04 Jun EC 320
Question
1 of 4
Homework 3
EC 320
Analytical Exercises
1) Consider the simple linear regression model:
€
Yi = ?1 + ?2Xi + ui
Recall that the OLS estimator for the parameter
€
?1 is:
Show that the formula for
€
b1 can equivalently be written as:
€
b1 = ?1 +
1
n ? aiX ?
?
? ?
?
?ui
i?1
n
? .
In other words, show that:
€
Y ? b2X = ?1 +
1
n ? ai
X ?
?
? ?
?
?ui
i?1
n
?
Hint: To get started on this problem, remember from class that we can write as:
€
b2 = ?2 + ai
ui
i=1
n
? .
2 of 4
2) In the previous question, you showed that
€
b1 = ?1 +
1
n ? aiX ?
?
? ?
?
?ui
i?1
n
? . Assuming that the
classical assumptions are true, show that
€
b1 is an unbiased estimator of
€
?1.
3) The Gauss-Markov theorem states that OLS estimates are BLUE. What word does
each letter in the acronym BLUE stand for? Give an intuitive definition for each of
these words.
Computer Exercises
1) In this problem you will use the EAEF dataset #1 that you worked with in the
previous homework assignment. Again, this dataset is posted on Blackboard under
the filename “EAEF01.wf1”. After downloading this file, you should be able to open
it in Eviews.
a) Does educational attainment depend on intellectual ability? To investigate this,
estimate a simple linear regression model where S is the dependent variable and
ASVABC is the independent variable. Interpret the estimated parameter on
ASVABC. Comment on the value of the
€
R2
.
b) Do earnings depend on education? To investigate this, estimate a simple linear
regression model where EARNINGS is the dependent variable and S is the
independent variable. Interpret the estimated parameter on S. Comment on the
value of the
€
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