Segregation patterns in cities: ethnic clustering without skill differences

“Spatial mismatch” is a social phenomenon wherein the area of job offered by firms and the residence of unemployed job applicants geographically differ. Theoretical explanations for the spatial mismatch hypothesis proposed by Kain (1968) are provided by, for example, Brueckner and Martin (1997) and Brueckner and Zenou (2003).

See, for example, Fujita (1989, Chapter 4, Part I) for the segregation mechanism by income level for multiple types of households. As for the theoretical literature on segregation mechanisms, see Fujita and Thisse (2013, Chapters 6 and 7) who consider social interactions in a land market model without assuming a city center as exogenously given. In addition, the body of research from this perspective includes Mossay and Picard’s (2013) segregation analysis.

Nevertheless, we do not deny the existence of an ethnicity bias in skill levels. Coulton et al. (1996) suggest that the geographical concentrations of poverty and affluence can be partially explained by racial and ethnic segregation. Clark and Blue (2004) examine the relationship between residential separation and income or education level.

In addition to these US city examples, in Tokyo, foreign residents from North America or Europe, who are as wealthy as native Japanese residents, tend to reside in clusters in Minato, Setagaya, or Shibuya Wards. See http://​www.​toukei.​metro.​tokyo.​jp/​gaikoku/​2015/​ga15010000.​htm (in Japanese).

Some may deem that the way in which educational factors affect ethnic segregation is a sort of negative externality. For example, in the US context, whites may avoid living close to blacks because blacks are less educated, and thus have children who perform worse at school, which may lead to negative externalities for white children. However, as in the example of the clustering of American or European residents in Tokyo, these negative externalities caused by minorities’ lesser educational attainments are not the only factor creating ethnic segregation, because such a large gap in educational level among foreign residents from rich countries and native Japanese might not exist. Nevertheless, American and European children in Tokyo are likely to choose international schools rather than Japanese public schools, which is indicated by the fact that a large proportion of international schools in Tokyo are located in Minato Ward, where American and European residents are clustered.

Note that in this study, clustering does not mean industrial clustering or agglomeration as is used in new economic geography contexts.

When considering the mechanism of segregation by ethnicity, especially in the context of the USA, whites’ prejudice against minorities is a key issue. Rose-Ackerman (1975), Yinger (1976), and Courant and Yinger (1977) consider a situation in which white residents hesitate to live close to black residents because of the negative externalities created by such residential proximity.

Kanemoto (1980, Chapter 7) suggests ways in which to express the externalities stemming from proximity to another type of household. Thus, this study defines externalities from proximity to the same type of household by employing Kanemoto’s (1980) model, in which externalities are defined as negative ones that affect the utility levels of other ethnicity groups when near another community’s residence.

An attempt was made to adopt a bid rent approach to deal with the topic in question, considering a spatially continuous city in the study; however, this makes the analysis cumbersome. Thus, a new economic geography model was adopted.

Some may suspect the existence a certain level of ethnicity bias. For example, in the Unites States, Hispanics and African Americans are likely to be less educated than the Whites, so that \(\kappa _X>\kappa _x\) may hold. However, as mentioned in Sect. 1, one cannot necessarily assert that the high-skilled ratio of the majority is greater than that of the minority. In addition, in the present model, skill levels are exogenously given for each ethnicity. For a model in which skill differences endogenously emerge through neighborhood interactions in the presence of peer community influence, see Bénabou (1993) and Bénabou (1996). Further, Billings et al. (2014) empirically examines the effects of racial segregation on educational attainment.

Here, although goods transportation cost is ignored, consumer commuting cost is not; such as assumption has also been employed in the context of a traditional bid rent curve analysis (Fujita 1989).

This expression of residential externality from different racial households living in a neighborhood is borrowed from Kanemoto (1980). It may be questioned as to why the ethnicity externality term \(X_e^j\) is not a level but a share. As mentioned in Sect. 1, local governments’ decisions are more likely to be influenced by minority residents, that is, if they are not negligible. In other words, the ethnicity composition of the area may be directly related to the level of ethnic clustering utility, making the employment of a share more rationalizable than a level.

