ECON 4135
Additional seminar exercise for week 44
We are concerned with analysing the demand for beer in a sample of households. Our sample
reports observations on 5 variables: the quantity of beer demanded in litres (QB ) , the price of
beer (PB) , the price of other liquor ( PL) , a price index of the remaining goods and services
on the households’ budgets (PR) , and finally the households income (INC ). All prices are in
US$. Our small data set is taken from the file: table8-3.dat, which is supplementary material
to the book: Undergraduate Econometrics by R. Carter Hill, W. E. Griffiths, G.G. Judge, and
is listed below. To get the data into Stata, copy and paste.
We are not certain of what will be the appropriate specification of this demand so we will try
different forms. We start with the ln-ln functional form:
(1) ln(QBi )  0  1 ln( PBi )  2 ln( PLi )  3 ln( PRi )  4 ln( INCi )   i
where  i denotes the random disturbances.
Question A. How will you interpret the regression parameters in this demand function.
Use Stata to estimate this model on the supplied data.
Question B. Do you think the signs of the estimates are reasonable? Substantiate your
assertions. Explain how the numbers in the column P  t in the regression output from Stata
are calculated.
Standard consumer demand theory tells us that if prices and income increase by the same
proportion we should expect no change in the quantity demanded. The consumers are said to
have no money illusion.
Question C. Show that the assumption of no money illusion applied to the demand function
(1) implies the restriction:
(2) 1   2  3   4  0
Question D. Use results and information from your regression to test the hypothesis:
H 0 : 1   2  3   4  0
against
with significance level   0.05 .
H a : 1   2  3   4  0
Now we are told that the ln-ln functional form (1) has certain theoretical drawbacks. In
addition to (1) we thus wish to analyse two forms which are linear in the relative price and the
real income.
1
(3) QBi  1  2 ( PLi PBi )  3 ( PRi / PBi )  4 ( INCi PBi )  ui
(4) QBi  0 (1 PBi )  1  2 ( PLi / PBi )  3 ( PRi / PBi )   4 ( INCi / PBi )  vi
where u i and vi denote random disturbances.
Use Stata to estimate the regression equations (3) and (4).
Question E. Which of the two equations (3) or (4) do you think is appropriate for testing the
assumption of no money illusion? State the reason for your choice and explain how you
would test this hypothesis.
Question F. Assume that the number of household members ( Ni ) has been wrongly excluded
from the regressions (3) and (4). What could be meant by this? Choose one of these
regressions for further study, and explain formally how this misspecification affects the OLS
estimates of the  ' s when:
(i) N i is uncorrelated with the explanatory variables already used in the equation.
(ii) N i is correlated with the explanatory variables already used in the equation.
QB
81.7
56.9
64.1
65.4
64.1
58.1
61.7
65.3
57.8
63.5
65.9
48.3
55.6
47.9
57.0
51.6
54.2
51.7
55.9
52.1
52.5
44.3
57.7
51.6
53.8
50.0
46.3
46.8
51.7
49.9
PB
1.78
2.27
2.21
2.15
2.26
2.49
2.52
2.46
2.54
2.72
2.60
2.87
3.00
3.23
3.11
3.11
3.09
3.34
3.31
3.42
3.61
3.55
3.72
3.72
3.70
3.81
3.86
3.99
3.89
4.07
PL
6.95
7.32
6.96
7.18
7.46
7.47
7.88
7.88
7.97
7.96
8.09
8.24
7.96
8.34
8.10
8.43
8.72
8.87
8.82
8.59
8.83
8.86
8.97
9.13
8.98
9.25
9.33
9.47
9.49
9.52
PR
1.11
0.67
0.83
0.75
1.06
1.10
1.09
1.18
0.88
1.30
1.17
0.94
0.91
1.10
1.50
1.17
1.18
1.37
1.52
1.15
1.39
1.60
1.73
1.35
1.37
1.41
1.62
1.69
1.71
1.69
INC
25088
26561
25510
27158
27162
27583
28235
29413
28713
30000
30533
30373
31107
31126
32506
32408
33423
33904
34528
36019
34807
35943
37323
36682
38054
36707
38411
38823
38361
41593
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