In the theoretical part of the paper, the authors assume that the income distribution of a neighborhood is only a function of the income distribution oat a more aggregated level times a weight. However, this assumption seems implausible since adjacent neighborhood tend to have significant impact on neighborhood j. A large literature suggest that gentrification of neighborhood j will significantly positive spillover effects to adjacent neighborhood (see for example, the introduction part of Hornbeck 2017).
In the theoretical part of the paper, the authors assume that the income distribution of a neighborhood is only a function of the income distribution oat a more aggregated level times a weight. However, this assumption seems implausible since adjacent neighborhood tend to have significant impact on neighborhood j. A large literature suggest that gentrification of neighborhood j will significantly positive spillover effects to adjacent neighborhood (see for example, the introduction part of Hornbeck 2017).