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This extension of the Blattberg and George (1991) shrinkage estimator, while an important methodological contribution, will represent an improvement in this particular application only if the demographic and competitive characteristics of each trade area add to the information about price elasticities already contained in the store-level data. Alan's Figure 1 shows that the least squares estimates (shown as clear diamonds) are related to the Bayesian prediction based on demographics. Note however, that the least-squares estimates were not constrained in any way, and still seem to carry a relationship to the demographics of the market area. This seems to indicate that the sales response data already have the demographic information embedded in them.
Fortunately, there is an easy way of disconfirming this hypothesis, by including Blattberg & George's model in the comparison of in-sample and out-of-sample MSE's shown in Alan's paper (Figure 4). The contribution of demographics in explaining differences in consumer response to price and promotions can be demonstrated by showing that the out-of-sample MSE for the proposed model is smaller than for the Blattberg & George (1991) model.
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