Study week on the econometric approach to development planning

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Monograph

Identifikator:: 1824422792

URN:: urn:nbn:de:zbw-retromon-217476

Document type:: Monograph

Title:: Study week on the econometric approach to development planning

Place of publication:: Amsterdam [u.a.]

Publisher:: North-Holland Publ. Co. [u.a.]

Year of publication:: 1965

Scope:: XLVII, 1259 S.; graph. Darst.

Digitisation:: 2022

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Dynamic structure and estimation in economy-wide econometric models / FranklinM. Fisher, Massachuetts Institute of Technology - Cambridge, Mass. - U.S.A.

Collection:: Economics Books

SEMAINE D ETUDE SUR LE ROLE DE L'ANALYSE ECONOMETRIQUE ETC. 303 ancorrelated with lagged values of low-numbered disturbances. Further, either B or all V(6) (A >o) have zeros evervwhere on the principal diagonal. If (R.1), (R.2), and (R.3*) hold, every term in (2.4) will be triangular, so that W(o) will likewise be triangular as re- quired. Further, W(1) will also be triangular rather than zero and will have zeros on its principal diagonal, but this will be all that is needed, since if B is triangular no lagged endogenous variable appears in an equation of (2.1) explaining a lower- numbered current endogenous variable. Intuitively, the general necessity of no serial correlation for the consistency of least squares is that an element of y,_, is influenced by an element of «, ;. If that element of u,_, is itself correlated with a lower-numbered element of #,, then the corresponding element of y,_, cannot be assumed to be uncor- related with that element of u,. Even if V(8) is triangular for 8>0 (or even diagonal) and B is not triangular, the dynamics of the system will carry serial correlation into relations between any current disturbance and any current endogenous variable. If both V(6) and B are triangular, however, such effects are only carried toward higher-numbered equations. That triangularity of both V(6) for all 6>>0 and B are generally necessary in the presence of serial correlation may be seen from the fact that since D is triangular, the terms in (2.4) will generally not otherwise be triangular and the fact that if B is not triangular, even triangularity of W(1) will not suffice. (The condition as to the principal diagonals can be easily seen to be required by considering a single-equation model). Of course, as is also the case for the assumption of the diagonality of V(0), even if such assumptions fail generally, similar weaker assumptions concerning certain off-diagonal ele- ments may hold and yield the consistency of ordinary least squares for certain equations. The indicated assumptions are necessary for such consistency in all equations, however. (Such weaker conditions are fairly readily obtained from the genera lization of the current discussion given in a later section’ Lo Fisher - pag. C,

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