The debate about immigration is often cast in terms of the alleged threat to American jobs. But in fact those who move to the U.S. are prodigious employment creators. First-generation immigrants or their children had founder roles in more than 40% of the Fortune 500, including such marquee companies as AT&T (No. 11), Procter & Gamble (No. 31), Goldman Sachs (No. 74), Pfizer (No. 51), eBay (No. 180), Google (No. 46), Intel (No. 53), Kraft (No. 156), Cigna (No. 97), and Kohl’s (No. 151).

In fact, the U.S. may be losing ground as a magnet for global entrepreneurs, thanks to a backlog in the visas that allow them to start new businesses. Last year efforts to boost available green cards and create a new visa class for immigrant entrepreneurs fizzled. Now foreign-born scientists and entrepreneurs are leaving the U.S., while such countries as Australia, Canada, Chile, China, and Singapore look to attract them. Says Duke University professor Vivek Wadhwa, author of The Immigrant Exodus: Why America Is Losing the Global Race to Capture Entrepreneurial Talent: “The United States is losing a key growth engine.”

IMM.06.16.14 chart part 2

IMM.06.16.14 chart part 2

But visas are limited, the process is onerous and lengthy, and immigrants are beginning to return home.

376,000: The number of permanent-resident visas available each year. No single nationality can claim more than 7% of these cards.

4.3 million: People waiting for green cards in 2013, according to a U.S. State Department report, up from 3.5 million in 2009.

180,000: Number of Chinese students who returned to their home country in 2011, up from 50,000 in 2008.

Sources: Partnership for a New American Economy; Kauffman Foundation and Duke University; Center for China and Globalization

This story is from the June 16, 2014 issue of  Fortune.