In this paper we propose an estimation method for the empirical study of theoretical auction models. We focus on first-price sealed bid and descending auctions and we adopt the private value paradigm, where each bidder is assumed to have a different private value, only known to him, for the object that is auctioned. Following McFadden (1989) and Pakes and Pollard (1989), our proposed method is based on simulations. Specifically, the method relies on a simulated nonlinear least squares objective function appropriately adjusted so as to obtain consistent estimates of the parameters of interest. We illustrate the proposed method by studying a market of agricultural products, where descending auctions are used. Our analysis takes into account heterogeneity of the auctioned objects and the fact that only the winning bid is observed. We estimate the parameters that characterize the distribution of the unobserved private values for each auctioned object.