I adapt the Generalised Method of Moments to deal with nonlinear models in which a …nite number of isolated parameter values satisfy the moment conditions. To do so, I initially study …rst-order underidenti…ed models whose expected Jacobian is rank de…cient but not necessarily 0. In both cases, the proposed procedures yield efficiency gains and underidenti…cation tests with standard asymptotics. I study separately non-linear in parameters but linear in variables models and fundamentally non-linear models without separation of data and parameters. I illustrate the proposed inference procedures with a dynamic panel data model and a non-linear regression model for discrete data.

Keywords: Finite set, Generalised Method of Moments, Identi…cation test.
JEL: C10