Logically Consistent Market Share Models

Cover Logically Consistent Market Share Models
Logically Consistent Market Share Models
Philippe Naert
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: 0. 9979 and given d = 0. 008, r should be less than 0. 010121.
21 Footnotes By ' itrinsically nonlinear forms we mean equations which cannot be linearized.
2 In fact, we should add a disturbance term e. . Since we will be dealing with expectations e will be deleted. ' 3 A similar theorem was derived by Schmalensee ([12], pp. 47-49). In his demonstration, he makes use of the properties of the row kernel of the matrix. Our proof is more concise and generalizes Schmalensee's theorem.
4 Note that
... r could be time-dependent, that is, the constraint on y is u'y = r . For example, if the dependent variable were brand sales, q. , their sum should add up to industry sales, Q, which may be time dependent. In the formulation of the theorem the c are then replaced by c. , The proof is not affected except that r becomes r and c. Becomes c .
If S . , were zero for all i and k, none of the X's would be explana- tory variables. If at least one of the X's is a true explanatory variable, s and k can always be chosen such that 6 j^ ii^ o.


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