Item Aggregates and Price Elasticity

Abstract

This study provides analytical results on the systematic relationship

between the elasticities obtained from item-aggregated data and those from

SKU level data. It is shown that the brand level (or any aggregate level)

elasticities are share-weighted averages of SKU elasticities. As SKUs in

a brand are substitutes each other in general, the own brand elasticities

would be smaller in magnitude than the own SKU elasticities and the crossbrand

elasticities will be larger than cross-SKU elasticities. It is also found

that when the SKU level demand function is given by a homogeneous

logit model with the latent utility being linear in price, the price sensitivity

parameter estimated from the brand level data should be the same as that

from SKU level data if the brand level model fits data well and the brand

prices are given by the weighted averages of SKU prices with the weights

being within-brand SKU shares.