Developing a Synthetic Socio-Economic Index through Autoencoders: Evidence from Florence's Suburban Areas

Abstract: The interest in summarizing complex and multidimensional phenomena often related to one or more specific sectors (social, economic, environmental, political, etc.) to make them easily understandable even to non-experts is far from waning. A widely adopted approach for this purpose is the use of composite indices, statistical measures that aggregate multiple indicators into a single comprehensive measure. In this paper, we present a novel methodology called AutoSynth, designed to condense potentially extensive datasets into a single synthetic index or a hierarchy of such indices. AutoSynth leverages an Autoencoder, a neural network technique, to represent a matrix of features in a lower-dimensional space. Although this approach is not limited to the creation of a particular composite index and can be applied broadly across various sectors, the motivation behind this work arises from a real-world need. Specifically, we aim to assess the vulnerability of the Italian city of Florence at the suburban level across three dimensions: economic, demographic, and social. To demonstrate the methodology's effectiveness, it is also applied to estimate a vulnerability index using a rich, publicly available dataset on U.S. counties and validated through a simulation study.