Quantile regression methods for first-price auctions

TL;DR

This paper develops a novel quantile regression framework for analyzing first-price auctions, enabling estimation of bidders' private values and testing hypotheses using observed bids, with applications to timber auctions.

Contribution

It introduces a new quantile regression approach for private values in first-price auctions, including estimation techniques, hypothesis testing, and extensions with sieve methods.

Findings

Quantile regression for private values can be derived from bid data.

The framework allows testing of auction model specifications.

Application to USFS timber auctions demonstrates its practical utility.

Abstract

The paper proposes a quantile-regression inference framework for first-price auctions with symmetric risk-neutral bidders under the independent private-value paradigm. It is first shown that a private-value quantile regression generates a quantile regression for the bids. The private-value quantile regression can be easily estimated from the bid quantile regression and its derivative with respect to the quantile level. This also allows to test for various specification or exogeneity null hypothesis using the observed bids in a simple way. A new local polynomial technique is proposed to estimate the latter over the whole quantile level interval. Plug-in estimation of functionals is also considered, as needed for the expected revenue or the case of CRRA risk-averse bidders, which is amenable to our framework. A quantile-regression analysis to USFS timber is found more appropriate than the homogenized-bid methodology and illustrates the contribution of each explanatory variables to the private-value distribution. Linear interactive sieve extensions are proposed and studied in the Appendices.