2.1 Background literature
At a general level, this work relates to the literature that analyzes racial groups SES dynamics. In an influential article Hirschman studies the evolution of the SES of Asians, Blacks, Hispanics and White men in the United States between 1960 and 1976 (Hirschman and Wong
1984). His main finding is that the socioeconomic status of high SES minorities tends to converge, or even surpass, that of the Whites, whereas disadvantaged minorities (e.g. Black) constantly lag behind. Although many decades have passed, we find that very similar dynamics still characterize American society. Other studies concentrate on the evolution of one of the dimensions of SES over time (generally wages) finding that differences across racial lines tend to be stable over time [see Leicht (
2008) and references therein]. We contribute to this literature by studying from a dynamic perspective the interactions among the SES of the various groups.
Two other strands of literature that are relevant to our analysis are studies investigating (i) how the SES of one group influences the attitude of out-group members toward that group and (ii) how the attitudes of the out-group members toward a group influence the SES of that group. Taken together, (i) and (ii) show that the interactions among groups are influenced by their respective SES via attitudes. However, while there is a general consensus in the literature that racial group SES affects racial interactions (Branton and Jones
2005; Taylor and Reyes
2014), scholars disagree on the direction of this effect. On the one hand, literature on racial group competition and threat argues that minorities with high SES foster negative attitudes in the dominant White group (Blumer
1958; Blalock
1967). This occurs because as minorities improve their social standing in society Whites perceive that they are encroaching their privileged position. Conversely, the group contact hypothesis predicts that higher SES levels of racial minorities can trigger positive attitudes in the majority group (Allport
1954). In this view, an equal social standing facilitates positive inter-group contacts. Looking at the SES-attitudes relationship from the opposite perspective, various strands of research investigate impact of attitudes on the allocation of resources among racial groups (Pager and Karafin
2009; DeSante
2013). This literature shows that racial attitudes create differences in key determinants of SES across racial groups [e.g. job positions (Pager and Karafin
2009), wages (Holzer and Ihlanfeldt
1998; Huffman and Cohen
2004), and government assistance (DeSante
2013)]. To summarize, variations in the SES of a racial group can affect the distribution of resources across racial groups. This, in turn, can trigger shifts in SES measures of the various groups within a society.
Another related strand of literature investigates directly how variations in one component of the SES of a group affects the SES of other groups (Cohen
1998). In this regard, it is important to distinguish two ways in which these effects can take place. On the one hand, changes in the socioeconomic standing of a group always have an effect on the SES of the other groups because SES is an inherently relative concept (Brown
2007). If one group improves its condition while the other remains stable, the position of the latter becomes relatively worse. On the other hand, research on the interactions between racial groups’ SES highlights that variations in SES measures of a racial group can trigger variations in SES measures of other racial groups in absolute terms. For instance, variations in the size of minority populations may lead to reductions/increases in the economic well-being of different racial groups (Tigges and Tootle
1993; Cohen
1998; Albrecht et al.
2005). In this regard, Cohen (
1998) finds a negative relation between concentrations of Blacks and their earnings. Moreover, he finds a positive relation between the number of Blacks and the earnings of Whites. Therefore, there is a relationship between groups’ SES that goes beyond the mere shift in the relative position of the groups.
On this background, the emergence of a prismatic society complicates the analysis, because a multi-racial society is a fertile environment for the emergence of nuanced relationships among racial groups. And indeed, a growing body of literature is investigating social patterns in a multi-groups framework (Wilkinson
2014). The present work contributes to this literature by offering a rigorous mathematical approach to test in a quantitative and replicable way how
n racial groups interact and influence each other SES.
2.2 Conceptual framework of the analysis
An important methodological premise to this study is defining in a clear and detailed way the SES measure, because SES is a multidimensional and contextual concept that can be measured using many different indicators (Braveman
2005; Berkowitz
2015; Berzofsky et al.
