A General Result on Observational Equivalence in a Class of Nonparametric Structural Equations Models

This paper examines observational equivalence in a class of nonparametric structural equations models under weaker conditions than those currently available in the literature. It allows for several endogenous variables, does not impose differentiability or continuity of the equations which are part of the structure, and allows the unobserved errors to depend on the exogenous variables. The usefulness of the main result is illustrated by deriving observational equivalence conditions for some models including nonparametric simultaneous equations models, additive errors models, multivariate triangular models, etc. Some of these yield well known results as special cases.