Medicare-for-all and other versions of universal coverage being proposed for the U.S. by several presidential hopefuls wouldn’t necessarily lead more people to seek hospital care, a new analysis suggests.

Critics of Medicare-for-all have raised concerns that it might lead to a surge in use of inpatient services, because people with comprehensive health insurance tend to use more hospital care than people with bare-bones benefits, researchers noted online in Annals of Internal Medicine.

Some previous studies suggest this surge might materialize, but other studies also suggest that hospital use only rises dramatically when more beds are available and staffed for an anticipated spike in utilization.

To see how universal coverage might play out today, researchers looked at the two biggest expansions of health benefits in U.S. history: the implementation of Medicare and Medicaid from 1966 and the Patient Protection and Affordable Care Act (ACA) in 2014.

Using data from the National Health Interview Survey (1962 to 1970), they found that hospital discharges averaged 12.8 per 100 people in the three years before implementation of Medicare and Medicaid and 12.7 per 100 people in the three years afterward.

And based on data from the Medical Expenditure Panel Survey (2008 to 2015), with the ACA, discharges dropped from 9.4 per 100 people in the three years before the law to 9.0 per 100 people in the three years afterward.

“Contrary to expectations, overall hospitalizations didn’t rise after both expansions—suggesting that universal coverage expansions like Medicare-for-all also won’t cause a surge in hospitalizations,” said Dr. Adam Gaffney, lead author of the study and president of Physicians for a National Health Program, an organization that advocates for Medicare-for-all.

The expectation when previously uninsured people get health coverage is that they will start using every kind of care, including hospital care, driving up costs, Gaffney, also an instructor at Harvard Medical School in Boston, said by email.

In the current study, while some populations did increase their use of hospital care, the increases were offset by reductions among others.

For example, after the introduction of Medicare and Medicaid, hospital use increased among elderly and low-income persons but decreased among younger and higher-income persons.

This suggests that major coverage expansions result in shifts in who uses the hospital, but not increases in overall hospital use, the study team concludes.

One limitation of the study is that it only looked at hospital care—which only accounts for about one-third of total healthcare spending. These coverage expansions might mean something different for outpatient or clinic visits, or prescription drug use, which are also big drivers of health spending.

“When it comes to prescription drugs, there is no supply limit as there is with hospital beds in the case of hospital care,” Gaffney said. “So we probably would expect a more unconstrained increase in prescription drug use after Medicare-for-all, relative to hospital care.”

It’s also possible that expanding insurance extends coverage mostly to people who aren’t at high risk of hospitalization, like young, healthy people who rarely see doctors, said Dr. Anupam Jena, a researcher at Harvard Medical School and Massachusetts General Hospital in Boston who wasn’t involved in the study.

“It’s very clear from many studies that insurance expansion or insurance coverage raises health care costs, despite the argument sometimes made that better insurance leads to better primary care which then leads to lower overall costs,” Jena said by email. “That isn’t true—insuring more people costs more money, but for a wealthy society such as ours, that in many people’s minds is still the right thing to do.”