This paper studies asymptotic properties of likelihood-based estimators and test statistics for models which are partially identified. We concentrate on local or global identification problems which are linked to ("structural") reparameterisations, where the original ("reduced form") parameters are identified. The problem is approached via local asymptotic analysis of likelihood ratio functions. Applications include simultaneous equation models under limited information, testing for cointegration in VAR models, and testing structural hypotheses on cointegrating vectors.