  We propose a semiparametric method to estimate the density of private values
in first-price auctions. Specifically, we model private values through a set of
conditional moment restrictions and use a two-step procedure. In the first step
we recover a sample of pseudo private values using Local Polynomial Estimator.
In the second step we use a GMM procedure to estimate the parameter(s) of
interest. We show that the proposed semiparametric estimator is consistent, has
an asymptotic normal distribution, and attains the parametric ("root-n") rate
of convergence.
