Asymptotic Hierarchies in an Economic Model
The dynamic specification of the various equations of an economic model and the numerical results associated with their estimation imply varying sluggishness of the different variables involved. This feature has extremely important outcomes on the dynamic evolution of the macroeconomic system. This problem is generally studied through the computation of the eigenvalues of the system under review, approximated by its linear-stationary state space correspondent. The dynamical behavior of some variables is mainly described in the short to medium run by their autoregressive structure. More generally, this is the well-known problem of assignment of eigenvalues to variables (see for instance Kuh et al (1985), Malgrange (1989), or Schoonbeek (1984).) One can also study the system in terms of blocks. The relevant concept is that of “near decomposability” investigated by depth by Ando et al (1963) for linear systems. They showed that, if the system is undecomposable, but can be decomposed into blocks with links between blocks “weak” relatively to links within blocks, then each block behaves, up to a certain horizon T1, “almost” independently of each other. Furthermore, after T1 and before T2, each block can be described by one representative variable, the behaviour of which is driven by the largest eigenvalue of the block. At last, after T2, all variables of the model are driven by the largest eigenvalue.
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