Measuring and Testing Advertising-Induced Rotation in the Demand Curve

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) q_i =a_i +b_iY+∑ⁿ c_ijp_j +∑ⁿ d_ijA_j +γ_ip_iA_i +e_iAge5+ f_iFafh
jj

nn

(3)    q_i = ai + b ^ln(^r / P *) ⁺ ∑ cij ln Ρj ⁺∑ dj ln Aj ⁺ Yiln Pi ln Ai ⁺ eiln Age 5⁺ f ln Fa^fh

jj

(4)    ln q_i= a_i + b_iln(K / P *) + ∑cj_j ln p_j + ∑d_ij ln A_j + γ_iln p_i ln Α_i + e_i ln Age 5 + fi ln Fafh

jj
nn

w_id lnq_i = a_i + b_idlnQ + ∑c_ijd ln p_j +∑d_ijdlnA_j +γ_id ln p_id ln A_i + e_id ln Age5
jj

+ f_id ln Fafh

nn

(6)    wi = ai ^{+ b}iln(^/P*) ⁺ ∑cij lnPj ⁺∑dj lnAj ⁺ YilnPi lnAi⁺ ei ln Age^{5 +} f lnFa^fh

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 p_iq_i is group
expenditure; P* denotes Stone’s geometric price index (lnP* = ∑_i⁴₌₁ w_i ln p_i); the

<<   <   5   6   7   8   9   10   11   >   >>