EC2030 UNIVERSITY OF WARWICK Summer Examinations 2017/18 Applied Econometrics Time Allowed: 3 hours, plus 15 minutes reading time during which notes may be made (on the question paper) BUT NO ANSWERS...

EC2030
UNIVERSITY OF WARWICK
Summer Examinations 2017/18
Applied Econometrics
Time Allowed: 3 hours, plus 15 minutes reading time during which notes may be made (on the
question paper) BUT NO ANSWERS MAY BE BEGUN.
Answer ALL questions in SECTION A (32 marks total) and ANY FOUR questions from
SECTION B (17 marks each). Answer Section A questions in one booklet and Section B
questions in a separate booklet.
Statistical Tables and a Formula Sheet are provided. Approved pocket calculators are allowed.
Read carefully the instructions on the answer book provided and make sure that the particulars
equired are entered on each answer book. If you answer more questions than are required and do
not indicate which answers should be ignored, we will mark the requisite number of answers in the
order in which they appear in the answer book(s): answers beyond that number will not be
considered.
Section A: Answer ALL Questions
1. Yi is the income of individual i. Y1i and Y0i represent the potential incomes of individual i if
the individual had (Ti = 1) and hadn’t (Ti = 0) entered an in-work training program,
espectively. State whether the following statements are true or false:
(a) Y1i is only observable if Ti = 1. (1 mark)
(b) Y1i − Y0i represents the individual causal effect of the program and can be observed if
individuals are randomised into and out of the program. (1 mark)
(c) E[Y1|T = 1]− E[Y0|T = 0] represents the average causal effect. (1 mark)
(d) The average selection effect is E[Y0|T = 1]− E[Y0|T = 0] and is zero in expectation if
individuals were randomised into the program. (1 mark)
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2. The following regression is estimated using OLS:
Ŷi = 0.03
(0.02)
+ 0.04
(0.01)
Xi (1)
We are interested in estimating the causal effect of X on Y .
(a) An important variable, T , has been omitted from the model. T is thought to be
co
elated with both X and Y . Explain how this is likely to be biasing the OLS
estimator of the causal effect. (2 marks)
(b) Unfortunately, there is no data on T . A further regression is run:
X̂i = 0.02
(0.01)
+ 0.05
(0.01)
Zi (2)
Explain under what conditions Z will be useful as an instrument for X. (2 marks)
3. The mean and variance of weekly wages are XXXXXXXXXXand 150.21, respectively, for a random
sample of 19 male nurses. The mean and variance of weekly wages are XXXXXXXXXXand 136.98,
espectively, for a random sample of 18 female nurses. Stating any assumptions you make,
answer the following:
(a) Test for equality of variances in male and female wages. (1 mark)
(b) Test if mean wages of male and female nurses are equal against the two-sided
alternative. (2 marks)
(c) Calculate and intepret the p-value of the test in part (b). (1 mark)
4. Let X ∼ N(20, 100), Y ∼ N(30, 25) and W = 10 + 2X + Y . Further, suppose
cov(X, Y ) = 9.5. Answer the following:
(a) What is the probability that X ≤ 10? (1 mark)
(b) What is the probability that Y ≥ 30? (1 mark)
(c) What is the expected value and variance of W . (1 mark)
(d) What is the probability that 45 ≤ W ≤ 81? (1 mark)
5. 25 households randomly entered into a microcredit program. Their mean income was 100.21
with a standard deviation of XXXXXXXXXXFor an independent random sample of 22 households not
entered into the microcredit program mean income was 90.21 with a standard deviation of
11.21.
2
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(a) Suppose the true effect of the program on mean income is 5.3. Choosing a 10%
significance level, what is the probability of rejecting a null of no effect against a
two-sided alternative. (2 marks)
(b) On a diagram represent whether your calculated probability in (a) would
increase/decrease or remain the same if the true impact of the program was a reduction
of 2.5 and not XXXXXXXXXXmarks)
6. In Fe
uary 2015, State A in the US made it illegal to own a gun. In the nea
y state, State
B, gun ownership was legal. Tim suggests using a crime survey to estimate the impact of the
law change on number of gun crimes. Let Gpst represent the number of gun crime a
ests in
police station p, state s at time t where t = 0 if the a
ests took place between March 2014
and January 2015 and t = 1 if the crimes took place between March 2015 and Jan 2016.
(a) Without controlling for any other factors, specify a regression model that would allow
you to test whether the law impacted the number of gun crimes. Interpret each of the
coefficients in your regression model. (2 marks)
(b) In order for your regression to provide strong evidence of a causal effect of the law what
assumption needs to hold? Suggest one way you could provide supporting evidence fo
the assumption. (2 marks)
7. The following OLS regression is estimated on a random sample of 1201 individuals from the
UK population:
ln(wagei) = 5.198
(0.122)
XXXXXXXXXX
(0.0073)
schooli XXXXXXXXXX
(0.0032)
experi XXXXXXXXXX
(0.0147)
ZIQi (3)
Where ln(wagei) is the natural log of wages; schooli is years of school; experi is years of
experience and ZIQi is standardised IQ score (that is, mean 0 and variance 1).
