The impact of the assimilation of migrants on the well-being of native inhabitants: A theory

https://doi.org/10.1016/j.jebo.2014.12.010Get rights and content

Highlights

  • We present a theory that links the well-being of native inhabitants with variation in the extent of assimilation of migrants.

  • Recent empirical findings are yielded as predictions of the theory.

Abstract

We present a theory that systematically and causally links the well-being of native inhabitants with variation in the extent of the assimilation of migrants. Recent empirical findings are yielded as predictions of the theory.

Introduction

In a study of the effect of migration into a country on the life satisfaction of the native population, Akay et al. (2014) present an array of findings. These findings will be summarized shortly. Akay et al. search for an explanation for the patterns observed. They dismiss several possible explanations, and suggest ad hoc ones for their reported findings. However, there is no unifying theory on offer, nor an overall model that can yield all the findings they report on assimilation-intensity and well-being. The usefulness of a unifying theory is obvious: it can generate an array of testable predictions and facilitate an orderly and logical interpretation of the findings obtained. A solid theory can also provide a clear guide as to what to look for in harvesting and employing the data. And it can pinpoint where gaps still exist in relating the data to the theory. It is the purpose of this paper to present a theory that systematically and causally links variation in the assimilation of migrants with impact on the well-being of native inhabitants.

The impact of migration on the well-being of the native inhabitants is one of the most intensively studied topics in migration research. A typical approach has been to estimate the elasticity of earnings and/or of the employment rate of the native inhabitants (or of subgroups of the native inhabitants) with respect to migration. A less common approach relates the gain to the native inhabitants to the tax proceeds collected from the migrants. An intermediate variable here is the host country's specific human capital that the migrants choose to acquire. The idea (cf. Stark, 2010) is that the greater this capital, the greater the migrants’ productivity, the higher their earnings, the higher the income tax collected from them and, consequently, the greater the gain to the native inhabitants. The received literature then assesses the repercussions of migration for the well-being of the native inhabitants via moves occurring in the economic space, which is perfectly reasonable, though this is not the only space that matters. In this paper we build on the idea that the assimilation of migrants impinges on the well-being of the native inhabitants, but we take a different course. In the spirit of Akay et al. (2014), we look at how the well-being of the native inhabitants is impacted by moves made by the migrants in social space. The move places the migrants in the reference group of the natives. The “length” of the move (the intensity of assimilation) determines the migrants’ income.

We characterize a group of individuals (a population) by the multiset of the incomes of the members of the group, X. We employ the following operations and definitions. First, by a sum over a multiset we mean a sum over its elements with repetitions accounted for. As an example, for X={1,1,2,2} we have that xXx=1+1+2+2. Second, by disjoint groups X and Y we mean that the sets of the individuals whose incomes constitute the multisets X and Y are disjoint. For example, having disjoint groups of migrants and of native inhabitants means that there is no individual who is both a migrant and a native inhabitant (although the sets of the incomes of the migrants and of the native inhabitants need not be disjoint). Third, for disjoint groups X and Y we define the combined group XY as the multiset sum of X and Y.1 For example, for X={1,1,2} and Y={1,2,3} we will have a combined group XY={1,1,1,2,2,3}.2

For a reference group characterized by a multiset of incomes of its members, X, we define the relative deprivation of an individual whose income is y asRDy|X1|X|xXmaxxy,0,where |X| is the size of reference group X (the number of members who constitute reference group X).3 From this definition it follows that the individual whose relative deprivation we measure need not be a member of the group with respect to which the individual's relative deprivation is calculated. For example, we may compute the relative deprivation of a native inhabitant, henceforth a native, with respect to a reference group of migrants. The aggregate relative deprivation of a group characterized by a multiset of incomes Y, with respect to a reference group characterized by a multiset of incomes X, is the sum of the levels of relative deprivation of the individuals in Y, calculated with respect to the individuals in X:ARD(Y|X)yYRDy|X=1|X|yYxXmaxxy,0.

