WASHINGTON — Eager to defend a prolonged government shutdown over his border wall, President Donald Trump is pretending that he’s holed up nonstop at the White House waiting for a deal with Democrats. He’s also rewriting history regarding his promise to make Mexico pay for the wall.

TRUMP: “The building of the Wall on the Southern Border will bring down the crime rate throughout the entire Country!” — tweet Sunday.

THE FACTS: His statement that people in the country illegally are a special menace to public safety is at odds with plentiful research.

Multiple studies from social scientists and the libertarian think tank Cato Institute have found that people in the U.S. illegally are less likely to commit crime than U.S. citizens, and legal immigrants are even less likely to do so.

A March study by the journal Criminology found “undocumented immigration does not increase violence.”

The study, which looked at the years 1990 through 2014, said states with bigger shares of such people have lower crime rates.

As well, a study in 2017 by Robert Adelman, a sociology professor at University of Buffalo, analyzed 40 years of crime data in 200 metropolitan areas and found that immigrants helped lower crime.