Bayesian Inference in Structural Second-Price Auctions with Gamma Distributed Common Values
(English)Manuscript (preprint) (Other academic)
Our paper explores possible limitations of the Gaussian model in Wegmann and Villani (2011) due to intrinsically non-negative values. The relative performance of the Gaussian model is compared to an extension of the Gamma model in Gordy (1998) within the symmetric second price common value model. A key feature in our approach is the derivation of an accurate approximation of the bid function for the Gamma model, which can be inverted and differentiated analytically. This is extremely valuable for fast and numerically stable evaluations of the likelihood function. The general MCMC algorithm in WV is utilized to estimate WV's eBay dataset from $1000$ auctions of U.S. proof coin sets, as well as simulated datasets from the Gamma model with different degrees of skewness in the value distribution. The Gaussian model fits the data slightly better than the Gamma model for the particular eBay dataset, which can be explained by the fairly symmetrical value distribution. The superiority of the Gamma to the Gaussian model is shown to increase for higher degrees of skewness in the simulated datasets.
Probability Theory and Statistics
Research subject Statistics
IdentifiersURN: urn:nbn:se:su:diva-57274OAI: oai:DiVA.org:su-57274DiVA: diva2:415129