Let the well-being of an individual depend positively on the individual's income, and negatively on the individual's relative deprivation, which arises from comparing his income with the incomes of others in his reference group(s); income is desirable, relative deprivation is undesirable. A brief foray into the subject of relative deprivation and a discussion of the significance of relative comparisons to well-being are in Sorger and Stark (2013). To enable us to draw inference from the aggregate relative deprivation of the native inhabitants to their well-being, we take the utility functions of the native inhabitants to be linear in relative deprivation with the same linear coefficient across all the native inhabitants. That is, the utility function of a native inhabitant who compares his income y with reference group X takes the form u(y|X)=f(y)aRD(y|X), where a>0 and f() is a strictly increasing function.4 We measure the well-being of the group of natives, N, whose members compare their incomes with the members of reference group X, as sum of the utility levels of the members of N:W(N|X)=yNu(y|X)=yNf(y)ayNRD(y|X)=yNf(y)aARD(N|X).

Holding constant the incomes of the natives, we can gauge the change in the well-being of the natives, brought about by assimilation of the migrants (which is tantamount to adding the migrants to the reference group of the natives), by the change in the aggregate relative deprivation of the natives. The magnitude of such a change is determined by the intensity of assimilation of the migrants. Different intensities affect the positioning of the assimilating migrants in the native inhabitants’ reference group.

With this measure of well-being in hand, we schematically present a series of constellations.

In Constellation I, the migrants, whose incomes are 1 each, constitute their own reference group, as do the natives whose incomes are 3 and 5. There is no assimilation. The migrants do not affect the relative deprivation nor the well-being of the natives.

In Constellation II, the migrants assimilate, thereby moving, so to speak, into the social space of the natives; the migrants are now included in the reference group of the natives. Because the intensity of assimilation is moderate, the migrants’ incomes remain lower than the incomes of the natives. This assimilation lowers the relative deprivation of native “3” and does not affect (leaves at zero) the relative deprivation of native “5.” Thus, the aggregate relative deprivation of the natives is lowered and their well-being rises.

In Constellation III, the migrants assimilate perfectly or “completely,” replicating the incomes of the natives. This assimilation leaves the aggregate relative deprivation and well-being of the natives intact.

In sum: when the migrants’ level of assimilation is intermediate (Constellation II), the natives’ well-being is affected positively; when the migrants do not assimilate (Constellation I), the effect on the well-being of the natives is “zero;” and when the migrants assimilate completely (Constellation III), the effect on the natives’ well-being is “zero” too. These are exactly the results obtained by Akay et al. In their words: “We find that the positive effect of immigration on natives’ life satisfaction is a function of the assimilation of immigrants in the region. Immigration's well-being effect is higher in regions with intermediate assimilation levels and is essentially zero in regions with no or complete assimilation” (p. 72).

Our proposed theory yields an additional prediction, not tested by Akay et al.: when the assimilation level of the migrants is as per Constellation IV, the natives’ well-being is lowered:

In Constellation IV, the migrants assimilate more intensively than in Constellation II. An assimilation of such an extent increases the relative deprivation of “3” and leaves unchanged the relative deprivation of “5.” The aggregate relative deprivation of the natives increases and their well-being takes a beating.

We next generalize the preceding examples of migrants’ assimilation and its impact on the well-being of the natives. To this end, we specify a condition under which assimilation is detrimental or beneficial to the well-being of the natives: for assimilation to favor the well-being of the natives, the relative deprivation experienced by the natives from comparison with the assimilating migrants has to be lower than the relative deprivation experienced by the natives from comparison with fellow natives.

Section snippets

A general framework

To begin with, we state and prove a lemma that will enable us to calculate the aggregate relative deprivation of a group of individuals with respect to a combined reference group.

Lemma 1

For disjoint groups X and Y, the aggregate relative deprivation of group Z calculated with respect to the combined reference group XY is

ARD(Z|XY)=|X||XY|ARD(Z|X)+|Y||XY|ARD(Z|Y).

Proof

For any individual zZ we have thatRD(z|XY)=1|XY|xXYmaxxz,0=1|XY|xXmaxxz,0+yYmaxyz,0=|X||XY|1|X|xXmaxxz,0+|Y||XY|1|Y|y

Conclusion

Inspired by the findings of Akay et al. (2014), we formulated a simple theory that enables us to predict the impact of the assimilation of migrants on the well-being of the native inhabitants. Founded on the concept of relative deprivation, the theory tracks how the inclusion of migrants in the comparison group of the natives affects the well-being of the natives. We find that the crucial determinant in this regard is the relationship between the relative deprivation experienced by the natives

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We are indebted to William Neilson for advice and encouragement, and to Agata Gorny and Ewa Zawojska for enlightening comments. The support of Georgetown University Edmund A. Walsh School of Foreign Service in Qatar is gratefully acknowledged.

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