Finite-Sample Auction Inference Using Transaction Prices

原文摘要

We first provide inference on the quantile function of the bid distribution in firstprice or descending auctions, and the quantile function of the value distribution in second-price or ascending auctions, with a known number of bidders with symmetric independent private values. Specifically, we provide finite-sample, nonparametric, tuning parameter-free, uniform confidence bands for these quantile functions when observing only the transaction price. We also show how these bands can be used to construct confidence intervals for many counterfactuals and economic quantities that are functionals of the value distribution. Some confidence intervals inherit the same properties of our bands, besides having conservative instead of exact coverage, while others require asymptotic arguments and/or tuning parameters. Even if the observed number of bidders varies across auctions, our bands’ finite-sample coverage is exact, assuming exogenous participation. With a fixed number of bidders, we also derive uniform confidence bands robust to auction-level unobserved heterogeneity. This includes new partial identification results that bound the bid or value quantile function in terms of the transaction price quantile function. Empirically, our new methodology is applied to timber auction data to examine heterogeneity across appraisal value and number of bidders, which helps assess the combination of symmetric independent private values and exogenous participation, and to provide confidence intervals for the optimal reserve price and the economic benefit of running the auction instead of a random lottery.

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