02256cam a22002417 4500001000600000003000500006005001700011008004100028100002200069245011100091260006600202490004100268500001400309520131300323530006101636538007201697538003601769700001801805710004201823830007601865856003701941856003601978w0085NBER20160628071738.0160628s1975 mau||||fs|||| 000 0 eng d1 aCooley, Thomas F.10aOn the Identification of Time Varying Structuresh[electronic resource] /cThomas F. Cooley, Kent D. Wall. aCambridge, Mass.bNational Bureau of Economic Researchc1975.1 aNBER working paper seriesvno. w0085 aMay 1975.3 aThe 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web.1 aWall, Kent D.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w0085.4 uhttp://www.nber.org/papers/w008541uhttp://dx.doi.org/10.3386/w0085