Modeling Expectations with Noncausal Autoregressions

This paper is concerned with univariate noncausal autoregressive models and their potential usefulness in economic applications. We argue that noncausal autoregres- sive 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 also be used to determine to what extent the expectation, and, hence, current value of an economic variable depends on its past realized and future expected values. Dependence on future values suggests that the underlying economic model has a nonfundamental solution. We show in the paper how the parameters of a noncausal autoregressive model can be estimated by the method of maximum likelihood and how related test procedures can be obtained. Because noncausal autoregressive models cannot be distinguished from conventional causal autoregressive models by second order properties or Gaussian likelihood, a detailed discussion on their speci�cation is provided. As an empirical application, we consider modeling the U.S. inflation dynamics which, according to our results, depends only on its expected future values.