On the measurement of “grayness” of cities

Motiram, Sripad (1); Vakulabharanam, Vamsi (2) (2018). 'On the Measurement of "Grayness" of Cities' Paper presented at the annual conference of the HDCA, Buenos Aires, Argentina 2018.


It is being increasingly acknowledged that the world is predominantly urban, and urbanization will continue into the foreseeable future. Urbanization in recent times has been driven by growth of cities in developing countries. Projecting into the future, the United Nations estimates that several of the largest cities in the world (e.g. Delhi, Shanghai, Mexico City) will be located in the global South. This paper is therefore concerned with group-based ("horizontal") disparities within cities, particularly cities in developing countries. Many cities in the world are characterized by severe disparities among groups. The particular facet of group-based disparity that we are interested in can be illustrated by the following examples. Lower castes and upper castes live in Indian cities which can be divided into several wards. Blacks and Whites live in American cities which have distinct neighborhoods or administrative divisions. Working classes and elites inhabit almost all cities in the world, which are characterized by some form of spatial division. What is common to all these examples is the presence of groups that can be ordered on some attribute, in a context with identifiable spatial heterogeneity. Lower castes and upper castes can be ordered in terms of their historical advantage or experience of discrimination. Similar is the case for Blacks and Whites. Working classes and elites can be ordered by their status in the society. Apart from this, we may have more "tangible" information available to order these groups, e.g. average incomes or wages. Essentially, we are interested in a phenomenon that is a combination (or intersection) of spatial segregation and more conventional (income or expenditure-based) inequality. We refer to this phenomenon as "Grayness". When Grayness is high, groups that can be ordered display a high degree of spatial co-existence in the context of modest inequality. When Grayness is negligibly small, cities become "stark".

Our focus on space is inspired by the recent recognition in social sciences and humanities of the importance of explicit considerations of space. Scholars have argued that such a "spatial turn" and the idea of "spatial justice" have conferred both theoretical and practical advantages, e.g. the discourse on the "right to the city", which has assumed political salience. One of the important ideas in this literature is that space and society are intricately linked ("sociospatial dialectics"). Space is not an inert given, and individuals and groups shape it, even as it influences them. Our attempt is to bring these ideas to bear on the literature in welfare economics, particularly the literature that builds on the capability approach. While the above body of knowledge has seen contributions mostly from non-economists, prominent economists like Amartya Sen (e.g. in his Lewis Mumford lecture) have recognized that spatial patterns influence outcomes like crime. Other economists have argued that spatial location confers both advantages and disadvantages to individuals and groups. Essentially, the spatial location and capability set of an individual are intertwined.

In light of the above, we consider an abstract city that is comprised of multiple spatial units. The population of the city, and in each spatial unit is divided into several groups which can be ranked in a pre-determined manner. Apart from his/her group identity, we have information on an economic attribute (income) of an individual. We lay down the desirable properties of a "Grayness Index" and develop a simple and intuitive index which satisfies these properties, and which incorporates the trade-off that a society chooses to make between interpersonal and group-based equity. Like the Human Development Index (HDI), the Grayness index is a multidimensional one and incorporates the idea from the literature on residential segregation that the "interaction" or "mixing" of different groups is "good".

With the exception of a few studies, the literature on segregation has largely dealt with categories that are not ordered. Hence, this study fills an important gap and builds upon a few previous studies that have considered ordered groups. Using data from a unique survey that we designed and conducted, we implement the Grayness Index on two Indian cities: Hyderabad and Mumbai. We also implement it on some American cities and show that the Grayness Index of Indian cities is high compared to the selected American cities. We hypothesize that this maybe an important characteristic of Indian cities vis-a-vis cities in the developed world.

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