17/06/2021 Quiz: ECMT2150 Final Exam
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ECMT2150 Final Exam
Started: Jun 17 at 17:00
Quiz Instructions
ECMT2150 INTERMEDIATE ECONOMETRICS
FINAL EXAMINATION
TIME ALLOWED = 130 minutes (plus 30 minutes to upload your responses for Sections B, C, D, E and
F to the separate drop box on the Assignments page)
Statistical tables and formulas are provided here: Formula sheets and tables Final.pdf
(https://canvas.sydney.edu.au/courses/33558/files/16246298/download?download_frd=1)
I would suggest downloading them and having them open in another window or printing them out.
Read all the instructions on the Home page carefully before beginning the exam
There are SIX (6) SECTIONS in this exam – SECTIONS A, B, C, D, E and F
ANSWER ALL QUESTIONS
Marks allocated for each question are indicated.
Total points available are 100.
All questions are shown inside this quiz.
Good luck!
Section A [30 marks]
Questions 1 – 11
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Answer all 11 questions in Section A in the Quiz.
2 ptsQuestion 1
True
False
When estimating a model with a binary dependent variable using OLS, all of the
Classical linear model assumptions can be satisfied.
2 ptsQuestion 2
True
False
The least absolute deviations (LAD) estimator in a linear model minimizes the sum of
the absolute value of the residuals.
2 ptsQuestion 3
True
If is an unbiased and consistent estimator of , the distribution of tends toward
a standard normal distribution as the sample size grows.
𝛽 ̂ 𝑗 𝛽𝑗 𝛽
̂
𝑗
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False
2 ptsQuestion 4
True
False
Missing data, if that data is missing at random, does not cause bias or inconsistency
in the OLS estimator.
3 ptsQuestion 5
Angela, Jack and Oliver are discussing the concept of linearity of econometric
models. They are faced with the scatterplot below, illustrating the relationship
between the dependent variable (y) and independent variable (x) in a simple
regression model:
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Jack
No-one
Oliver
All three of them.
Angela
Angela notices the nonlinear relationship between the variables. She concludes that
estimating a simple regression with OLS is not possible because the relationship in
the figure above is not linear. Jack disagrees and mentions that it is possible to use
OLS to estimate a nonlinear model. Oliver disagrees with both of them and suggests
that it is possible to incorporate the nonlinearities and use OLS even with the clear
nonlinear relationship between two variables.
Who is most likely to be correct?
3 ptsQuestion 6
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F distribution with 3 numerator and 318 denominator degrees of freedom
t-distribution with 318 degrees of freedom
F distribution with 3 numerator and 321 denominator degrees of freedom
F distribution with 3 numerator and 317 denominator degrees of freedom
None of the other possible answers are correct.
t-distribution with 317 degrees of freedom
I run the following regression investigating the impact of the number of bedrooms on
house prices, on a random sample of houses from Sydney:
where:
houseprice = the sale price of the house in $
bedrooms = the number of bedrooms
land = the area of the block of land the house is on, in m
baths = the number of bathrooms
Assume the CLM assumptions hold.
My results from Stata are as follows:
I test for the overall significance of the model. The correct distribution and associated
degrees of freedom under the null hypothesis for the test of overall significance are:
ln(ℎ𝑜𝑢𝑠𝑒𝑝𝑟𝑖𝑐𝑒) = + 𝑏𝑒𝑑𝑟𝑜𝑜𝑚𝑠 + 𝑙𝑎𝑛𝑑 + 𝑏𝑎𝑡ℎ𝑠 + 𝑢𝛽0 𝛽1 𝛽2 𝛽3
2
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t-distribution with 321 degrees of freedom
3 ptsQuestion 7
assumes the unobserved effect is uncorrelated with each explanatory variable
cannot be used if the key explanatory variable is constant over time
assumes the unobserved effect is correlated with each explanatory variable
is more convincing than fixed effects for policy analysis using aggregate data
The random effects estimator
3 ptsQuestion 8
Heteroskedasticity-robust t statistics are justified only if the sample size is small.
