By Dennis Fox

ISBN-10: 9058920496

ISBN-13: 9789058920492

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Such an approach could turn out to be useful in a category in which expansion effects play an important role. However, in a sales model, one needs to model seasonal effects and the category expansion or category contraction explicitly. In order to analyze changes in actual behavior of a brand manager, that is, changes in the use of instruments like price and display, one needs methods to test for structural changes in time series variables. Upon doing so, we build on the findings in Srinivasan et al.

These restrictions imply that the model parameters can be estimated from a multivariate reduced-form model with I − 1 equations. The dependent variable in each of the I − 1 equations is the natural logarithm Mit , for i = 1, 2, . . , I − 1. The of a relative market share. More formally, it is ln mit ≡ ln M It base brand I can be chosen arbitrarily. Of course, one is usually interested in predicting Mit and not in the logs of the relative market shares. It is then important to recognize that, first of all, exp(E[ln m it ]) is not equal to E[mit ] and that, secondly, E[Mit /MIt ] is not equal to E[Mit ]/E[MIt ], where E denotes the expectation operator.

IT ) . Given an estimate of σI2 , this relationship can be used to obtain 2 . estimates of σ12 , . . 27) ˜ When taking the square where one should include the appropriate ML estimator for Σ. roots of the diagonal elements of this matrix, one obtains the appropriate standard errors. 2 Modeling market shares Log-centering approach The above estimation routine is based on the reduced-form model, which is obtained from reducing the system of equations using the base-brand approach. An alternative method is the, what is called, log-centering method advocated by Cooper and Nakanishi (1988).

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