Semester One Final Examinations, 2019 ECON7310 Elements of Econometrics
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This exam paper must not be removed from the venue

School of Economics
EXAMINATION
Semester One Final Examinations, 2019
ECON7310 Elements of Econometrics

This paper is for St Lucia Campus students.
Examination Duration: 120 minutes
Reading Time: 10 minutes

Exam Conditions:
This is a Central Examination
This is a Closed Book Examination - specified materials permitted
During reading time - write only on the rough paper provided
This examination paper will be released to the Library

Materials Permitted In The Exam Venue:
(No electronic aids are permitted e.g. laptops, phones)
An unmarked Bilingual dictionary is permitted
Calculators - Casio FX82 series or UQ approved (labelled)

Materials To Be Supplied To Students:
1 x 14 Page Answer Booklet
1 x Multiple Choice Answer Sheet

Instructions To Students:
Part A: Answer all questions on the Multiple Choice Answer Sheet
Part B: Answer all questions in the Answer Booklet
Formulas and F Table are on page 10
Additional exam materials (e.g., answer booklets, rough paper) will be provided
upon request.
Total Questions: 17
Total Marks: 50
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Semester One Final Examinations, 2019 ECON7310 Elements of Econometrics
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Semester One Final Examinations, 2019 ECON7310 Elements of Econometrics
Part A:
Answer ALL Questions on the Multiple Choice Answer Sheet.
Each Question has only ONE correct answer and is worth 2 marks (30 Marks
Total):
1. In the multiple regression model, the t-statistic for testing that the slope is significantly
di↵erent from zero is calculated:
(a) by dividing the estimate by its standard error.
(b) from the square root of the F-statistic for significance of the model.
(c) by multiplying the p-value by 1.96.
(d) using the adjusted R2 and the confidence interval.
2. The OLS estimators of the coecients in multiple regression will have omitted variable
bias:
(a) only if an omitted determinant of Yi is a continuous variable.
(b) if an omitted variable is correlated with at least one of the regressors, even though
it is not a determinant of the dependent variable.
(c) only if the omitted variable is not normally distributed.
(d) if an omitted determinant of Yi is correlated with at least one of the regressors.
3. In the regression model Yi = 0 + 1Xi + 2Di + 3(Xi ⇥ Di) + ui, where X is a
continuous variable and D is a binary variable, 3:
(a) indicates the slope of the regression when D = 1.
(b) has a standard error that is not normally distributed even in large samples since
D is not a normally distributed variable.
(c) indicates the di↵erence in the slopes of the two regressions.
(d) has no meaning since (Xi ⇥Di) = 0 when Di = 0.
4. Assume that you had estimated the following quadratic regression model \TestScore =
607.3+ 3.85Income 0.0423Income2. If Income increased from 10 to 11 ($10,000 to
$11,000), then the predicted e↵ect on TestScores would be:
(a) 3.85.
(b) 3.85-0.0423.
(c) Cannot be calculated because the function is non-linear.
(d) 2.96.
Examination continues on the next page.
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Semester One Final Examinations, 2019 ECON7310 Elements of Econometrics
5. A study based on OLS regressions is internally valid if:
(a) the errors are homoskedastic, and there are no more than two binary variables
present among the regressors.
(b) you use a two-sided alternative hypothesis, and standard errors are calculated
using the heteroskedasticity-robust formula.
(c) weighted least squares produces similar results, and the t-statistic is normally
distributed in large samples.
(d) the OLS estimator is unbiased and consistent, and the standard errors are com-
puted in a way that makes confidence intervals have the desired confidence level.
6. The analysis is externally valid if:
(a) the statistical inferences about causal e↵ects are valid for the population being
studied.
(b) the study has passed a double blind refereeing process for a journal.
(c) its inferences and conclusions can be generalized from the population and setting
studied to other populations and settings.
(d) some committee outside the author’s department has validated the findings.
