On the Border with Economic Incentives

I read a post on Andrew Samwick's blog about improving border control using economic incentives. We could do a much better job of controlling who enters our country via the southern border with Mexico if Mexico would put more effort into securing their side of the border. Currently Mexico has an incentive to allow illegal immigrants into the U.S. because illegal workers send a lot of money back to Mexico. In the post it says that we could create an incentive for Mexico to reduce illegal immigration by creating a guest worker program where we would reduce the number of guest workers allowed into the U.S. by two for every illegal worker. With such a program, Mexico would benefit more by helping to prevent illegal immigration than by allowing it. I think this is a good idea, the problem I see is trying to figure out how many illegal workers we have here in the U.S. The current estimate of illegal workers today is between 11 and 20 million. So, we know how many illegal workers we have here now .... give or take about 5 million.