This dissertation consists of four chapters contributing to the development of microeconometric methodology, with a particular emphasis on questions of identification. The methodological problems discussed are motivated by substantive questions about the causes of urban segregation and of long term unemployment. Chapter 1 develops static and dynamic models of sorting in which location choices depend on the location choices of other agents as well as prices and exogenous location characteristics. In these models, demand slopes and hence preferences are not identifiable without further restrictions because of the absence of independent variation of endogenous composition and exogenous location characteristics. Four solutions of this problem are presented and applied to data on neighborhoods in US cities: The first three use exclusion restrictions, based on either subgroup demand shifters, the spatial structure of externalities, or the dynamics of prices and composition in response to an amenity shock. The fourth tests for multiplicity of equilibria in the dynamics of composition, using the test proposed in chapter 2. The empirical results consistently suggest the presence of strong social externalities, that is, a dependence of location choices on neighborhood composition. Chapter 2 proposes an estimator and develops an inference procedure for the number of roots of functions which are nonparametrically identified by conditional moment restrictions. The estimator is superconsistent, and the inference procedure is based on non-standard asymptotics. This procedure is used to construct confidence sets for the number of equilibria of static games of incomplete information and of stochastic difference equations. In an application to panel data on neighborhood composition in the United States, no evidence of multiple equilibria is found. Chapter 3 proposes a test for path dependence in discrete panel data based on a characterization of stochastic processes that are mixtures of Markov Chains. This test is applied to European Community Household Panel data on employment histories. The data allow to reject the null of no path dependence in all subsamples considered. Chapter 4 discusses identification in nonparametric, continuous triangular systems. It provides conditions which are both necessary and sufficient for the existence of control functions satisfying conditional independence and support requirements. Confirming a commonly noticed pattern, these conditions restrict the admissible dimensionality of unobserved heterogeneity in the first stage structural relation, or more generally the dimensionality of the family of conditional distributions of second stage heterogeneity given explanatory variables and instruments. These conditions imply that no such control function exists without assumptions that seem hard to justify in most applications. In particular, none exists in the context of a generic random coefficient model.