The Federal Reserve stopped fighting the markets over the pace of the ease of inflation and the direction of monetary policy.

That was the message from the Fed Chair Jerome Powell during the press conference that followed the end of FOMC's regular meeting on Wednesday.

The two sides have been engaged in a tug-of-war over the direction of monetary policy and how quickly inflation is easing after reaching multi-year highs late last year.

Markets have been taking the position that inflation is easing at a rapid pace. Therefore, they advocate an end to rate hikes sooner than later, followed by rate cuts.

The nation's central bank has been cautiously taking the position that inflation is coming down at a slower pace. Therefore, it has a long way to go before bringing inflation to its target of 2%, ending and reversing rate hikes.

The sticking point in the debate is the lag in calculating some components of the Consumer Price Index (CPI). One of them is housing cost, a significant part of the CPI, which is sensitive to home prices.

When housing prices rise, the cost of owning or renting a home increases, raising the overall cost of living measured by the CPI. As a result, it leads to higher inflation, as measured by the change in the CPI, and affects the decisions of both consumers and policymakers.

By contrast, a decline in housing prices can lead to lower inflation and a decrease in the overall cost of living as measured by the CPI. As a result, it has a positive impact on the economy, as it can make housing more affordable for consumers, but it can also be a sign of economic hardship.

The problem is that home prices are reported with a delay, causing biases in CPI calculations. In recent months the bias is on the upside as home prices have been declining in the last couple of months rather than rising, as was the case six months ago.

While the market recognized and acted on this bias, the Fed looked the other way. For instance, in the conference sessions following the October and December meetings, the Fed chair pushed back against the market view that inflation is much lower than the official numbers indicate, emphasizing that more needs to be done.

But that changed in the last session, when the Fed chair recognized the problem, changing the monetary policy narrative to "data dependent" rather than "much more work to be done."

"As expected, the Fed increased the federal funds rate by 25 basis points," Phillip Neuhart, director of market and economic research at First Citizens Wealth Management, told International Business Times.

"Whether the Fed hikes the overnight rate once more as futures believe, or potentially twice as indicated in the FOMC's projections, the Fed is closer to the end of the current tightening cycle than the beginning."

Still, a "data dependent" policy doesn't necessarily mean that the Fed is done with interest rate hikes as bullish market participants concluded following the Fed chair's comments, fueling a rally on both the equity and the debt markets on Wall Street.

"We're nearing the end of rate hikes, but the Fed is still clearly implying that its fight against inflation is far from over, " Callie Cox, US Investment Analyst at eToro, told IBT. "That, in itself, should give investors pause. But, on the other hand, rates are historically high, which could constrain growth, capital, and confidence."