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 this end we show the links between the techniques of structural and VAR model building on the one hand, and the econometric profiles of dynamic modelling on the other. The solutions engendered by both approaches, which share a common difference-equation ancestry, call for a matrix polynomial inversion by either Taylor or Laurent expansions. The former is true for classical econometrics, where unit roots are ruled out, whereas the latter comes to the fore in time-series econometrics, with unit roots and cointegration as an added value. The derivation of the intended result, as well as the econometric interpretation of the solutions, rest on a neat algebraic and statistical apparatus.