This dissertation provides computationally intensive, yet feasible methods for inference in a very general class of partially identified econometric models. Let P denote the distribution of the observed data. The class of models we consider are defined by a population objective function Q ([straight theta], P ) for [straight theta] ∈ Θ. The point of departure from the classical extremum estimation framework is that it is not assumed that Q ([straight theta], P ) has a unique minimizer in the parameter space Θ. The goal may be either to draw inferences about some unknown point in the set of minimizers of the population objective function or to draw inferences about the set of minimizers itself. To this end, we study two distinct definitions for confidence regions. In the first formulation, the object of interest is some unknown point [straight theta] ∈ Θ 0 (P ), where Θ0 (P ) = arg min[straight theta]∈Θ Q ([straight theta], P ), and so we seek random sets that contain each [straight theta] ∈ Θ 0 (P ) with at least some prespecified probability asymptotically. In the second formulation, the object of interest is Θ0 ( P ) itself, and so we seek random sets that contain this set with at least some prespecified probability asymptotically. We also extend these two notions of confidence regions to situations where the object of interest is the image of some unknown point [straight theta] ∈ Θ0 ( P ) or the image of Θ0 (P ) under a known function. For each of these notions of confidence regions, we construct random sets satisfying the desired coverage property under weak assumptions. We also provide conditions under which the confidence regions are uniformly consistent in level. Finally, we illustrate the use of our methods with an empirical study of the impact of top-coding of outcomes on inferences about the parameters of a linear regression.
