Case for using the Theil indices to measure spatial disparities by income at the sub-municipal level

This working paper develops the methodology proposed by Insee to study social mixity from an economic perspective, using the single criterion of declared household income. The method is based on the use of geolocalized tax data and Theil indices. This type of index has two particularly interesting properties for the social segregation analysis. First, it is multi-group index, i.e. it simultaneously measures the segregation of all social groups, without focusing on extreme social groups (richest / poorest). On the other hand, it is decomposable. Its spatial decomposition provides information on the contribution of certain neighbourhoods to total segregation, and its decomposition by social group provides information on the influence of a given group on total multi-group segregation. The main difficulty lies in the non-linear nature of the Theil indices, which limits their interpretation to ordinal considerations. Furthermore, the calculation of Theil indices does not take into account spatial autocorrelation, i.e. the geographical configuration of neighborhoods is not taken into account in determining the town-level of segregation.

This methodology is applied to the study of segregation at the sub-municipal level within the 53 largest French cities, over the period from 2004 to 2019. For this purpose, the population is equally divided into five income groups, and the cities are divided into 200-metre squares for the calculation of segregation indices. The results, presented in Gerardin and Pramil (2023), show in particular that the poorest and richest populations live in the least mixed neighbourhoods, and that, over the 15 years studied, spatial disparities measured by income have increased in most large cities.