Stock markets are heading for a wild ride this year as central bankers strap on their bullet-proof vests and test investors’ willingness to accept higher interest rates. Last week’s share price crashes, which in two days wiped $4 trillion off the value of markets around the world, was just a foretaste of the battle to come.

In the days following Monday’s crash, share values have recovered strongly only to dive again as competing theories about the path of interest rates and the likely impact on economic growth fight for attention.

Most investors want the era of cheap borrowing to continue and many are willing to sell their shareholdings if it looks like coming to an end. Without low interest rates, they cannot borrow and invest cheaply, especially in the assets that for the past decade have gone up every year by much more than their salary – property and shares. Countless businesses have also come to rely on low borrowing costs to keep going, and investors fear they might go bust should their bank raise loan rates.

Weaning companies and investors off their addiction was never going to be easy, even 10 years after central banks first put their stimulus packages in place, and despite warnings that these measures need to end. For some time, the US Federal Reserve has taken on the role of the advance guard, forging a path towards higher rates for others to follow. But its campaign got off to a faltering start.

Back in 2013 it was forced to retreat when it signalled in the mildest terms that it would begin withdrawing its quantitative easing programme. The main effect of QE was to drive down long-term interest rates, allowing investors to borrow cheaply not just over one or five years, but for 30 years. And so its withdrawal was as much of a blow for some fund managers as an immediate rate rise.

Wall Street and markets in Europe and Asia, where heavy selling turned into a rout, forced Fed officials to retreat. The Fed adopted a more incremental approach. It gave markets more warning and spaced out the policy decisions. As it entered 2017, US interest rates had trebled, but only from 0.25% to 0.75%.

Yet the economy was booming more than ever. The Fed appeared ready to get tougher, and with justification, according to Karen Ward, chief market strategist for the UK and Europe at JP Morgan Asset Management. After the heavy lifting needed to get the industrialised world back from bankruptcy, she said, “economies are now rested”.

On the floor of the New York Stock Exchange last week. Photograph: Brendan Mcdermid/Reuters

Ward, who until recently was an adviser to the chancellor, Philip Hammond, said: “Households and businesses are feeling better about the future. They do not need a boost in quite the same way. Central banks can ease off the accelerator without troubling either growth or markets.”

For the past year, health checks on the global economy have reported the patient doing much better than expected. On Friday 2 February a member of the committee that sets US interest rates repeated his warning that he couldn’t take much more good news without voting to calm things down. That would mean one or two more interest rates rises than most investors were expecting.

Not long after Robert Kaplan spoke, figures showed US average earnings growth almost hitting 3%. It was yet another piece of good news and proved to be the tipping point for a plunge in share values, dwarfing the so-called taper-tantrum crash that greeted the Fed’s first attempt at tightening its interest-rate policy.

Ken Odeluga, a market analyst at investment firm City Index, says the Fed is “vindicated by green shoots in personal income growth” in pressing ahead with rate increases.

Investors had decided that Kaplan and his Fed colleagues were, at last, likely to make good on the threat of rates as high as 3% by 2019. On the following Monday the Vix index, which forecasts stock market volatility, jumped above the 30 mark that signals a crash. The tumble on Friday 2 February became a rout. By the end of the day, the Dow Jones industrial average had suffered its biggest ever one-day fall. Another fall of more than 1,000 points came on Thursday.

Also on Thursday, the Bank of England governor, Mark Carney, and the other eight members of Threadneedle Street’s monetary policy committee said investors should bet on earlier and more frequent rate rises than previously forecast. That probably means four rate rises in the next two years, starting in May.

Bank of England Governor Mark Carney has indicated that interest rates will soon need to rise. Photograph: Victoria Jones/AFP/Getty Images

In the Bank’s quarterly inflation report, which forecasts inflation, GDP growth and the course of interest rates over the next two years, Carney said that the UK remained resilient and a return to higher borrowing costs was justified. The FTSE 100, which had tumbled from a high point above 7700 earlier in the year to 7280, slumped another 100 points.

The Bank of England takes a slightly different route to the Fed in arguing its case. It says that Brexit has permanently damaged the UK economy and it will therefore be operating at full capacity at a lower GDP growth rate. Effectively, this means it takes only a low growth rate to push up inflation. Given that inflation is already above the Bank’s target of 2%, it must use its main tool – higher borrowing costs – to bring down inflation.

Investors can seek respite in the eurozone, where the European Central Bank is still adding to the pile of assets in its QE programme, and Japan, where the central bank is keeping rates low despite the best period for growth in more than a generation.

Paul Donovan, global chief economist at Swiss investment bank UBS, says he tried to persuade investors against selling in the recent crash, telling them that higher rates were no threat to one of the best periods for growth in postwar history.

“However, growth is modest and there are no signs of overheating or of central banks tightening monetary policy too quickly,” he adds.

Strong growth figures from the US economy are also tempered by lack of wage growth among low-income workers, which limits the Fed’s room for manoeuvre. “If you look closely at the average earnings figures from the US it shows that the lion’s share is going to professional and managerial grades. It’s not filtering down to the shop floor,” Donovan says.

The prospect of a Brexit talks collapsing does little to disturb his view; neither do policy tantrums in the White House. It is possible, he says, that in a couple of years’ time, politicians will make mistakes that disturb his benign picture, but in the meantime, global growth is strong enough and broad enough to stay on course.

Carney and the new Fed boss, Jerome Powell, who succeeded Janet Yellen last week, will want to stand by their rate-rise predictions, wanting investors to be the first to blink in a battle of wills. But they have a chink in their armour. Both central banks have a remit to use higher interest rates to bring down inflation above 2%, except that inflation has been running at 2.1% in the US for the past two years, and while it jumped to 3% last year in the UK, it is due to fall this year without any increase in borrowing costs.

So the betting must be that without the scary prospect of rampant inflation, the Fed and the Bank of England find themselves in a war of words that only adds to stock market volatility.