Throughout the primary season, leading Republican presidential candidates vied over who could bash immigrants the hardest. And they were promising more than border walls. Donald Trump is the most extreme immigrant-blamer; according to his website, “Providing healthcare to illegal immigrants costs us some $11 billion annually. If we were to simply enforce the current immigration laws and restrict the unbridled granting of visas to this country, we could relieve healthcare cost pressures on state and local governments.”

As with many of Trump’s claims, this one is wrong. But unlike some of his other falsehoods, the media has left this one unchallenged. Trump’s $11 billion figure comes from an obviously biased study that’s based on outlandish assumptions.

For instance, it counts as “immigrants” millions of U.S. citizens — children who were born in the U.S. of immigrant parents. It also assumes that immigrant families have high health care costs, ignoring a raft of data showing that immigrants use little care. For instance, nearly half (48 percent) of noncitizen immigrant children never see the doctor in the course of a year.

Finally, Trump’s source assumes that every penny of immigrant kids’ health care costs are borne by the taxpayers. Yet a recent study in the respected journal Health Affairs found that unauthorized immigrants families pay the vast majority of their own health care bills, either out-of-pocket, or by buying private insurance. Indeed, 40 percent of newly arrived immigrants have private insurance.

Trump’s numbers don’t just exaggerate taxpayers’ costs for immigrants’ care, they ignore the billions that immigrants pay in taxes. Compared to other Americans, immigrants are younger, healthier and more likely to be male and part of the workforce. That means that an outsized share of immigrants pay the payroll taxes that support Medicare and Social Security, while few are eligible to draw benefits from these programs.

Employers are required to check a Social Security card when hiring a new worker. But they don’t have to check that it’s valid. The IRS happily accepts (and passes on to Medicare and Social Security) payments made under invalid Social Security numbers.

Consequently, millions of undocumented immigrants work and pay taxes under fake or borrowed Social Security numbers. The Social Security Administration estimates that undocumented immigrants pay $13 billion annually into the Social Security trust funds. And, in studies we did at Harvard and the City University of New York, we found that undocumented immigrants contribute billions more to Medicare.

Without immigrants — and especially unauthorized immigrants — Medicare’s Trust Fund would be broke. Each year, immigrants pay about $11 billion more in Medicare taxes than Medicare pays for their care. And undocumented immigrants contribute the lion’s share of this subsidy.

And, just like everyone else, unauthorized immigrants pay sales taxes every time they shop and property taxes (indirectly) when they pay their rent, contributing $11 billion annually in state and local taxes.

While unauthorized immigrants contribute billions in taxes, they use shockingly little health care. Most of the federal health programs they help pay for (like Medicare, Medicaid and the ACA’s plans) exclude them. And those who pay for private coverage use very little care, so their premiums effectively subsidize other enrollees with private insurance.

As physicians, we believe that medical care must be available to everyone residing in the U.S. However, if Trump and other politicians are concerned about “relieving healthcare cost pressures on state and local governments” they should champion fair immigration policies that assure a steady flow of immigrants who come here wanting to work and willing to pay taxes, and don’t need much medical care

Dr. Leah Zallman is a research scientist at the Institute for Community Health, a primary care doctor at Cambridge Health Alliance, and an instructor of medicine at the Harvard Medical School. She is a health services researcher who focuses on health disparities, with specific areas of focus including immigrant health and access to care for vulnerable populations.

Dr. Steffie Woolhandler is a co-founder of Physicians for a National Health Program. She is professor of public health at the City University of New York and visiting professor of medicine at Harvard Medical School. She is also a primary care physician at Cambridge Hospital in Cambridge, Mass.