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Inflation was expected to be up in October, but the pace of inflation was worse than expected, hitting a level it has not seen since December 1990. The consumer price index rose 6.2% year over year and on a monthly basis, CPI increased 0.9%, both significantly above estimates.

There's no easy fix if the Federal Reserve is ultimately proven wrong about the inflation being "transitory," and the Fed's view is a concern, according to Harvard University professor Jason Furman, a former chairman of President Obama's Council of Economic Advisers.

The Fed's mandate includes maximum employment and inflation targeting, but Furman said in an interview with CNBC's "Squawk Box Europe" on Wednesday that the current bout of inflation is defying the expectations of many.

"What we are seeing is inflation before the unemployment rate gets all the way to where we want it to get," Furman said. "Some people didn't think we could have inflation before you have unemployment below 3.5%, or some number like that."

Last week's nonfarm payroll report for October showed the unemployment rate to be at 4.6%, a pandemic low.

"It turns out, in the short run, you try to push too hard, too fast, and the economy can't make the adjustment on the real production side, and you end up with more inflation and that's what we are seeing," Furman said.

"I think the Fed has been a little bit behind the curve and they are going to be tested next year," he added.

Furman is not the only former Obama economic adviser to doubt Fed policy, with Larry Summers, who served under both President Obama and President Clinton, being one of the early and most vocal critics of Fed policy and the danger of inflation.

Jason Furman, chairman of the U.S. Council of Economic Advisors, speaks during an interview outside the White House in Washington, D.C.

Andrew Harrer | Bloomberg | Getty Images

In recent months, Fed chair Jerome Powell has called inflation" frustrating" and has said it will last "well into next year," but he has stuck to his messaging about inflation being largely tied to the pandemic and supply chain issues that will pass.

Inflation has been expected to peak this quarter at 5.9%, with the 6.2% reported on Wednesday ratcheting up fears about a central bank that has lost control of the inflation argument.

At the Fed press conference last week timed to its tapering announcement, Powell countered claims the Fed has not moved fast enough. "I don't think that we're behind the curve. I actually believe that policy is well-positioned to address the range of plausible outcomes, and that's what we need to do," Powell said.

Furman noted in a tweet on Wednesday that he has been concerned since the summer that faster-than-expected inflation could only go two ways: either an upward or a downward revision of inflation in the future."

"The upward parts have happened more than the downward parts," he wrote on Wednesday.

Furman said that can still change, and as the Fed has argued, the inflation trend reverse, but he isn't betting on an easy time for the Fed next year.

In his interview with CNBC, the former Obama economic adviser said that if the Fed is correct, and inflation comes back down to 2.3% in 2022, which was the median forecast from its last FOMC meeting, "then they are fine."

By one economic indicator from the shipping market, inflation may be peaking.

But if inflation is closer to 3% next year, which Furman thinks is "more plausible," then the Fed will have a serious test.

"They will need to shift off their game plan and raise rates faster than they are currently telegraphing," he said.

Powell said last week that the current level of inflation is not consistent with price stability and that the central bank would "use our tools as appropriate to get inflation under control."

A Fed forced to act sooner could mean increasing the pace of its just-announced bond taper before making the more drastic move to raise rates, though on Wednesday the market was increasing bets that the Fed will have to raise rates sooner rather than later. Stocks dove on Wednesday after the hotter-than-anticipated inflation.

While he supported President Obama's Covid financial relief plan, Furman told CNBC the plan "was larger than it needed to be" and that has played a role in the inflation now being experienced in the economy.

While some economists also have worried about an era of stagflation, Furman said that shouldn't be a concern since the unemployment rate is coming down, and will continue to decline.

But to combat the inflation, at this point, "there's not a great playbook," Furman said.

Among options that the government can pursue in addition to a change in Fed policy would be a dramatic lowering of tariffs, especially on China, which would reduce inflationary pressures and help supply chains.

President Biden said in a statement on Wednesday about the rising prices that "reversing this trend is a top priority for me."

Current White House Council of Economic Advisers member Jared Bernstein told CNBC on Wednesday that administration efforts to fix the supply chain bottlenecks, and to vaccinate more Americans including children, will lead to an improving economy and he stressed Covid's role in the current inflationary pressures.

When Covid hit there was a massive shift from in-person services to goods demand, and savings went up as people stopped eating out and staying in hotels, and that combined with the financial relief provided by the government led to even greater savings and demand which have ultimately contributed to the issues at ports. "I just don't think there's a coherent story about inflation without recognizing Covid's role, and every forecast I've seen has it settling down in the second half of next year," Bernstein said.

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Fed 'behind the curve' on inflation, says former Obama economist Jason Furman - CNBC