Topological Data Analysis in an Economic Context: Property Tax Maps

Property tax is a significant index which reflects housing quality and even the community structure of a neighborhood. Historically, economics has offered various methods to analyze living standards and policy effectiveness using property tax. In this paper we introduce a topological approach to explore local housing patterns. We use methods from topological data analysis (TDA) to analyze 210 property tax maps sampled from 21 cities. We then utilize clustering and dimension reduction methods to classify samples and identify features of the local tax patterns. By evaluating the topological features, we are able to identify the property tax value structure within each sample, and provide an efficient general classification. The resulted clustering is distinct from past measures, and we also evaluate its relationship between local land use and indicators of regional demographic heterogeneity.