By Nicole Goodkind, CNN

Federal Reserve policy is based on trust. The central bank’s ability to maintain stable prices depends on the public’s confidence that it can deliver. But after more than a year of interest rate hikes and attempts to cool the economy, prices are still rising at a pace well above the Fed’s 2% goal and the public is becoming increasingly weary.

Market movements have become increasingly disconnected from Fed messaging. Recent data has shown that inflation is still hot, and that the economy is rip-roaring. On Thursday, JPMorgan Chase (JPM) CEO Jamie Dimon publicly expressed his doubt in the central bank’s ability to control inflation.

That’s why Fed officials will be desperately hoping for any sign that their disinflationary policies are working when the January Personal Consumption Expenditures report is published on Friday. The reading, however, is expected to show an acceleration in prices.

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What’s happening

When people trust the Fed to keep inflation low and stable, they are more likely to hold long-term expectations about prices that align with the central bank’s objectives. This, in turn, can help make it easier for the central bank to achieve its inflation targets.

But if the public expects that inflation will be higher in the future, they may demand higher wages while companies may raise prices for goods and services. This, in turn, can create a self-fulfilling prophecy in which inflation expectations become embedded in the economy, making it harder for the Fed to achieve its policy objectives.

Dimon eroded some of that trust on Thursday. “I have all the respect for [Fed Chair Jerome] Powell, but the fact is we lost a little bit of control of inflation,” the head of the largest US bank said in an interview with CNBC.

Dimon added that he expects that interest rates could “possibly” remain higher for longer, and that it may take the Fed “a while” to return to its goal of 2% inflation.

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‘Living with inflation’

Blackrock analysts wrote in a note Thursday that “we think we are going to be living with inflation. We do see inflation cooling as spending patterns normalize and energy prices relent — but we see it persisting above policy targets in coming years.”

“Equity bulls and even Chair Powell have bragged about anchored expectations for inflation and how consumers and investors believe it is moving in the right direction,” said Lisa Shalett, chief investment officer for Morgan Stanley Wealth Management. Recent data, however, raises questions about whether inflation progress is stalling and the Fed will now need to “tread carefully.”

Fed officials are highly aware of this problem. At their last policy meeting, “a number” of participants warned that an insufficiently restrictive policy stance could lead to prolonged inflationary pressures where people start to expect inflation to remain high.

What to watch: PCE inflation is the Fed’s preferred measure. If that data comes in higher than expected it could increase the likelihood of a larger rate hike of a half percentage point in March.

Analysts expect January’s core PCE, which strips away volatile food and energy data, to rise 0.4% from December and by 4.3% year-over-year. A January reading of that magnitude would be a tick higher than December’s, though the annual data would be lower.

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