Dissecting income segregation: Impacts of concentrated affluence on segregation of poverty

ABSTRACT

This article investigates how income inequality shapes residential segregation by income. Using agent-based modeling, it develops a residential preferences model that is capable of generating results mimicking empirical income segregation patterns. Simulation analysis shows how varying income inequality produces differential residential mobility outcomes that alter income segregation profiles. The model is used to capture the distinct impacts of households’ moves into richer or poorer neighborhoods, and how these impacts are further differentiated with respect to the moving household’s income. The article demonstrates how aggregating such diverse outcomes of micro-level interactions at a meso-level can help us to better understand the changes in macro-level income segregation patterns. Analyzing residential mobility patterns carefully, the article suggests that i) segregation of affluence and of poverty can trigger each other via initiating cascades of residential mobility and housing prices, and ii) increasing income inequality can disrupt housing market and lead to shortages in affordable housing, which can yield high residential instability and eviction rates among the poorest stratum.

KEYWORDS:

• Agent-based modeling
• analytical sociology
• concentration of affluence
• concentration of poverty
• eviction
• income inequality
• income segregation
• residential segregation

Acknowledgments

I am indebted to Gönenç Yücel, Yaman Barlas, and Dolunay Uğur for their helpful comments on the earlier versions of this article. I also would like to thank Emily Erikson, Andy Papachristos, Joscha Legewie, Oylum Şeker, Tuna Kuyucu, Elizabeth Roberto, Richard Breen, Vida Maralani, the participants of the Center for Research on Inequalities and the Life Course workshop at Yale University, and Socio-Economic System Dynamics research group at Boğaziçi University. All mistakes, of course, are my own.

Notes

¹ The model presented here purposefully leaves out some other significant drivers of income segregation such as racial segregation, prejudice, and discrimination; housing and urban policies such as zoning laws and rent control; home ownership, wealth distribution and inequality; spatial particularities of the cities, and the like. It does so purposefully to gain analytical leverage because including these would make this model notoriously complicated to analyze the main research questions namely how income inequality affects residential preferences, housing market, and the interaction between the two, and eventually gets spatially sorted and lead to income segregation. While it might be promising further research to complicate the findings of this article by introducing these other factors into the simulation model, this study is just a humble beginning of sorting out the mechanisms that translate income inequality into spatially uneven distributions of income, which is already an analytically complex problem to deal with even in the absence of these aspects. I discuss the role of these omitted factors and some related experiments that I did with this model in the discussion section.

² Although while calculating the overall segregation level they weight segregation of the poorest and the richest least, it is still important to focusing on these parts to provide a complete panorama of the segregation experienced in a city.

³ For a sophisticated and thorough review of the literature on residential segregation as well as the related modeling studies, see the special issue of Journal of Mathematical Sociology on Fossett’s work (2006a, 2006b; Skvoretz, 2006) and Bruch and Mare’s works (2006, 2012).

⁴ Although they frame their study around the concept of wealth and I choose income instead, our studies are still comparable, because in both, wealth and income serves the same purposes of affordability and of informing SES levels of residents. Moreover, I also abstain from using similar concepts of class segregation or economic segregation as I think they need more conceptual elaboration than income segregation.

⁵ Minimum income segregation occurs when income distribution in each neighborhood mirrors that of the city as a whole. Maximum income segregation occurs when there is no income variation within any of the neighborhoods (i.e. every household in a neighborhood has the same income) while each neighborhood’s income differs from one another.

⁶ I coded and executed my model in Net Logo (Wilensky, 1999).

⁷ Similarly, without decoupling SES and income, it is not possible to have nouveau riche, who has high income but low SES, which can create unpredictable dynamics in housing market as gentrification does.

⁸ In the model, the budget and the income of a household equal to each other for the sake of simplicity.

⁹ Benard and Willer (2007) found that higher values of the correlation between income and SES lead to higher levels of segregation. I experimented with different levels of correlation as well and found the same impact. In the simulations, the coefficient is taken as 0.7, yielding 0.9 correlation between income and SES on average.

¹⁰ To gain analytical leverage, other determinants of SES are not specified in the model such as race or ethnicity, jobs, and family. They are purposefully ignored by the modeler and can be thought as if they are combined under the rubric of desirability in a single random variate b following similar distributions to income distribution.

¹¹ The number of neighborhoods is determined such that the distortion in the extreme ends of income segregation profile is minimized. The reason of doing is to ensure that 1% of population can fill a neighborhood (so that any H(p) value can practically hit its maximum value of 1).

¹² The households in my model, as in reality, have some tolerance of residing in a house in which they would not prefer. More specifically, if the rent is less than (100+tolerance) % of their budget and the status level is higher than (100- tolerance) % of their SES, then the household is satisfied and stays put. However, if either of these two conditions is not satisfied, then the household wants to move to a better (with respect to their budget and SES) house. In the experiments that I report here, the tolerance level is determined as 33%. Sensitivity analyses showed the findings are resilient, but they are clearer when it is around 33%. For the sake of clarity, I dropped the tolerance expression from the text and simply referred to the budgets and SES levels as if they are absolute.

