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Modeling Expectations with Noncausal Autoregressions
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EUI ECO; 2008/20
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LANNE, Markku, SAIKKONEN, Pentti, Modeling Expectations with Noncausal Autoregressions, EUI ECO, 2008/20 - https://hdl.handle.net/1814/8714
Abstract
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 vari-
able is affected by expectations and how expectations are formed. Noncausal autore-
gressive models can also be used to examine the related issue of backward-looking
or forward-looking dynamics of an economic variable. 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. Motivated by economic applications
we explicitly use a forward-looking autoregressive polynomial in the formulation of
the model. This is different from the practice used in previous statistics literature
on noncausal autoregressions and, in addition to its economic motivation, it is also
convenient from a statistical point of view. In particular, it facilitates obtaining like-
lihood based diagnostic tests for the speci ed orders of the backward-looking and
forward-looking autoregressive polynomials. Such test procedures are not only useful
in the speci cation of the model but also in testing economically interesting hypothe-
ses such as whether the considered variable only exhibits forward-looking behavior.
As an empirical application, we consider modeling the U.S. in ation dynamics which,
according to our results, is purely forward-looking.