New research from Zillow shows that there are nearly 21 million empty nester households — those are homes with at least two empty bedrooms, no kids, and that have been owned and occupied for more than a decade by folks over 55.

People in that category you could maybe expect to start trading down or moving elsewhere. But despite the need to address the U.S. housing shortage, the sale of empty nester homes isn’t likely to do much to solve the crisis.

One of the big reasons is that younger people simply don’t want what older people are selling.

“The empty nesters are located in places where job prospects for their younger children are not as good,” explained Tim Savage, a clinical assistant professor at the NYU SPS Schack Institute of Real Estate.

Empty nesters are most common in Buffalo, Cleveland or Detroit. But meanwhile, the tech sector has accelerated the millennial and Gen Z migration to bigger cities, Savage said.

“It attracts young, talented people, and in turn, it attracts firms who want young, talented people,” he said.

On top of that, “homeowners are aging in place,” said Mark Eppli, director of the James A. Graaskamp Center for Real Estate at the University of Wisconsin, Madison.

That’s partly because most of them have mortgages at under 4%, but is also just a personal preference. “They get comfortable with the church they’re going to, with the drugstore they go to, the grocery store, to the bar, whatever it may be,” Eppli said.

It helps that employers are moving to smaller metro areas, he added. Though the big metro areas need zoning laws that’ll make it easier to build there, NYU’s Savage noted.