On the Indeterminacy of New-Keynesian Economics

We study identiÞcation in a class of three-equation monetary models. We argue that these models are typically not identiÞed. For any given exactly identiÞed 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 identiÞcation. In our Þrst 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 [1] 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. Non Technical Summary This paper is about the general lack of identiÞcation in linear rational expectations models. It has become common practice in applied monetary economics to estimate single equations using instrumental variables. In a recent paper, Clarida, Gali and Gertler [4] estimate a monetary policy rule and they use their estimated rule to argue that monetary policy before 1980 was very different from policy after 1980. Their work has been criticized in a number of recent papers for failing to pay sufficient attention to the fact that identiÞcation is a property of a system. In general one cannot identify a single equation without making assumptions about the nature of other equations in the model. We go beyond this literature by drawing attention to a dimension of the identiÞcation problem that is potentially more serious if one hopes to use careful econometrics to help to design economic policies that maximize welfare. We study identiÞcation in a class of three-equation monetary models and show that, using data from a single policy regime, it is not possible to tell whether a given period was associated with a policy that was driven purely by fundamental shocks; or whether sunspots also played a role. For any given exactly identiÞed 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 identiÞcation. In our Þrst 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 [1] 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