Specification Bias
a. Specification mistake  suppose an important variable,
X
2
, is left out of the regression model.
The
true
model is:
0
1
1
22
i
i
ii
Y
X
Xu
b
bb
=
+++
But, you assume:
0
11
i
Y
Xv
aa
=
++
(What CRM assumptions have been violated? Assumption #1 and Assumption #3.)
b. What happens  Verbally.
Your model assumes only
X
1
causes
Y
to change,
but
in truth, the variable
X
2
also causes
Y
to change.
The effects of
X
2
on
Y
are not accounted for in your model.
As a result, the effect of
X
2
Y
gets
tangled up
with the effect of
X
1
Y
.
We can't get a clear picture
of how changes in
X
1
affect changes in
Y
.
c. What happens  Mathematically.
The estimator that you use is:
1
2
1
ˆ
i
i
1
i
x y
=
x
a
∑
∑
This will be
biased
To show this take the expected value of the estimator and use the
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This note was uploaded on 12/08/2011 for the course ECON 312 taught by Professor Daniellass during the Winter '10 term at UMass (Amherst).
 Winter '10
 DanielLass

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