7. The main advantage of using panel data over cross sectional data is that it:
(a) gives you more observations.
(b) allows you to analyze behavior across time but not across entities.
(c) allows you to control for some types of omitted variables without actually ob-
serving them.
(d) allows you to look up critical values in the standard normal distribution.
8. In panel data, the regression error:
(a) is likely to be correlated over time within an entity
(b) should be calculated taking into account heteroskedasticity but not autocorrela-
tion
(c) only exists for the case of T > 2
(d) fits all of the three descriptions above
Examination continues on the next page.
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Semester One Final Examinations, 2019 ECON7310 Elements of Econometrics
9. In the binary dependent variable model, a predicted value of 0.6 means that
(a) the most likely value the dependent variable will take on is 60 percent.
(b) given the values for the explanatory variables, there is a 60 percent probability
that the dependent variable will equal one.
(c) the model makes little sense, since the dependent variable can only be 0 or 1.
(d) given the values for the explanatory variables, there is a 40 percent probability
that the dependent variable will equal one.
10. When having a choice of which estimator to use with a binary dependent variable, we
use:
(a) probit or logit depending on which method is easiest to use in the software
package at hand.
(b) probit for extreme values of X and the linear probability model for values in
between.
(c) OLS (linear probability model) since it is easier to interpret.
(d) the estimation method which results in estimates closest to your prior expecta-
tions.
11. When estimating probit and logit models,
(a) the t-statistic should still be used for testing a single restriction.
(b) you cannot have binary variables as explanatory variables as well.
(c) F-statistics should not be used, since the models are nonlinear.
(d) it is no longer true that the R¯2 < R2.
12. The rule-of-thumb for checking for weak instruments is as follows: for the case of a
single endogenous regressor:
(a) a first stage F must be statistically significant to indicate a strong instrument.
(b) a first stage F > 1.96 indicates that the instruments are weak.
(c) the t-statistic on each of the instruments must exceed at least 1.64.
(d) a first stage F < 10 indicates that the instruments are weak.
Examination continues on the next page.
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Semester One Final Examinations, 2019 ECON7310 Elements of Econometrics
13. The two conditions for a valid instrument are:
(a) corr(Zi, Xi) = 0 and corr(Zi, ui) 6= 0.
(b) corr(Zi, Xi) = 0 and corr(Zi, ui) = 0.
(c) corr(Zi, Xi) 6= 0 and corr(Zi, ui) = 0.
(d) corr(Zi, Xi) 6= 0 and corr(Zi, ui) 6= 0.
14. The following are reasons for studying randomized controlled experiment in an econo-
metrics course, with the exception of:
(a) at a conceptual level, the notion of an ideal randomized controlled experiment
provides a benchmark against which to judge estimates of causal e↵ects in prac-
tice.
(b) when experiments are actually conducted, their results can be very influential,
so it is important to understand the limitations and threats to validity of actual
experiments as well as their strength.
(c) randomized controlled experiments in economics are common.
(d) external circumstances sometimes produce what appears to be randomization.
15. If the causal e↵ect is di↵erent for di↵erent people, then the population regression
equation for a binary treatment variable Xi, can be written as:
(a) Yi = 0 + 1Xi + ui.
(b) Yi = 0 + 1iXi + ui.
(c) Yi = 0i + 1iXi + ui.
(d) Yi = 0 + 1Gi + 2Dt + ui.
Examination continues on the next page.
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Semester One Final Examinations, 2019 ECON7310 Elements of Econometrics
Part B:
Short answer questions – answer all questions in the Answer Booklet.
Marks are as indicated. Total value: 20 marks.
Formulas and F table are on page 10.
1. The cost of attending your college has once again gone up. Although you have been
told that education is investment in human capital, which carries a return of roughly
10% a year, you (and your parents) are not pleased. One of the administrators at your
