Question

2. Huang and others (1980) estimated the following demand for coffee: In 0, -1.279-0.1647h P+0.5115h I, +0.1483n P,-0.0089T, -0.096D,-0.157D, +0.0097D, (-2.14) (1.23) (0.55) (3.36) (-3.34) (-6.03) (-0.37) Where: Q- pounds of coffee P price of coffee per pound in 1967 prices IPer capita income in thousands of 1967 dollars P' Price of tea in 1967 prices T time variable 1961-quarter 1 through 1977-quarter 4 D1 Dummy variable -1 for the first quarter D2- Dummy variable -1 for the second quarter Ds- Dummy variable -1 for the third quarter In natural log. a. Interpret each of the coefficients and statistical significance of P, I, P' and T. b. would you conclude that the Demand for coffee is price elastic? c. Are coffee and tea substitute or complementary goods? d. Among the dummy variables, which one is the reference category? What does that mean? e. Interpret each of the dummy coefficients and their statistical significance.

Answer 1

a. Assuming that the data set is large enough, we'll assume 'infinite' degrees of freedom, and a t-distribution with infinite degrees of freedom is a normal distribution.

So, we'll consider an independent variable to be significant at 5% level of significance if |t- value| > 1.96.

Significance:
The following factors seem to be statistically significant, because the |t-value| > 1.96:
1. P = price of coffee
2. T = Time variable

Interpretations:
1. ln(P), coefficient = -.0.1647, so there is an negative relationship between Q and ln(P)
2. ln(I), coefficient = 0.5115 , there is a positive relationship between Q and ln(I), although this seems to be insignificant.
3. ln(P'), coefficient = 0.1483, indicates that tea and coffee are substitutes, relationship seems to be insignificant.
4. ln(T), coefficient = -.0089, indicates an inverse relationship


b.

Price elasticity is less than 1 in magnitude. So, coffee is price inelastic.

c. Substitute goods, demand for coffee is positively related to price of tea.

d. The reference category pertains to 'quarter-4'

e. The |t-value| > 1.96 for quarter 1 and quarter 2. This means that the sales in quarter 3 is very similar to that in quarter 4.

The coefficient for quarter 1 and 2 are negative, which indicates that the sales in quarter 1 and 2 are much lower than that in quarter 4.  The sales in quarter 3 is very similar to that in quarter 4.

The order is:

Quarter 3 >= Quarter 4 > Quarter 1 > Quarter 2

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