We use multifractal analysis to explore the process by which housing prices and income distributions interact in several cities. This technique allows the gathering of statistical information, represented by a curve called the spectrum, which takes into account the spatial pattern of the distributions at multiple scales. In turn, this information can be interpreted in terms of inequality and segregation . We use agent-based modelling to test different housing development scenarios aiming at reducing economic segregation by positively influencing the spectra.
Our model represents people relocating inside a city. The agents make their decisions according to three decisive parameters for our purpose: their evolving salary, the price distribution of housing inside the city, and their preferences in terms of the economic composition of their neighbourhood. In our context, neighbourhoods are defined by a topology which includes proximity through the transport system. We base the attributes of the model on New York data. The model is flexible and extensible, and can be built upon to accommodate other potentially meaningful parameters such as racial segregation or rules allowing the city to sprawl.
An autonomous model is first calibrated to represent the regular movements and price adjustments induced by people moving in and out of the city. Then, major perturbations of the price distribution are introduced (in our case representing different ways of developing low-cost housing stock and the construction of a new underground line). The model is run for a representative period of time. The multifractal spectra are computed along the process and the scenarios are sorted depending on their influence on inequality.