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ECOM20001 Final Exam
This is a preview of the draft version of the quiz.
Started: Oct 11 at 16:20
Quiz Instructions
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Semester Two Assessment, 2021
Faculty/Dept: Faculty of Business and Economics, Department of Economics
Subject Number: ECOM20001
Subject Name: Econometrics 1
Writing Time: 3 hours
Reading: 30 minutes
Start and End Times (for students without an Alternative Exam Arrangement
(AEA))
Exam Start: 3:00 PM Australian Eastern Standard Time (AEST) on
Tuesday 09/11/2021
Exam End: 6:30 PM Australian Eastern Standard Time (AEST) on Tuesday
09/11/2021
You must start and submit your exam within this 3:00 PM - 6:30 PM
AEST time window.
The exam will end automatically at the 6:30 PM cut-off time
Students in different time zones are reminded to be mindful of relevant
time zone differences
Start and End Times (for students with an Alternative Exam Arrangement
(AEA))
Refer to your AEA for the the Exam Start and End times.
Open Book Status: Open Book
Additional Information
11/10/2021, 16:20 Quiz: ECOM20001 2021 S2 Final Exam
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Exam timetable information can be found on my.unimelb.edu.au
Instruction to Students
This examination contributes 70% to the final subject mark for ECOM20001
The exam includes 4 sections, 25 questions, and 100 marks in total.
Answer all questions using the Canvas LMS quiz tool.
Section A: multiple choice
Sections B, C, D: type in answers directly into the text boxes provided for
each question
Questions overview
Section A (20 marks)
10 questions (Q1 to Q10). Each question carries 2 marks.
Section B (36 marks)
3 questions (Q11, Q12, Q13). Each question carries 12 marks.
Section C (22 marks)
6 questions (Q14, Q15, Q16, Q17, Q18, Q19).
Section D (22 marks)
6 questions (Q20, Q21, Q22, Q23, Q24, Q25).
Exam Conditions
All exams will be moderated.
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submit your exam for grading.
Attachments for the Exam
Please download the following PDF attachment before starting the exam by
clicking on the link.
formulas.pdf (formula sheet)
Good luck!
SECTION A: MULTIPLE CHOICE (20 points)
This section contains 10 questions (Q1-Q10).
2 ptsQuestion 1
H0: B1=B2 vs. H1: B1!=B2 (where != means “not equals”)
H0: B3=0 vs. H1: B3!=0
H0: B1=B2=0 vs. H1: at least one of B1!=0 or B2!=0
None of the above
Consider the following regression: Y_i = B0 + B1 X1_i + B2 X2_i + B3 (X1_i *
X2_i) + u_i. Suppose we wanted to test whether the partial effect of X1_i is the
same as the partial effect of X2_i. What are the correct null and alternative
hypotheses?
2 ptsQuestion 2
In a sample with n=61 observations you run a regression with k=5 regressors and
obtain a standard error of the regression (SER) of SER=12. The sample variance
of Y is 132. What of the following statement about the R-squared (R2) is correct?
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R2 = 0
0 < R2 < 0.5
R2 = 0.5
R2 > 0.5
2 ptsQuestion 3
0.2
0.8
0.08
none of the above
Suppose we are interested in the relationship between weather (X=0 means no
rain; X=1 means rain) and stock market performance (Y=0 means stock market
falls; Y=1 means stock market rises). Suppose the joint distribution of X and Y is
given as P(X=0, Y=0)=0.32, P(X=0, Y=1)=0.48, P(X=1, Y=0)=0.08, P(X=1,
Y=1)=0.12. What is the probability of raining conditional on a stock market fall?
2 ptsQuestion 4
Reject null at the 1% significance level
Reject null at the 5% significance level, but not at the 1% significance level
Reject null at the 10% significance level, but not at the 5% significance level
Not reject null at the 10% significance level
Suppose you estimate a single linear regression of Y on X and obtain a slope
estimate of B1=-12 with a standard error of SE(B1)=2. Suppose that you wanted
to test the null hypothesis that the true value of B1 is -16 against the alternative
that it is not equal to -16. Which of the following is correct?
