The first two chapters of this dissertation study identification of a new class of demand models termed \textit{perturbed utility models}. The first chapter provides sufficient conditions under which structural functions in these models can be uniquely determined from knowledge of conditional means. The second chapter proposes a definition of complementarity/substitutability for these models and shows how to recover this measure from data.

The third chapter of this dissertation studies inference in a class of partially identified models. Specifically, this chapter provides a finite-sample power comparison between two existing tests of moment inequalities.