By J.P. Nelson, Michael R. Baye
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Extra resources for Advertising and Differentiated Products (Advances in Applied Microeconomics, Vol. 10)
However, they use aggregate annual data for advertising, which is the same across all cross-sectional units, and they do not report the method of deﬂation for advertising expenditures. Saffer (1997) measures advertising at the metropolitan level, but studies its effect on trafﬁc fatalities rather than consumption, and does not attempt to account for lag structures. Finally, neither Goel and Morey (1995) nor Saffer (1997) analyze the time-series properties of their data, which leaves open the question of whether key variables like consumption and advertising are nonstationary and/or cointegrated.
However, this possibility was rejected, since elasticities from the (singleequation) double-log model were similar to the system estimates. A ﬁnal reason for the insigniﬁcant own-advertising effect for milk may be related to data. Speciﬁcally, the model uses annual data, which could lead to bias since the data interval exceeds the purchase interval (Clarke, 1976). Quoting from Duffy (1990, p. 247), “annual data . . ” However, this critique would imply that none of the advertising effects is signiﬁcant, which clearly is not the case (Table 1, model (1h)).
Y1, y2, . . , yn) is cointegrated, then the data generating process takes the form of a vector error-correction (VEC) model written as p ⌬Yt = 0 + ⌸Yt Ϫ 1 + j ⌬Yt Ϫ j + t (3) j=1 where Yt ϵ (y1t, y2t, . . , ynt)Ј is an (n ϫ 1) vector, ⌬ is a ﬁrst-difference operator, 0 is an (n ϫ 1) vector of constants, j ( j = 1, 2, . , p) and ⌸ are (n ϫ n) matrices, and t is an (n ϫ 1) vector of white noise errors (Engle & Granger, 1987). Note that the ⌸ matrix shown in (3) can be expressed as ⌸ = ␣␤Ј, where ␤Ј is a collection of stacked cointegrating vectors representing the long-run relationships among the variables, and ␣ is a vector of short-run “speed of adjustment” coefﬁcients measuring the speed with which the system returns to equilibrium.