Modeling Concurrency of Events in Online Auctions Via Spatio-Temporal Semiparametric Models

Abstract

We introduce a semiparametric approach for modeling the effect of concurrent events on an outcome of interest. Concurrency manifests itself as temporal and spatial dependencies. By temporal dependency we mean the effect of an event in the past. Modeling this effect is challenging since events arrive at irregularly spaced time intervals and thus the standard definition of time-lags does not apply. Our concurrency model also takes spatial effects into account. We interpret the meaning of "space" in a slightly non-traditional way in order to conceptualize the more abstract notion of space among a set of item-features. We motivate our model in the context of eBay's online auctions. In particular, we model the effect of concurrent auctions on an auction's price. Our concurrency model consists of three components: a transaction-related component that accounts for auction-design and bidding-competition, a spatial component that takes into account similarity among item-features, and a temporal component that accounts for events in the past. To construct each of these model components, we borrow ideas from spatial modeling and from the mixed model methodology. We also develop a new time-lag metric to handle unevenly-spaced time series by interpreting a time-lag as the information distributed over a certain time-window in the past and by incorporating this information via inclusion of appropriate summary measures. We illustrate the power of this model by applying it to a large and diverse set of laptop auctions crawled off 1 eBay.com. We show that our model results in superior predictive performance compared to a set of competitor models. Our model also allows for new insight into the factors that drive price in eBay's online auctions and their relationship to bidding-competition, auction-design, product-variety and temporal learning effects.

Keywords: Nonparametric model, distance measure, dissimilarity, spatial model, timelag, mixed model, online auction, E-Bay