Regulation models are a special class of contract models that have received a lot of attention from economists in the last few decades. This continuous interest has been motivated by an increasing need in designing regulatory policies in a world where decentralization and delegation of public services play an important role. A more recent and less rich strand of economic literature is devoted to the structural analysis of contract theory models. The economic setting underlying these models gives rise to complex nonlinear inverse problems and hence the difficulties in uniquely recovering the primitives of the model from the data. The novelty of our paper comes from the fact that we globally identify the static version of a classical adverse selection model and we also provide a quantile estimation procedure for the parameter of interest along with a discussion of the asymptotic properties of our estimator. We also present two extensions where we allow for semiparametric forms of the cost function