America's inflation headache is gone, top economist Steve Hanke says. Paul Krugman and Mohamed El-Erian aren't so sure.

• US inflation fell to a two-year low of 3% in June, dividing experts on whether the threat is over.
• Top economist Steve Hanke said the headache is gone and the Fed has things under control.

Soaring prices have squeezed American households and businesses, spurred the Federal Reserve to hike interest rates at a historic pace, and stoked fears of a brutal recession. One leading economist says the threat is over, after official data released on Wednesday showed inflation fell to a two-year low of 3% in June. Two of his peers aren't so sure.

"The inflation story is history," Steve Hanke told CNBC on Thursday. The professor of applied economics at Johns Hopkins attributed the decline from 9.1% to 3% over the past year to shrinking money supply. He also predicted the Fed will quickly reach its target of 2% annual price growth if it keeps tightening.

"It's all about money," the former economic adviser to President Ronald Reagan said, adding that it's "utter rubbish" to focus on non-monetary causes of inflation.

Hanke also dismissed concerns that the Fed faces a painful, protracted battle to rein in stubborn inflation. "Things aren't sticky," he said.

Paul Krugman struck a more cautious tone in a Wednesday tweet, noting the stellar inflation reading of 3% for June might reflect seasonal adjustments and could be revised upward. While private-sector surveys also point to cooling price growth, he warned the latest figure could still be a "head fake," and said "history makes me nervous."

The Nobel Prize-winning economist and retired Princeton and MIT professor laid out a couple reasons why inflation may have plunged without causing major fallout over the past year. He suggested that prices may have temporarily surged due to pandemic-related disruptions that have now dissipated. Also, the labor market might be so tight that inflation could fall sharply without a material rise in unemployment, he said (the Phillips Curve shows inflation and unemployment are inversely related.)

Even if inflation is on the retreat, interest rates may need to remain high to prevent a resurgence, Krugman continued.

"Fwiw I don't think the Fed was wrong to raise rates; it may even need to keep them high given the economy's surprising resilience," he tweeted. "But there's now a very strong case for pausing and looking around."

Mohamed El-Erian, Allianz's chief economic adviser and the former CEO and co-chief investor of PIMCO, also weighed in via tweet on Thursday.

He emphasized that market sentiment has swung wildly in recent months, from hope for a "soft landing" where the Fed crushes inflation without tanking the economy, to fear of a "hard landing" where the central bank's fight causes a recession, to excitement for "no landing" where the economy grows without interruption and shrugs off inflation.

"I suspect that whether it sticks this time around is likely to be more a function of the inflation dynamics and, therefore what the #FederalReserve does, than the #economy's endogenous #growth dynamics," he said about the narrative of a soft landing.

El-Erian's comment raises the prospect that inflation could rear its head again, forcing the Fed to keep hiking rates and trigger a recession.