Piecewise Pseudo-Maximum Likelihood Estimation for Risk Aversion Case in First-Price Sealed-Bid Auction

Abstract

In the literature, more and more clues show that the bidders indeed tend to risk averse. But as a good structure estimation procedure in first-price sealed-bid auctions, the traditional PPMLE (Piecewise Pseudo-Maximum Likelihood Estimation) approach is only applicable to the risk neutrality case. This study generalizes this approach to the risk aversion case, and obtains a simple estimation procedure for the Pareto family of private costs. In the procedure, the estimation order of distribution parameters of private costs is not important, which is different from the traditional PPMLE method. Though there is no unique estimator for ? 1 and ?, some guidance is given for real-world applications on the basis of our Monte Carlo simulation experiments. What's more, this procedure can be reduced further, if one is only interested in estimating the private costs. Extensive simulation experimental results indicate that our approach outperforms or matches at least the traditional one in the case of risk neutrality, and is applicable to the risk aversion case.