Empirically feasible solutions and explicit dynamics for rational expectation models
This paper views economic dynamics as a set of stochastic difference equations whose solutions are vector autoregressive moving average (VARMA) models. We assume some give-and-take between the original specification of rational expectations (RE) models and corresponding VARMA reduced forms as solutions, with a view to obtaining the simplest RE specification and linear VARMA estimation. The literature contains a great variety of RE specifications, identifying restrictions on the structure, and reduded forms. \textit{L. J. Christiano} [Int. Econ. Rev. 28, 33-49 (1987)] lists eight money demand models for the identical German hyperinflation data, yielding widely different estimates of the RE parameters. A version of the Sargent-Wallace model in Christiano yields even a `wrong sign' for the coefficient of the inflation variable. We suggest ways of avoiding special purpose software (e.g., constrained maximum likelihood, generalized method of moments, etc.) to estimate RE models. Sometimes modest revisions of RE specifications yield VARMA reduced forms estimated by off-the-shelf VARMA software. By avoiding special purpose software, questions of the best fit, the best forecast, minimal state representation, etc., can be addressed with powerful tools developed by statisticians and engineers. The plan of the paper is as follows. Section 2 shows that our approach to the specification of the RE models is general enough to encompases a varied economic behavior. We derive the VARMA\((n,n^*)\) reduced form. Section 2.1 discusses identification. Section 2.2 discusses a scalar special case of the adaptive expectations RE structure with an ARMA(1,1) reduced form. Section 3 and an appendix have generalizations and new interpretations of famous RE models. Energy price dynamics is studied at the end of Section 3. Section 4 discusses \textit{J. S. Fackler} and \textit{S. C. Krieger's} [J. Bus. Econ. Stat. 4, 71-80 (1986)] numerical example, and Section 5 contains some final remarks.
scientific article; zbMATH DE number 906599
scientific article