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By Dennis Fox

ISBN-10: 9058920496

ISBN-13: 9789058920492

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4). Every vector (M1t , . . , MIt ) generated this way amounts to a draw from the joint distribution of the market shares at time t. Using the average over a sufficiently large number of draws we calculate the expected value of the market shares. By the weak law of large numbers we have 1 L→∞ L L (l) Mit = E[Mit ]. 45) l=1 For finite L the mean value of the generated market shares is an unbiased estimator of the market share. The estimate may differ from the expected market share, but this difference is only due to simulation error and this error will rapidly converge to zero if L gets large.

Due to the properties of the forecasting errors and the determinant operator this measure is invariant for the choice of the omitted brand. A large determinant corresponds to large forecasting errors. We find that imposing restrictions while they are not valid is worse than the other way around. That is, estimating a model with full competition when in fact the true model has restricted competition yields a better performing model than when a model with restricted effects were estimated. Moreover, standard econometric theory tells us that inappropriate parameter restrictions imply omitted variable bias.

5 Model selection Attraction models are often considered for forecasting market shares. It is usually assumed that, by imposing in-sample specification restrictions, the out-of-sample forecasting accuracy will improve. Exemplary studies are Brodie and Bonfrer (1994), Danaher (1994), Naert and Weverbergh (1981), Leeflang and Reuyl (1984), Kumar (1994) and Chen et al. (1994), among others. A summary of the relevant studies is given in Brodie et al. (2001). A common characteristic of these studies, an exception being Chen et al.

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Advanced econometric marketing models by Dennis Fox

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