Neighborhood effects and the distribution of income in cities

The aim of this paper is to explain patterns of household income within an urban area. A particular pattern common to US cities is for a concentration of the poor in the inner city, with higher-income households farther out, and then lower-income households even farther out. It is the non-monotonicity of this pattern that makes it an interesting and difficult phenomenon to explain. This paper shows how this phenomenon can arise due to a mix of population growth and neighborhood effects (externalities). The paper constructs a model of a linear city with inhabitants of different incomes and with properties of varying quality. Computationally, the paper is novel by its use of an agent-based approach. Instead of modeling the city by a set of equilibrium conditions, it determines the outcome according to the decisions of a large number of individual agents, using a simulated auction market that allocates households to properties dynamically. The structure of the city evolves over time in response to the collective outcome of individual decisions. Simulation of the model finds that population growth combined with neighborhood effects can produce a non-monotonic pattern of income. Sensitivity analysis shows how the outcome depends on the characteristics of the city. In particular, it is found that the speed of population growth is very significant. This is important as US cities, particularly in the West and South, have been characterized by rapid population growth.