On the Measurement of “Grayness” of Cities

We consider a situation where individuals belonging to multiple groups inhabit a space that can be divided into smaller distinguishable units, a feature characterizing many cities in the world. When data on an economic attribute (in our case, income) is available, we conceptualize a phenomenon that we refer to as “Grayness”—a combination of spatial integration based upon group-identity and income. Grayness is high when cities display a high degree of spatial coexistence in terms of both identity and income. We lay down some desirable properties of a measure of Grayness and develop a simple and intuitive index that satisfies them. We provide an illustration by using data from the Indian city of Hyderabad, and selected American cities.