Econometrics – Assignment I/Fall 2015

Question 1
For each of the following, select the single most appropriate option to complete the
statement and brie
y explain your choice :
1.  An estimate is
a) robust if it has the smallest variance possible.
b) a random number.
c) biased if its expected value equals the population value.
d) another word for estimator.
2.  The slope estimator,
1
, has a smaller standard error, other things equal, if
a) there is less variation in the explanatory variable, X.
b) there is a large variance of the error term, u.
c) the sample size is larger.
d) the intercept,
0
, is small.
3.  To decide whether or not the slope coecient is large or small,
a) you should analyze the economic importance of a given increase in X.
b) the slope coecient must be dierent than zero.
1
c) the (1-0.1)*100 % condence interval for the slope parameter does not include
zero.
d) you should change the scale of the X variable if the coecient appears to be too
small.
4.  The t-statistic is calculated by dividing
a) the MLE estimator by its standard error.
b) the slope by the standard deviation of the explanatory variable.
c) the OLS estimator minus its hypothesized value of zero by the standard error of
the estimator.
d) the slope by 1.96.
5.  Under the least squares assumptions (zero conditional mean for the error term,
X
i
and
Y
i
being i.i.d., and
X
i
and
u
i
having nite fourth moments), the OLS estimator
for the slope and intercept
a) has an exact normal distribution for n > 15.
b) is BLUE.
c) has a normal distribution even in small samples.
d) is consistent.
6.  When there are omitted variables in the regression, which are determinants of the
dependent variable, then
a) you cannot measure the eect of the omitted variable, but the estimator of your
included variable(s) is (are) unaected.
b) this has no eect on the estimator of your included variable because the other
variable is not included.
c) this will bias the OLS estimator of the included variable if the omitted variable
is correlated with the included variable.
d) the OLS estimator is biased.
2
7.  The overall regression F-statistic tests the null hypothesis that
a) all slope coecients are zero.
b) all slope coecients and the intercept are zero.
c) the intercept in the regression and at least one, but not all, of the slope coecients
is zero.
d) the slope coecient of the variable of interest is zero, but that the other slope
coecients are not.
8.  If the estimates of the coecients of interest change substantially across specica-
tions,
a) then this can be expected from sample variation.
b) then you should change the scale of the variables to make the changes appear to
be smaller.
c)  then  this  often  provides  evidence  that  the  original  specication  had  omitted
variable bias.
d) then choose the specication for which your coecient of interest is most signi-
cant.
9.  The interpretation of the slope coecient in the model
ln(
Y
i
) =
0
+
1
(
X
i
) +
u
i
follows :
a) a 1% change in X is associated with a
1
% change in Y.
b) a change in X by one unit is associated with a
1
change in Y.
c) a change in X by one unit is associated with a 100
1
% change in Y.
d) a 1% change in X is associated with a change in Y of 0
:
01
1
.
3

Econometrics – Assignment I/Fall 2015

Question 1
For each of the following, select the single most appropriate option to complete the
statement and brie
y explain your choice :
1.  An estimate is
a) robust if it has the smallest variance possible.
b) a random number.
c) biased if its expected value equals the population value.
d) another word for estimator.
2.  The slope estimator,
1
, has a smaller standard error, other things equal, if
a) there is less variation in the explanatory variable, X.
b) there is a large variance of the error term, u.
c) the sample size is larger.
d) the intercept,
0
, is small.
3.  To decide whether or not the slope coecient is large or small,
a) you should analyze the economic importance of a given increase in X.
b) the slope coecient must be dierent than zero.
1
c) the (1-0.1)*100 % condence interval for the slope parameter does not include
zero.
d) you should change the scale of the X variable if the coecient appears to be too
small.
4.  The t-statistic is calculated by dividing
a) the MLE estimator by its standard error.
b) the slope by the standard deviation of the explanatory variable.
c) the OLS estimator minus its hypothesized value of zero by the standard error of
the estimator.
d) the slope by 1.96.
5.  Under the least squares assumptions (zero conditional mean for the error term,
X
i
and
Y
i
being i.i.d., and
X
i
and
u
i
having nite fourth moments), the OLS estimator
for the slope and intercept
a) has an exact normal distribution for n > 15.
b) is BLUE.
c) has a normal distribution even in small samples.
d) is consistent.
6.  When there are omitted variables in the regression, which are determinants of the
dependent variable, then
a) you cannot measure the eect of the omitted variable, but the estimator of your
included variable(s) is (are) unaected.
b) this has no eect on the estimator of your included variable because the other
variable is not included.
c) this will bias the OLS estimator of the included variable if the omitted variable
is correlated with the included variable.
d) the OLS estimator is biased.
2
7.  The overall regression F-statistic tests the null hypothesis that
a) all slope coecients are zero.
b) all slope coecients and the intercept are zero.
c) the intercept in the regression and at least one, but not all, of the slope coecients
is zero.
d) the slope coecient of the variable of interest is zero, but that the other slope
coecients are not.
8.  If the estimates of the coecients of interest change substantially across specica-
tions,
a) then this can be expected from sample variation.
b) then you should change the scale of the variables to make the changes appear to
be smaller.
c)  then  this  often  provides  evidence  that  the  original  specication  had  omitted
variable bias.
d) then choose the specication for which your coecient of interest is most signi-
cant.
9.  The interpretation of the slope coecient in the model
ln(
Y
i
) =
0
+
1
(
X
i
) +
u
i
follows :
a) a 1% change in X is associated with a
1
% change in Y.
b) a change in X by one unit is associated with a
1
change in Y.
c) a change in X by one unit is associated with a 100
1
% change in Y.
d) a 1% change in X is associated with a change in Y of 0
:
01
1
.
3