The Federal Reserve delivered its first interest rate cut in more than four years yesterday. It was a declaration of victory over once hot, hot, hot inflation. And mortgage rates responded by fluctuating in kind of a weird way. The average 30-year fixed weekly rate dropped from 6.2% to 6.09% and the daily rate rose from 6.15% to 6.17%. They might seem like tiny changes, but it matters to anyone who wants to buy a home—think of the total cost of a mortgage over its 30-year lifespan.

But there is a fight that the central bank hasn’t won. Although it might not be its fight at all.

During a post-meeting press conference, Fed Chair Jerome Powell was asked if interest rate cuts would reignite demand in the housing market and send prices soaring—again. His answer was telling: once mortgage rates come down, the lock-in effect will ease. People will start to sell their homes, and when they do, they’ll buy homes, too. So it isn’t clear how much extra demand the cut could trigger. To him, it seems that piece only side-steps the crux of the country’s housing crisis.

“I mean, the real issue with housing is that we have had and are on track to continue to have not enough housing, and so it’s going to be challenging,” Powell said. “It’s hard…to zone lots that are in places where people want to live...All of the aspects of housing are more and more difficult, and you know, where are we going to get the supply? And this is not something that the Fed can really fix.”

He continued: “But I think as we normalize rates, you’ll see the housing market normalize. And I mean, ultimately, by getting inflation broadly down and getting those rates normalized and getting the housing cycle normalized, that’s the best thing we can do for householders. And then the supply question will have to be dealt with by the market and also by government.”

It’s interesting. So we know the Fed doesn’t set mortgage rates, but it can influence where they go. Case in point: mortgage rates won’t plummet in the aftermath of yesterday’s decision, because they’ve already fallen so much because the cut was priced in from expectation alone. Still, lower rates are coming. Either way, when the pandemic began, the central bank slashed interest rates; they were emergency cuts. Mortgage rates were already pretty low, but they kept falling. Rock-bottom mortgage rates and the ability for work from wherever fueled a housing boom.

Then roughly two years later when inflation became a problem, the Fed raised interest rates, and mortgage rates soared. The shock pushed the housing world to a standstill. Last year existing home sales fell to their lowest level in close to three decades. Even now, data out today showed existing home sales dropped 2.5% in August from the prior month and 4.2% from one year ago. So the central bank absolutely plays a role in housing, but its movements only power temporary phenomenons. The Fed doesn’t build houses, as Powell said in Fed Speak.

Our problem is that the country is missing millions of homes, and the shortfall is keeping prices aloft, that’s what housing policy analysts and urban economists and real estate executives will tell you. Some say we’ve been under building since the Great Financial Crisis; some say it goes back further, to land-use regulations and policy failures decades ago. People can’t afford homes, and it’s not only because of high mortgage rates.

It isn’t the first time Powell has taken this stance. Earlier this year, as he testified to the Senate Banking Committee, Powell explained that problems associated with the lock-in effect, resulting from higher mortgage rates “will abate as the economy normalizes and as rates normalize…But we’ll still be left with a housing market nationally, where there is a housing shortage.”

This story was originally featured on Fortune.com