Spectral Representation of a Linear Dynamic Econometric Model with Stochastic Coefficients
Until now, in analyzing dynamic properties of econometric models the usual procedure was to treat the estimated regression coefficients as fixed parameters according to the classical theoretical specification of these models. In the sequel an approach which explicitly considers the stochastic nature of the estimated regression coefficients in order to test the Frisch hypothesis is applied. Hence, besides the uncertainty originated by the specification of equations which is considered by regarding the influence of the residuals, the risk of the estimation procedure is now taken into account. Studying the stochastic nature of the estimated regression coefficients gives information about the sensitivity and the stability of cycles with regard to variations in the structural parameters as, in the following, all estimated second-order moments will be taken as fixed. According to this approach, the spectral matrices in (2.8) or (2.14) contain random variables. Hence, one has to derive from these relationships the distributions or first- and second-order moments of the spectra given the distributions or first- and second-order moments of the structural parameters.
KeywordsCovariance Neral Income Coherence Resi
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