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ECOM30001: Basic Econometrics

创建日期：2024-05-10 18:03:52

所属分类：数学mathematics

标签： ECOM30001

Basic Econometrics

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ECOM30001: Basic Econometrics

Time Allowed: TWO Hours
Reading Time: 15 minutes
This examination paper contributes 60 percent to the assessment in ECOM30001.
This examination consists of four (4) questions in total.
You must answer ALL four questions.
Each question is worth twenty (20) marks for a maximum of 80 marks.
The examination paper should be inserted in the back of your answer booklet at the end
of the examination.
The following items are authorized in the examination room:
-Casio FX-82 (any suffix) calculator
This exam has 19 pages.
The paper may not be removed from the exam room.
Answer all questions in the examination booklet(s) provided.
The examination contains a formula sheet starting on page 14.
The examination contains critical values for a number of distributions starting on page 17.
Page 2 of 19
Question 1
a) [5 marks] Consider the following econometric model:
yi = β0 + β1Xi + εi
What is meant by the term heteroskedasticity in the random error? What are the con-
sequences for the OLS estimator if you ignore heteroskedasticity in the random error εi?
Briefly outline how you would test for the presence of heteroskedasticity using White’s
test. Your answer should clearly state the null and alternative hypotheses, the test statis-
tic and its distribution.
b) [5 marks] Consider the following econometric model:
yi = β0 + β1X
∗
i + εi
Consider the following measurement equation relating the observed value for X to the
‘true’ value X∗:
Xi = X
∗
i + υi
with COV(X∗i , εi) = 0 and COV(υi, εi) = 0.
What is meant by the term classical measurement error? Clearly explain the implications
for the OLS estimator of β1 if the explanatory variable X
∗ is observed with (classical)
measurement error.
c) [5 marks] Consider the following econometric model:
yt = β0 + β1Xt + εt
What is meant by the term autocorrelation in the random error? Clearly explain the
consequences for the OLS estimator if you ignore autocorrelation in the random error εt.
Briefly outline how you would test for first order AR(1) autocorrelation in the random
error. Your answer should clearly state the null and alternative hypotheses, the test
statistic and its distribution.
Page 3 of 19
d) [5 marks] Consider the following regression:
∆ inft = β0 + β1 inft−1 + β2 ∆ inft−1 + β3 ∆ inft−2 + β4 ∆ inft−3 + β5 ∆ inft−4 + εt
where inf represents the quarterly inflation rate. This econometric model was estimated
using the method of Ordinary Least Squares (OLS) for the period 1948:Q1 to 2016:Q1
and the results are presented in Figure 1.

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Figure 1: OLS Regression Results: Question 1 (d)
Outline how you would test whether the series for the quarterly inflation rate was sta-
tionary or not. Your answer should clearly state the null and alternative hypotheses, the
test statistic and its distribution. Using the results in Figure 1, what is the value of the
Augmented Dickey-Fuller test statistic? At the 5% level of significance, explain whether
the sample evidence is consistent with the null hypothesis. Based upon the estimation
results presented in Figure 1, the p-value associated with the Augmented Dickey-Fuller
test is 0.0080.
Page 4 of 19
Question 2
Consider the following demand function for airline seats on routes in a large country:
lnpasseni = β0 + β1lnfarei + β2lndisti + β3lndist
2
i + εi (1)
where:
passeni = average (log) number of passengers per day on route i
farei = average (log) fare on route i, in dollars
lndisti = average (log) distance of route i, in miles
conceni = average market share of largest carrier on routei
and ln(X) denotes the natural logarithm of variable X.

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Figure 2: OLS Regression Results for Model (1)
a) [3 marks] The estimation results from estimating model (1) by the method of Ordinary
Least Squares (OLS) are reported in Figure 2. At the 5% level of significance, test
the hypothesis that the price elasticity of demand for air travel is elastic, that is the
price elasticity of demand is less than -1. Your answer should clearly state the null and
alternative hypotheses, the distribution of the test statistic, and your decision.
b) [3 marks] Do you think that the condition COV(fare, ε|dist) = 0 is likely to be satisfied?
Clearly explain why or why not. Explain the consequences for the OLS estimator if this
condition is not satisfied.
c) [4 marks] Consider a variable concen that might be suitable as an instrumental variable
for ln (fare). This variable is a measure of market concentration, measured by the market
share of the largest carrier on the route. Clearly, explain the two conditions that must be
satisfied for the variable concen to be a valid instrumental variable. Do you think these
two conditions are likely to be satisfied? Why or why not?
Page 5 of 19
d) [2 marks] Consider the following first stage:
lnfarei = pi0 + pi1 conceni + pi2lndisti + pi3lndist

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