The term “compositional effects” is used here to refer to a range of observations about how using group averages can paint a misleading picture about how individuals are doing. This does strike down a small but significant minority of objections to immigration.

Compositional effect for means

Suppose country A has a mean income of $1000 per capita per annum and country B has a mean income of $10000 per capita per annum. Suppose a worker with an income of $2000 per annum in country A moves to country B, and sees his income rise to $5000 per annum. Further, suppose that the income of no other individual is affected.

From an individual perspective, this is a Pareto improvement: at least one person is better off, and nobody is worse off. However, the means of both countries have gone down, because country A lost an above-average earner and country B gained a below-average earner. In other words, looking at group means paints a very different picture compared to looking at, and tracking, individuals.

Compositional effect for variation

The example is harder to illustrate numerically, but the idea is that migration can increase the variation in incomes or other measures within each country while decreasing the global variation. This variation may be measured using conventional measures such as standard deviation or the Gini coefficient. The story may be a little different for different measures of variation. For instance, in his paper Economics and Emigration: Trillion-Dollar Bills on the Sidewalk (PDF, 24 pages), Michael Clemens writes (Page 9 of the paper, Page 91 in the print edition):

Furthermore, if a man from Morocco triples his income by moving to France, the effects on inequality of outcomes within Morocco and within France are both contingent: they depend on where in Morocco’s income distribution he came from, and where in France’s income distribution he goes to. But the effects on inequality of outcomes for France and Morocco collectively almost certainly declines.

Remedies

Some of the problems associated with compositional effects can be remedied using measures such as income per natural, which tracks and aggregates the income of people based on their country of birth rather than their current country of residence/citizenship.

Compositional effects and analytical nationalism

In a policy analysis for the Cato Institute titled Thinking Clearly about Economic Inequality, Will Wilkinson considers how compositional effects and analytical nationalism can lead people to view immigration as an inequality-increasing mechanism, despite the improvement in everybody’s living standards and the reduction in world inequality:

Consider immigration. Looking at that issue through the prism of conventional economic analysis or liberal egalitarian political thought tends to simply take for granted what might be called “analytical nationalism.” Afterall, income statistics are kept by governments on a national level. Of course, the mere fact that most useful economic data are collected by nation-states about individuals and families within their physical jurisdictions is irrelevant to the task of determining the morally relevant pattern of incomes. If you focus only on the shifting pattern of incomes among legal residents within the statistics-keeping jurisdiction (the United States), you can easily lose track of the real story of human welfare and social justice. [Page 14]

Wilkinson continues:

Consider a discussion of the effects of immigration on income inequality from three eminent political scientists: Nolan McCarty,Keith T. Poole, and Howard Rosenthal, in their recent book
Polarized America: The Dance of Ideology and Unequal Riches:

The new immigrants are predominantly unskilled. They have contributed greatly to the economy by providing low-wage labor, especially in jobs that American citizens no longer find desirable. They also provide the domestic services that facilitate labor market participation by highly skilled people. On the other hand, immigrants have also increased inequality both directly, by occupying the lowest rungs of the economic ladder, and indirectly, though competition with citizens for low-wage jobs. Yet as noncitizens they lack the civic opportunities to secure the protections of the welfare state. Because these poor people cannot vote, there is less political support for policies that would lower inequality by redistribution [emphasis added by Wilkinson].

This is a sadly typical example of the distortions of analytical nationalism. If we were to assume a natural and mundane moral perspective, from which all people involved are taken into account and assumed to have equal worth — that is, if we assume the perspective of moral egalitarianism — what we would see is a profound reduction in both poverty and economic inequality. If the question is “What happened to the people in this scenario?” then the answer is “The poorest people became considerably wealthier, narrowing the economic gap between them and the rest.” But what actually happened seems either invisible or irrelevant to the authors, which certainly suggests that their analytical framework leaves something to be desired. Here’s how the passage I highlighted might be more accurately stated:

Immigration decreased inequality both directly, by sharply increasing the wages of low-skilled, foreign-born workers,and indirectly, through remittance payments to low-income relatives at theimmigrants’ places of origin. Due to the widespread opposition of American voters to liberalizing immigration, very large additional reductions in poverty and inequality have been forgone.

[Page 14-15]

Wilkinson also wrote a slightly modified version of this paper of his own paper in a blog post titled Analytical Nationalism vs. What Actually Happens.