Classical versus VAR econometrics: the Janus head effect in economic dynamic modelling

The aim of this paper is that of giving a finer insight into the analytic foundations of vector autoregressive models (VAR) in comparison with classical econometric models. To target such a goal we establish a bridge between the techniques of structural and VAR model building in the backstage, and the econometric profiles of dynamic modelling on the forefront. The solutions engendered by both approaches, which unfold a common difference-equation ancestry, ask for a matrix polynomial inversion by either Taylor or Laurent expansions. The former case occurs in classical econometrics, where unit roots are ruled out, whereas the latter comes to the fore in time-series econometrics, with unit roots in the backstage and cointegration as an added value. The derivation of the intended result, as well as the econometric reading keys of the solutions, rest on a neat algebraic and statistical apparatus.