Abstract

Machine learning models are increasingly used for credit scoring and loan allocation. The EU AI Act classifies such systems as high-risk, requiring audits for bias and discrimination. Yet even when gender is formally excluded, ML models can reconstruct protected attributes through proxy variables and nonlinear feature interactions. Moreover, standard mean-based fairness assessments may miss bias that concentrates at specific points of the score distribution. Existing audit approaches address proxy detection and distributional analysis in isolation, and structured documentation standards for financial applications remain largely absent.
This paper proposes an integrated statistical framework for auditing gender bias in AI-based lending decisions, illustrated with administrative data from a German building society (Bausparkasse). The framework combines two complementary analyses applied to the predictions of ML credit models. The first identifies which covariates serve as robust proxies for gender by adapting a sequential Bayes-factor-based detection procedure that accumulates evidence across repeated data perturbations, yielding a continuous evidence measure rather than a binary classification from a single model run. The second applies distributional decomposition methods - building on the Firpo-Fortin-Lemieux (2009) recentered influence function framework - to decompose gender gaps in model-generated scores or loan outcomes at multiple quantiles into contributions from observable characteristics and an unexplained residual.
The two analyses inform each other in interpretation. The proxy detection identifies what carries gender signal in the model’s input space; the distributional decomposition reveals where in the model’s output distribution gender differences concentrate. When the explained component at a given quantile is driven by variables flagged as strong gender proxies, the fairness interpretation differs substantively from cases driven by genuinely gender-neutral characteristics. Both analyses are embedded in a structured audit framework comprising documentation templates (data cards and model cards adapted for financial AI), proxy variable criteria informed by the detection results, and reproducibility standards.