The Sealed-Bid Abstraction in Online Auctions

This paper presents five empirical tests of the popular modeling abstraction that assumes bids from online auctions with proxy bidding can be analyzed "as if" they were bids from a second-price sealed-bid auction. The tests rely on observations of the magnitudes and timings of the top two proxy bids, with the different tests stemming from different regularity assumptions about the underlying distribution of valuation signals. We apply the tests to data from three eBay markets--MP3 players, DVDs, and used cars--and we reject the sealed-bid abstraction in all three data sets. A closer examination of these rejections suggests that they are driven by less experienced bidders. This consistent rejection casts doubt on several existing theories of online auction behavior and suggests some demand estimates based on the abstraction can be biased. To assess the direction and magnitude of this bias, we propose and estimate a new model in which some bidders conform to the abstraction while other bidders bid in a reactive fashion. Because reactive bidding can be at least partially detected from the data, we are able to estimate the underlying distribution of demand and compare it to what the sealed-bid abstraction implies. We find that our proposed model fits the data better, and our demand estimates reveal a large potential downward bias were we to assume the second-price sealed-bid model instead.