university/college does not make the situation better by telling you that you pay more
because the reputation of your institution is better than that of others. To investigate
this hypothesis, you collect data randomly for 100 national universities and liberal
arts colleges from the 2000-2001 U.S. News and World Report annual rankings. Next
you perform the following regression,
where Cost is Tuition, Fees, Room and Board in dollars, Reputation is the index
used in U.S. News and World Report (based on a survey of university presidents
and chief academic ocers), which ranges from 1 (“marginal”) to 5 (“distinguished”),
Size is the number of undergraduate students, and Dpriv, Dlibart, and Dreligion are
binary variables indicating whether the institution is private, a liberal arts college, and
has a religious aliation. The numbers in parentheses are heteroskedasticity-robust
standard errors.
(a) Indicate whether or not the coecients are significantly di↵erent from zero.
(2 marks)
(b) For the null hypothesis that the coecient on Size is equal to zero, you find that
the relevant p-value is 0.062. Based on this, should you eliminate the variable
from the regression? Why or why not? (2 marks)
(c) You want to test simultaneously the hypotheses that Size = 0 and Dilbert = 0.
Your regression package returns the F -statistic of 1.23. Explain if you would
reject the null hypothesis? (2 marks)
(d) In order to have a significant e↵ect of Size, you re-compute the standard errors
by forcing the assumption of homoskedasticity onto your estimation. The results
are as follows:
Examination continues on the next page.
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Semester One Final Examinations, 2019 ECON7310 Elements of Econometrics
Calculate the t-statistic on the Size coecient and perform the hypothesis test
that its coecient is zero (2 marks). Explain if this test is reliable. (2 marks)
Examination continues on the next page.
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Semester One Final Examinations, 2019 ECON7310 Elements of Econometrics
2. A researcher investigating the determinants of crime in the United Kingdom has data
for 42 police regions over 22 years. She estimates by OLS the following regression,
ln(cmrt)it = ↵i + t + 1unrtmit + 2proythit + 3 ln(pp)it + uit
for i = 1, 2, . . . , 42 and t = 1, 2, . . . , 22 (but excluding 1), where cmrt is the crime
rate per head of population, unrtm is the unemployment rate of males, proyth is the
proportion of youths, pp is the probability of punishment measured as (number of
convictions)/(number of crimes reported). ↵ and are area and year fixed e↵ects,
respectively, where ↵i equals one for area i and is zero otherwise for all i, and t is
one in year t and zero for all other years for t = 2, . . . , 22. Again, 1 is not included.
(a) Explain unobservable factors that the terms ↵ and are likely to pick up in this
context (2 marks) and discuss the advantages of using panel data for this type
of investigation. (2 marks)
(b) Estimation by OLS using heteroskedasticity and autocorrelation-consistent stan-
dard errors results in the following output, where the coecients of the fixed
e↵ects are not reported:
What is the e↵ect of a ten percent increase in the probability of punishment?
Explain your answer. (2 marks)
(c) You want to test the null hypothesis that the area fixed e↵ects are all irrelevant
at 1% level. You find that the F-statistic is 135.28 for this hypothesis testing.
What is the relevant degrees of freedom you should use here? (2 marks)
Explain, completely and concisely, whether or not you reject the null. (2 marks)
End of Examination
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Semester One Final Examinations, 2019 ECON7310 Elements of Econometrics
Some Formulas:
• Pr(|Z| > 1.645) = 0.1, Pr(|Z| > 1.96) = 0.05, and Pr(|Z| > 2.576) = 0.01 for
Z ⇠ N (0, 1).
• SER =
q
1
nk1
Pn
i=1 bu2i and RMSE =q 1nPni=1 bu2i
• R2 = ESSTSS = 1 SSRTSS
• ESS =Pni=1(bYi Y )2, TSS =Pni=1(Yi Y )2, SSR =Pni=1 bu2i
• R2 = 1 n1nk1 SSRTSS
• bjj
SE(bj) approx⇠ N (0, 1)
• bj ± d⇥ SE(bj) where d is the critical value
F table:
Source: Stock and Watson (2015) “Introduction to Econometrics,” Updated Third
Edition, Pearson.
End of Examination
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