Warsh said he's been encouraged by inflation expectations easing recently, but the current level still isn't good enough.

"If there were people in household or the business sector, in the financial markets, who thought that this central bank was going to be comfortable with an inflation objective above 2%, well, I guess they'd be disappointed," he said. "We're going to deliver price stability in the U.S."

The Fed's preferred gauge showed core inflation at 3.4% in May, with the headline all-items index even higher at 4.1%.

—Jeff Cox

One key part of the Warsh revamp at the Fed is how it utilizes data in its policy decisions. The chairman said he's hoping that in a year, the central bank has a totally different approach.

"My hope, my aspiration, is that nine-12 months from now we're going to be using new technologies to understand what's happening in the real economy in a contemporaneous real-time way that positions us as central banker to make better decisions," he said.

Long a critic of conventional data tools provided by government agencies, Warsh said "the conventional wisdom" is his least favorite data point.

— Jeff Cox

Bank of England Governor Andrew Bailey said central bankers were monitoring issues that could carry tail risk and potentially trigger financial instability.

"We look at the increase in leverage in core government bonds markets. These markets have changed substantially," he said. "[Another] thing we've seen in the course of the last few months is an increase in leverage in equity markets — you look at hedge fund leverage in equity markets, you look at leverage in exchange-traded fund markets, those things are changing."

"If you look at private credit, the question we're asking is, are those the things that actually can move from tail risk into a broader consequence?" he added.

Bailey also said the Bank of England is monitoring asset valuations.

"We are living in a world where you've got quite a divergence between how bond yields are moving and how equity markets are moving," he said. "A lot of this comes back to … AI. Frontier AI is obviously high on the list. We've got quite a list of things that we're looking at at the moment."

— Chloe Taylor

Leaders of Warsh's five task forces to examine Fed policy likely will be released soon.

"We have news to come. I can tell you likely next week who will be the outside experts," he said. "Some of them would have been folks in seats like this in prior years, some would have been academics in the audience. But we really tried to find the best minds [in the ] economics profession among practitioners, experienced hands, including people from countries outside the U.S."

"We're not asking for de Tocqueville to come to America, but sometimes we need a foreigner to sort of see things clearly," Warsh added.

— Jeff Cox

Lagarde said she took the point that Europe is lagging in AI investment and the development of frontier companies leading breakthroughs in the space.

But she added that she thought Europe and the U.S. "are sort of hostage to each other" when it comes to making progress.

"We need those frontier companies, but they need the market," she said. "When Europe represents 25% of the revenues of many of those hyperscalers — we need each other. We are in this game together."

She added: "There will be healthy competition, I'm sure, but we depend on each other. We can't dispense of them, and they can't dispense of the revenue source that we constitute. So we are in this together."

— Chloe Taylor

Warsh pushed back on President Donald Trump's pressure campaign against the central bank, saying its independence would not change regardless of what the president wants.

"We've been an independent central bank for a very long time," Warsh said. "We're going to be an independent central bank at this moment, and you're going to see no changes on that."

The comments mark an early test for Warsh, who replaced Jerome Powell as Fed chair after Trump spent years attacking Powell over interest rates and accusing him of moving too slowly to lower borrowing costs.

Powell, whose term as Fed chair ended this year, repeatedly defended the central bank's independence and said Fed officials would make decisions based on economic data, not political pressure.

– Luke Fountain

Fed Chair Kevin Warsh said inflation remains too elevated even as Fed officials have become more open-minded about AI and its implications for being deflationary.

"We're all in the price stability business, that might not be our only business, but if there was a common thing I heard over the last couple of days, it was open-mindedness on these questions of AI, open-mindedness on productivity, but we've all looked around, and we've seen that prices are too high," Warsh said.

He sees taming inflation as the Fed's primary objective despite growing optimism about AI-driven gains on the supply side of the economy.

— Yun Li

Warsh declined to speculate on the long-term ramifications of the artificial intelligence boom after saying previously that he thought it ultimately would help ease inflation.

"The AI shock is leading to a boom in capital expenditures," he said. "We see that first and foremost in demand, but I'm confident we're going to see it in supply at some point. So, we're spending most of our time trying to monitor those developments."

Asked by CNBC's Sara Eisen whether AI would boost inflation, Warsh demurred.