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2 ptsQuestion 5
The OLS estimator is the best linear unbiased estimator
The variance of the error term is the same for any X
A linear regression model fits better than a nonlinear regression model
The variance of the OLS estimator can be estimated
Which of the following statements are wrong under homoskedasticity?
2 ptsQuestion 6
An additional bar per 10,000 population is associated with an increase of 10 infected
individuals per 1,000 population
An additional bar per 10,000 population is associated with an increase of 1 infected
individual per 1,000 population
An additional bar per 10,000 population is associated with an increase of 0.1 infected
individuals per 1,000 population
An additional bar per 10,000 population is associated with an increase of 0.01 infected
individuals per 1,000 population
Suppose you run a single linear regression of Infect_i = B0 + B1 Barden_i + u_i
where Infect_i is the number of infected individuals per 10,000 population in area i
and Barden_i is the number of bars per 1,000 population in area i. If you obtained
a B1 estimate of 10, which of the following would be the correct interpretation?
2 ptsQuestion 7
The slope estimate must be positive
Suppose X is the regressor and Y is the dependent variable. Suppose there is
classical measurement error in X. When we regress Y on X, which of the following
statement is correct?
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The slope estimate must be close to zero
The slope estimate may be negative or positive
None of the above
2 ptsQuestion 8
Yes
No
We need to know the sample mean to answer the question
There is not enough information
Suppose we carry out hypothesis testing on the population mean of a random
variable. Suppose from a random sample with a very large sample size you
compute a 95% confidence interval for the population mean of [-1, 3.9]. Further,
suppose that you wanted to test the null hypothesis that the population mean
equals 4 against the alternative that it is not equal 0. Would you reject the null at
the 1% level of significance?
2 ptsQuestion 9
It is the elasticity of Y_i with respect to X_i
A 1-unit increase in X_i yields a 100B1% increase in Y_i
A 1-unit increase in X_i yields a B1% increase in Y_i
A B1 unit increase in X_i yields a 1% increase in Y_i
Consider the following regression: ln(Y_i)=B0 + B1 X_i + u_i. Which of the
following is the correct interpretation of B1?
2 ptsQuestion 10
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X and Y are statistically independent because raining cannot affect the stock market
X and Y are statistically independent
X and Y are not statistically independent
X has a causal effect on Y if X and Y are not statistically independent
Suppose we are interested in the relationship between weather (X=0 means no
rain; X=1 means rain) and stock market performance (Y=0 means stock market
falls; Y=1 means stock market rises). Suppose the joint distribution of X and Y is
given as P(X=0, Y=0)=0.32, P(X=0, Y=1)=0.48, P(X=1, Y=0)=0.08, P(X=1,
Y=1)=0.12. Which of the following is correct?
SECTION B (36 points)
This section contains 3 questions (Q11, Q12, Q13).
12 ptsQuestion 11
We are interested in estimating casual effect of yoga exercise on health.
Answer the following questions. Show your working. Wherever relevant, you
should write down the estimation equation, define all the variables that you
would use, and briefly describe the hypothesis test involved. (Hint: when
conducting the test, do not impose restrictions on the sign of the effect.)
(a)(3pts) Suppose we have a data set for all residents in Melbourne. There are
two variables: individual’s health score (SCORE); individual’s number of hours of
yoga exercise per week (YOGAHRS). Suppose individuals who regularly do yoga
exercise also tend to eat more unhealthy food (e.g., they indulge themselves after
exercising). Assume that eating more healthy food results in better health, all else
being equal. Write down the equation for the single linear regression of SCORE
on YOGAHRS, and then explain what the direction of the omitted variable bias
would be for the slope coefficient on YOGAHRS.
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(b)(3pts) Suppose someone in a health organization suggests a randomized
controlled trial, which randomly selects half of the Melbourne residents to be given
a free yoga mat. Suppose you have data on all Melbourne residents' health scores
and whether each individual is given a free yoga mat. Explain how you would
evaluate the effect of this policy using regression.
