Commercial and Residential Mortgage Defaults: Spatial Dependence with Frailty

We investigate the spatial dependence between commercial and residential mortgage defaults. A new class of observation-driven frailty factor models is introduced to do so. The idea of dynamic parameters embedded in the class of GAS models is utilized to estimate dynamic models of default risk with potentially multiple factors which are driven by stratified grouping of large panels of mortgage loan records. The score dynamics in the models is driven by so-called generalized residuals, and have therefore a fairly intuitive interpretation of ARMA-like dynamics. The asymptotic analysis recognizes the fact that we deal with both cross-sectional and time series data features. The proposed models are computationally easy to implement and therefore attractive in big data applications, something that gives them a considerable advantage in comparison to the typical latent factor frailty models proposed in the literature. Our empirical analysis demonstrates strong spatial dependence between commercial default and residential defaults.