Modeling Reputation as a Time-Series: Evaluating the Risk of Purchase Decisions on eBay*

Reputation systems based on buyer feedback play an important role in today's online markets. In this article, we provide a rigorous methodology to establish a relationship between a seller's feedback history and risk of default. We validate this method against eBay's reputation system, using a dataset of terminated users (Not‐A‐Registered‐User or NARU) and the feedback left for them by buyers. By treating feedback rating data as a function of time, we characterize the tendency of change in seller feedback ratings in order to predict the behavior of a seller. We find that NARU sellers have significantly more negative feedback in their final weeks. Applying functional principal component analysis and classification tree methods, we find that when projecting the feedback data to an appropriate space, NARU and non‐NARU sellers can be distinguished at better than 92% accuracy. We use this to provide a quantitative mechanism for evaluating the risk of trading with a seller who has less than perfect feedback, and offer advice on how much a buyer should offer to pay, given an asking price on a commodity item and a seller's feedback history.