(c)(6pts) Suppose the manager thought that the experiment was too expensive.
Instead, the manager held free yoga lessons in five suburbs of Melbourne
(Carlton, Parkville, Southbank, Docklands, Flemington) in February 2021.
Suppose you have data on all Melbourne residents' health scores in January 2021
and February 2021. Explain how you would use a differences-in-differences model
to evaluate the effect of this policy. You should also describe how you define the
treatment and control groups and pre- and post-policy periods in the data.
12 ptsQuestion 12
Consider the following population linear regression model of individual
consumption: Y = 30 + 0.2X + u, where Y is yearly consumption (in thousand
dollars), X is the individual’s yearly income (in thousand dollars), and 30+0.2X is
the population regression line. Suppose we generate artificial data for 3
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individuals using this model. This artificial sample, which consists of 3
observations, is shown in the following table:
Observation X Y E(Y|X) u
Predicted value of Y
(Yhat)
Residual
(uhat)
1 30 50 V1 V2 45 5
2 70 V4 44 ? V3 -10
3 110 ? ? ? ? V5
Suppose we know that in this artificial sample, the sample mean of Y is 60, the
sample variance of Y is 300, the sample variance of X is 1600, and the sample
covariance between X and Y is 600. Assume these summary statistics hold in all
parts of this question.
Answer the following questions. Show your working.
(a)(2pts) What are the values of V1 and V2?
(b)(3pts) Compute the OLS regression line of the regression of Y on X. (Hint:
Assume the OLS regression line continue to hold in parts (c)-(e).)
(c)(2pts) What are the values of V3 and V4?
(d)(2pts) Compute the value of V5 using the information given by the table alone.
Briefly explain how you obtain this result.
(e)(3pts) Compute the R-squared of the regression in part (b). Show your
working.
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12 ptsQuestion 13
Consider the regression model Y = B0 + B1 X1 + B2 X2 + u. Suppose you want to
test the null hypothesis H0: B1 + 2 B2 = 0, versus the alternative hypothesis H1:
B1+ 2 B2 != 0 (!= means "not equal to"). The data set consists of 300
observations.
Answer the following questions. Show your working. In all places that are
relevant, you should describe the test statistic and critical-value (or p-value)
used.
(a)(6pts) Describe TWO different ways of transforming the regression to conduct
the test.
(b)(2pts) Suppose we use an F-statistic to conduct the test. What are the degrees
of freedom associated with this test statistic?
(c)(2pts) Let G(.) be the CDF of the F-distribution for the F-statistic in part (b).
Denote the actual F-statistic by F_act. Suppose G(F_act)=0.07. Do you reject the
null hypothesis at the 10% significance level? Briefly explain why.
(d)(2pts) Suppose you find that the F-test in part (b)-(c) and the test in part (a)
yield identical p-values. Do you think this result is correct? Briefly explain your
reasoning.
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SECTION C (22 points)
This section contains 6 questions (Q14, Q15, Q16, Q17, Q18, Q19).
A data set of 5,000 workers contains the following variables:
LNEARN: logarithm of annual earnings
AGE: age in years
AGE_SQ: square of AGE
LNAGE: logarithm of AGE
Regression output with HC standard errors is shown below:
Dependent variable:
LNEARN
(1) (2)
LNAGE 0.491
(0.040)
AGE 0.098
(0.007)
AGE_SQ -0.001
(0.0001)
CONSTANT 8.955 8.572
(0.150) (0.152)
R2 0.037 0.069
Answer the following questions. Show your working. (Hint: You may want to
take a screenshot of the regression output so you don't have to scroll up
and down when you answer the questions.)
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4 ptsQuestion 14
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Discuss the result in regression (1) by interpreting the coefficient estimate on
LNAGE and discussing its statistical significance. Then, based on regression (1),
compute the 95% confidence interval for the coefficient on LNAGE.