¹³ Note that this is in contrast with the existing models of segregation, where agents usually seek and are able to find the best available alternative (Benard & Willer, 2007, p. 156; Fossett, 2006a, p. 232). More importantly, to the best author’s knowledge, the researchers of income segregation using agent-based models have not tried to model the agents with bounded rationality. In fact, I experimented and saw that how unrealistic assumptions of perfect rationality, which can be calibrated to bounded rationality with little effort, lead to the erroneous results such that the impact of income inequality on income segregation becomes negligible.

¹⁴ The weight of income in determining the rents is calibrated to be 0.2 in the benchmark model. It is assumed that the weight of Moore neighborhood and the neighborhood are equal and 0.5. If there is no one in the Moore neighborhood of a household, then the weight becomes 0.33 instead of 0.25.

¹⁵ The empty house multiplier is approximated by the amount of excess housing supply. It is equal to vacancy rate.

¹⁶ Moore neighborhood covers the 8 immediate neighbors of the ego agent. If there are no one living in the Moore neighborhood, then only the average SES of all neighbors is used.

¹⁷ For empirical examples, see (Reardon, 2011; Reardon & Bischoff, 2011; Reardon & Firebaugh, 2006). Nevertheless, as it is discussed before, H(p) curves can take shapes other than the ideal U-shape. For instance, when Gini coefficient is around 0.55, the left tail of the H(p) curve violates a perfect U-shape. I will explain this later.

¹⁸ Reardon and Bischoff (2011) interprets H(10) and H(90) as reference points for segregation of poverty and affluence, respectively. Such a point-wise approach may be easier to interpret the results or since their data contains samples of income thresholds, such point-wise approach is more valid than using the polynomial estimates. Nevertheless, this can be misleading. For example, it is possible to have a case where the segregation of the poorest 10% increases, the segregation of the poorest 5% can decrease. As I have the whole population’s data by virtue of simulation, I focus on the larger portions of the left and right tails of the curve as interpretations of segregation of poverty and of affluence, for example focusing on the poorest percentiles between 1–20% or 25% and on the richest percentiles between 75% or 80–99%.

¹⁹ Here, aggregating the richest and poorest at 25% is a just heuristic. The reason of such aggregation at a meso-level is highlight and magnifies the typical impact of a rich or poor household’s residential mobility.

²⁰ Similarly, when we make the 2^nd quarter to commit to status-seeking and 3^rd quarter to economical moves, we see that while segregation experienced in the middle income percentile decreases, segregation of poverty and segregation of affluence slightly increases, respectively.

²¹ I have experimented with using median income and SES instead of mean in calculating the housing prices and qualities, and the results show that segregation of poverty becomes larger than segregation of affluence. Similar results are observed for larger values of the weight of income parameter used in the price calculation function. The results of these experiments are available from the author by request. I thank one of the reviewers for stimulating this insight.

²² It is important to stress that an ideal U-shape is not the only possible form of income segregation profile. Yet, it is the most intuitive one; commonsense suggests that the poorest and richest households should be the most segregated. Moreover, while it is known from empirical studies that segregation profiles approximate U-shape (Reardon, 2011; Reardon & Bischoff, 2011), recall that their sampled empirical data do not let them to draw complete H(p) curves. The model here enables us to have the information of each household in our population and hence to draw H(p) curves completely, including the extreme ends of income distribution.

²³ Recalling the calculation of H(p), the more fully the selected people (for the corresponding p-value) fills a neighborhood, the higher H(p) values we have since it is the ratio of the selected people in a neighborhood that matters. Hence, if the poorest 10% spread to the same neighborhoods with the poorest 25%, then H(10) will inevitably be lower than H(25). If, on the other hand, the poorest 10% is not as spread as the poorest 25%, but concentrated on a limited subset of neighborhoods that the poorest 25% is spread over, then we would have H(10) higher than H(25), as we see with the illustration of richest 10% vs. 25%.

²⁴ There are two other possible reasons of observing local integrations. First, it can be due to the size of census tracts or neighborhoods calculated in H(p). Imagine a large neighborhood such that it can accommodate 5% of the population and suppose that poorest 4% of the population lives in the same neighborhood. Recalling the calculation of H(p), inevitably, H(4) will be lower than H(5). This suggest that the size of census tracts matter in calculating income segregation with rank order information index, and in fact, this justifies further Reardon and Bischoff’s effort to delineate geographical scale of income segregation (2011; Reardon & O’Sullivan, 2004). Yet, the hills in the model’s segregation profile output do not stem from this explanation since it is eliminated by having neighborhood sizes around 1% of population (see footnote 11). Second, hills on income segregation profiles can stem from some voluntary mismatches between neighborhoods and houses, and households. As the discussion of the smaller U-shapes in Figure 6 suggests, sometimes further stratification and segregation might be deemed unnecessary with respect to households’ expectations. For example, the richest 1% households may not mind whether they reside in the utmost richest neighborhood in the city; they simply may be content as long as they are among the richest, say, 5%.

²⁵ I did not account for eviction and homelessness in my model and hence, the households who pay rents beyond their budgets can stay put though they are constantly searching for a cheaper option.

²⁶ I do not discuss the experiments and the results here in detail for space considerations. They are available from the author by request.