The Dynamic Factor Network Model with an Application to Global Credit Risk 
In recent years, economists have become increasingly interested in analyzing social and economic networks. These networks arise naturally in many fields of economics. Key examples are the input-output matrix of an economy, international trade relationships, and interbank lending networks. The relevance of studying such networks is evident, since the interactions of economic agents, such as firms, households, and governments, are generally at the core of economic activity. However, the econometric tools necessary for the empirical analysis of data that reflect pairwise interactions between economic agents, which we refer to as network data, are still in their infancy. In particular, most existing statistical methods focus on static networks and do not address models of the dynamic behavior of time-varying networks; see also the discussions in Kolaczyk (2009).
In this study, the authors develop a dynamic modeling framework for analyzing network data, with probabilistic link functions that depend on stochastically time-varying parameters. They carry out a Monte Carlo simulation to investigate the finite sample properties of their novel, importance sampling procedure, and, in an empirical study, they analyze credit-risk spillovers between 61 financial firms throughout the world from 2007 through 2015.
Key Findings
- The authors show that their dynamic binary network model can be collapsed into a low-dimensional binomial vector series, which is used to sample the time-varying effects from the importance densities in a manner that improves considerably on existing methods. Variational approximation techniques are introduced to sample the random cross-section effects. Both importance samplers allow for a computationally feasible maximum likelihood estimation.
- The Monte Carlo results suggest that the estimators are well centered around their associated true parameter values, even for networks with a small number of nodes. The results show large computational gains of the proposed binomial collapsing, with computations gains growing fast with the size of the network. For example, for a moderate network with 100 nodes and 250 time periods, the construction of the importance sample with the authors' proposed methods is 10 times faster than using the collapsing method of Jungbacker and Koopman (2015).
- In the empirical study, the estimated latent block structure suggests that the nodes can be partitioned into two groups. The first group is associated with large U.S. banks and large European banks (global banks). The second group consists of the remaining mostly European (local) banks, which supposedly have a smaller global scope. The estimated latent factors suggest a strong increase in spillovers within and between all groups during the 2008 financial crisis and the sovereign debt crisis. The heterogeneous effects show that spillovers from global to local banks are most sizeable during the entire sample, while those from local to global banks are generally smaller. Moreover, spillovers among local European banks global banks became elevated during the European debt crisis and again from 2014 until the end of the sample period.
Implications
The authors’ dynamic factor model is sufficiently general and flexible for all practical purposes. On the other hand, the parametric structure is parsimonious since many features of the model are treated by stochastic variables. The authors show that the small-sample properties of their proposed solution are favorable, in terms of both estimation accuracy and computational efficiency. With respect to the empirical study, further extensions and precision in the proposed network structure would be needed in order to observe links at the country level and within common bank characteristics. Such developments would be of special interest to financial regulators and supervisors.
Abstract
We introduce a dynamic network model with probabilistic link functions that depend on stochastically time-varying parameters. We adopt the widely used blockmodel framework and allow the highdimensional vector of link probabilities to be a function of a low-dimensional set of dynamic factors. The resulting dynamic factor network model is straightforward and transparent by nature. However, parameter estimation, signal extraction of the dynamic factors, and the econometric analysis generally are intricate tasks for which simulation-based methods are needed. We provide feasible and practical solutions to these challenging tasks, based on a computationally efficient importance sampling procedure to evaluate the likelihood function. A Monte Carlo study is carried out to provide evidence of how well the methods work. In an empirical study, we use the novel framework to analyze a database of significance-flags of Granger causality tests for pair-wise credit default swap spreads of 61 different banks from the United States and Europe. Based on our model, we recover two groups that we characterize as "local" and "international" banks. The credit-risk spillovers take place between banks, from the same and from different groups, but the intensities change over time as we have witnessed during the financial crisis and the sovereign debt crisis.