Topics in Dynamic Model Analysis : Advanced Matrix Methods and Unit-Root Econometrics Representation Theorems PDF

by Mario Faliva, Maria Grazia Zoia

Part of the Lecture Notes in Economics and Mathematical Systems series

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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 dy- namic 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 vari- ables 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 represen- tation theorem approach.

The final form solution - algebraic technicalities apart - arises in the wake of classical difference equation theory, display- ing besides a transitory autonomous component, an exogenous one along with a stochastic nuisance term.

This follows from a properly defined ma- trix function inversion admitting a Taylor expansion in the lag operator be- cause of the assumptions regarding the roots of a determinant equation pe- culiar to SEM specifications.