Immigrant entrepreneurs comprise a large portion of start-ups. In fact, according to a recent study, more than half of the Silicon Valley start-ups had at least one foreign-born founder, and across the country the figure was just over one-quarter. These were astonishing findings given that just 13 percent of the U.S. population is foreign-born.

U.S. immigrants are about twice as likely to become entrepreneurs as native-born Americans. They make up around 13% of the...