Reihan Salam discusses the idea.
The problem with Kenny’s proposal, in my view, is that if we are going to set a tariff, $50,000 is almost certainly not the “correct” price. Kenny’s concern is that the price might be too high, yet the findings of Miao Chi and Scott Drewianka suggest otherwise. Moreover, his thought experiment stipulates that a $50,000 tariff would lead to an influx of 1 million, but of course we don’t know what the market-clearing price would be. In the first year of the new system, in light of pent-up demand, the $50,000 tariff might lead to far more than 1 million immigrants, which in turn might lead to a backlash against immigration tariffs.
The way to fix the number slots, Salam argues, is with an auction of immigration slots, rather than a tariff. But I do not see why this is an instance where it is easier to know the number of slots than the correct price. (Not that i have any idea about what the correct price would be.)
When I thought about this issue nine years ago, I wrote
The tax rate for guest workers would provide a means with which to fine tune the competition between domestic and foreign workers. If we believe that foreign workers are driving domestic wages too low, we can raise the tax on foreign workers. On the other hand, if the economy is at full employment and we want continued expansion without inflationary pressure, we could lower the tax on foreign workers.
I was talking about a high payroll tax for guest workers, not about an immigration fee.
Note that the employers of illegal immigrants would much prefer a quota to something like my payroll tax proposal.