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GaussMarkov Theorem – Under 4 assumptions + homoskedasticity, OLS is BLUE
1)
Linear in Parameters
– Population model is
0
1
y
x
u
β
=
+
+
Violations:
•
Including irrelevant variables does not affect unbiasedness but increases variance if correlated with relevant variable of interest.
•
Omitting relevant variable will bias estimator and generally decrease variance unless uncorrelated with all included variables.
2)
Random Sampling
3)
Zero Conditional Mean 
E(  )
E( )
0
u x
u
=
=
Corr( , )
0
u x
=
a
Cov( , )
0
u x
=
a
Cov( , )
Corr( , )
or
sd( )sd( )
u x
u x
u
x
u x
u x
u
x
σ
ρ
σ σ
= =
Represents two assumptions in one:
E(  )
E( )
u x
u
=
and E( )
0
u
=
.
u
and
x
are assumed to be random variables that follow a
joint probability distribution
The assumption E(  )
E( )
u x
u
=
is very important; it implies, among other things, that
u
and
x
are uncorrelated
(i.e., not linearly related). The assumption
E( )
0
u
=
is not crucial as long as an intercept term is included in the equation (intuitive explanation).
Violations:
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 Spring '03
 Johnson
 Econometrics

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