In Search of Lost Edges: A Case Study on Reconstructing Financial Networks
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To capture the systemic complexity of international financial systems, network data is an important prerequisite. However, dyadic data is often not available, raising the need for methods that allow for reconstructing networks based on limited information. In this paper, we are reviewing different methods that are designed for the estimation of matrices from their marginals and potentially exogenous information. This includes a general discussion of the available methodology that provides edge probabilities as well as models that are focussed on the reconstruction of edge values. Besides summarizing the advantages, shortfalls and computational issues of the approaches, we put them into a competitive comparison using the SWIFT (Society for Worldwide Interbank Financial Telecommunication) MT 103 payment messages network (MT 103: Single Customer Credit Transfer). This network is not only economically meaningful but also fully observed which allows for an extensive competitive horse race of methods. The comparison concerning the binary reconstruction is divided into an evaluation of the edge probabilities and the quality of the reconstructed degree structures. Furthermore, the accuracy of the predicted edge values is investigated. To test the methods on different topologies, the application is split into two parts. The first part considers the full MT 103 network, being an illustration for the reconstruction of large, sparse financial networks. The second part is concerned with reconstructing a subset of the full network, representing a dense medium-sized network. Regarding substantial outcomes, it can be found that no method is superior in every respect and that the preferred model choice highly depends on the goal of the analysis, the presumed network structure and the availability of exogenous information.
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