termdlnQ = ∑i4=1widlnqi is the Divisia volume index; Age5 is the proportion of the
U.S. population less than age five; Fafh is the ratio of food-away-from home
expenditures to food-at-home expenditures; time subscript for each variable is
suppressed here for ease of derivation of the rotation effect. For ease of discussion,
equations (2) - (6) are denoted as models A - E if the price-advertising interaction
terms are not included and models F - J otherwise. Following Kinnucan et al. (2001,
p. 5), these (conditional) models treat non-alcoholic beverages as a weakly separable
group since Moschini et al. (1994) found empirical evidence supporting the
commonly used separability assumption in modelling food demand.
Table 1 summarizes the own-price elasticities in absolute values,
advertising’s effects on the own-price elasticities which are derived in the
appendices A and B, and their decomposition into the rotation and shift effects. The
first column lists the own-price elasticities (ηi ,s).5 Taking the logarithmic partial
differential of ηi with respect to advertising expenditure Ai yields ∂ lnηi /∂ln Ai,
which is reported in the second column. Finally, by adding the shift effect (αii) to
the ∂ lnηi /∂ln Ai, we have the rotation effect (∂ln∆i /∂ln Ai) according to equation
(1).
Implications from table 1 are threefold. First, an econometric test of whether
advertising affects the own-price elasticity is a joint test of a curve rotation and shift
(Kinnucan and Zheng 2004), echoing our conclusion made in the beginning of the
second section that curve rotation is neither necessary (as shown in model C) nor
sufficient (as shown in model A) for advertising to alter the own-price elasticity.