Inference for the neighborhood inequality index

The neighborhood inequality (NI) index measures aspects of spatial inequality in the distribution of incomes within the city. The NI index is defined as a population average of the normalized income gap between each individual's income (observed at a given location in the city) and the incomes of the neighbors, living within a certain distance range from that individual. This paper provides minimum bounds for the NI index standard error and shows that unbiased estimators can be identified under fairly common hypothesis in spatial statistics. These estimators are shown to depend exclusively on the variogram, a measure of spatial dependence in the data. Rich income data are then used to infer about trends of neighborhood inequality in Chicago, IL over the last 35 years. Results from a Monte Carlo study support the relevance of the standard error approximations.