Relevance of Functional Flexibility for Heterogeneous Sales Response Models: A Comparison of Parametric and Semi-Nonparametric Models

Abstract

So far studies estimating sales response functions on the basis of store-specific data either consider heterogeneity or functional flexibility. That is why in this contribution a model is developed possessing both these features. It is a multilayer perceptron with store-specific coefficients which follows a hierarchical Bayesian framework. An appropriate Markov Chain Monte Carlo estimation technique is introduced capable to satisfy theoretical constraints (e.g. sign constraints
on elasticities). The empirical study refers to a data base consisting of weekly observations of sales and prices
for nine leading brands of a packaged consumer good category. The data were acquired in 81 stores over a time span of at least 61 weeks. The multilayer perceptron is compared to a strict parametric multiplicative model and turns out to be clearly superior in terms of posterior model probability. This result indicates the benefits of using a flexible model even if heterogeneity is dealt with. Estimated sales curves and elasticities demonstrate that both models differ with regard to implications on price response.