Some may oppose the assumption that land is equally consumed and owned by residents in the same area (public land ownership by area). Thus, we introduce certain modifications to the model in terms of land consumption and ownership. First, we remove the assumption that each resident in the same area consumes the same amount of land, and assume public land ownership, where residents obtain the same share of total land rent in the city. Numerical exercises show that the outcome does not contradict the analytical solutions of the original model; thus, the result obtained from the main analysis on the basis of this assumption can be deemed robust. Details of the analysis can be made available upon request.

Here, we simply assume fixed working hours, such that the high-skilled labor supply equals the total amount of high-skilled labor.

See “Appendix 1” for the proof.

Note that, in this model, “cluster” does not mean industrial clustering but residential clustering in terms of ethnicity.

(M_ HD/LS) stands for a pattern in which Majority, High-skilled workers Disperse across areas and Low-skilled workers cluster in the Suburb. (M_ HC/LS) means that Majority, High-skilled workers cluster in the Center and Low-skilled workers cluster in the Suburb.

The possible residential patterns of the minority are derived in almost the same manner as those of the majority. Details are provided for readers upon request.

(m_HC/LS) stands for a pattern where the minority, High-skilled workers cluster in the Center and Low-skilled workers who cluster in the Suburb. (m_HC/LD) stands for a pattern where as for the minority, High-skilled workers cluster in the Center and Low-skilled workers Dispersed across both areas.

If \(\lambda _{xh} \ne 1\), some high-skilled minority workers commute because their workplaces are in the center. (Note that if \(\lambda _{xh} \ne 1\), some high-skilled minority workers live in the suburb.) Similarly, if \(\lambda _{xl} \ne 0\), some low-skilled minorities commute because their workplaces are in the suburb. (Note that if \(\lambda _{xl} \ne 0\), some low-skilled minority residents live in the center.) For a further discussion, see “Appendix 2”.

For the proof, see “Appendix 3”.

See “Appendix 4” for the proof.

The stability notion used here is that of local stability with respect to relocation dynamics to higher utility locations.

For the derivation, see “Appendix 5”.

Since the proof is similar to that in the cases of (M_HD/LS)(m_HC/LC) in “Appendix 5”, it has been omitted.

I thank an anonymous referee for suggesting this clear restatement of Proposition 1.

Pattern \(\hbox {L}\tau \hbox {-mC}\) stands for a residential pattern where for a Low \(\underline{\tau }\) (commuting cost), minority residents cluster in the Center.

In this model, there is no stable interior equilibrium for the minority residential distribution. For a further discussion, see “Appendix 6”.

See “Appendix 6”.

I thank an anonymous referee for suggesting this clear restatement.

Pattern \(\hbox {H}\tau \hbox {-mD}\) stands for a residential pattern in which for a High \(\underline{\tau }\) (commuting cost), minority households Disperse across both areas. Pattern \(\hbox {H}\tau \hbox {-mC}\) denotes a residential pattern where for a High \(\underline{\tau }\), minority households cluster in the Center.

If \(\psi _h \equiv N_h^C/\sum _{j\in \{C,S\}}N_h^j<1/2\), both high- and low-skilled workers commute in vain without reducing congestion, because if no one commutes, then \(\psi _h=1/2\). \(\psi _h>1/2\) means that some low-skilled workers choose to commute when the entire majority group chooses to commute. The possibility that this situation occurs is excluded from the list of possible residential patterns 1-5 of the minority group (Sect. 3.2).

In fact, this outcome \((\varDelta V_{xh}(\lambda _{xh})\mid _{\lambda =(1,0,1,0)} >0)\) comes from the assumption \(\kappa _X=\kappa _x=1/2\). If this assumption is not given (for instance \(\kappa _x<1/2\)), \(\varDelta V_{xh}(\lambda _{xh})\mid _{\lambda =(1,0,1,0)}\) can take a negative value. This implies that the stable interior equilibrium \(\lambda _{xh}^*\) can emerge at a certain level of \(\tau \).

Drawing the quadratic function \(g_h(\lambda _{xh})\) helps us to check this proof.