The research department of a multinational has constructed a model for the company’s worldwide sales. The research team collected quarterly sales (in millions of dollars) for 15 years and estimated the following two models:

ΔS = 12.58 + 0.5 (Q1) + 0.2 (Q2) + 0.8 (Q4) + 0.25 Δ(X1) – 0.5 Δ(X2) + 0.3 Δ(X3)

R-squared 0.42

ΔS = 10.48 + 0.19 Δ(X1) – 0.55 Δ(X2) + 0.22 Δ(X3)

R-squared 0.15

Where
S: is dollar value of the company’s sales
Q1, Q2, Q4: are dummy variables identifying the corresponding quarter of the year
X1: is the amount of the company’s advertising expenditures
X2: is the dollar value of sales of the company’s main competitor in the market
X3: is the dollar value of the company’s investment in R&D four quarters ago

• Explain why a dummy variable for the third quarter of the year is not included in the model
• Would you say that the demand the company faces is characterized as seasonal?
• Based on the information you have, can you tell anything about the company’s sales across quarters in a typical year?
• Based on their preferred specification, the researchers spotted that the estimated coefficients of advertising and investment in R&D are very similar. Discuss a procedure that they could follow in order to test whether these variables have a (statistically) similar effect on the company’s sales.