Mehmet Soytas
Applied Econometrics I, Summer, 2009
Monday, June 1, 2009
Duration : 120 min.
MIDTERM EXAM SOLUTIONS
1.
State whether the following statements are TRUE or FALSE (Provide an explanation in either case,
only TRUE or FALSE answers will not get any partial credit). (
30 points
)
a. Imagine you regressed earnings of individuals on a binary variable (°Male±) which takes on the
value 1 for males and is 0 otherwise, and another binary variable (°Female±) which takes on the
value 1 for females and is 0 otherwise (You suppressed the constant term from the regression)
Because females typically earn less than males, you would expect the coe¢ cient for Male to have
a positive sign, and for Female a negative sign.
FALSE. Since you suppressed the constant term from the regression, there is no
"Dummy variable Trap" in this regression. Remember you will have a dummy vari
able trap if you include both dummy variables along with the constant term. However
now the coe¢ cients on Male and Female will represent the sample averages of earn
ings for these groups. Therefore both coe¢ cient will be positive,but the coe¢ cient
on Male being higher than Female.
b. To test whether or not the population regression function is linear rather than a polynomial of
order
r
, check whether the regression
R
2
for the polynomial regression is higher than that of the
linear regression.
FALSE. The regression
R
2
will always increase by addition of new variables into
the regression.
In order to test the nonlinear polynomial speci°cation, you should
conduct an
F
test on the coe¢ cients of all terms other than the linear one. Namely,
if the population regression function with a polynomial of order
r
is :
Y
i
=
°
0
+
°
1
X
i
+
°
2
X
2
i
+
°
3
X
3
i
+
::::
+
°
r
X
r
i
+
u
i
,then
H
0
:
°
2
= 0
; °
3
= 0
; :::; °
r
= 0
. If you reject the null
hypothesis, then you can conclude the regression function is nonlinear rather than
linear.
c. If the estimates of the coe¢ cients of interest change substantially across di/erent speci²cations
of multiple regression model, then this often provides evidence that the original speci²cation had
omitted variable bias.
TRUE. The omitted variable bias happens if the independent variables in the re
gression are correlated with the omitted variables. The basic sign of the existence of
the correlation is that the coe¢ cient on the independent variable changes when the
omitted variable is included in the regression.
d. You don³t have to worry about imperfect multicollinearity in the multiple regression model because
OLS estimates will be always unbiased.
TRUE and FALSE. You don±t have to worry about the consistency of the parameters
since they will be unbiased under the imperfect multicollinearity. However you may
still worry about the statistical inference you will make using the coe¢ cients. Since
imperfect multicollinearity causes standard errors of the coe¢ cients to be
in²ated
which may cause incorrect inference when you conduct hypothesis testing involving
signi°cance of the coe¢ cients.
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 Summer '08
 Staff
 Econometrics, Regression Analysis, Yi, coe¢ cients

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