A solution to the global identification problem in DSGE models

We develop an analytical framework to study global identification in structural models with forward-looking expectations. Our identification condition combines the similarity transformation linking the observationally equivalent state space systems with the constraints imposed on them by the model parameters. The key step of solving the identification problem then reduces to finding all roots of a system of polynomial equations. We show how it can be done using the concept of a Gröbner basis and recently developed algorithms to compute it analytically. In contrast to papers relying on numerical search, our approach can prove whether a model is identified or not at a given parameter point, explicitly delivering the complete set of observationally equivalent parameter vectors. We present the solution to the global identification problem for several popular DSGE models.