Discrete Time-to-Event Regression Analysis Under Left-Truncation with Applications to Consumer Finance

with Jackson P. Lautier, PhD, FSA, CERA, MAAA, Bentley University

Abstract:

Asset-backed securities (ABS) play a vital role in financing American consumer automobile debt.  Recently, economic analysis into ABS has benefited from the public release of data, which provides a new, rich source of loan level consumer auto loan information. Because this loan lifetime data is discrete-time and subject to random left-truncation, however, it is nontrivial to analyze. This has attracted recent study, but there is still no suitable approach to model this ABS loan lifetime data that incorporates regression coefficients for the lifetime of interest.  

We thus generalize the conditional, bivariate distribution to link to covariates, while keeping the left-truncation distribution unspecified. We solve the high-dimensional, constrained likelihood-based parameter estimation problem numerically, using a block coordinate descent design. Under suitable regularity conditions, we provide the complete large sample, multivariate normal distribution of the estimators. This allows for large sample inference into variable and model selection. We both prove all results and verify them through simulation studies.

Our methods are then applied in an economic study of borrower prepayment behavior for 1,553 consumer auto loans from the 2017-3 Ally Auto Receivables Trust ABS bond. We find that borrowers with pick-up trucks prepay slower, all else equal, among other consumer finance insights.