Introduction to Econometrics
Worksheet week # 6
1. In 1986 Frederick Schut and Peter VanBergeijk published an article in which they
attempted to see if the pharmaceutical industry practiced international price discrimination
by estimation by estimating a model of the prices of pharmaceuticals in
a cross section of 32 countries. The authors felt that if price discrimination existed,
then the coeﬃcient of per capita income in a properly speciﬁed price equation would
be strongly positive. The reason they felt that the coeﬃcient of per capita income
would measure price discrimination went as follows: the higher the ability to pay,
the lower (in absolute value) the price elasticity of demand for pharmaceuticals and
the higher the price a price discriminator could charge. In addition, the authors expected
that prices would be higher if pharmaceutical patents were allowed and that
prices would be lower if price controls existed, if competition was encouraged, or if
the pharmaceutical market in a country was relatively large. Their estimates were:
Pi = 38.22+ 1.43
0.21)
GDPNi − 0.6
0.22)
CV Ni + 7.31
6.12)
PPi − 15.63
6.93)
DPCi − 11.38
7.16)
IPCi ,
where:
Pi . . . the pharmaceutical price level in the i-th country divided by that
of the United States
GDPNi . . . per capita domestic product in the i-th country divided by that of
the United States
CV Ni . . . per capita volume of consumption of pharmaceuticals in the i-th
country divided by that of the United States
PPi . . . a variable equal to 1 if patents for pharmaceutical products are
recognized in the i-th country and equal to 0 otherwise
DPCi . . . a variable equal to 1 if the i-th country applied strict price controls
and 0 otherwise
IPCi . . . a variable equal to 1 if the i-th country encouraged price competition
and 0 otherwise
(a) Develop and test appropriate hypotheses concerning the regression coeﬃcients
using the t-test at the 5 percent level. Do you think Schut and VanBergeijk
concluded that international price discrimination exists? Why or why not?
(b) Set up 90 percent conﬁdence intervals for each of the estimated slope coeﬃcients.
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2. Using data wage.csv estimate the model describing the impact of education and
experience on wage:
wage = β0 + β1educ + β2exper + β3exper2
+ ε
(a) Import data into Gretl from the csv ﬁle.
(b) Generate variable exper2
.
(c) Why we include this variable into the model?
(d) Estimate model with and without exper2
, compare R2
and R2
adj.
(e) Comment on the signs and signiﬁcance of β1, β2, and β3 in the model with
exper2
.
(f) Test the following hypotheses in the model with exper2
:
- test for the overall signiﬁcance of the regression;
- education has a signiﬁcant impact on wage;
- experience has a signiﬁcant impact on wage.
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3. Answer the following questions about a data on the sales prices of houses in the UK.
The variables in this study are:
HPRICEi Sales price for house i
ASSESSi Assessed price of house i
LOTSIZEi Size of lot (in m2) for house i
BDRMSi Number of bedrooms for house i
BATHi Number of bathrooms for house i
OCEANi Dummy variable indicating that house i is located within 1 mile of the ocean
LAKEi Dummy variable indicating that house i is located within 1 mile of the lake
URBANi Dummy variable indicating that house i is located in an area classiﬁed as urban
INTERCEPT Intercept in the model
SSE Sum of squared residuals
Table 3 lists coeﬃcients with standard errors in parentheses below the coeﬃcients.
Table 1: Results of regressions
Dependent variable HPRICEi, n = 238
(1) (2) (3) (4) (5) (6) (7)
ASSESSi 0.90 0.90 0.91 0.90 0.89 0.90
(0.03) (0.03) (0.03) (0.03) (0.03) (0.03)
LOTSIZEi 0.0035 0.00059 0.00059 0.00057 0.00058 0.00059 0.00060
(0.00002) (0.00002) (0.00002) (0.00002) (0.00002) (0.00002) (0.00002)
BDRMSi 11.5 9.74 7.65 8.74 10.43
(2.32) (3.11) (3.29) (3.54) (3.77)
BATHi 3.57 3.78
(2.24) (1.11)
OCEANi 15.6 14.32 16.76 15.32 14.56
(11.43) (5.21) (4.32) (4.98) (7.01)
URBANi 9.54 10.29 12.32
(8.99) (5.43) (5.22)
LAKEi 11.36 12.87 11.98
(4.28) (8.32) (6.43)
INTERCEPT 261.9 -38.91 -40.30 -43.21 - 36.54 -42.37 -38.44
(11.98) (6.78) (7.32) (6.99) (5.87) (7.22) (9.43)
SSE 145.69 142.99 136.66 134.54 135.38 135.22 136.54
R2
0.143 0.158882 0.196118 0.208588 0.203647 0.204588 0.196824
(a) Using the reported regressions, could you test whether the value of the house
near water was diﬀerent from the value of the house away from the water at the
5% level, controlling for assessed value, lot size and the number of bedrooms?
If so, perform the test. If not, explain what results you would need to do the
test.
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(b) Could you test whether the number of bathrooms changes the value of the house
controlling for the assessed value, lot size and the number of bedrooms at the
5% level? If so, perform the test. If not, explain what results you would need
to do the test.
(c) Can you test whether the assessed value and the number of bedrooms are jointly
signiﬁcant, controlling for the lot size? If so, perform the test at 5% level. If
not, explain what you would need to perform this test.
(d) Could you test whether all of the 7 listed variables (excluding the intercept) are
jointly signiﬁcant at the 5% level? Be sure to state any assumptions you make.
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