The OLS estimators are the best linear unbiased estimators if heteroskedasticity is present.
Heteroskedasticty causes inconsistency in the OLS estimators.
It is possible to obtain F statistics that are robust to heteroskedasticity of an unknown form.
Which of the following is true of heteroskedasticity?
3 ptsQuestion 9
What will you conclude about a regression model if the Breusch-Pagan test results in
a small p-value, for example, less than 0.1?
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The model has a homoscedastic error variance.
The model contains heteroskedasticty.
The model omits some important explanatory factors.
The model contains dummy variables.
3 ptsQuestion 10
The sampling variance of the 2SLS estimator is smaller than the variance for the ordinary
least square estimator.
The 2SLS estimator is equal to the instrumental variable (IV) estimator when we have 1
instrumental variable available.
It can only be used when we have cross-sectional data.
For identification we require fewer instruments than endogenous variables.
Which of the following is true of the 2SLS estimator?
4 ptsQuestion 11
In your own words, explain why a high R-squared is not an indication that an
estimated OLS coefficient from a model is a
causal estimate of the impact of on . What other factors are relevant to assess
whether is a causal estimate?
𝛽 ̂ 1 𝑦 = + + … + + 𝑢β0 β1𝑥1 𝛽𝑘𝑥𝑘
𝑥1 𝑦
𝛽 ̂ 1
Edit View Insert Format Tools Table
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p 0 words
Section B [16 marks]
There is 1 question with 6 parts, (1) – (6), in Section B.
Upload your answers to all questions in Section B in the
assignment dropbox.
We have a 2-year panel of data from 93 Sydney suburbs, for 2005 and 2010.
Suburbs vary in terms of their access to public transport and over the 5 years from
2005 to 2010, the extent of transport linkages for many suburbs changed
substantially. We have a continuous index, links , developed by urban planners that
measures the density of public transport linkages. The index takes values between 0-
100 with 100 corresponding to the highest level of public transport linkages.
it
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We are investigating the impact of public transport linkages on housing prices. Our
model is:
(B1)
where:
HP = the average house price in suburb i in year t
pop = the population of suburb i in year t
avginc = the average income of residents of suburb i in year t
links = the index of public transport linkages for suburb i in year t
Yr2010 = a year dummy variable equal to 1 if the year is 2010, and 0 if the year is
2005
(1) [2 marks] Give one (1) example of the kind of variable captured by the term in
model (B1).
(2) [3 marks] What is the crucial assumption we must make so that the random
effects (RE) estimator is consistent? Under this assumption, why is RE preferred to
pooled OLS?
(3) [4 marks] Outline the key idea of the fixed effects (FE) transformation underlying
the FE estimator.
We find the following results when we estimate Model (B1) by random and fixed
effects:
ln (𝐻 ) =𝑃𝑖𝑡 + 𝑌 𝑟 + ln (𝑝𝑜 )β0 δ0 2010𝑡 β1 𝑝𝑖𝑡
+ ln (𝑎𝑣𝑔𝑖𝑛 ) + 𝑙𝑖𝑛𝑘 + +β
2
𝑐𝑖𝑡 β3 𝑠𝑖𝑡 𝑎𝑖 𝑢𝑖𝑡
it
it
it
it
t
𝑎𝑖
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(4) [2 marks] Interpret the estimated coefficient on the Year2010 dummy variable in
the random effects model.
(5) [2 marks] Notice that the coefficient on the log of the population ( ) is statistically
significant when we use the RE estimator but is insignificantly different from zero
when we use the FE estimator. Provide a likely reason for this.
(6) [3 marks] For model (B1), which estimator do you prefer, RE or FE? Briefly
explain why.
𝛽 ̂ 1
Section C [14 marks]
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There is 1 question with 5 parts, (1) – (5), in Section C.
Upload your answers to all questions in Section C in the
assignment dropbox.
