Nonparametric panel estimation of online auction price processes

In this study, we examine the price process of eBay online auctions. We pool sparse and unevenly spaced bidding histories of individual auctions, resulting in an unbalanced panel of bids. Since the price processes of online auctions are monotonically increasing within individual auctions and exhibit a substantial degree of heterogeneity, we propose a monotone series estimator for panel data with auction-specific slopes for a common relative price growth curve. We generalize Ramsay’s (1998, J R Stat Soc B 60(2):365–375) monotone series estimator to fit our panel model of the price process. We apply the proposed model and estimator to eBay auctions of a popular hand-held device (a Palm PDA). The results are shown to capture closely the overall pattern of observed price dynamics. In particular, the early bidding, mid-auction bidding drought, and end-auction bid sniping are well approximated by the estimated price curve.