Econometrics
Prepare your answers to the following questions as neatly as you can.
1. Based on quarterly observations for the period 1961-I through 1977_II the following demand function
for coffee has been estimated:
Where
Q = pounds of coffee consumed per capita
P = the relative price of coffee per pound at 1967 prices
I = per capita personal disposable income 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
Ln = natural log
And the numbers in brackets under the coefficients are “t” ratios.
a) How would you interpret the coefficients of P, I and P’?
b) Is the demand for coffee price elastic?
c) Are coffee and substitute or complementary products?
d) How would you interpret the coefficients of T?
e) What is the trend rate of growth or decline in coffee consumption?
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 dummy variables is statistically significant?
k) Is there a pronounced seasonal pattern in coffee consumption? If so, what accounts for it?
l) Which is the benchmark quarter in this example? Would the results change if we choose another
quarter as the base quarter?
m) The above model only introduces differential intercept dummies. What implicit assumption is made
here?
n) How would you rewrite the model to take into account differential slope dummies?
2. In a regression of weight on height involving 51 students, 36 males and 15 females, the following
regression results were obtained:
1. Weighti = -232.06 + 5.566 Heighti
t = (-5.20) (8.62)
2. Weighti = -122.96 + 23.82 Dumsexi + 3.74 Heighti
t = (-2.59) (4.01) (5.16)
3. Weighti = -107.95 + 2.01 Dumsexi + 3.51 Heighti + 0.326 Dumhti
t = (-1.23) (0.02) (2.61) (0.20)
Where weight is in pounds, height is in inches, and
Dumsex = 1 for males
= 0 otherwise
Dumht = the interactive or differential slope dummy
(i.e. Dumht = (Dumsex) × (Height)
a) Which regression would you chose, 1 or 2? Why?
b) If 2 is preferable but you chose 1, what kind of error are you making?
c) What does the Dumsex coefficient in 2 suggest?
d) In model 2 the differential intercept dummy is statistically significant whereas in model 3 it is statistically insignificant. What accounts for this change?
e) Between models 2 and 3, which one would you choose? Why?
f) In models 2 and 3 the coefficient of Height variable is about the same but the coefficient of the
dummy variable for sex changes dramatically. Any idea what is going on?
To answer questions d), e), and f), use the following correlation matrix.
Height Dumsex Dumht
Height 1 0.63 0.67
Dumsex 0.63 1 0.99
Dumht 0.67 0.99 1
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