Mental models of immigration

Glen Whitman ponders the difference between my preferences and Kerry Howley's on immigration:

I won’t weigh in on the topic itself, fascinating though it is. I’m more interested in trying to parse why they disagree. One interpretation of Kerry vs. Megan is that they differ in their preference ordering. Kerry’s preferences look like this:
{more legal immigration}
pref {guest-worker program}
pref {status quo}
whereas Megan’s, apparently, look like this:
{more legal immigration}
pref {status quo}
pref {guest-worker program}.
That is, Kerry and Megan would both ideally like to see expanded legal immigration, but since that’s a political dead letter, they are consulting their second preferences. Their second preferences differ, because Megan thinks the negative consequences of a guest-worker program are bad enough to make it worse than the status quo.

But here’s an alternative interpretation of Kerry vs. Megan: They have the same preferences (both consider a guest-worker program superior to the status quo, as in the first ordering above),but they have different political strategies. Kerry, thinking that expanded immigration is not going to happen, pushes her second preference for a guest-worker program. Megan, thinking expanded immigration might still be in the cards, opposes a guest-worker program because it could siphon support from the superior alternative.

(Clearly, it’s Megan’s position that I’m less clear about.

Economists have a tendency to represent simple verbal things in more complicated jargon, in part because this is occasionally clarifying, and in part because it is fun. And hell, it's New Years Eve, so I can't resist trying my own model.

Let's suppose a simple model where there are five classes of people: foreigners, illegal immigrants, guest workers, permanent legal immigrants, and Americans. Represent them by the letters f, g, i, l and a. Assume that for each there is a population P, with one interesting variable dimension, W. Take as stylized facts that:

Wa > Wl > Wg > Wi > Wf

and population growth is exogenous to American migration flows so that global population can be simply represented by the following equation:

Pf = Pworld - (Pa + Pl + Pg + Pi)

Global welfare will then be described by the equation:

Wworld = PaWa + PlWl +PiWi + PgWg + PfWf

Right now, for our purposes, Pg = 0. Kerry would like to see it increased to much greater than 0. I would like it to stay 0.

Glenn is right, I think, that for both of us the first preference is a scenario in which legal immigration is increased, so that in twenty years, our population and culture have been enriched by hordes of assimilated foreigners merrily remitting financial and human capital back to their home countries:

Wa + Pa +
Wl + Pl +
WgNo changePg No change
WiNo changePi -
Wf + Pf -

But since this is politically infeasible, Kerry turns to a guest-worker program as second-best. Here, I think, is Kerry's mental model of what happens with a guest worker program:

WaNo changePa No change
WlNo changePl No change
WgNo changePg +
WiNo changePi -
Wf + Pf -

This, obviously, represents an unambiguous Pareto improvement, especially since we both anticipate that current American immigration policy will make Pi fall no matter what we do about guest workers; indeed, I think Kerry views guest worker programs as a possible way to alleviate anti-illegal sentiment.

My mental model, however, extends over multiple time periods. In time period one, you import a large number of guest workers who impose adjustment costs on their neighbors, including other immigrants with whom they compete for resources. In time period two, those guest workers go home and are supposed to be replaced by new guest workers. However, the frictional costs of those guest workers has increased opposition to both legal immigration, and the guest worker program. So in time period 1, things look like this:

Wa - Pa No change
Wl - Pl No change
WgNo changePg +
Wi - Pi No change
Wf + Pf -

In period two, one of two things happens (possibly both): there are significant changes in the law and our institutions in order to better contain guest workers; or the guest worker program and the legal immigration program are curtailed in order to appease rising anti-immigration sentiment. I fear an outcome like this:

Wa - Pa -
Wl - Pl -
WgNo changePg -
Wi - Pi -
WfNo changePf +

In other words, I'm not holding out for some awesome future that both Kerry and I would probably agree is first best, but would probably also agree is not currently politically feasible. I'm against guest worker programs because I think it is possible to do much worse than the status quo, and that guest worker programs will probably reduce American welfare, immigrant welfare, and the total number of foreigners represented by (Pl + Pg + Pi).

Obviously, I don't think that P=1 for my scenario. But it doesn't have to be all that close to one for guest worker programs to start looking a lot less attractive.