We are researching the health care costs of child obesity. We have data on a random
representative sample of 8544 Australian children that allows us to estimate the
following model:
(C1)
where
HealthCosts = total annual Medicare costs for child i
ChildBMI = child i’s BMI (body mass index) – an index based on height and
weight used to assess whether an individual is underweight, of a healthy weight or
overweight. Higher values are associated with being more overweight.
(1) [3 marks] Provide an intuitive explanation for why a child’s BMI (ChildBMI ) is
likely to be endogenous in model (C1). What does this imply about
?
(2) [1 mark] Given your answer to part (1), what is the impact on our estimate for if
we estimate model (C1) using OLS?
(3) [3 marks] An alternative to OLS is to use an Instrumental Variable (IV) estimator.
A potential instrument for a child’s BMI (ChildBMI) is the BMI of their biological mother
or father. Our data set fortunately has the BMI of the mother (motherBMI). What
conditions must the instrumental variable motherBMI satisfy in order for the IV
estimator to be consistent? Indicate whether these conditions can be tested.
𝐻𝑒𝑎𝑙𝑡ℎ𝐶𝑜𝑠𝑡 = + 𝐶ℎ𝑖𝑙𝑑𝐵𝑀 +𝑠𝑖 β0 β1 𝐼𝑖 𝑢𝑖
i
i
i
𝐸(𝑢|𝐶ℎ𝑖𝑙𝑑𝐵𝑀𝐼)
𝛽 ̂ 1
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(4) [5 marks] When we estimate Model (C1) by OLS and by IV we find the following
estimated coefficient on ChildBMI:
with a standard error = 0.013
with a standard error = 0.068
Interpret the OLS and IV estimates. Explicitly compare the coefficient estimates and
their standard errors. Do these estimates suggest that child BMI affects the cost of
health care?
(5) [2 marks] Given the OLS and IV estimates in part (4), does the variable ChildBMI
appear to be related or unrelated to other factors that affect health costs? Provide a
brief explanation for your answer.
= 0.051𝛽 ̂ 1,𝑂𝐿𝑆
= 0.123𝛽 ̂ 1,𝐼𝑉
i
Section D [13 marks]
There is 1 question with 6 parts, (1) – (6), in Section D.
Upload your answers to all questions in Section D in the
assignment dropbox.
We are interested in assessing the impact of alcohol taxes on deaths from road or
traffic accidents.
Suppose we have two samples of data on the number of deaths by traffic accident in
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60 local council areas, some in NSW and some in Queensland. In the year 2011,
NSW increased the tax rate on alcoholic beverages. The first sample is from 2010
before the change in tax rates, and the second is from 2013 after the change in the
taxes. During this period, there was no change in alcohol taxes in Queensland. The
hypothesis we wish to test is that the increase in the tax rate in reduces the number of
deaths by traffic accidents.
We use a difference-in-difference model on the pooled data from 2010 and 2013. We
find the following results:
(D1)
where
fatalityrate = annual fatality rate, equal to the number of deaths per 10,000
population
NSW = a dummy variable equal to 1 if the council area is in NSW and 0 otherwise
Yr2013 = a dummy variable equal to 1 if the year is 2013 and 0 otherwise
(1) [2 marks] Which council areas are in the treatment group and which are in the
control group?
(2) [1 mark] From the results in (D1), what is the average fatality rate from traffic
accidents across the Queensland council areas in 2010?
(3) [1 mark] From the results in (D1), what is the average fatality rate from traffic
accidents across the NSW council areas in 2013?
(4) [3 marks] What is the interpretation of the coefficient on (NSW x Yr2013)?
(5) [3 marks] We have not included any other explanatory or control variables in
=𝑓𝑎𝑡𝑎𝑙𝑖𝑡𝑦𝑟𝑎𝑡𝑒ˆ
𝑁 = 120
10.205 − 0.053 𝑁𝑆𝑊 − 0.188 𝑌 𝑟2013 − 1.315 (𝑁𝑆𝑊 × 𝑌 𝑟20
(2.290) (0.029) (0.158) (0.351)
= 0.098𝑅
2
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Model (D1). State one advantage of including additional relevant and exogenous
explanatory variables in the model. Suggest one variable that you think would be
useful and appropriate to include in the model.
