Empirically, a rotation in the demand curve can be determined by estimating
a demand equation (or system of equations) with price and advertising entered as
interaction terms and testing whether the interaction terms are significant.
Following Cramer (1973) five widely-used demand models - a linear model, a semi-
log model, a compensated double-log model motivated by Alston, Chalfant, and
Piggott (2002), a Rotterdam model, and a linear approximate almost ideal demand
system (AIDS) - are specified to test whether advertising rotates demand curves as
follows:
(2) qi =ai +biY+∑n cijpj +∑n dijAj +γipiAi +eiAge5+ fiFafh
jj
nn
(3) qi = ai + b ln(r / P *) + ∑ cij ln Ρj +∑ dj ln Aj + Yiln Pi ln Ai + eiln Age 5+ f ln Fafh
jj
(4) ln qi= ai + biln(K / P *) + ∑cjj ln pj + ∑dij ln Aj + γiln pi ln Αi + ei ln Age 5 + fi ln Fafh
jj
nn
(5)
wid lnqi = ai + bidlnQ + ∑cijd ln pj +∑dijdlnAj +γid ln pid ln Ai + eid ln Age5
jj
+ fid ln Fafh
nn
(6) wi = ai + biln(^/P*) + ∑cij lnPj +∑dj lnAj + YilnPi lnAi+ ei ln Age5 + f lnFafh
jj
where i indexes the four beverages (n = 4) in the non-alcoholic group (fluid milk,
juices, soft drinks (including carbonated soft drinks and bottled water), and coffee
and tea; pi, qi, wi, and Ai, are the price, demand, budget share, and advertising for
group i; d ln denotes the logarithmic first-difference operator; Y = ∑i4=1 piqi is group
expenditure; P* denotes Stone’s geometric price index (lnP* = ∑i4=1 wi ln pi); the
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