Semi-structured multi-state delinquency model for mortgage default

TL;DR

This paper introduces a semi-structured multi-state model combining additive predictors and neural networks to analyze mortgage delinquency transitions, balancing interpretability and flexibility.

Contribution

It develops a novel semi-structured modeling framework that integrates structured effects with neural networks for discrete-time multi-state transition analysis.

Findings

The model effectively recovers baseline and covariate effects in simulations.

It shows modest but consistent improvements in prediction accuracy over benchmarks.

Adding macroeconomic indicators yields limited additional benefit in out-of-time predictions.

Abstract

We propose a semi-structured discrete-time multi-state model to analyse mortgage delinquency transitions. This model combines an easy-to-understand structured additive predictor, which includes linear effects and smooth functions of time and covariates, with a flexible neural network component that captures complex nonlinearities and higher-order interactions. To ensure identifiability when covariates are present in both components, we orthogonalise the unstructured part relative to the structured design. For discrete-time competing transitions, we derive exact transformations that map binary logistic models to valid competing transition probabilities, avoiding the need for continuous-time approximations. In simulations, our framework effectively recovers structured baseline and covariate effects while using the neural component to detect interaction patterns. We demonstrate the method using the Freddie Mac Single-Family Loan-Level Dataset, employing an out-of-time test design. Compared with a structured generalised additive benchmark, the semi-structured model provides modest but consistent gains in discrimination across the earliest prediction spans, while maintaining similar Brier scores. Adding macroeconomic indicators provides limited incremental benefit in this out-of-time evaluation and does not materially change the estimated borrower-, loan-, or duration-driven effects. Overall, semi-structured multi-state modelling offers a practical compromise between transparent effect estimates and flexible pattern learning, with potential applications beyond credit-transition forecasting.