Bayesian Inference in Structural Second-Price common Value Auctions
AbstractStructural 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 Hortaçsu (2003). 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. The analysis is also extended 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 carefully collected dataset from eBay with bids and covariates from 1000 coin auctions. It is demonstrated 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.
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Bibliographic InfoPaper provided by Sveriges Riksbank (Central Bank of Sweden) in its series Working Paper Series with number 242.
Length: 33 pages
Date of creation: 01 May 2010
Date of revision:
Bid function approximation; eBay; Internet auctions; Likelihood inference; Markov Chain Monte Carlo; Normal valuations; Variable selection;
Other versions of this item:
- Wegmann, Bertil & Villani, Mattias, 2011. "Bayesian Inference in Structural Second-Price Common Value Auctions," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 382-396.
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-05-29 (All new papers)
- NEP-ECM-2010-05-29 (Econometrics)
- NEP-ORE-2010-05-29 (Operations Research)
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