Econ2280 Introductory Econometrics
2018 Semester 1
Tutorial Problem Set 5
1
Question 1 (T-test in STATA)
Consider the multiple linear regression of Y on X1 and X2 , and this regression satis…es the classical linear model assumptions (CLM assumptions). We
would like to perform the T-tests based on the STATA output based on the
below data set.
Observation number
1
2
3
4
5
6
7
8
X1
4
4
5
7
6
5
3
6
X2
0:5
0:6
0:8
0:75
0:4
0:35
0:5
0:5
Y
15
17
20
22
18
17
13
20
1. Test whether X1 and X2 are individually statistically signi…cant at 5%
signi…cance level.
2. Test whether X2 is statistically signi…cant at 10% signi…cant level.
3. Test H0 :
1
= 4 against H1 :
1
< 4 at 5% signi…cance level, where
is the coe¢ cient of X1 in the MLR model.
4. Test H0 :
1
1
1
= 3 against H1 :
1
> 3 at 5% signi…cance level, where
is the coe¢ cient of X1 in the MLR model.
1
5. Test H0 :
2
2
2
= 10 against H1 :
2
6= 10 at 5% signi…cance level, where
is the coe¢ cient of X2 in the MLR model.
Question 2 (Hypothesis testing in the application of economics)
Consider the Cobb-Douglas production function in a model form,
Yt = At Kt Lt "t
where "t is the error term in this multiplicative model,At ; Kt ; Lt and Yt are
the technology level, capital level, level of labor, GDP in year t:
1. Convert the model into a multiple linear regression model.
2. It is known that the model in part (a) satis…es the classical linear
model assumptions. Also, it is famously known that under
it is displaying the constant returns to scale; under
+
+
= 1,
> 1, it is
displaying the increasing returns to scale. Propose the method to test
whether the economy is undergoing the increasing returns to scale,
with the steps you would like to proceed.
3
Question 3 (Model with interaction term and
quadratic term)
Suppose the model below satis…es classical linear model assumptions:
log (wage) =
0
+
1 exper
+
2 educ
+
3 exper
educ + u;
where wage, exper and eudc refer to annual wage, years of experience and
years of education, respectively.
1. Interpret all coe¢ cients of the independent variables used in the model.
2
2. Do you think the interpretations in part (1) are useful economically?
Explain individually.
3. Propose two possible amendments in specifying the model that gives
a more useful and meaningful interpretation for all coe¢ cients of the
independent variables.
4. Interpret the coe¢ cients of the independent variables in the two models speci…ed in (3).
If we re…ne the model as following,
log (wage) =
0
+
1 exper
+
2 educ
+
3 exper
educ +
4 educ
2
+ u;
5 Interpret all coe¢ cients of the independent variables used in the model.
6 Do you think the interpretation of
Explain.
3
4
in (5) is useful economically?