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Conditions for Identification in Nonparametric and Parametric Models
Charles S. Roehrig
Abstract
It is argued that most econometric models are nonparametric and that parameterizations should typically be viewed as approximations made for purposes of estimation. These parameterizations should not be used to judge identification when they are not a precise representation of prior information. Identification in a nonparametric context is defined and theorems are developed that aid in judging the identifiability of both nonparametric and parametric models. The application of parametric models extends previous research as it applies to a broad range of models including those that are nonlinear in variables and/or parameters. The application to nonparametric models results in a simple necessary condition for identifiability. Furthermore, when this condition is met and when the structure is nonlinear (as defined in the paper), all functions are identifiable. Examples are given that illustrate the usefulness of these results for determining sources of identification.
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