Since day one of his campaign for president, Donald Trump has linked illegal immigration with crime. Vice President Pence recently did it as well during a visit to the Texas-Mexico border to tout how “this administration has been taking decisive steps to enforce our laws; secure our borders; taking dangerous drug dealers off our — violent criminals off our street.”

But there is no link between illegal immigration and crime — even in a border state like Texas.

The Texas Department of Public Safety preserved the results from immigration checks when people are arrested and convicted of crimes, unlike other states. This allowed me to check immigration statuses against criminal convictions and compare them to the share of illegal immigrants in Texas’ population. The results are in a new brief I wrote for the Cato Institute, showing that illegal or legal immigrants are less likely to be convicted of crimes than native-born Americans.

Let’s examine the raw numbers: In 2015, natives were convicted of 409,063 crimes, illegal immigrants were convicted of 13,753 crimes, and legal immigrants were convicted of 7,643 crimes in Texas.

Natives were convicted of a disproportionate 95 percent of all crimes, although they only made up 83 percent of Texas’ population. Illegal immigrants, making up just six percent of the population, were convicted of only three percent of the crimes. And legal immigrants were even less crime prone, making up 11 percent of the population but receiving only two percent of criminal convictions.

Even in a Republican-governed border state like Texas with law enforcement officials very concerned about illegal immigration — and with a reputation for enforcing criminal laws to the hilt — illegal immigrants appear less crime-prone than natives.

This holds true even for particularly violent crimes. Many Americans are concerned about murders committed by illegal immigrants, notably the killing of Kate Steinle in San Francisco in 2015. Steinle’s killing was a tragedy but, as the Texas crime data shows, it is a remarkably rare one, at least in the Lone Star state. There were 951 total homicide convictions in Texas in 2015. Of those, native-born Americans were convicted of 885 homicides, whereas illegal and legal immigrants face 51 and 15 such convictions, respectively.

In other words, there were 2.9 murder convictions of illegal immigrants in Texas for every 100,000 of them living there that year. That’s compared to 3.9 convictions of native-born Americans for every 100,000 natives. Once again, legal immigrants were the most peaceful as there were only 0.51 homicide convictions for every 100,000 legal immigrants.

Thus, homicide conviction rates for illegal and legal immigrants were 25 percent and 87 percent below those of natives, respectively. Per capita, there were fewer convictions against illegal immigrants for every crime except for gambling, smuggling, vagrancy and kidnapping —crimes that account for a mere 0.18 percent of all criminal convictions in Texas in 2015.

There is a potential criticism of our findings so far. Illegal immigrants might not be convicted of many crimes because they get out on bail and skip town before the courts can convict them. After all, most of them are from Mexico and there’s little stopping them from returning if they think they’ll be convicted of a crime. However, the arrest data shows results that are very similar to the convictions data. For virtually every crime, legal or illegal immigrants are less likely to be arrested than native-born Americans.

Illegal immigrants who commit violent and property crimes should be deported after serving their sentences. The United States does indeed have more crime than other developed countries — but it’s inaccurate to scapegoat immigrants for this problem, or to portray them as more bloodthirsty or less law-abiding.

So even if Pence claims that stopping violent crime or drug dealing starts with more security at the border, illegal immigrants’ low conviction rate for serious crimes such as murder should put the worries of many Texans to rest. There are many reasons to be concerned about illegal immigration, from cultural impacts to the economy, but criminality is not one of them.