Distribution-valued Causal Machine Learning: Implications of Credit on Spending Patterns

Fintech lending has become a central mechanism through which digital platforms stimulate consumption, offering dynamic, personalized credit limits that directly shape the purchasing power of consumers. Although prior research shows that higher limits increase average spending, scalar-based outcomes obscure the heterogeneous distributional nature of consumer responses. This paper addresses this gap by proposing a new causal inference framework that estimates how continuous changes in the credit limit affect the entire distribution of consumer spending. We formalize distributional causal effects within the Wasserstein space and introduce a robust Distributional Double Machine Learning estimator, supported by asymptotic theory to ensure consistency and validity. To implement this estimator, we design a deep learning architecture comprising two components: a Neural Functional Regression Net to capture complex, nonlinear relationships between treatments, covariates, and distributional outcomes, and a Conditional Normalizing Flow Net to estimate generalized propensity scores under continuous treatment. Numerical experiments demonstrate that the proposed estimator accurately recovers distributional effects in a range of data-generating scenarios. Applying our framework to transaction-level data from a major BigTech platform, we find that increased credit limits primarily shift consumers towards higher-value purchases rather than uniformly increasing spending, offering new insights for personalized marketing strategies and digital consumer finance.