Based on quarterly observations for the United States for the period 1961-1 through 1977-11, H. C. Huang, J. J. Siegfried, and F. Zardoshty14 estimated the following demand function for coffee. (The figures in parentheses are t values.)
In Qt = 1.2789 - 0.1647 In Pt + 0.5115 In It + 0.1483 In P't
t =(-2.14)(1.23)(0.55)
- 0.0089T - 0.0961 D1t- 0.1570D2t - 0.0097D3tR2 = 0.80
t = (- 3.36)(- 3.74)(- 6.03)(- 0.37)
where Q = pounds of coffee consumed per capita
P = the relative price of coffee per pound at 1967 prices
I = per capita PDI, in thousands of 1967 dollars
P' = the relative price of tea per quarter pound at 1967 prices
t = the time trend with t = 1 for 1961-I, to t = 66 for 1977-II
D1 = 1 for the first quarter
D2 = 1 for the second quarter
D3 = 1 for the third quarter
In = the natural log
a. How would you interpret the coefficients of P, I, and P'?
b. Is the demand for coffee price elastic?
c. Are coffee and tea substitute or complementary products?
d. How would you interpret the coefficient of t?
e. What is the trend rate of growth or decline in coffee consumption in the United States? If there is a decline in coffee consumption, what accounts for it?
f. What is the income elasticity of demand for coffee?
g. How would you test the hypothesis that the income elasticity of demand for coffee is not significantly different from 1?
h. What do the dummy variables represent in this case?
i. How do you interpret the dummies in this model?
j. Which of the dummies are statistically significant?
k. Is there a pronounced seasonal pattern in coffee consumption in the United States? If so, what accounts for it?
1. Which is the benchmark quarter in this example? Would the results change if we chose another quarter as the base quarter?
m. The preceding model only introduces the differential intercept dummies. What implicit assumption is made here?
n. Suppose someone contends that this model is misspecified because it assumes that the slopes of the various variables remain constant between quarters. How would you rewrite the model to take into account differential slope dummies?
o. If you had the data, how would you go about reformulating the demand function for coffee?