This preview shows pages 1–3. Sign up to view the full content.
Lecture Notes 10
Econ 410 – Introduction to Econometrics
1
Instrumental Variables Regression
Instrumental variables (IV) regression is a way to obtain consistent estimators of the
regression coefficients when one or more of the regressors are correlated with the error
term. This correlation might arise for different reasons: omitted variables, errorsin
variable, simultaneous causality….
In IV regression, the variables in the regression model are called:
•
endogenous variables, if they are correlated with the error term;
•
exogenous variables, if they are not correlated with the error term.
Let
X
be
an
endogenous
va
r
iab
le
.
The
idea
of
IV
reg
ress
ion
is
to
th
ink
X
as
composed of two parts: one that is correlated with
u
and the other one that is not. If we
had information that allowed us to isolate this second part, than we could focus on the
variations of
X
that are not correlated with the error term and disregard the part of
X
that causes problems to the OLS estimator.
The information about the movements in
X
that are uncorrelated with
u
is obtained
from one or more additional variables that are called instrumental variables
(or
instruments
). IV regression uses these instruments to isolate the movements in
X
that are
uncorrelated with
u
which in turns permits to estimate consistent OLS coefficients.
Regression model with one regressor
Consider the model:
i
i
i
u
X
Y
+
+
=
1
0
β
β
If
()
0
,
≠
i
i
u
X
corr
, then
0

≠
i
i
X
u
E
and the OLS estimators
0
ˆ
β
and
1
ˆ
β
are biased and
inconsistent.
Let
Z
be the instrument that we want to use to isolate the movements in
X
that are
uncorrelated with
u
. For
Z
to be a valid instrument, it must satisfy two conditions:
1)
Instrument relevance
:
0
,
≠
i
i
X
Z
corr
This condition ensures that the movements in
Z
are related to the movements in
X
.
2)
Instrument exogeneity
:
0
,
=
i
i
u
Z
corr
This condition ensures that the part of the movements in
X
that is captured by
Z
is
exogenous (that is, not correlated with the error term).
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Lecture Notes 10
Econ 410 – Introduction to Econometrics
2
Two Stage Least Squares Estimator
The Two Stage Least Squares (TSLS) estimator is a common IV estimator that can be used
when one or more of the regressors are correlated with the error term. The TSLS estimator
is obtained in two stages.
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 07/28/2010 for the course ECON 410 taught by Professor Staff during the Fall '08 term at Wisconsin.
 Fall '08
 Staff
 Econometrics

Click to edit the document details