TY  - JOUR
AU  - Cooley,Thomas F.
AU  - Wall,Kent D.
TI  - On the Identification of Time Varying Structures
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 85
PY  - 1975
Y2  - May 1975
UR  - http://www.nber.org/papers/w0085
L1  - http://www.nber.org/papers/w0085.pdf
N1  - Author contact info:
Thomas F. Cooley
Department of Economics
Stern School of Business
44 West 4th Street, Room 7-88
New York, NY  10012-1126
Tel: 212/998-0870
Fax: 212/995-4218
E-Mail: tcooley@stern.nyu.edu

Kent D. Wall
AB  - The identifiability of reduced form econometric models with variable coefficients is investigated using the control theoretic concepts of uniform complete observability and uniform complete controllability. First, a variant of the state space representation of the traditional reduced form is introduced which transcribes the underlying non-stationary estimation problem into one particularly suited to a Kalman filtering solution. Using such a formulation, observability and controllability can be called upon to obtain a necessary and sufficient condition for identification of the specific parameterization. The results so obtained are completely analogous to those already established in the econometric literature, namely, that the parameters of the reduced form are always identified subject to the absence of multicollinearity(referred to as "persistent excitation" in the control literature). How-ever, now the multicollinearity condition is seen to depend on the structure of the parameter variations as well as the statistical nature of the explanatory variables. The verification of identifiability thus reduces to a check for uniform complete observability which can always be affected in econometric applications. Some consistency results are also presented which derive from the above approach.
ER  -