Modeling Expectations with Noncausal Autoregressions

We argue that noncausal autoregressive models are especially well suited for modeling expectations. Unlike conventional causal autoregressive models, they explicitly show how the considered economic variable is affected by expectations and how expectations are formed. Noncausal autoregressive models can be used to examine the related issue of backward-looking or forward-looking dynamics of an economic variable. Our formulation of the model differs from that in the previous literature, and it facilitates obtaining tests of the orders of the backward-looking and forward-looking polynomials, i.e., determining the quot;order of forward-lookingnessquot;. Because noncausal autoregressive models cannot be distinguished from conventional causal autoregressive models by second order properties or Gaussian likelihood, a detailed discussion on their specification is provided. As an empirical application, we consider modeling the U.S. inflation dynamics which, according to our results, is purely forward-looking