2015). In particular, traditional measures of SES include education, income, employment—sometimes called the “big three”—but also wealth, household tenure, parental education, and so on. SES-related measures are sometimes used as single items or suitably combined (Branton and Jones
2005; Braveman
2005; Berkowitz
2015; Berzofsky et al.
2015), and are often operationalized as a single ordinal categorical variable (e.g., poor/nonpoor, less than high school/high school/more than highschool, or low/middle/upper wealth). Moreover, measures of SES can have a different scope and range from a neighborhood (identified via ZIP codes, census tracts, and census blocks) to areas as large as states and regions. As both single and composite measures of SES have some disadvantages, it is widely understood that there cannot be one universally accepted indicator, and the debate is still open on which are the most reliable (Alsabbagh
2016). It was noted that (i) the indicators should carry as much relevant information as possible, (ii) the indicators used should be clearly spelled out, including their limitations, (iii) and the impact of non accounted factors should be explicitly stated (Braveman
2005). We try to follow these guidelines to build our measure of SES. In detail, we adopt a multi-dimensions approach that accounts for measures of income, employment, group numerosity, and life expectancy. We focus on income and employment because they constitute natural dimensions to study interracial dynamics and the reciprocal impact of the various groups on their respective SES. Moreover, recent studies show that measures of income, even considered alone, have a high predictive power on relevant outcome variables (Alsabbagh
2016).
In addition, to develop a more comprehensive indicator of SES, we aggregate also information relative to groups’ political power and health status. We account for the former by considering group numerosity, because size can positively influence the political strength of a group in a democratic society. This is even more so in societies, such as the American one, in which minorities’ political turnout is positively correlated with increases in their relative group size (Fraga
2016). We account for the latter by including information on life expectancy, which is widely recognized as an indicator of various dimensions of SES [e.g. exposure to pollutants, eating habits, access to health services, exposure to violent crimes, etc. (Harper
2007; Lynch and Kaplan
2000)]. Admittedly, our indicator overlooks some important component of SES, like education and wealth. We do not include these factors due to data availability and because they cannot be aggregated in a straightforward way with the other measures of SES considered. For example, unlike the variables that we consider, education is not a continuous variable. And indeed, the “amount” of education is traditionally expressed using categories (e.g. high school, bachelor, master etc.). Then, in order to include a measure of education in the proposed SES index it would be necessary to build an ad hoc continuous version of the “amount” of education (e.g. as a weight varying in the interval [0,1]).
However, we remark that in principle our approach is well suited also when accounting for measures of wealth and education. Similarly, provided that the relevant data is available, the analysis can be replicated at a State level or even at a county level. While the indicators chosen are far from foreign to the literature, we adopt a different strategy to aggregate them. Instead of obtaining the composite SES measure as a weighted average of their single indicators (Sackett
2009; Higdem
2016), we opt for a multiplicative form. This choice allows us to approximate the behavior of American courts in tort cases when calculating damages awards. As noted by Avraham and Yuracko, race-based tables of wage and life expectancy are commonly used to define the compensation owed to a victim of a tort (Avraham and Yuracko
2017). Assume that in a car accident a White and a Black child of the same age die. Simplifying to the extreme, if these tables are used a court will determine compensation multiplying the predicted wage of each child for his expected work-life (adjusted according to the specific circumstances of the case). Because Whites generally live longer and have higher wages, the parents of the White child will be awarded higher damages. This approach has a relevant practical impact on how resources are allocated within the society. For instance,
ceteris paribus for a firm it is cheaper to pollute in a “Black neighborhood” than in a “White neighborhood” because the expected liability is lower (Avraham and Yuracko
2017). In turn, the choice of the firm to locate in a Black neighborhood further reduces the SES of the Blacks, as an increased pollution is likely to decrease life expectancy. Due to the practical relevance of these considerations, we build our SES indicator following the same logic and multiply income, expected life and employment rate. Last, we correct the result of this product for the size of the group.
