Semiparametric Estimation of First-Price Auction Models

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.