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Regional Sales Response Functions (SRF) with Stochastic Derivative Constraints

Sales response function have become increasingly important to model panel data on sales across regional units and time. Regional marketing strategies involve usually a fixed and a flexible spending component which could interact with the sales responses if sales managers decide to react fast according to new market situations. A recent article of Kao et al. (2005) suggested to use a class of production functions under optimal constraints to estimate the sales responses to marketing strategies. In this paper we generalize this approach to spatially and time correlated data sets with one up to K endogenously determined decision variables and show how to estimate them by MCMC as in [4]. The new modeling approach leads to a multivariate equation system and will be demonstrated using simulates data and data from a pharma-marketing survey in German regions.