A New Index for Comparing the Diversity of Population Inflows and Population Stocks

A New Index for Comparing the Diversity of Population Inflows and Population Stocks The paper introduces a new “diversification index” (DIV), which compares the composition of the current or recent population inflow and the composition of pre-existing population stock, with positive (negative) values signifying a process generating more (less) diversity in the stock. Higher absolute values for DIV signify larger differences in the composition of the inflows and the pre-existing stocks of population. DIV is easy to compute and interpret, adaptable to handle population inflows or outflows, and widely applicable to a variety of phenomena. The paper defines DIV, discusses its properties, and calculates it for several hypothetical cases as a way of showing its intuitive appeal, such as how it would reflect a neighborhood gentrification scenario. DIV indices for both race and income groupings are computed from 1992 to 2006 for three neighborhoods in Chicago to demonstrate how inter-temporal trends in DIV provide insights into neighborhood dynamics. Finally, the paper discusses extensions, potential weaknesses, and other caveats related to the use of DIV in future applied research. A great deal of social scientific effort has been invested in the development of numerous indices for describing multi-group compositional characteristics of a stock of population defined by differences in some demographic, economic, ethnic or other dimension. Examples of such indices include nominal entropy (Theil’s Information), ordinal entropy, and Simpson’s D (Hirschman-Herfindahl); see Reardon and Firebaugh (2002) and Reardon et al. (2006) for evaluative reviews. Less research has been devoted to measuring compositional characteristics of flows of population, though the aforementioned indices typically may be applied to measuring flows as well as stocks. No index has yet been developed, however, that compares the compositions of an inflow of population and the baseline stock of population on a group-by-group basis. Such a comparative index would be useful for gauging the degree to which the composition of the inflow either matches that of the stock (and thus the degree to which the current stock is tending to remain stable) or differs from it (and thus the degree to which the current stock is tending toward more or less diversity over time due to its inflows). The “diversification index” (DIV) introduced in this paper aims to do exactly this. DIV compares the composition of the current or recent population inflow and the composition of pre-existing population stock on a group-by-group basis, with positive (negative) values signifying a process generating more (less) diversity in the stock. Higher absolute values for DIV signify larger aggregate differences in the composition of the inflows and the pre-existing stocks of population, based on group-by-group comparisons. DIV is easy to compute, easy to interpret, and widely applicable to various phenomena. This approach is quite distinctive from standard measures of inter-group diversity, which indeed could be applied to both a flow and a stock to suggest a difference in their degrees of diversity. These standard measures do not, however, 1 Population can be thought of either as residents of a geographic area or members of a nonspatial collection, such as occupation or standard industrial classification.