The Bank of England's inflation debate has spilled into the open as the chief economist and governor clash

• The Bank of England's chief economist warned strong inflation could be dangerous in his final speech in the job.
• A day later, the Bank's governor shot him down, saying people shouldn't overreact to price rises.
• It is emblematic of the debate about inflation going on inside central banks and across markets.

Central bankers usually prize consensus. But a rift about inflation at the Bank of England has spilled into public view.

The Bank's departing chief economist Andy Haldane used his final speech in the job to warn his fellow central bankers that they're underestimating the risks of strong inflation on Wednesday.

He said the threat of strong price rises was "rising fast" and that "everyone would lose" if the cost of living grew sharply. Haldane said inflation could hit 4% at the end of the year from 2.1% in May, and recommended nipping it in the bud.

A day later, the Bank's governor Andrew Bailey used a major speech to say it's "important not to overreact" to strong price rises, which he argued will be temporary. He said central banks risk hurting the economic recovery by cutting back support too soon due to unwarranted fears about inflation.

The two speeches highlight the lively debate going on inside central banks and among investors about whether sharp inflation - as seen in the US and UK in recent months - will be temporary.

Read more: 'Inflation could destroy today's darlings': An equities chief overseeing $7.5 billion has been preparing for inflation since June. Here's his playbook and 2 sectors set to surge

In the US, Federal Reserve Chair Jerome Powell has repeatedly said strong inflation will prove transitory. On Thursday, the BoE's Bailey echoed that message, saying bottlenecks in the economy should soon ease.

The market now appears to be buying the central bankers' line. One closely watched US bond-market gauge of inflation, the 5-year breakeven rate, has fallen considerably from May's 13-year high of 2.7% to around 2.47% on Thursday.

And tech stocks, which do better when investors think inflation will be lower, have jumped over the last month, with the Nasdaq index up more than 6% over the period.

Yet like the BoE's Haldane, Fed official James Bullard has warned that inflation may be stronger than expected. He's one of a number of Fed officials to say interest rates may have to rise sooner than initially expected.

In the eurozone, European Central Bank governing council member Jens Weidmann has said the ECB should cut bond purchases due to "upside risks" of inflation.

Big-name investors like Mohamed El-Erian, who's chief economic advisor at Allianz, are also concerned the Fed and other central banks are wrong on inflation.

However, a recent Bank of America survey found 73% of fund managers agree with the Fed's argument that strong inflation will be fleeting.

Hugh Gimber, global market strategist at JPMorgan Asset Management, told Insider that "the inflation debate is not going to be settled for several quarters. It's going to be well into next year before we know conclusive answers about how sticky inflation is."

He said it has the potential to create jitters in the markets over the coming months, particularly in bonds, as investors assess exactly how much support central bankers are willing to give.