The nature of the inflation problem in the eurozone is changing, and interest rates will need to be higher for longer than policymakers and investors once estimated, Christine Lagarde, the president of the European Central Bank, said on Tuesday.

While the shocks that pushed the region’s inflation rate above 10 percent late last year, such as supply chain bottlenecks during the pandemic and the surge in energy prices after Russia’s invasion of Ukraine, have started to wane, their impact is still passing through the economy. That’s making inflation more persistent, Ms. Lagarde said at the central bank’s 10th annual conference in Sintra, Portugal.

The slower decline in inflation “is caused by the fact that inflation is working its way through the economy in phases, as different economic agents try to pass the costs on to each other,” Ms. Lagarde said. Companies have passed on costs to customers, and now workers are trying to catch up from lost wages caused by high prices.

Central bankers from across Europe and further afield, from Canada to South Africa, including Chair Jerome H. Powell of the Federal Reserve and Andrew Bailey, governor of the Bank of England, have gathered in Sintra at a challenging time for policymakers as they battle to bring inflation down without causing unnecessary economic pain.

Central banks around the world have aggressively raised interest rates, and while the full impact of these moves has not been felt yet in different economies, policymakers are trying to determine if they have a handle on the inflation problem.

Earlier this month, the European Central Bank, which sets policy for the 20 countries that use the euro currency, raised interest rates to their highest level since 2001 and said more increases were likely to follow. Consumer prices in the eurozone rose 6.1 percent in May from a year earlier, the slowest pace in more than a year. But policymakers are still concerned about core inflation, which strips out food and energy prices, and is one way to measure how deeply price pressures are embedding in the economy. That measure declined to 5.3 percent in May, from 5.6 percent the previous month.

The central bank “will have to bring rates to sufficiently restrictive levels and keep them there for as long as necessary,” Ms. Lagarde said on Tuesday.

For inflation in the eurozone to return to the central bank’s target of 2 percent, companies have to absorb higher wage costs and accept lower profit margins, she added.

Last year, companies were able to pass on higher costs quickly, partly because customers were unable to discern whether higher prices were being caused by high company costs or the pursuit of bigger profits, she said. And so profits contributed about two-thirds to domestic inflation, compared with one-third, which was the average over the previous two decades.

Workers are now seeking higher pay to make up their lost purchasing power. The central bank expects wages to rise 14 percent by the end of 2025 as they return to prepandemic levels, once adjusted for inflation.

Inflation can be pushed down, and workers can make up some lost wages, if monetary policy is restrictive enough, Ms. Lagarde said. For this to work, policy needs to restrain the economy by dampening demand so companies can’t completely pass on the cost of higher wages to their customers. If that doesn’t happen, inflation will remain stubbornly high.

The central bank will need to have “more persistent policy” to tackle signs of longer-lasting inflation, Ms. Lagarde said. That means keeping interest rates at restrictive levels until policymakers are sure that the wage catch-up has been resolved.

“We have made significant progress,” Ms. Lagarde said. “But faced with a more persistent inflation process, we cannot waver, and we cannot declare victory yet.”

The central bank won’t be able to say in the near term with confidence whether the peak in interest rates has been reached, she added.

The evening before, central bankers were given a stern warning from the International Monetary Fund. “Inflation is taking too long to get back to target,” Gita Gopinath, the first deputy managing director of the organization, said in a speech.

Ms. Gopinath set the tone for the conference, which runs through Wednesday, arguing that central banks needed to go further to bring down inflation, despite the economic costs.

Even with the actions global central banks have taken, “the battle won’t be easy,” Ms. Gopinath said. “Financial stresses may intensify, and growth may have to slow more.”

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