Principles of Econometrics
Mid-Term
March 3rd, 2010
João Valle e Azevedo
Paulo Júlio
Time for completion: 70 min
For each question, identify the correct answer.
For each question, there is one and only one correct answer.
A correct answer is worth 1 point; an incorrect answer shall be attributed 0 points.
Mark your choice on the answer sheet provided at the end of this examination paper.
EITHER USE A PENCIL OR DO NOT MAKE CORRECTIONS.
Identify your answer sheet with your name and student number
1. OLS stands for what in Econometrics?
(a) Optimally Linearized Solution
(b) There is no such thing in Econometrics
(c) The only rock band that Econometricians are crazy about
(d) Ordinary Least Squares
(e) None of the answers above is correct
2. When choosing observations from a population of interest that will be studied using
Cross-Section Econometrics, we should:
(a) Chose all the elements of the population, even if it costs e 700 billion
(b) Make sure all observations have the same probability of being chosen
(c) Select the largest (feasible) number of observations
(d) b) and c) are correct
(e) a) and b) are correct;
(f) All of the above are correct
(g) None of the above is correct
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3. When can the intercept in the linear regression model,
preted?
0,
be meaningfully inter-
(a) when the range of the independent variables includes zero.
(b) when the range of the dependent variables excludes zero.
(c) when the range of the independent variables excludes zero.
(d) when the range of the dependent variables includes zero.
(e)
0
can always be meaningfully interpreted.
4. Consider the model y = 0 +
as x increases when 2 < 0?
1x +
2x
2
+ u. How will the slope of the curve change
(a) the slope will increase as x increases.
(b) the slope will not change as x increases.
(c) the slope will decrease as x increases.
(d) the answer depends on
1.
(e) none of the answers above is correct.
5. Consider a multiple linear regression model verifying the Gauss-Markov assumptions. The OLS estimators have a low sampling variance if:
(a) The total sum of squares of each regressor is low
(b) The total sum of squares of each regressor is high
(c) The variance of the error term is high
(d) The variance of the error term is low
(e) The regressors are highly correlated in the sample
(f) a) and c) above
(g) b) and d) above
(h) b, d) and e) above
(i) a), d) and e) above
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6. In a linear regression model, if the error term is not homoskedastic, then
(a) the OLS estimator is no longer unbiased.
(b) we cannot guarantee the OLS estimator is BLUE.
(c) we cannot guarantee the OLS estimator is the minimum variance unbiased
estimator.
(d) the OLS estimator is useless.
(e) both (b) and (c) are true.
(f) both (b) and (d) are true.
(g) all of the above.are true
7. The test of overall signi…cance of the model is a test to ascertain:
(a) if the regression is estimated correctly.
(b) if all coe¢ cients, including the intercept, are equal to zero.
(c) if all coe¢ cients, excluding the intercept, are equal to zero.
(d) if we need to add additional regressors to the model.
(e) both (a) and (c) are true.
(f) both (c) and (d) are true.
8. Suppose a researcher wants to test the hypothesis that coe¢ cient i is equal to
a in a multiple linear regression model. What is the di¤erence in the alternative
hypothesis between a one-tailed test and a two-tailed test?
(a) the alternative hypothesis for a one-tailed test is either H1 :
i > a and for a two-tailed test it is H1 : i 6= a.
(b) the alternative hypothesis for a one-tailed test is H1 :
tailed test it is H1 : i 6= a.
(c) the alternative hypothesis for a one-tailed test is H1 :
tailed test it is H1 : i = a.
(d) the alternative hypothesis for a one-tailed test is H1 :
tailed test it is either H1 : i < a or H1 : i > a.
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i
< a or H1 :
i
= a and for a two-
i
6= a and for a two-
i
6= a and for a two-
9. Suppose a researcher estimates the following model yb = b0 + b1 x1 + b2 x2 and wants
to test the null hypothesis of H0 : 1 = 0 against the alternative H1 : 1 6= 0 at
a 5% signi…cance level. Let n denote the number of observations and assume the
Classical Linear Model assumptions hold. Which of the following is true?
(Note: tobs denotes the observed t-statistic for that test and tx%
df denotes the x
percentile of the t-distribution with df degrees of freedom)
(a) He should reject the null hypothesis if jtobs j > t97:5%
n 3 .
(b) He should reject the null hypothesis if jtobs j > jt95%
n 3 j.
(c) He should reject the null hypothesis if jtobs j < jt2:5%
n 3 j.
(d) He should reject the null hypothesis if jtobs j < jt5%
n 3 j.
(e) both (b) and (c) are correct.
(f) both (a) and (d) are correct.
(g) we do not have enough information to answer this question.
10. Suppose a researcher estimates the following model yb = b0 + b1 x1 + b2 x2 and
wants to test the null hypothesis of H0 : 1 = 2 = 0 against the alternative H1 :at
least one i 6= 0; i = 1; 2 at a 5% signi…cance level. Let n denote the number of
observations and assume the Classical Linear Model assumptions hold. Then:
j
(Note: tobs
denotes the observed t-statistic for parameter j and tx%
df denotes the
x percentile of the t-distribution with df degrees of freedom. Fobs denotes the
x%
observed F-statistic for that test and F(df
1;df 2) the x percentile of the F -distribution
with (df 1; df 2) degrees of freedom)
97:5%
1
2
(a) He should reject the null hypothesis if jtobs
j > jt97:5%
n 2 j and jtobs j > jtn 2 j.
