A functional estimation approach to the first-price auction models

Abstract

This paper introduces new methods of identification and estimation of the first-price sealed bid auction model and compares them with the previous existing ones.The first method of estimation allows us to estimate directly (through an iterative algorithm) the cumulative distribution function of the private values without estimating the private values beforehand. In the second method, we use a quantile approach. Although the first-price auction is a complex nonlinear inverse problem, the use of quantile leads to a linearization of the model. Thus, in contrast with the existing methods we are able to deduce a closed-form solution for the quantile of the private values. This constructive identification allows for a one-stage estimation procedure that can be performed using three regularization methods: the Tikhonov regularization, the Landweber–Friedman regularization and the kernels.We conduct a Monte Carlo experiment to compare our methods of estimation by c.d.f. and quantiles with the methods of estimation developed by Guerre et al. (2000), Marmer and Shneyerov (2012), and Hickman and Hubbard (2015).Some extensions of the model are considered: asymmetric bidders, affiliation, conditional models to exogenuous variables, and the observation of only the winning bids.