From The Mythical Connection Between Immigrants and Crime – WSJ:

…numerous studies going back more than a century have shown that immigrants—regardless of nationality or legal status—are less likely than the native population to commit violent crimes or to be incarcerated. A new report from the Immigration Policy Center notes that while the illegal immigrant population in the U.S. more than tripled between 1990 and 2013 to more than 11.2 million, “FBI data indicate that the violent crime rate declined 48%—which included falling rates of aggravated assault, robbery, rape, and murder. Likewise, the property crime rate fell 41%, including declining rates of motor vehicle theft, larceny/robbery, and burglary.”

A separate IPC paper from 2007 explains that this is not a function of well-behaved high-skilled immigrants from India and China offsetting misdeeds of Latin American newcomers. The data show that “for every ethnic group without exception, incarceration rates among young men are lowest for immigrants,” according to the report. “This holds true especially for the Mexicans, Salvadorans, and Guatemalans who make up the bulk of the undocumented population.”

It also holds true in states with large populations of illegal residents. A 2008 report by the Public Policy Institute of California found that immigrants are underrepresented in the prison system. “The incarceration rate for foreign-born adults is 297 per 100,000 in the population, compared [with] 813 per 100,000 for U.S.-born adults,” the study concludes. “The foreign-born, who make up roughly 35% of California’s adult population, constitute 17% of the state prison population.”

[…]

Every immigrant here illegally has already broken a law, though that doesn’t mean they are predisposed to crime. In a 2005 paper, the Federal Reserve Bank of Chicago reported that more recently arrived immigrants are even less crime-prone than their predecessors. In 1980 the incarceration rate of foreign nationals was about one percentage point below natives. A decade later that had fallen to a little more than a percentage point, and by 2000 it was almost three percentage points lower.

[…]

How do you balance border security and labor-market demand? Should relatives of people already here continue to be given an immigration preference? Is it time to move toward a skills-based immigration system similar to Canada’s? How should the federal government treat border states and cities that bear the upfront costs of illegal entries? Is walling off the southern border feasible? Would it make the U.S. safer? And what should be done about the estimated 12 million undocumented people already living here?