I like the set-up of this model because it gets at what I believe is a key element of the immigration debate - how we value the welfare of people outside our borders relative to the welfare of citizens within our borders. As Alan Krueger says:
There are no simple answers on immigration policy because different people can legitimately assign different weights to the welfare of new immigrants, recent immigrants, and various groups of natives.
Here's the introduction and conclusion to the paper:
Optimal Migration: A World Perspective, by Jess Benhabib and Boyan Jovanovic, NBER WP 12871, January 17, 2007 [open link]: 1 Introduction All rich industrialized countries severely restrict immigration. While the extent of the restrictions varies by country and by period, they nevertheless are at odds with the basic tenets of free trade, and in deep contradiction with some of the most cherished values of liberal democracy: that there should be no job discrimination based on nationality, ethnicity, race or gender. While we deplore job discrimination directed at citizens, we also design immigration laws that exclude foreign nationals out of our countries and our job market. It follows that there must be costs associated with immigrants that are borne by the citizens of a country, or otherwise the borders would be open.
Several reasons may be given to explain restrictive immigration policies in terms of the costs that immigrants impose on the citizens of a country. The most obvious is a distributional argument cast in terms of political economy. The median voter whose income derives mostly from wages will wish to keep out the unskilled immigrants who will depress his wage. Others, more controversially, stress the cost of social services that low-skilled immigrants impose on the citizens, or adopt the communitarian view that shared values, customs and culture constitute a social good that would be diluted by immigration, an argument that has often been used to keep the undesirables out. Finally, one can argue that positive output externalities emanating from the average level of human capital will be depressed by immigrants with low human capital stocks who cause congestion, disutility, and have a negative impact on output per capita. Since the goal of this paper is not to identify the nature and scope of the costs of immigration borne by citizens, we will model the latter explanation by externalities emanating from the average level of human capital, a framework which is quite simple, and which may be modified or reinterpreted to capture direct labor-market effects on wages, or negative cultural externalities from low skilled immigrants.
We study the welfare implications of restrictive immigration policies from the world perspective, while allowing for costs of migration to the host and source countries. We ask what the optimal immigration policy would be, given a social welfare function that parametrically weighs the citizens of the industrialized, human-capital rich countries and those of the third world. One might simply expect that as the welfare weight is continuously shifted from the citizens of the first to the third world, optimal immigration policy, in terms of the proportion of third world citizens allowed to emigrate, would increase continuously. Our results indicate that this is not so: if populations are homogeneous in the skills within a country but differ across countries, there is a threshold relative welfare weight assigned to the third world citizens at which optimal immigration policy shifts from zero immigration to maximal immigration. If populations are heterogenous in skill to labor ratios, then under egalitarian social welfare weights, or, a fortiori, with weights that favor natives of the low average skill country, the optimal policy is to let the least skilled emigrate, up to a threshold skill level, from the low to the high average skill country. A simple and quick calibration shows that this implies that optimally up to 3.2 billion low-skilled people should emigrate from the third world to the OECD. If on the other hand, social welfare weights favor the natives of the high-skill country, optimal immigration policy may be no immigration at all, or an immigration policy that allows only the highly skilled to emigrate from the low- to the high-average-skill country.
With globalization, pressures to design redistributive and immigration policies that increasingly take a world rather than national perspective are likely to mount. Thus, if the political perspective shifts from a national to an international one, more consistent with values of liberal democracy applied globally, the optimal immigration policy will require a drastic change. Of course other factors, including political costs of policy transition, or political resistance in host countries, may imply a more gradual shift over time. This paper, while allowing for the costs of immigration, shows a basic thrust or tendency calling for a shift in immigration policy as we move towards a world democracy.
Egalitarian optimal immigration policy from the world perspective, taking into account the economic costs of immigration to the host and source countries, may still require a significant and abrupt relaxation of the restrictive immigration policies currently imposed by the rich countries. With increasing globalization, the third world countries are likely to acquire a greater voice and request greater access to world labor markets. It will probably become harder for richer countries to justify their non-discriminatory and redistributive welfare policies at home, while denying access to their labor markets to citizens of poorer countries, basing the exclusion simply on ethnicity and nationality. While the deep contradictions between the democratic values of the West and the limitations on free access to world labor markets based on nationality have only recently began to surface, they are likely to become increasingly apparent in the future, and enter political discourse through international organizations like the UN or the World Bank. Political negotiations and compromises, however, may at best yield a gradual relaxation of restrictions on labor mobility, as in the case of a slowly expanding EU or the phased legalization of illegal immigrants in the US, rather than an abrupt switch to free immigration that an egalitarian parametrization of our model suggests.
We thank the NSF for support and Matthias Kredler for doing all the calibrations and producing the associated plots.
 Freedberg and Hunt (1995) report that all but 100 million of the world’s 6 billion people live in the country of their birth.
 Protectionist arguments have recently been made against the mobility of capital, on the grounds that some multinational corporations do not pay a “living wage” in third world countries. Yet none of the pundits against outsourcing has advocated opening up of the borders to immigrants in order to improve their lot.
 See for example Borjas(2003), and Borjas and Katz (2005). For the opposing view see Card (2005). For a more recent reconsideration of this debate, see Peri and Ottaviano (2006).
 See the edited volume by Warren F. Schwartz (1995), and in particular the essays in the volume by Jules Coleman and Sarah Harding, and by Michael Trebilcock. For studies suggesting that immigrants do not impose large negative social externalities see National Research Council (1997) and Butcher and Piehl (1998).
 The International Organization for Migration estimates that currently there are 191 million transnational migrants worldwide comprising 3% of the global population. See http://www.iom.int/jahia/page254.html
 By contrast, however, the French Interior Minister Sarkozy recently declared “It is the right of our country, like all the great democracies of the world, to choose which foreigners it allows to reside on our territory.” See http://www.migrationpolicy.org/pubs/Backgrounder2_France.php