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Problem Set 3
Economics 103
Introduction to Econometrics
Due Thursday, February 20, 2009
True/False/Explain
1.
In the regression model: Y=
β
0
+
β
1
female
+
β
2
education
+
ε
,
β
2
represents the
intercept for females.
False,
β
0
+
β
1
is the intercept for females
2.
In the model Y =
β
0
+
β
1
log(X) +
ε
, the effect of X on Y does not depend on
the level of x.
False, dy/dx =
β
1
/X so the effect of X on Y depends on the level of X.
3.
In the model Y =
β
0
+
β
1
X +
β
2
X
2
+
ε
the effect of X on Y does not depend on
the level of x.
False, dy/dx =
β
1
+ 2
β
2
X is the effect of X on Y which depends on the level of X.
4.
An insignificant coefficient (not statistically different from zero) means you
should not include that variable in the model.
False, we should consider other factors such as whether the adjusted Rsquared
increases.
We also might introduce omitted variable bias into the model if we
drop that variable
5.
In the regression model: Y=
β
0
+
β
1
female
+
β
2
education
+
β
3
education*female+
ε
,
β
3
represents the return to education for females.
False,
β
2
+
β
3
represents the return to education for females
6.
If you estimate the regression model: Y=
β
0
+
β
1
female
+
β
2
education
+
β
3
education*female+
ε
, where Y is earnings, the constant term will represent
the average earnings for men and Beta1 will represent the average earnings for
women.
False,
β
0
represents the average earnings for men with no
education, and
β
0
+
β
1
represents the average earnings for women
with no education.
7.
In the multiple regression model, the Adjusted
R
2
cannot be negative.
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View Full DocumentFalse, the adjusted Rsquared can be negative if
1
1
1
1
1
1
)
1
(
1
1
)
1
(
1
0
1
)
1
(
1
2
2
2
2
2
2
n
k
R
n
k
n
n
R
n
k
n
R
R
n
k
n
k
n
n
R
k
n
n
R
8.
In the multiple regression model, the Adjusted
R
2
is the same as the RSquared
when the explanatory variables are all statistically significant.
False, the Rsquared and adjusted Rsquared are only the same if k=1 (we only
estimate the model with a constant).
9.
Under perfect multicollinearity, the OLS estimator cannot be computed.
True, perfect multicollinearity means that one of the explanatory variables can
always be expressed linearly in terms of the others. Therefore, under perfect
multicollinearity it is impossible to compute the OLS estimator since it is
impossible to change one variable while holding all other variables constant
10.
Wages tend to be lower in the south than other regions (total of 4 regions), as seen
by the following estimated model:
ln(wage)=1.56+.05north+.15west+.12northeast
If instead we include south and drop north, then the coefficient on south will be
.05 and all the other coefficients (including the intercept) will stay the same.
False, the equation will become ln(wage) = 1.61  .05south + .09west +
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 Winter '07
 SandraBlack
 Econometrics

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