Tentan
NEGB01&NEGB22 Ekonometri
Tuesday 25th of May 2021
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There are 5 questions.
This exam gives a maximum of 20 points.
Each (sub)question has the same number of points.
10 points are required to pass the exam.
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No dictionaries, no calculators.
You can answer the questions in English or Swedish.
Some friendly advice:
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Write clearly and write on each pages the number of the question answered.
If you cannot solve an entire question completely, don't give up! Hand in your
solutions and indicate where you got stuck, rather than handing in a blank
paper.
Allocate your time proportionally among the questions.
Good Luck!
Klaas Staal
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1. SPSS & Some Multiple Choice Questions
Consider the following SPSS output:
Graph 1
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Graph 2
Suppose, in addition, that the auxiliary regression of ‘tenure’ on ‘years of education’,
‘years of potential experience’ and ‘age’ gives an R2 equal to 1.
a.
b.
c.
d.
Give the regression model that is estimated in this SPSS output.
What is the interpretation of the estimated intercept?
What is the interpretation of the first estimated slope coefficient?
What is the interpretation of the fourth estimated slope coefficient?
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e. Some multiple choice questions. For each question, give the subindex of the
question (i, ii, iii, iv) and the corresponding answer (1, 2, 3, …, 16).
i) In the regression model 𝑢𝑢𝑡𝑡 = 𝜌𝜌𝑢𝑢𝑡𝑡−1 + 𝜀𝜀𝑡𝑡 , 𝜌𝜌 is the:
(1)
Coefficient of autocorrelation;
(2)
First-order coefficient of autocorrelation;
(3)
Coefficient of autocorrelation at lag 1;
(4)
All of the above.
ii) If the error terms 𝑢𝑢𝑡𝑡 satisfy the assumptions of the classical linear
regression model, then in the regression model 𝑢𝑢𝑡𝑡 = 𝜌𝜌𝑢𝑢𝑡𝑡−1 + 𝜀𝜀𝑡𝑡 , the
expected value of 𝜌𝜌 is:
(5)
-1;
(6)
0;
(7)
1;
(8)
Between -1 and 1.
iii) The estimation method that accounts for the fact that observations
coming from populations with greater variability are given less weight
than those coming from populations with smaller variability is:
(9)
OLS;
(10) GLS;
(11) MLE;
(12) 2SLS.
iv) In the regression model 𝑌𝑌𝑖𝑖 = 𝛽𝛽1 𝑋𝑋0𝑖𝑖 + 𝛽𝛽2 𝑋𝑋1𝑖𝑖 , if 𝛽𝛽1is the intercept
coefficient then the value that 𝑋𝑋0𝑖𝑖 can take are::
(13) All zeros;
(14) All ones;
(15) Any value;
(16) Any positive value.
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2. SPSS & Some Multiple Choice Questions
Continue with using the model and SPSS output in Question 1.
a. Independent from the estimation, explain which sign you would expect for
the third slope coefficient.
b. What is the meaning of the estimated value of the standardized coefficient
for “years of education”?
c. Why are the estimated slope coefficient(s) (not) jointly statistically
significantly different from 0 at the 5% significance level?
d. Why would you (not) expect a perfect multicollinearity problem if the model
in Question 1 is extended with tenure and age?
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e. Some multiple choice questions. For each question, give the subindex of the
question (v, vi, vii, viii) and the corresponding answer (17, 18, 19, …, 32).
v) Which estimation method obtains BLUE estimators when estimating a
regression model in the presence of autocorrelation?
