Another important decision the econometrician has to make is whether to use parametric or nonparametric methods. With nonparametric methods, the analysis is flexible and the results are not driven by preliminary assumptions. However, due to limitations in the data or the complexity of the theoretical model, one often has to make para- metric assumptions to simplify the estimation. Typically parametric assumptions are made about the distribution from which the bidders draw their valuations. That allows closed form solutions to the equilibrium bid functions and therefore the use of maxi- mum likelihood methods. In the first essay of this thesis, I use nonparametric methods. In the other two essays, I have to make some standard parametric assumptions about the distributions of the error terms in the reduced form econometric models.