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Bayesian Inference in Structural Second-Price Common Value Auctions
Stockholm University, Faculty of Social Sciences, Department of Statistics.
Stockholm University, Faculty of Social Sciences, Department of Statistics.
2011 (English)In: Journal of business & economic statistics, ISSN 0735-0015, E-ISSN 1537-2707, Vol. 29, no 3, 382-396 p.Article in journal (Refereed) Published
Abstract [en]

Structural econometric auction models with explicit game-theoretic modeling of bidding strategies have been quite a challenge from a methodological perspective, especially within the common value framework. We develop a Bayesian analysis of the hierarchical Gaussian common value model with stochastic entry introduced by Bajari and Hortacsu. A key component of our approach is an accurate and easily interpretable analytical approximation of the equilibrium bid function, resulting in a fast and numerically stable evaluation of the likelihood function. We extend the analysis to situations with positive valuations using a hierarchical gamma model. We use a Bayesian variable selection algorithm that simultaneously samples the posterior distribution of the model parameters and does inference on the choice of covariates. The methodology is applied to simulated data and to a newly collected dataset from eBay with bids and covariates from 1000 coin auctions. We demonstrate that the Bayesian algorithm is very efficient and that the approximation error in the bid function has virtually no effect on the model inference. Both models fit the data well, but the Gaussian model outperforms the gamma model in an out-of-sample forecasting evaluation of auction prices. This article has supplementary material online.

Place, publisher, year, edition, pages
2011. Vol. 29, no 3, 382-396 p.
Keyword [en]
Bid function approximation, eBay, Internet auctions, Likelihood inference, Markov chain Monte Carlo, Normal valuation, Variable selection
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:su:diva-66979DOI: 10.1198/jbes.2011.08289ISI: 000292316500005OAI: oai:DiVA.org:su-66979DiVA: diva2:470081
Note
authorCount :2Available from: 2011-12-28 Created: 2011-12-22 Last updated: 2017-12-08Bibliographically approved
In thesis
1. Bayesian Inference in Structural Second-Price Auctions
Open this publication in new window or tab >>Bayesian Inference in Structural Second-Price Auctions
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The aim of this thesis is to develop efficient and practically useful Bayesian methods for statistical inference in structural second-price auctions. The models are applied to a carefully collected coin auction dataset with bids and auction-specific characteristics from one thousand Internet auctions on eBay. Bidders are assumed to be risk-neutral and symmetric, and compete for a single object using the same game-theoretic strategy. A key contribution in the thesis is the derivation of very accurate approximations of the otherwise intractable equilibrium bid functions under different model assumptions. These easily computed and numerically stable approximations are shown to be crucial for statistical inference, where the inverse bid functions typically needs to be evaluated several million times.

In the first paper, the approximate bid is a linear function of a bidder's signal and a Gaussian common value model is estimated. We find that the publicly available book value and the condition of the auctioned object are important determinants of bidders' valuations, while eBay's detailed seller information is essentially ignored by the bidders. In the second paper, the Gaussian model in the first paper is contrasted to a Gamma model that allows intrinsically non-negative common values. The Gaussian model performs slightly better than the Gamma model on the eBay data, which we attribute to an almost normal or at least symmetrical distribution of valuations. The third paper compares the model in the first paper to a directly comparable model for private values. We find many interesting empirical regularities between the models, but no strong and consistent evidence in favor of one model over the other. In the last paper, we consider auctions with both private-value and common-value bidders. The equilibrium bid function is given as the solution to an ordinary differential equation, from which we derive an approximate inverse bid as an explicit function of a given bid. The paper proposes an elaborate model where the probability of being a common value bidder is a function of covariates at the auction level. The model is estimated by a Metropolis-within-Gibbs algorithm and the results point strongly to an active influx of both private-value and common-value bidders.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm University, 2011. 11 p.
Keyword
Asymmetry, Bid function approximation, Common values, Gamma model, Gaussian model, Markov Chain Monte Carlo, Private values, Variable selection, Internet auctions
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-57278 (URN)978-91-7447-276-9 (ISBN)
Public defence
2011-06-10, hörsal 3, hus B, Universitetsvägen 10 B, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Epub ahead of print. Paper 2: Manuscript. Paper 3: Manuscript. Paper 4: Manuscript.

Available from: 2011-05-12 Created: 2011-05-05 Last updated: 2013-07-12Bibliographically approved

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