Discrete-Time Survival Modelling with Dynamic Industrial Graphs for Mortgage Credit Risk

Mortgage credit risk may exhibit dependence across economically connected areas, even when they are geographically distant. However, current models typically represent cross-area dependence through fixed geographical neighbourhoods, potentially overlooking economic connections that extend beyond physical proximity and evolve over time. These models may fail to capture shared risks among geographically distant but economically similar areas, and cannot describe a changing dependence of risk; it therefore risks retaining economically obsolete connections while omitting newly emerging ones. This paper uses similarities of industrial composition as a measure of economic proximity and develops a discrete-time survival model with dynamic industrial graphs to capture evolving cross-area dependence in mortgage default risk. The resulting graphs are reconstructed annually, allowing both their topology and edge weights to change as regional industrial compositions evolve. Jointly combining a proper conditional autoregressive process with a first-order autoregressive process governs the temporal cross-area dependence and the temporal persistence in latent risk simultaneously. The model is estimated using Integrated Nested Laplace Approximation and evaluated on U.S. mortgage loan-level data against the static industrial graph specifications. The results show that the proposed dynamic model achieves better in-sample fit and out-of-sample discrimination, while its estimated parameters indicate substantial graph-induced cross-area dependence and temporal persistence. These findings demonstrate the value of allowing economically defined neighbourhoods to evolve when modelling mortgage default risk.