Description
Classical econometrics – which plunges its roots in economic theory with simultaneous equations models (SEM) as offshoots – and time series econometrics – which stems from economic data with vector autoregr- sive (VAR) models as offsprings – scour, like the Janus’s facing heads, the flowing of economic variables so as to bring to the fore their autonomous and non-autonomous dynamics. It is up to the so-called final form of a dy­namic SEM, on the one hand, and to the so-called representation theorems of (unit-root) VAR models, on the other, to provide informative closed form expressions for the trajectories, or time paths, of the economic vari­ables of interest. Should we look at the issues just put forward from a mathematical standpoint, the emblematic models of both classical and time series econometrics would turn out to be difference equation systems with ad hoc characteristics, whose solutions are attained via a final form or a represen­tation theorem approach. The final form solution – algebraic technicalities apart – arises in the wake of classical difference equation theory, display­ing besides a transitory autonomous component, an exogenous one along with a stochastic nuisance term. This follows from a properly defined ma­trix function inversion admitting a Taylor expansion in the lag operator be­cause of the assumptions regarding the roots of a determinant equation pe­culiar to SEM specifications.
