  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.
