Inference for the neighborhood inequality index

The neighborhood inequality (NI) index measures aspects of spatial inequality in the distribution of incomes within a city. The NI index is 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 located within a certain distance range. The approach overcomes the Modiable Areal Units Problem affecting local inequality measures. This paper provides minimum bounds for the NI index standard error and shows that unbiased estimators can be identied under fairly common hypothesis in spatial statistics. Results from a Monte Carlo study support the relevance of the approximations. Rich income data are then used to infer about trends of neighborhood inequality in Chicago, IL over the last 35 years.