Two recent stories about heinous crimes allegedly committed by people living in the country illegally have again prompted immigration hard-liners to mischaracterize such migrants as a menace to public safety. The crimes at issue here are indeed serious, but the suspects’ immigration status has little to do with their criminal acts.

One man in San Francisco stands accused of posing as a Lyft driver to rape female ride-hailers, and another man in Whittier, Calif., has been charged with taking a chain saw to his wife, who somehow managed to survive the horrific attack. The alleged rapist is from Peru; the alleged chainsaw-wielder is from Mexico, and had been deported back there 11 times since 2005, Immigration and Customs Enforcement officials told reporters.

To suggest that these men reflect the threat posed by people living in this country illegally, however, is just as ridiculous as suggesting that Timothy McVeigh illustrates the threat posed by Army veterans. A number of studies have found that immigrants — whether here legally or not — commit crimes at lower rates than do native-born Americans. In fact, one study of people living in Texas found that immigrants who are undocumented commit fewer crimes than legal immigrants.

Our country’s identity and economy are inextricably tied to immigration.

Some hard-liners shrug off that reality and argue that an individual crime would not have occurred if the perpetrator had been kept out of the country. But that argument doesn’t persuade. It echoes the death penalty advocates who say executions might not deter others from killing, but executing a convicted killer deters that particular person from killing again. That’s no way to frame policy.

Violent criminals living in the country illegally shouldn’t be here, and the government is right to track them down and seek their deportation. But holding up individual violent crimes as a broad indictment of immigrants does nothing to suggest a solution for the problem of illegal immigration.

That the chain-saw assailant had been deported nearly a dozen times is evidence that border enforcement needs to be more effective (and no, a wall running the length of the border will not help). It is not evidence that people living here under the radar pose a public safety risk. The vast majority of immigrants, regardless of their legal status, are here trying to improve their lives and those of their families.

The reality is that our country’s identity and economy are inextricably tied to immigration. Granted, we’ve succumbed to bouts of xenophobia and racism in the past when deciding who is allowed to settle here.

It wasn’t that long ago that the U.S. heavily favored immigrants from northwest Europe and strictly curtailed arrivals from Asia, policies that changed with the 1965 Immigration Act. Regardless, for more than a half-century the U.S. has been the globe’s top destination for immigrants, and about one-fifth of the world’s immigrants now call the U.S. home.