As standard manipulations allow us to write each SES index as a logit model, we perform the quantitative analysis using the class of LV models introduced in Marasco et al. (
2016a). These models are a powerful tool to study and forecast the interaction among different entities in a given environment. At a general level, LV models have the advantage of being able to capture every possible kind of interaction (i.e. mutualism, predator-prey, commensalism, competition, amensalism, and neutralism). For this reason, they are widely used in natural sciences, and are becoming more and more widespread in a variety of domains in social sciences [see Modis (
1999), Romano (
2013), Marasco et al. (
2016a) and references therein]. There are two main factors that explain why traditionally LV models have been used more frequently in natural sciences. First, the most used LV models are
autonomous, i.e., the model equations contain only constant coefficients as in Tsai and Li (
2009), Chiang (
2012), Lin (
2013), Lakka (
2013), Duan et al. (
2014), Cerqueti et al. (
2015), thus, the kind and the intensity of the interaction is assumed to be constant over time. Intuitively, this is a greater limitation for studies in social sciences than for
some studies in natural sciences. For example, it is very unlikely that sheeps and wolves change the way in which they interact, and therefore modeling them respectively as preys and predators for the whole time horizon is a perfectly reasonable choice. On the contrary, phenomena in social sciences are usually characterized by a high variability of competitive roles. For instance, an appropriate marketing campaign can turn a firm that used to be a prey of another into a predator. Similarly, we expect that ethnic groups do not have a constant pattern of interaction (Brandt et al.
2014), thus autonomous LV systems are generally not an appropriate choice to model this social dynamics. Second, in most cases the analytical solutions of LV models—especially in the nonautonomous case—are not known in a closed form. Therefore, the parameters of the model have to be estimated using expensive numerical fitting procedures. This is not always possible in many domains of social sciences that are plagued by data scarcity. The LV model presented in Marasco et al. (
2016a), Romano (
2016) overcomes both problems. On the one hand, it is a nonautonomous model and therefore the competing entities are allowed to change their competitive roles over time. On the other hand, the analytic solutions are known and therefore the quantitative analysis is significantly easier and requires less data. Importantly, the analytical solutions of this class of LV models are in the form of a
logit model introduced by McFadden (
1973), extensively used in every area of social sciences, and also in studies analysing socioeconomic status and race (Bayer and McMillan
2005). Therefore, besides its properties, this model has the additional advantage of being coherent with the mainstream approach to the quantitative study of many social phenomena. Differently from Marasco et al. (
2016a), in this paper we can easily design the scenarios since the SES functions are linked in a known way to the components of groups’ SES (i.e., income, employment, group numerosity, and life expectancy).
2.3 Scenario method in public policy
The scenario method consists in developing
“a set of hypothetical events set in the future constructed to clarify a possible chain of causal events as well as their decision points” (Kahn and Wiener
1967). In particular, scenario planning allows to forecast future dynamics by presenting the crucial elements of a given problem in a systematic and coherent way (Burt and Heijden
2003; Amer et al.
2013). If appropriately applied, it is a powerful tool to approach complex problems characterized by a high degree of uncertainty in a more rational and effective way (Kahn
1962). Moreover, in settings dominated by uncertainty, scenarios are useful for
“highlighting implications of possible future system discontinuities, identifying nature and timing of these implications, and projecting consequences of a particular choice or policy decision” (Amer et al.
2013). Not surprisingly, the literature identifies a correlation between the degree of uncertainty characterizing a given domain and the use of the scenario method (Malaska
1984). As in many policy domains the debate is dominated by the concept of uncertainty (e.g. environmental law (Sachs
2011), health law (Sadeleer
2006), financial law (Pacces and Romano
2015)), scenario planning can be a useful tool also for policy makers. We contribute to the scenario literature in two ways. First, many of the scenario applications in the public policy area often remain at a qualitative level. We complement this literature by proposing a deterministic modeling approach that translates into deterministic predictions the set of possible narratives. Second, we apply the scenario methodology to a domain that is extremely appropriate for scenario analysis due to its complexity and uncertainty, yet in which scenarios—to the best of our knowledge—have not been applied before.