Seemingly Unrelated Equations: Shrinkage Estimation of Price and Promotional Elasticities, Journal of the American Statistical Association
Consider the problem where a retailer or manufacturer wants to estimate product price and promotional elasticities based on supermarket scanner data. Classical linear modeling suffers from the following aggregation dilemma. Price and promotional elasticities appear to vary considerably among chains and brands so that one overall model is too restrictive. Alternatively, the use of a different model for each chain and brand leads to noisy and often nonsensical estimates of separate elasticities because of excessive data variation. To resolve this dilemma, shrinkage estimation procedures are proposed. By borrowing strength across chains and brands, these procedures reduce variability while providing flexibility that allows for separate elasticity estimates. Application of these procedures to a large data set yields not only more reasonable model estimates but also improved predictive power.
Blattberg, Robert. 1991. Seemingly Unrelated Equations: Shrinkage Estimation of Price and Promotional Elasticities. Journal of the American Statistical Association. 86(414): 304-315.