Estimating market-level multiplicative models of promotion effects with linearly aggregated data: A parametric approach

Marketing researchers may be confronted with biases when estimating response coefficients of multiplicative promotion models based on linearly aggregated data. This paper demonstrates how to recover the parameters obtained with data which are aggregated in a compatible way with such models. It provides evidence that the geometric means of sales and of prices across stores can be predicted with accuracy from their arithmetic means and standard deviations. Employing these predictions in a market-level model results in parameter estimates which are consistent with those obtained with the actual geometric means and fairly close to coefficients derived at the individual store level.