ECONOMICS 140
Professor Enrico Moretti
4/12/2010
Lecture 10
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ANNOUNCEMENTS
Today, we will finish chapter 13. You should skip
13.6.1. Then we will cover chapter 18, which is
related to chapter 13. Then we might start on
chapter 14, but I doubt it will happen.
On April 19
th
, we will finish chapter 14 and cover
16. To refresh your memory, chapter 14 is the
current chapter and it covers four of the problems
with regression models. Chapter 18 proposes some
solutions to fix that. You should skip 18.5. Chapter
16 covers two more problems with regression
models.
We will skip chapter 15 and 17. Chapter 15 is a
fairly technical treatment of a system of equations. I
don’t think it will be a useful chapter for most
people and covers far more material then what you
will need. Chapter 17 is about the time series of
econometrics. For example, stock crisis and GDP
where variables are linked to the passing of time. If
anyone is interested in either of these two topics, I
will be happy to further discuss this with you during
office hours.
On April 26
th
, we will have practice problems in
class. I will post them in advance and I encourage
you to solve them before class.
The week of April 26
th
, I will have extra office
hours. There will still be section this week.
There is no lecture the week of May 3
rd
, but there
will still be sections. I will have extra office hours
this week.
I will post a problem set tonight and it will be due
on April 19
th
. I will send out an email about the
exact dates and times of the extra office hours.
LECTURE
Recap of Last Lecture
Last lecture, we left off in chapter 13 talking about
measurement error. Think about the model where
y=
β
0
+
β
1
x
1
* +
Ε
x
1
* is unobserved
x
1
= x
1
* + U
We made some assumptions about U last week.
What are they?
1. The mean of U is zero. E[U] = 0
2. x
1
* and U are uncorrelated. E[x
1
* U]= 0
3. E[U E]= 0
y=
β
0
+
β
1
(x
1
–U) +
Ε
y=
β
0
+
β
1
x
1
–
β
1
U) +
Ε
where 
β
1
U + E are the residual
E[
β
1
– (b
12
β
1
)
.
If
β
1
is positive, then the attenuation bias is
negative.
Student:
What does the E[x
1
* U]= 0 mean?
This is the covariance of x
1
* and U.
What it means
in words is that the measurement error has nothing
to do with x
1
. Let’s look at an example with
schooling. I want to find the relationship between
schooling and wages so I call up different
individuals and ask them. Some will underreport
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 Regression Analysis, measurement error, UC Board of Regents, ASUC Lecture Notes, Lecture Notes Online, Compulsory Schooling Laws

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