Identification Problems in SDGE Models with an illustration to a small Macro model

We study identification in a class of linear rational expectations models. For any given exactly identified model, we provide an algorithm that generates a class of equivalent models that have the same reduced form. We use our algorithm to show that a model proposed by Jess Benhabib and Roger Farmer is observationally equivalent to the standard new-Keynesian model when observed over a single policy regime. However, the two models have different implications for the design of an optimal policy rule