Guy Sorman wrote about a Gary Becker idea for this in a recent CapX article. According to Sorman, Becker’s idea runs something like this:

The immigrant takes a risk, and often pays intermediaries to have access to the accumulated capital available in the host country. Becker therefore proposed that the right to enter a country, and apply for a work visa for various periods of time, should be priced and sold. This is already the case in most developed countries, but it only concerns wealthy investors. Fixing a price on all work visas would allow poorer people—who may get into debt to invest for their future—to have access to privileges now reserved to the wealthiest. This right to a paying visa would suppress most of, if not all, illegal immigration and make border controls, as well as the war on evaders (who would become rarer) easier.

Or not. The idea’s presentation leaves unanswered the mechanism for how possession of a visa would make border controls easier: someone still has to be at the border checking the visa, and someone still has to be…somewhere…tracking the visa and its holder’s departure by the visa’s indicated deadline.

Also left unanswered is the mechanism that makes a bought and paid for visa suppressive of illegal immigration. The man who’s leaving his home country and entering his target country exactly because he has no money and wants a better job is unlikely to be able to afford the visa. Coyotes, you say? They only bring a fraction of illegals across.

Also left unanswered is the mechanism that makes a bought and paid for visa useful when another significant fraction of illegal immigrants enter the target country to (re)join their families who already are here. The cost of illegal entry vs bought and paid for visa entry makes that choice obvious.