However, he noted that it's a good problem to have rather than "years back" when companies relied on "financial engineering" and buying back their own shares of stock for prosperity.

"Right now they're investing in the future because their expectation is the supply side of the economy will expand, and if it does, that has huge implications for monetary policy," he said. "But again, I'm not going to make a judgment now."

— Jeff Cox

European Central Bank President Christine Lagarde said that the bank's Governing Council "had the perfect monetary policy circumstances" to enact a rate hike last month, when it became the first major central bank to raise its key interest rate in response to the energy shock caused by the U.S.-Iran war.

"When you have your inflation outlook up, your core inflation up, when you have the underlying inflation also indicating that it's also trending up as well and that you're only going back to your 2% target at the end of 2028 … you have the obvious decision — and it was so obvious that we had unanimity within the board of the Governing Council," she told the panel.

— Chloe Taylor

Warsh promised that the Fed under his watch would "chart a new course" but offered no details on what that involves, including whether he thinks an interest rate hike is imminent.

"There's a lot of late breaking news on a series of these things, and we get into that room and shut the door, we're going to have the good debate," the central bank leader said. "But I don't have much more for you than that."

Earlier, Warsh praised ECB President Christine Lagarde, who expressed her own opposition to the type of "forward guidance" that the Fed chairman disdains.

"I liked her when we met 20 years ago when she was finance minister. After that answer, I love her," he said.

— Jeff Cox

Investors are closely watching every new comment and statement by Federal Reserve Chairman Kevin Warsh, but he may not be able to do much to curtail what's ahead for the economy, according to TS Lombard.

"Our bet now is that the economy will dictate a much more significant path of hiking than the market currently expects especially next year," wrote TS Lombard's chief economist, Freya Beamish, in a Wednesday note. "Given the scale of change in dynamics in this economy, how Warsh reacts will be dominated by how the economy is behaving."

Beamish added that Warsh's perspectives and policy wishes aren't unimportant. However, she added that his views won't fundamentally alter where rates will go eventually, but rather could change the timing of when to expect any changes.

"The key question is whether Warsh is going to fight the trends of the new macro regime or flow with them," she wrote. "If Warsh chooses to fight, delaying necessary rate adjustments will likely force the Fed to hike a lot more down the line."

— Davis Giangiulio

ADP private payrolls data, a precursor to Thursday's official jobs report, came in a little light Wednesday morning. Private sector employment grew by 98,000 for June, down from 122,000 in May and a bit below the forecast for 110,000.

The data comes ahead of June's nonfarm payrolls data, which is expected to show a 115,000 increase in jobs, down from 172,000 added in the prior month, according to the Dow Jones consensus estimate. The unemployment rate is expected to hold steady at 4.3%.

Yields were little changed following the ADP data. The 2-year Treasury yield is yielding 4.2%, around levels it spiked to following Kevin Warsh's first Federal Reserve rate decision last month, where he laid out a focus on "price stability" during his news conference.

— John Melloy

Federal Reserve officials have made significantly fewer public appearances in the two weeks following the June policy meeting, a potential early sign that Chairman Kevin Warsh is encouraging a lower-profile communications strategy, according to Bank of America.

There have been just 12 speeches and interviews by Fed officials since the June FOMC meeting, including events scheduled through the end of this week, according to strategists at Bank of America. That compares with an average of about 23 appearances over the same two-week period after Fed meetings since 2022.

"This may be a sign that FOMC participants are heeding Chair Warsh's desire to speak less," the firm said in a note. "But it may also be due to the July 4 holidays and Fed speakers having little to add to the guidance issued in June. Time will tell whether this is a new trend or just noise."

— Yun Li

Federal Reserve Chairman Kevin Warsh will have the opportunity to show more of what will motivate his policy positions when he appears Wednesday at the central bank forum in Portugal.

One of the big areas of early focus for the central bank leader, who took office in May, will be the Fed's "reaction function," or what criteria it will use when making interest rate decisions. Warsh has argued that policymakers have spent too much time trying to predict the future, with a spotty record of doing so.

One of five task forces Warsh has set up is expected to focus on how the Fed communicates its thinking behind policy moves.

"I think it's important that we, as central bankers, are transparent in communicating how we're making decisions," Cleveland Fed President Beth Hammack said Tuesday in a CNBC interview, also from the ECB forum.

— Jeff Cox