95%
1
2
(b) He should reject the null hypothesis if jtobs
j > jt95%
n 3 j and jtobs j > jtn 3 j.
95%
(c) He should reject the null hypothesis if Fobs > F(2;n
3) .
95%
(d) He should reject the null hypothesis if Fobs > F(n
3;2) .
95%
(e) He should reject the null hypothesis if Fobs > F(3;n
3) .
(f) both (a) and (c) are correct.
(g) both (a) and (d) are correct.
(h) we do not have enough information to answer this question.
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\ =
For the next three questions, consider the following estimated model log(w)
2
10; 42 + 0; 06school + 0; 02male + 0:04exper 0:001exper , where w is the wage
(in Euros), school is the number of years of schooling, male is a dummy variable
which takes the value of 1 if the individual is a male and 0 otherwise, and exper
is the number of years of professional experience. Assume that the Gauss-Markov
assumptions hold.
11. What can you conclude about the e¤ect of years of schooling on wages:
(a) we cannot conclude anything, since the e¤ect of schooling on wages depends
on whether the individual is a male or a female.
(b) an additional year of schooling increases wages by 0,06%.
(c) an additional year of schooling increases wages by 0,6%.
(d) the coe¢ cient 0; 06 is the elasticity of wages with respect to the number of
years of schooling.
(e) the coe¢ cient 0; 06 is the semi-elasticity of wages with respect to the number
of years of schooling.
(f) both (b) and (e) are correct.
(g) none of the above.
12. Which of the following statements is true:
(a) all males in the sample earn 2% more than females.
(b) a male earns 2% more than females on average, ceteris paribus.
(c) on average, females have to invest more in education in order to have the same
wage than males, ceteris paribus.
(d) both (b) and (c) above are correct.
(e) none of the above is correct.
13. What can you conclude regarding the e¤ect of experience on wages:
(a) an additional year of experience implies an increase in wages of 4% on average,
ceteris paribus.
(b) an additional year of experience implies an increase in wages of 0.04% on
average, ceteris paribus.
(c) the e¤ect of an additional year of experience on wages depends on the level of
experience itself.
(d) we can not infer the impact of an additional year of experience on wages.
(e) none of the answers above is correct.
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14. In the context of the simple linear regression model y =
following is NOT true?
0
+
1 x + u,
which of the
(a) the point (x; y) always lies on the regression line
(b) the sum of the residuals is always zero
(c) the average of the …tted values of y is the same as the average of the observed
values of y
(d) there are always as many points above the …tted line as there are below it
(e) the regression line minimizes the sum of the squared residuals
(f) both (c) and (d)
(g) both (a) and (d)
15. Take an observed (that is, estimated) 95% con…dence interval for a parameter
of a multiple linear regression. If you increase the con…dence level to 99% then,
necessarily:
(a) The length of the con…dence interval decreases
(b) The length of the con…dence interval remains unchanged
(c) The length of the con…dence interval increases
(d) None of the answers above is correct
16. In a multiple linear regression, changing the units of measurement of the dependent
variable (by multiplying it by some constant) will a¤ect all except which of the
following?
(a) the estimated intercept parameter
(b) the estimated slope parameter
(c) the Total Sum of Squares of the regression
(d) the R-squared of the regression
(e) the estimated standard error of the regression
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17. A …tted regression equation is given by Y^ = 20 + 0; 75X. What is the value of the
residual at the point X = 100, Y = 90?
(a) 5
(b)
5
(c) 0
(d) 15
(e) None of the above
18. In a multiple linear regression context, the R-squared measures:
(a) the correlation between each regressor and the dependent variable
(b) the amount of variation in the dependent variable
(c) the squared covariance between the squared regressors and the squared dependent variable
(d) the Residual Sum of Squares as a proportion of the Total Sum of Squares
(e) the Explained Sum of Squares as a proportion of the Total Sum of Squares
19. Under the Gauss-Markov assumptions in the multiple linear regression model, the
OLS estimator is BLUE. This means what?
(a) The OLS estimator is an Avatar
(b) The OLS estimator has wavelength between 440 and 490 nanometers
(c) The OLS estimator supports FC Porto
(d) None of the answers above is correct
20. "The Ordinary Least Squares (OLS) estimator of a slope coe¢ cient is unbiased"
means:
(a) the estimated slope coe¢ cient will always be equal to the true parameter value
(b) the estimated slope coe¢ cient will get closer to the true parameter value as
the size of the sample increases
(c) the estimated slope coe¢ cient will be equal to the true parameter if the sample
is large
(d) the mean of the sampling distribution of the slope parameter is zero
(e) if (in…nitely many) random samples of the same size are taken, the average of
the estimated slope coe¢ cients will be equal to the true parameter
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ANSWER SHEET
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Number:
Mark your answers with an X in the table below.
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EITHER USE A PENCIL OR DO NOT MAKE CORRECTIONS
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