Aggregate market response models comprise variables which are defined as sums (e. g., of sales, of advertising budgets) or averages (e. g., of prices) across persons or households for a certain store, retail chain, region, etc. We consider sales or market shares of brands in one product category as dependent variables and marketing variables ( e. g. prices, advertising budgets, etc.) as independent variables. Estimates of the effects of marketing variables which are either too high or too low can be avoided by functional flexibility, latent heterogeneity and by taking endogeneity into account. Avoiding such biases is especially important if we want to derive implications for marketing decision making. Researchers should switch to flexible methods as these usually perform much better even for new data than better known parametric alternatives. Such a switch seems to be quite feasible as the often heavy data limitations of previous decades have been overcome, at least in consumer goods marketing. Another motivation for such a change is offered by the fact that in many studies functional flexibility turns out to be the most important factor. We compare three flexible approaches, multilayer perceptron, splines regression and kernel regression which have been applied to determine aggregate market response functions. We recommend to use the multilayer perceptron, which is a form of artificial neural net, because of better statistical performance, lower computation time and robustness for extrapolated data. Researchers can avoid problems of flexible methods such as overfitting and implausible estimation results (e. g., higher sales at higher prices) by careful selection of model complexity and by introducing restrictions to ensure, e. g., monotone or concave shapes. In models with latent heterogeneity parameters are not constant, but vary according to a continuous or a finite mixture distribution. We distinguish two types of latent heterogeneity, a) heterogeneity within regions or within stores across consumers, and b) heterogeneity across retail chains or stores. We observe that in aggregate response modeling continuous mixtures have been applied more often. Moreover, as a rule continuous mixtures beat finite mixtures. Most studies with parametric response functions which also allow for latent heterogeneity obtain a better statistical performance than related models with constant parameters. Many of these studies also show that heterogeneous models lead to different implications for optimal decision making, e. g., optimal pricing. Therefore researches should regularly investigate latent heterogeneity if they use parametric aggregate market response models. A marketing variable is endogenous if it is related to an unobserved factor which also determines the dependent variable. Endogeneity arises, for example, if management raises prices or advertising budgets because unobserved preferences of customers change in favor of the respective brand. If marketing variables are endogenous, classical methods provide biased estimates of their effects. Frequently instrumental variable methods are used to correct these biases, but finding appropriate instrumental variables is often difficult. Researchers may bypass these difficulties by turning to instrument-free methods of which the copula-based approach seems to be most attractive one. If the assumptions of this approach do not hold, linking marketing variables to parameters of flexible aggregate response functions constitutes a viable alternative. If researchers are not interested in measuring the effects of marketing variables, but instead look on overall predictive performance, they can safely ignore the endogeneity problem. On the other hand, functional flexibility and to some degree latent heterogeneity are important because usually they lead to better predictions.
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