(17) OLS;
(18) GLS;
(19) MLE;
(20) 2SLS.
vi) Using the OLS estimation technique in the presence of autocorrelation
will lead to:
(21) Accurate t- and F-tests;
(22) Inaccurate t- and F-tests;
(23) Efficient estimates;
(24) Biased estimates.
vii) In the Park test ln 𝑢𝑢�𝑖𝑖2 = ln 𝜎𝜎 2 + 𝛽𝛽 ln 𝑋𝑋𝑖𝑖 + 𝜐𝜐𝑖𝑖 is the suggested regression
model. If we find 𝛽𝛽 to be statistically significantly different from zero, this
means that:
(25) The homoscedasticity assumption is satisfied;
(26) The homoscedasticity assumption is not satisfied;
(27) There is autocorrelation;
(28) There is no autocorrelation.
viii) Heteroscedasticity may arise due to various reasons. Which one of these
is NOT a reason:
(29) Extremely low or high values of the (in)dependent variables;
(30) Correlation of variables over time;
(31) Incorrect specification of the functional form of the model;
(32) Incorrect transformation of variables.
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3. SPSS & Some Multiple Choice Questions
Continue with using the model and SPSS output in Questions 1 and 2.
a. Do you think that there is a heteroscedasticity problem? Explain. On which
graph do you base your answer?
b. Do you think that there is an autocorrelation problem? Explain. On which
graph do you base your answer?
c. Do the Durbin-Watson d test of autocorrelation. That is, give the test
statistic, the critical values at the 5% significance level, and the interpretation
of the test outcome.
d. Is the estimated R2 statistically significantly larger than 0? Why (not)?
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e. Some multiple choice questions. For each question, give the subindex of the
question (ix, x, xi, xii) and the corresponding answer (33, 34, 35, …, 48).
ix) Multicollinearity is not a problem if the objective of the estimation is:
(33) Forecasting only;
(34) Prediction only;
(35) Getting reliable estimators of the parameters;
(36) Prediction or forecasting.
x) As a remedy to multicollinearity, which of the following may lead to a
specification bias?
(37) Transforming the variables;
(38) Adding new data;
(39) Dropping one of the collinear variables;
(40) First differencing the successive values of the variable.
xi) Dummy variables classify the data into:
(41) Inclusive categories;
(42) Mutually exclusive categories;
(43) Qualitative categories;
(44) Quantitative categories.
xii) Suppose you estimate the differentials in average annual salary of
professors for three categories – those employed at a fully governmentfunded college (𝐷𝐷1𝑖𝑖 ), those employed at a partially government-funded
college (𝐷𝐷2𝑖𝑖 ), and those employed at a private college (𝐷𝐷3𝑖𝑖 ), using
𝑌𝑌𝑖𝑖 = 𝛽𝛽1 + 𝛽𝛽2 𝐷𝐷2𝑖𝑖 + 𝛽𝛽3𝑖𝑖 𝐷𝐷3𝑖𝑖 + 𝑢𝑢𝑖𝑖 . 𝛽𝛽1 then represents the mean annual
salary of professors working in:
(45) Fully government aided colleges;
(46) Partially government aided colleges;
(47) Private colleges;
(48) All three colleges.
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4. SPSS & Linear Regression & Some Multiple Choice Questions
Continue with using the model and SPSS output in Questions 1, 2 and 3.
a. Are the residuals normally distributed? Why (not)?
b. Explain why adding the variable (years of education)2 can solve a potential
heteroscedasticity problem.
c. Suppose you want to estimate whether the effect of education on wages is
different for males and females. Give the regression model in which the
intercept and slope parameter of ‘years of education’ can differ by gender,
while keeping the effects of marriage and ‘years potential experience’
constant.
d. Test whether education has a positive effect on hourly wages at the 1%
significance level. Give the test statistic, the critical value and the test
outcome.
