ECONOMICS 140
Professor Enrico Moretti
4/05/10
Lecture 9
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LECTURE
I'm starting off today’s lecture where we left last
week. The broad theme of last week's and today's
lecture is problems with the regression model. As
we saw last week, there are six problems with the
regression model.
First problem is when we include irrelevant
variables. The second more serious problem is
when we exclude relevant variables. The third
problem is multicollinearity, the fourth problem is
measurement error, the fifth problem is
heteroscedacity and the sixth problem is data
scatter.
Today, we will cover problems number three, four,
and possibly number five.
Examples of Excluding Relevant Variables
Last week, I proved to you that when we exclude a
relevant variable, we will have a bias.
E[
= β
1
+ Bias
Bias= β
2
* Σx
2
(x
1

)
Σ (x
1

)
2
= β
2
* b
12
If β
2
= 0, then the variable omitted is not relevant to
the outcome.
If b
12
= 0, then there is no correlation between x
2
and
x
1
. This means that we are excluding a variable that
is not correlated with the variable of interest.
Remember that the true model is:
The estimated model is:
When we leave out the second beta variable, x
1
is
picking up two effects, the effect of x
2
and the true
effect of x
1
.
Student:
What about the fit even if x
1
and x
2
are
uncorrelated? Would the true equation have a better
fit than the estimated equation?
Even if x
1
and x
2
are uncorrelated, the goodness of
fit can only go up when we have more variables. I
have to stress that goodness of fit is a 2
nd
or 3
rd
order concern, one that we do not need to think too
much about.
Now I will pick up from where we left off last week
with some examples. Imagine if I wanted to explain
the relationship between your grade in this class and
IQ.
Example 1:
The true model is:
The estimated model is:
How does the estimated
β,
, relate to the
β
you get
from estimating the true model? My guess is that
your estimated beta will be too large compared to
the true
β. There will be
a positive bias. To what
extend is this true? It is true under two conditions:
1.
γ > 0
2.
b
12
> 0
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4/05/10
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 Spring '10
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 Regression Analysis, measurement error, UC Board of Regents, ASUC Lecture Notes, Lecture Notes Online

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