On the Indeterminacy of New Keynesian Economics

We study identification in a class of three-equation monetary models. We argue that these models are typically not identified. 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 provide four examples of the consequences of lack of identification. In our first two examples we show that it is not possible to tell whether the policy rule or the Phillips curve is forward or backward looking. In example 3 we establish an equivalence between a class of models proposed by Benhabib and Farmer and the standard new-Keynesian model. This result is disturbing since equilibria in the Benhabib-Farmer model are typically indeterminate for a class of policy rules that generate determinate outcomes in the new-Keynesian model. In example 4, we show that there is an equivalence between determinate and indeterminate models even if one knows the structural equations of the model