(8)
∂η ∂α
∂ ln A ∂ ln p ’
where η is (as before) expressed in absolute value. Thus, if advertising has no effect
on the own-price elasticity, then by (8) it must also be true that price has no effect on
the advertising elasticity. The latter inference contradicts an argument underlying
Chung and Kaiser’s (1999) analysis, namely that advertising would be more
effective at shifting the demand curve when prices are low than when prices are
high. As noted by Frisch (p. 180) equations such as (8) are invariant under a general
(non-linear) transformation of the utility function. Hence, the hypothesis based on
(8) that the advertising-price interaction effect should be non-zero is quite general.
Data and Estimation Procedures
The models F - J were estimated using U.S. annual time series data for the period
1970-2004. Variable definitions and some description statistics of the data are
reported in table 2. The price and quantity data were obtained from the U.S.
Department of Labor’s CPI Detailed Report (price of bottled water was obtained
from Beverage Marketing Corporation) and the U.S. Department of Agriculture’s
Food Disappearance Data, respectively; the advertising data were obtained from
private sources, chiefly Ad $ Summary published by Leading National Advertisers,
Inc. The price data were divided by the CPI for all items (1982-1984 = 100) to
remove the effects of inflation. A complete description of the data covering the
period 1970-1994, including sources, is available in Kinnucan et al. (2001, pp. 24-
28). Their data were updated in three aspects for use in this article: (i) ten more
years of data were collected to extend the data period to 2004, (ii) advertising
12
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