(a) At the 10% significance level test the hypothesis that the wage return to an additional
year of school is equal to half the wage return of a one standard deviation increase in IQ
score. Note cov(bschool, bZIQ) = − XXXXXXXXXXmarks)
(b) Calculate the p-value of the test in part (a) and illustrate on a diagram. (1 mark)
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8. The following regression is estimated via OLS on a random sample of 254 individuals:
Ĥi = 150.12
(4.53)
− 3.51
(1.23)
agei + 0.03
(0.1)
age2i
Where Hi is happiness (between 0 and 100) and agei and age2i are the age and age squared
of individual i. Standard e
ors are given in parentheses.
(a) Illustrate the regression with a diagram. (2 marks)
(b) Let Mi = 1 if an individual is male and Mi = 0 otherwise. Outline how would you test
for a difference in the relationship between happiness and age between males and
females. (2 marks)
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Section B: Answer FOUR Questions
Please use a separate booklet
9. Si are the observed end of second year test scores for individual i. Further, let S1i and S0i
epresent the potential test score of individual i if the individual had (T = 1) and hadn’t
(T = 0) attended support classes during the year, respectively. Answer the following
questions:
(a) What does S1i − S0i represent? (2 marks)
(b) What does E[S1|T = 1]− E[S0|T = 0] represent? (2 marks)
(c) What does E[S1|T = 1]− E[S0|T = 1] represent? (2 marks)
(d) When could you reasonably expect
E[S1|T = 1]− E[S0|T = 0] = E[S1|T = 1]− E[S0|T = 1]? (3 marks)
(e) Suppose a random sample of 26 students was taken. 12 students had taken support
classes and scored 72.11 on average with a standard deviation of XXXXXXXXXXstudents had
not taken support classes and scored 68.11 on average with a standard deviation of
4.12. Test for a difference in mean test scores between those who took and did not go
to support classes. State any assumptions you are making. (4 marks)
(f) Did the support classes increase the average test score marks? Briefly explain you
answer. (4 marks)
10. The following regression is estimated using OLS on a random sample of 524 individuals:
̂SPORT i = 10.51
(4.32)
+ 7.6
(2.31)
AGEi − 0.06
(0.01)
AGE2i XXXXXXXXXXMi XXXXXXXXXXUGi (4)
SPORTi is number of minutes of sport activities per week individual i does; AGEi and
AGE2i are the individuals age and age squared; Mi is = 1 if male and = 0 otherwise; UGi is
= 1 if they have an undergraduate degree and = 0 otherwise. The R2 = 0.32 and
RSS = 13100.
(a) Excluding the intercept, interpret the coefficients in the model. (3 marks)
(b) Test the hypothesis that age impacts the amount of sport if the R2 of the model
estimated without the age variables is XXXXXXXXXXmarks)
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(Question 10 continued overleaf)
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(c) Test the hypothesis that the impact of UG and male on sport is the same. Assume all
the OLS estimators are pairwise unco
elated. (3 marks)
(d) Estimating the model for 225 individuals who had an UG degree gave an RSS = 11202,
while for those without an UG degree the RSS = 9000. Test for a structural
eak
etween individuals with and without a degree. (4 marks)
(e) Suppose the true effect of male on minutes of sport is 10. Calculate the power of
ejecting a null hypothesis of no effect, at the 5% level, against the two sided
alternative. (4 marks)
11. A university is trailing online courses and is interested in understanding teacher evaluations.
Ei ∈ [0, 100] represents the evaluation of teacher i where 0 means completely unsatisfied and
100 is completely satisfied. All course material is online: there are no lectures or classes and
the only co
espondence is via forums. The following regression was estimated on an
independent random sample of 232 tutors.
Ei = 65.51
(4.32)
+ 10.11
(2.32)
Mi + 6.21
(3.32)
EXPi + 5.40
(1.32)
Y R2i − 10.51
(3.32)
Y R3i (5)
Mi = 1 if the teacher is male and zero otherwise. EXPi = 1 if the teacher has 2 or more
years experience at university level teaching and zero otherwise; Y R2i = 1 for year 2 modules
and zero otherwise; Y R3i = 1 for year 3 modules and zero otherwise.
(a) Interpret the intercept in the above model. (2 marks)
(b) The courses are three years in length, why is there no dummy variable for year 1
modules? (2 marks)
(c) Draw a graphic to represent the relationship between evaluation and year of study fo
males with less than two years of experience. Now draw the same graphic for females
with less than two years experience. (3 marks)
(d) Outline how you would use an F-test to test H0 : βY R3 = −3βY R2. (3 marks)
(e) The university was surprised to see the positive and significant sign on the male
coefficient. The regression was re-estimated with a new variable: Qi = 1 if the module
was quantitative and zero otherwise. The coefficients on Q and M in the new regression
are 5.12 and 5.06, respectively. What does this imply about the relationship between
male and quantitative models? (3 marks)
The coefficient on male was still statistically significant.