  Consumer credit services offered by e-commerce platforms provide customers
with convenient loan access during shopping and have the potential to stimulate
sales. To understand the causal impact of credit lines on spending, previous
studies have employed causal estimators, based on direct regression (DR),
inverse propensity weighting (IPW), and double machine learning (DML) to
estimate the treatment effect. However, these estimators do not consider the
notion that an individual's spending can be understood and represented as a
distribution, which captures the range and pattern of amounts spent across
different orders. By disregarding the outcome as a distribution, valuable
insights embedded within the outcome distribution might be overlooked. This
paper develops a distribution-valued estimator framework that extends existing
real-valued DR-, IPW-, and DML-based estimators to distribution-valued
estimators within Rubin's causal framework. We establish their consistency and
apply them to a real dataset from a large e-commerce platform. Our findings
reveal that credit lines positively influence spending across all quantiles;
however, as credit lines increase, consumers allocate more to luxuries (higher
quantiles) than necessities (lower quantiles).
