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Question 1
a)
Agree. On average OLS slope coefficient are on target even with heteroscedasticity, but are no longer
efficient.
b) true
The classical ttest is valid when the regressor is fixed and trended and autocorrelation among errors is
predominantly negative, and when the regressor is random and AR(1), like the errors, and
autocorrelation is moderately negative or positive.
Agree.
Parameters estimates are fitted by minimizing a WLS of residuals where the weights are
inversely proportional
to the variance of the errors. This is in contrast to OLS.
Disagree. The last slope B4 has for factor edi+agei. When we expand the expression we get 2*edi*agei
but no explanatory variable appears to be linearly correlated to another.
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View Full Document Disagree. The Durbin–Watson statistic is a test statistic used to detect the presence of autocorrelation
We would need to add slope dummy variables and an intercept dummy variable as well.
We want to test for a difference in the slope and the intercept. We therefore enter the categorical dummy variable children
and estimate for its slope b5. Children = {0,1} – We jump between models by pluggingin 0 or 1.
The model with children is written as: y= b1 + (b2+d1children)edi + (b3+d2children)agei + (b4+d3children)wagei +
b5children + ut.
We begin by testing to see if we can remove the dummy variables
Setting up a test of hypothesis as follows:
H(0): only edu, agei, wagei,and b1needed => b5 =0 – null hypothesis
H(a): dummy variables are needed,
=> d(15)=/=0
Rejection:
We use the following F test
F(obs.) =
(RSS(0)  RSS(a))/(df(0)  df(a))
__________________________________
RSS(a)/df(a)
We will perform a t test on the coefficient of the dummy variable.
1.
Work hour structure of married people without children = Work hour structure of married people with children
b5, =0
b5 =/=0
2.
Test for significant effect of dummy variable on pooled data
H
0
:
β
5
=0
H
1
:
β
5
≠0
Test for significant effect of children:
H
0
:
β
5
=0
H
1
: at least one of the parameters
β
14
is not zero
•
This hypothesis test follows the Fdistribution
•
The critical value of this test which is always onetailed is, F
α
,K,nK1
where
α
is the level of
significance
•
K represents the number of parameters set to zero (in this case two)
•
nK1 is the degrees of freedom in the unrestricted model
•
In the Ftable, the numerator degrees of freedom is K and the denominator degrees of freedom is
nK1
To test whether the multiple regression model with dummy variable for the “Children effect”
improved the regression model with 4 explanatory variable, I conducted
Wald’s F test. The test statistic is F, where the numerator is (SSEr – SSEur)/m, while
denominator is SSEur divided by DoF. The unrestricted model is the multiple regression
with the dummy, while the restricted model is the simple market model.
The F value of the test is 0.101, while critical F is 3.85 with degree of freedom of 1 in
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This note was uploaded on 11/18/2011 for the course ECON 570 taught by Professor Staff during the Fall '08 term at UNC.
 Fall '08
 Staff

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