# Econometrics Questionnaire

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EC252 AUTUMN MID-TERM PRACTICE TEST, 2021
1. Answer each of the following questions based on the estimated relations given in each case:
(a) [6 marks] What is the predicted change in y given a 2 unit change in x?
y? = 3.2 ? 6.4 x
(b) [6 marks] What is the predicted change in y given a 1 percent change in x?
y? = ?9.1 + 81.2 log(x)
(c) [6 marks] What is the predicted percentage change in y given a 1 unit change in x?
= ?3.6 + 0.022 x
log(y)
(d) [7 marks] What is the predicted percentage change in y given a 5 percent change in x?
= 0.22 ? 2.1 log(x)
log(y)
2. You are given the multiple regression model
y = ?0 + ?1 x1 + ?2 x2 + ?3 x3 + ?4 x4 + u,
(1)
where u is an unobserved error term.
(a) [5 marks] Classify the following as observable or unobservable: y, x1 , x4 , ?0 , ?3 , x3 .
(b) [5 marks] Is the following statement true of false?
“Adding another variable to the right hand side of (1) can never increase the explanatory power of the model.”
(c) You are interested in testing the null hypothesis
H0 : ?1 = 3
against the alternative
H1 : ?1 > 3.
(i) [3 marks] What is the name of the test you would use to test this hypothesis?
(ii) [5 marks] Give the formula of the test statistic, for a sample of size n.
(iii) [7 marks] Define all components of the test statistic in part (ii) above.
3.
(i) [5 marks] Suppose that Y is distributed as t432 . Find P (Y ? 1.96).
(ii) [5 marks] If W is an estimator of some parameter ?, is it generally true that M SE(W ) =
var(W )? If not, then when is it true?
(b) Consider the general multiple regression model
y = ?0 + ?1 x1 + ?2 x2 + . . . + ?k xk + u,
(2)
where u is an unobserved error term. Suppose that var(u|x1 , x2 , . . . , xk ) = ? 2 .
(i) [5 marks] Name one method for obtaining estimates of the ?i , i = 0, . . . , k. No
explanations necessary.
(ii) [10 marks] You are given the following two estimates for ? 2 :
s21 =
SSR
SSR
and s22 =
,
n
n?k?1
where n denotes sample size and SSR denotes the sum of squared residuals. Which
one provides an unbiased estimate of ? 2 ? Explain briefly.
4.
(a) [6 marks] State the Classical Linear Model (CLM) assumptions. Remember, there are
six of them and we called them MLR.1 through MLR.6.
(b) You are investigating the effects of smoking on stamina (measured by the variable stam)
for a sample of sports-persons who are all smokers. You find the following ordinary least
squares (OLS) regression results in a published paper:
d = ?8.65 ? 3.54 cigs + 1.98 train
stam
(0.43)
(0.46)
(0.30)
n = 103, R2 = 0.162.
where cigs is daily cigarette consumption, and train is daily training time, n is the sample
size, and R2 is the coefficient of determination.
(i) [6 marks] Interpret the intercept estimate. If you think this is plausible, explain why,
and if you think this is not plausible, explain why not. Explanations can be very
brief and still earn full marks.
(ii) [10 marks] Test the null hypothesis that daily cigarette consumption has no impact
on stamina against the two-sided alternative that cigarette consumption does have
an impact at the 1% significance level. The critical value for the test can be found
from the table on the last page of the test paper.
(iii) [3 marks] What does the value of R2 tell us?
Percentage points of Students t-distribution with ? degrees of freedom
Area ? under right-hand tail
@
?@@
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
40
60
100
?
0.25
0.10
.05
.025
.01
.005
1.000
0.816
0.765
0.741
0.727
0.718
0.711
0.706
0.703
0.700
0.697
0.695
0.694
0.692
0.691
0.690
0.689
0.688
0.688
0.687
0.684
0.683
0.681
0.679
0.677
0.674
3.078
1.886
1.638
1.533
1.476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1.333
1.330
1.328
1.325
1.316
1.310
1.303
1.296
1.290
1.282
6.314
2.920
2.353
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.708
1.697
1.684
1.671
1.660
1.645
12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
2.120
2.110
2.101
2.093
2.086
2.060
2.042
2.021
2.000
1.984
1.960
31.821
6.965
4.541
3.747
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
2.583
2.567
2.552
2.539
2.528
2.485
2.457
2.423
2.390
2.364
2.326
63.657
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.787
2.750
2.704
2.660
2.626
2.576
EC252-5/7-AU/ZA
1
UNIVERSITY OF ESSEX
Autumn Mid-Term Test, November 2021
INTRODUCTION TO ECONOMETRIC METHODS
Time allowed: 2 hours. Please see your exam timetable or check on FASER for the deadline to
The time allocated for this assessment includes time for you to download this question paper
The times shown on your timetable are in UK time. Please check online for a conversion to your
local time if you will be undertaking your assessment outside the United Kingdom.
Candidates are permitted to use:
Calculator, Textbook(s), Lecture materials, Statistical table of their choice
This paper consists of 4 questions.
Candidates must answer all 4 questions.
All questions carry equal weight.
must be written in the document(s) uploaded to FASER.
If you write your answers by hand please use a black pen and make sure the photos and/or scans in your
If you think there is an error in the wording of any question or the instructions are not clear, contact
the module lecturer immediately via email: a.gupta@essex.ac.uk A response will be sent to your
Essex Email Account (click!).
If you have a technical problem with FASER, please go to the IT Helpdesk (click!) to find contact details
work.
It is forbidden to communicate with any other candidate in any way during this assessment. Your response must be your own work. Procedures are in place to detect plagiarism and collusion.
EC252-5/7-AU/ZA
2
1. Answer each of the following questions based on the estimated relations given in each case:
(a) [6 marks] What is the predicted change in y given a 1 unit change in x?
y? = 2.3 + 1.1 x.
(b) [6 marks] What is the predicted change in y given a 4 percent change in x?
y? = ?1 + 4 log(x).
(c) [6 marks] What is the predicted percentage change in y given a 1 unit change in x?
= 1.2 x.
log(y)
(d) [7 marks] What is the predicted percentage change in y given a 3 percent change in x?
= 3 + 1.9 log(x).
log(y)
2. You are given the multiple regression model
y = ?0 + ?1 x1 + ?2 x2 + ?3 x3 + u,
(1)
where u is an unobserved error term and you have a sample of size n.
(a) [5 marks] Is the following statement true or false?
“Adding another variable to the right hand side of (1) can never decrease the explanatory
power of the model.”