ETF2100-ETF6510 Introductofy eConometrics

This question consists of five parts, part (a) to (e).

Consider a model explaining the weekly sales, S measured in 100’s cans sold, of a popular brand of

canned tuna (the “Blue Sea” brand) as a function of its price (P = price in cents), the price of a competitor

(PC, also in cents), and advertising. To capture advertising, the model includes a dummy variable DISP = 1

if there is a store display but no newspaper ad during the week for Blue Sen brand, and 0 otherwise, and a

dummy variable DISPAD = 1 if there is a store display and newspaper ads during the week for the Blue

Sea brand, and 0 otherwise. The model is as follows:

In(S) = B, + $2? + BPC + BaDISP + BsDISPAD + e

(1)

The estimated log-linear model using data from 52 weeks is as follows (standard errors in parentheses):

In(S) = 8.9800 – 0.0375 P + 0.0115 PC + 0.4240 DISP + 1.4310 DISPAD

(0.6460)

(0.0058)

(0.0045)

(0.1050)

(2)

(0.1560)

(se)

R? = 0.84 N = 52

To answer this question you may find the following useful for F critical values. When F(a,b) is distributed random variable with numerator degree of freedom a and denominator degree of freedom

3

F

• Pr(F(2,16) ? 3.20) = 0.95
• Pr(F(2,17) ? 3.195) = 0.95
• Pr(F(2,48) < 3.191) = 0.95
• Pr(F(1,47) ? 4.047) = 0.95

(a) (4 Marks) Interpret the estimated coefficient of Blue Sea’s price and the estimated coefficient of competitor’s price. Are the signs of the estimated coefficients what you would expect?

(b) (4 Marks) Interpret the estimated coefficient of DISP using the “rough” calculation, and interpret the estimated coefficient of DISPAD using the “exact” calculation. Report your answers to 1 decimal place.

(c) (3 Marks) Find the point prediction (using the natural predictor) for the weekly sales when the price of Blue Sea brand is 80 cents and the price of a competitor brand is 70 cents, during the week in which there is a store display but no newspaper ads for the Blue Sea brand.

(d) (5 Marks) We want to test the joint significance of the two advertising variables using the F-test.

Write down the restricted model that you would need to estimate and all the steps of this hypothesis test (including the test statistic, its distribution under Ho, and the rejection region). If you are told that the calculated F-test statistic, F*, for this test is 42.0, what can you conclude about the significance of advertising using 5% significance level?

(e) Explain what would happen if we add a dummy variable that takes value 1 if there is neither a store display nor newspaper ad during the week and 0 otherwise to the model and attempt to estimate it.