Semiparametric Estimation of First-Price Auction Models*

In this paper we propose a two-step semiparametric procedure to estimate first-price auction models. In the first-step, we estimate the bid density and distribution using local polynomial method, and recover a sample of (pseudo) private values. In the second-step, we apply the method of moments to the sample of private values to estimate a finite set of parameters that characterize the density of private values. We show that our estimator attains the parametric consistency rate and is asymptotically normal. And we also determine its asymptotic variance. The advantage of our approach is that it can accommodate multiple auction covariates. Monte Carlo exercises show that the estimator performs well both in estimating the value density and in choosing the revenue maximizing reserve price.