(6) [3 marks] Based on these findings, what simple policy advice could you give to
the state governments of Australia regarding taxes on alcohol? Please write no more
than 2 sentences.
Section E [12 marks]
There is 1 question with 6 parts, (1) – (6), in Section E.
Upload your answers to all questions in Section E in the
assignment dropbox.
We are researching the adoption of solar panels by Australian households. We have
the following model:
(E1)
where:
HasSolar = a dummy variable equal to 1 if the household’s residence has rooftop
solar panels, and 0 otherwise
income = household annual income
employed = the number of household members in employment
𝐻𝑎𝑠𝑆𝑜𝑙𝑎𝑟 = + 𝑖𝑛𝑐𝑜𝑚𝑒 + 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑑 + 𝑦𝑟𝑠𝑂𝑤𝑛𝑒𝑑 + 𝑢β
0
β
1
β
2
β
3
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yrsOwned = the number of years the household has owned the residence.
Our data is a random sample of Australian households and we have 1615
observations. You can assume .
(1) [3 marks] Referring to (E1) above, interpret the coefficient . You can assume it
is positive.
(2) [2 marks] You know that this model will suffer from heteroskedasticity. Why is this
the case?
(3) [2 marks] Define heteroskedasticity in your own words.
(4) [2 marks] Briefly describe the impact of this heteroskedasticity on your estimates.
(5) [2 marks] Briefly describe the impact of this heteroskedasticity on your inference.
(6) [1 mark] Name the simple strategy you could use in this model to deal with the
problem of heteroskedasticity and allow you to conduct inference.
𝐸(𝑢│𝑖𝑛𝑐𝑜𝑚𝑒, 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑑, 𝑦𝑟𝑠𝑂𝑤𝑛𝑒𝑑) = 0
𝛽2
Section F [15 marks]
There is 1 question with 4 parts, (1) – (4), in Section F.
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Upload your answers to all questions in Section F in the
assignment dropbox.
Anna is interested in understanding the factors surrounding smoking habits in
Australia. She estimates the model:
(F1)
by OLS using Stata and obtains the following results:
where:
cigs = number of cigarettes smoked in a day
lincome = the natural log of the individual’s income
lcigpric = the natural log of the price of a pack of cigarettes
age = individual’s age in years
agesq = age squared
educ = individual’s education attainment in years
female = a dummy variable equal to 1 if the individual is female and 0 otherwise
𝑐𝑖𝑔𝑠 = + 𝑙𝑖𝑛𝑐𝑜𝑚𝑒 + 𝑙𝑐𝑖𝑔𝑝𝑟𝑖𝑐 + 𝑎𝑔𝑒 + 𝑎𝑔𝑒𝑠𝑞β
0
β
1
β
2
β
3
β
4
+ 𝑒𝑑𝑢𝑐 + 𝑓𝑒𝑚𝑎𝑙𝑒 + 𝑓𝑒𝑚_𝑒𝑑𝑢𝑐 + 𝑢β
5
β
6
β
7
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Not saved
fem_educ = female x educ, that is, the interaction of female and educ
(1) [3 marks] Interpret , the estimated coefficient on lcigpric.
(2) [3 marks] John and his colleague James are both celebrating their birthdays
today. John has just turned 29 while James is now 32. Will the additional year of age
have the same effect on the number of cigarettes smoked per day for both? If yes,
explain why. If not, find the difference in the effect of an additional year of age on the
number of cigarettes smoked per day between John and James.
(3) [4 marks] Graph the relationship between the number of cigarettes smoked per
day and the number of years of education for males and females. Be sure to fully
label your graph.
(4) [5 Marks] One of your friends claims that the effect of education on the number of
cigarettes smoked per day does not differ by gender, that is, between males and
females. Find and report the 99% confidence interval that you can use to test this
hypothesis at the 1% level of significance. Conduct the hypothesis test. Be sure to
state the null and alternative hypotheses and provide a conclusion.
𝛽 ̂ 2
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