 4%. Inflation is way too high."

The fed funds rate is currently at 2.25%-2.50%, and central bankers are widely expected to approve another 0.75-point increase at their September 20-21 meeting.

On Thursday, Powell said the effort "will take some time and requires using our tools forcefully to bring demand and supply into better balance."

And until inflation cools, Clarida also said the Fed would effectively have a single mandate instead of its official dual mandate of price stability and maximum employment.

"The chair made clear: the Fed knows that if you squander price stability it's very hard to achieve and sustain maximum employment," he said. "So I think that they are data dependent, and the data says inflation is too high. So I think they're going at least to 4%."