1.1 Twovariable OLS:
distributions
73261 Econometrics
August 30
Wooldridge 2.5
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Announcements
p. 2
© CMU / Y. Kryukov
Quiz this Friday, covering the material
from this & previous week
HW#1 – will be complete by end of day
Due next Wed., Sept. 8
You can do all of it after today
Next Monday – Labor day
No class next Monday, Sept. 6
73

261 Aug

31
1.1 Two

variable OLS
Review & plan
p. 3
© CMU / Y. Kryukov
Up to now:
True coefficients
(
β
0
,
β
1
)
are constants
Our estimates
are random variables
Today
Distribution of the estimates
So we can tell how precise our estimates are
And do statistical tests
1
0
ˆ
,
ˆ
β
β
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Approach
p. 4
© CMU / Y. Kryukov
Want distribution of
’s
’s are functions of
X
i
’s and
Y
i
’s
Y
i
’s are function of
X
i
’s and
u
i
’s
We observe
X
i
’s
So we condition on them
I.e. we hold
X
i
’s fixed
Some books just have
X
i
as part of population
What could
’s be given
X
i
?
Only independent random variable is
u
i
Which affects
’s via
Y
i
’s
How do
’s depend on
Y
i
’s and
u
i
‘s?
β
ˆ
β
ˆ
β
ˆ
β
ˆ
β
ˆ