Identification and mis-specification issues in forward-looking models

Limited-information methods are commonly used to estimate forward-looking models with rational expectations, such as the "New Keynesian Phillips Curve" of Galli and Gertler (1999). In this paper, we address the issues of identification, which have been overlooked due to the incompleteness of the single-equation formulations. We show that problems of weak instruments can arise in these models, depending on the properties of the 'exogenous' variables, and that they are empirically relevant. We also uncover the link between identification and dynamic mis-specification, and examine the (lack of) power of
the Hansen test to detect invalid over-identifying restrictions. Finally, with regards to the New Phillips curve, we conclude that this equation is either weakly identified or mis-specified, casting doubts on its utility as a model of in ation dynamics.