ETC2410 Lecture Notes - F-Distribution, Unit Root, Bias Of An Estimator
Marking Guide
ETC2410/ETW2410/ETS2410/ETC3440
Introductory Econometrics
S2, 2017
Question 1, Part A: All students should attempt this part
(1.A.1) d
(1.A.2) d
(1.A.3) b
(1.A.4) e
(1.A.5) d
(1.A.6) a
(1.A.7) c
(1.A.8) b
(1.A.9) d
(1.A.10) c
Question 1, Part B: For ETC2410, ETW2410 and ETS2410 students only
(1.B.1) For people with the same IQ (or keeping IQ constant), an extra year of education
increases the predicted wage by 4%. [If conditioning on IQ is not there, 0 marks](1
mark)
(1.B.2) The second equation, because it removes the e¤ect of IQ. In the …rst equation, educ
not only represents years of education, but also acts as a proxy for relevant factors
that are correlated with education and can a¤ect wages, such as intelligence. The
second equation explicitly controls for IQ, so the coe¢cient of educ is closer to
what we are interested in. [If they only say the second equation without any
explanation, only half a mark. No need for them to include "omitted variable
bias" in their answer for full marks. As long as they talk about the importance of
controlling for the e¤ect of ability or intelligence, give full marks] (2 marks)
1
find more resources at oneclass.com
find more resources at oneclass.com
(1.B.3) The …rst equation. The …rst equation estimates the conditional expectation of
log(wage) conditional on education only, so when the only information we have is
education, the …rst equation is the one to use for prediction. [1 mark] Prediction:
\
log(wage) = 5:97+0:0612 = 6:69 )[wage =e6:69 = 804:32 dollars per week [1 mark]
Half a mark o¤ if the prediction is left as log(wage).
Question 1, Part C: For ETC3440 students only
The following two regressions are estimated using the …nal exam scores (final which is
a score out of 100), number of tutorials attended (tute_attend which is out of 10) and
the mid-term scores (midterm which is a score out of 100) for a random sample of 449
students. \
final = 40:09
(3:50) + 2:18
(0:39)tute_attend with ^= 14:22 (1)
\
final = 17:29
(3:50) + 1:50
(0:34)tute_attend + 0:44
(0:04)midterm with ^= 12:21 (2)
In the above equations, the numbers in parentheses below the parameter estimates are
standard errors and ^is the standard error of the regression.
(1.C.1)
final = 40:09 + 2:18 8 = 57:53
(1 mark)
(1.C.2) The second equation because it controls for academic ability by conditioning on
the midterm score. In the …rst equation tute_attend not only measures the e¤ect
of tutorial attendance but it also acts as a proxy for other students’ characteristics
that are correlated with tute attendence and may a¤ect the …nal score.[If they
only say the second equation without any explanation, only half a mark. No need
for them to include "omitted variable bias" in their answer for full marks. As
long as they talk about the importance of controlling for the e¤ect of ability or
intelligence, give full marks]
(2 marks)
(1.C.3)
\
final = 17:29 + 1:510 + 0:44 60 = 58:69
95% con…dence interval : (58:69 1:98 12:21;58:69 + 1:98 12:21)
= (34:514;82:866)
1 mark for the prediction and 1 mark for the con…dence interval. It is OK if they
use 1.96 instead of 1.98 to form the con…dence interval. The actual …gures on the
last line do not matter, if all else is correct, then full mark.
(2 marks)
Page 2of 9
find more resources at oneclass.com
find more resources at oneclass.com
Question 2 (15 marks)
2.a.(i) (2 marks)
We have; X0^u =X0yX^
=01 mark
And hence; X0y=X0X^
and ^
= (X0X)1X0y1 mark
2.a.(ii) (3 marks)
For an unbiased estimator we want: Eh^
i=. i.e. the expectation of the
estimated value to be equal to the actual value. 1 mark
Eh^
jXi= E h(X0X)1X0yjXi= E h(X0X)1X0(X+u)jXi1 mark
Eh^
jXi=+ (X0X)1X0E [ujX] = + (X0X)1X00=. Since the expec-
tation conditional on Xdoes not depend on X, the unconditional expection must
be . [OK if they have only shown that Eh^
jXi=] 1 mark
2.b.(i) (2 marks)
The coe¢cient on GV REM indicates that residing in a very remote area leads to
a reading score which is on average 28.13 points lower than for a student who lives
in a Metropolitan area. 1 mark
The coe¢cients imply that as the degree of remoteness increases (from Metropol-
itan to Provincial to Remote to Very Remote) the reading score falls. 0.5 marks
However, as the sample size is small (22 observations) the standard errors of the
coe¢cients are large so these di¤erences do not appear statistically signi…cant.
0.5 mark
2.b.(ii) (3 marks)
H0:ST = 0
H1:ST <01 mark
The test statistic is ST =se(ST ) = 5:68=0:89 = 6:38 0.5 marks
The test statistic follows a t distribution with nk1 = 22 51 = 16 degrees
of freedom. The signi…cance level is = 0:05 and the test is one-sided. Hence the
critical value is: t0:05;16 =1:746. As the test statistic is smaller than the critical
value, we reject the null hypothesis. We …nd that there is evidence that a high
student-teacher ratio reduces students’ reading scores. [Some students may say
that the critical value is 1:746 or even don’t mention the word “critical value” and
just read the number 1:746 from the table and use it. As long as it is clear that
they are using it appropriately (e.g. they say that they reject the null because
the test statistic is negative and its absolute value is larger than 1:746), then they
should get full mark.] 1.5 mark
Page 3of 9
find more resources at oneclass.com
find more resources at oneclass.com