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e. Some multiple choice questions. For each question, give the subindex of the
question (xiii, xiv, xv, xvi) and the corresponding answer (49, 50, 51, …, 64).
xiii) In the regression model 𝑌𝑌𝑖𝑖 = 𝛽𝛽1 + 𝛽𝛽2 𝑋𝑋2𝑖𝑖 + 𝛽𝛽3 𝑋𝑋3𝑖𝑖 + 𝑢𝑢𝑖𝑖 testing the overall
significance of the model using an F-test, the degrees of freedom used is
(k-1),(n-k), where k is equal to:
(49) 2;
(50) 3;
(51) 4;
(52) The sample size.
xiv) When the R2 for a regression model is equal to 0, the F value is equal to:
(53) Infinity;
(54) A high positive value;
(55) A low positive value;
(56) 0.
xv) Which of the following formulations of the Cobb-Douglas production
function is NOT intrinsically linear:
(57)
(58)
(59)
(60)
𝛽𝛽
𝛽𝛽
𝛽𝛽
𝛽𝛽
𝑌𝑌𝑖𝑖 = 𝛽𝛽1𝑋𝑋2𝑖𝑖2 𝑋𝑋3𝑖𝑖3 𝑒𝑒 𝑢𝑢𝑖𝑖 ;
𝛽𝛽
𝛽𝛽
𝑌𝑌𝑖𝑖 = 𝛽𝛽1𝑋𝑋2𝑖𝑖2 𝑋𝑋3𝑖𝑖3 + 𝑒𝑒 𝑢𝑢𝑖𝑖 ;
𝑌𝑌𝑖𝑖 = 𝛽𝛽1𝑋𝑋2𝑖𝑖2 𝑋𝑋3𝑖𝑖3 𝑢𝑢𝑖𝑖 ;
All of the above.
xvi) 𝑅𝑅� 2 can take values:
(61) Between 0 and 1;
(62) Between -1 and 1;
(63) Between -1 and 0;
(64) Less than +1.
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5. Linear Regression & Some Multiple Choice Questions
Continue with using the model and SPSS output in Questions 1, 2, 3 and 4.
a. State the Gauss-Markov Theorem.
b. Is the Gauss-Markov Theorem applicable in the regression model presented
in Questions 1, 2, 3, and 4? Why (not)?
Consider the following models:
Model A: 𝑌𝑌𝑡𝑡 = 𝛾𝛾1 + 𝛾𝛾2 𝑋𝑋2𝑡𝑡 + 𝛾𝛾3 𝑋𝑋3𝑡𝑡 + 𝜇𝜇𝐴𝐴𝐴𝐴
Model B: (𝑌𝑌𝑡𝑡 − 𝑋𝑋2𝑡𝑡 ) = 𝛿𝛿1 + 𝛿𝛿2 𝑋𝑋2𝑡𝑡 + 𝛿𝛿3 𝑋𝑋3𝑡𝑡 + 𝜇𝜇𝐵𝐵𝐵𝐵
c. Will the OLS estimates of 𝛾𝛾2 and 𝛿𝛿2 be the same? Why?
d. Will the OLS estimates of 𝛾𝛾3 and 𝛿𝛿3 be the same? Why?
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e. Some multiple choice questions. For each question, give the subindex of the
question (xvii, xvii, xix, xx) and the corresponding answer (65, 66, 67, …, 80).
xvii) If we multiply the explanatory variable by 1000 and re-estimate the
regression, the intercept coefficient and its standard error will:
(65) increase by 1000 times;
(66) decrease by 1000 times;
(67) remain the same;
(68) increase by (1/1000) times.
xvii) If in 𝑌𝑌𝑖𝑖 = 𝛽𝛽1 + 𝛽𝛽2 𝑋𝑋𝑖𝑖 + 𝑢𝑢𝑖𝑖 both Y and X are standardized variables, the
intercept term will be:
(69) Positive;
(70) Negative;
(71) Between -1 and 1;
(72) Equal to zero.
xix) “The regression model does not include the lagged value(s) of the
dependent variable as one of the explanatory variables.” This is an
assumption underlying which of the following tests of autocorrelation?
(73) Durbin-Watson d test;
(74) Runs test;
(75) Breusch-Godfrey test;
(76) Graphical method.
xx) Data on GDP, unemployment, and household expenditure are examples
of:
(77) Experimental data;
(78) Non-experimental data;
(79) Cross-section data;
(80) Time series data.
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