Identification Theory for Time Varying Models

39 Pages Posted: 26 May 2004 Last revised: 9 May 2021

See all articles by Thomas F. Cooley

Thomas F. Cooley

New York University - Leonard N. Stern School of Business; National Bureau of Economic Research (NBER)

Kent D. Wall

Naval Postgraduate School

Date Written: March 1976


The identification of time-varying coefficient regression models is investigated using an analysis of the classical information matrix. The variable coefficients are characterized by autoregressive stochastic processes, allowing the entire model to be case in state space form. Thus the unknown stochastic specification parameters and priors can be interpreted in terms of the coefficient matrices and initial state vector. Concentration of the likelihood function on these quantities allows the identification of each to be considered separately. Suitable restriction of the form of the state space model, coupled with the concept of controllability, lead to sufficient conditions for the identification of the coefficient transition parameters. Partial identification of the variance-covariance matrix for the random disturbances on the coefficients is established in a like manner. Introducing the additional concept of observability then provides for necessary and sufficient conditions for identification of the unknown priors. The results so obtained are completely analogous to those already established in the econometric literature, namely, that the coefficients of the reduced form are always identified subject to the absence of multicollinearity. Some consistency results are also presented which derive from the above approach.

Suggested Citation

Cooley, Thomas F. and Wall, Kent D., Identification Theory for Time Varying Models (March 1976). NBER Working Paper No. w0127, Available at SSRN:

Thomas F. Cooley (Contact Author)

New York University - Leonard N. Stern School of Business ( email )

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Kent D. Wall

Naval Postgraduate School

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United States

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