Table: Posterior Mean (
) and Standard Deviation (
) of the
Hyper-Distribution for the Cross-Price Elasticity Matrix using Average
Prices and prior k=.1
and covariance matrix 
. In this section we describe
the posterior mean for this hyper-distribution using a strong prior
(i.e., 
). We have selected this prior, since it is most
insightful to consider common store tendencies when we are willing to
express strong prior beliefs that they exist. Table 3 lists the price
elasticity matrix computed at the average prices. Along with the
central tendency is a measure of the standard deviation of the random
store-specific variation, i.e., the diagonal elements of the posterior
mean of 
. (Note 
gives the standard deviation of
the hyper-distribution and not the standard error of the estimates.)
For example Minute Maid 64 oz has an average own-price elasticity of
-2.84, with a standard deviation of .31 for store specific fluctuations.
Table: Posterior Mean () and Standard Deviation () of the
Hyper-Distribution for the Cross-Price Elasticity Matrix using Average
Prices and prior k=.1
The cross-price elasticity matrix is a 12 x 12 matrix, and summarizes information about substitution between products induced by price changes. The average of the own-price elasticities (diagonal elements) and cross-price elasticities (all off-diagonal elements) is -2.75 and .18 respectively. Also smaller sizes have larger own-price elasticities than larger sizes. Florida Gold is the most own-price sensitive brand with an own-price elasticity of -3.67. This is probably the result of the brand not engaging in a significant amount of national advertising, and not establishing a great deal of brand equity.
The mean and standard deviation of the constant, deal, lag, and feature coefficients in the hyper- distribution are provided in table 4. Since the dependent variable is the log of movement, the units of these parameters can be interpreted as percentage changes in movement. The large posterior standard deviations of the constants show that there is a great deal of diversity in the intercepts of the demand functions, which is the result of both preference and store size differences. The deal coefficients are typically small and dominated by the feature promotions. The lag coefficients are also very small, except Citrus Hill 96 ounce. The feature variables show strong promotional sensitivity, although the price discount given on feature must be added in to compute the full effect of feature promotions. The average feature coefficient is .60, with the most promotional sensitive brand being Florida Gold 64 ounce. Feature responses for national brands are largest followed by the store and then the premium tiers.