The Biden administration wants every large business to require Covid vaccinations for their workers. A federal rule could make that mandatory by next year. Some big companies, such as Goldman Sachs and United Airlines, aren’t waiting, with vaccine requirements in place now for all workers or those who enter a company work site.

But many companies don’t require their workers to get vaccinated—and there’s a surprising connection to the labor shortage that’s making it very hard for many companies to find workers. At the recent Milken Institute Global Conference, I moderated a panel discussion on the evolving workplace with five business leaders in different fields. I asked each whether their companies require employees to get a Covid vaccine. None of them do.

The main reason is that some employees would probably leave if forced to get vaccinated, and the labor shortage might make it difficult or impossible to replace them. “If you require vaccination, I think we could lose 10%, 20% of the work force,” Scott Myers, CEO of packaging firm Advanced Converting Works, said during the panel discussion. “It’s a huge percentage. When you look at manufacturing, there are other opportunities out there.”

David Dill, CEO of hospital chain LifePoint Health, says he might lose 2% to 3% of his workforce if the firm required vaccines. That would be enough to cause stress at 89 regional hospitals that already struggle to find enough workers. LifePoint’s hospitals are typically the only large medical facility in the regions they serve, but their employees still have other options. “We’re the only hospital in town in most of our communities, but we’re not the only health-care provider in town,” Dill said. Nurses or technicians, say, could leave the hospital to work at a doctor’s office.

All CEOs on the Milken panel said they’re trying to raise vaccination rates through education and persuasion efforts. In some instance, employees have to be vaccinated because local regulations or client policies require it. “Officially, we do not mandate a vaccine but it sure feels like it,” said Scott Hisey, CEO of Qualtek, an infrastructure firm. “As each of the states that we work in and our customers are requiring it, we’re slowly connecting the dots to a mandate.”

The Biden administration said in early September it would draft new rules requiring all employees at businesses with more than 100 workers to get vaccinated. That would cover about 100 million workers (including many already vaccinated) and ratchet up the nation’s overall vaccination rate. But the Labor Department hasn’t yet issued a final rule and it may not do so until next year.