  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.
