A common conservative refrain is that immigrants, once they enter the U.S., “immediately begin to depend on government welfare,” as Sen. Jeff Sessions of Alabama recently put it.

That’s simply not true, according to a Cato Institute study by Professor Leighton Ku and lecturer Brian Bruen, both of George Washington University’s health policy department.

Ku and Bruen looked at social welfare programs ranging from Medicaid to the food stamp program to the Children’s Health Insurance Program. Their findings: Poor immigrants consistently use welfare programs less than their native-born counterparts. Furthermore, when poor immigrants do participate in welfare programs, the cost is less, resulting in a lower bill for the taxpayer.

Take Medicaid. Noncitizen immigrant adults and children are about 25 percent less likely to be signed up for Medicaid than their poor native-born equivalents. When they do sign up, poor immigrant adults consume $941 less on average than poor native adults every year. The story is the same for poor immigrant children. Looking at CHIP data, the study finds poor immigrant children consume 565 fewer dollars than poor native-born children.

One hundred native-born adults eligible for Medicaid will cost the taxpayers about $98,000 a year. A comparable number of poor non-citizens — immigrants who have not naturalized — cost approximately $57,000 a year — a 42 percent lower bill than for natives. For children, citizens cost $67,000 and noncitizens cost $22,700 a year — a whopping 66 percent lower cost.

Average food stamp use tells a similar story. A poor native-born adult on food stamps receives about $1,091 a year worth of benefits while a non-citizen adult receives $825 — a 24 percent savings. Immigrants are also much less likely to receive food stamps: a noncitizen child is 37 percent less likely than a poor native-born child to receive food stamps.

Certainly it is true that immigrants use fewer benefits because they are not eligible for them. Legal immigrants cannot get welfare for their first five years of residency with few exceptions. Unauthorized immigrants, of course, are not eligible for welfare at all. But doesn’t this in itself undermine the notion that new immigrants “immediately” become government-dependent, as claimed by Sen. Sessions and his ilk?

Furthermore, even when immigrants are legally eligible for welfare, few of them take advantage of it. Immigrants are drawn to America’s labor markets, not to our welfare programs. Unauthorized immigration in 2012 was less than quarter of what it was in 2007, the last year of low unemployment. Since then, the number of Mexican unauthorized immigrants who left the country is about equal to those who immigrated. Food stamps and Temporary Aid to Needy Family benefits are way up since the beginning of the Great Recession, but immigrants stay away because the jobs are gone.

Milton Friedman, the free-market economist beloved by conservatives, had an interesting take on immigration: It’s “a good thing for the United States … so long as it’s illegal.” Translation: Friedman believed open immigration to be highly beneficial for the economy, provided those inexpensive laborers did not have access to welfare.

The findings from Cato’s new study should dampen the fears of free-marketeers who would support more legal immigration if it weren’t for the welfare concern.