Nonparametric identification

When one wants to estimate a model without specifying the functions and distributions parametrically, or when one wants to analyze the identification of a model independently of any particular parametric specification, it is useful to perform a nonparametric analysis of identification. This chapter presents some of the recent results on the identification of nonparametric econometric models. It considers identification in models that are additive in unobservable random terms and in models that are nonadditive in unobservable random terms. Single equation models as well as models with a system of equations are studied. Among the latter, special attention is given to structural models whose reduced forms are triangular in the unobservable random terms, and to simultaneous equations, where the reduced forms are functions of all the unobservable variables in the system. The chapter first presents some general identification results for single-equation models that are additive in unobservable random terms, single-equation models that are nonadditive in unobservable random terms, single-equation models that possess and index structure, simultaneous equations nonadditive in unobservable random terms, and discrete choice models. Then, particular ways of achieving identification are considered. These include making use of conditional independence restrictions, marginal independence restrictions, shape restrictions on functions, shape restrictions on distributions, and restrictions in both functions and distributions. The objective is to provide insight into some of the recent techniques that have been developed recently, rather than on presenting a complete survey of the literature.