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Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge
Edition 6ISBN: 130527010XIntroductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge
Edition 6ISBN: 130527010XConsider the simple regression model
y = ?0+ ?1x + u
and let z be a binary instrumental variable for x. Use (15.10) to show that the IV estimator 
can be written as
where 
and 
are the sample averages of 
and 
over the part of the sample with 
= 0, and where 
and 
are the sample averages of y. and x. over the part of the sample with 
= 1. This estimator, known as a grouping estimator, was first suggested by Wald (1940).
Verified
Step 1 of 2
Consider the simple regression model:
Consider 
be a binary instrumental variable for 
Consider 
is the number of observation with 
That implies
Also 
Consider 
is the average of 
for these 
observations
Consider 
is the average of 
for these 
observations
Consider there are 
observations with
such that 
is the average of 
for these 
observations and 
is the average of 
for these 
observations
Thus,
Where, 
is the overall average of 
for 
number of observations
The instrument variable estimator for 
is given by:
Now consider the numerator 
Now consider the denominator 
Hence,
Step 2 of 2
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