Econometrica: Jan, 1983, Volume 51, Issue 1

The Identification Problem in Systems Nonlinear in the Variables

https://doi.org/0012-9682(198301)51:1<175:TIPISN>2.0.CO;2-J
p. 175-196

Bryan W. Brown

This paper examines the identifiability of the coefficients of a single equation in a simultaneous equation model which is nonlinear only in the variables. The concept of identifiability in this model is motivated and developed using the closely related concept of observational equivalence. This framework is then utilized to develop necessary and sufficient conditions for identifiability when the disturbances are required to be independent of the exogenous variables. The approach recommended by Fisher is shown to yield sufficient but not necessary conditions for identifiability. For several relatively common special cases the necessary and sufficient conditions are found to simplify to the familiar rank condition for identifiability in the linear model.