Nonparametric Identification in Nonlinear Simultaneous Equations Models: The Case of Covariance Restrictions

Abstract

Nonlinear systems of simultaneous equations are ubiquitous in Economics. Despite their importance, relatively few results regarding the nonparametric identification and estimation in these models are available. Important advances by Matzkin (2015, ECMA) show that exclusion restrictions, as known in linear simultaneous equations models, can lead to nonparametric identification in nonlinear models. The point of departure of our analysis is a well-known fact (see, e.g., Fisher, 1966) that in linear simultaneous equations systems, traditional exclusion restrictions can under certain conditions be replaced with restrictions on the covariance structure of the unobservables. We extend those results to nonlinear systems with infinite dimensional parameters of interest. The key features of our nonparametric identification result are: (i) it is instrument free in that it does not use instrumental variables; and (ii) it is constructive, in the sense that it leads to a natural nonparametric estimator of the model parameters.