Consider the constant-term-only regression model Yt = 0 + ut, where ut follows the stationary AR(1) model
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![Consider the](https://dsd5zvtm8ll6.cloudfront.net/si.question.images/image/images11/909-M-S-L-R(8275)-1.png)
with mean 0 and variance
![Consider the](https://dsd5zvtm8ll6.cloudfront.net/si.question.images/image/images11/909-M-S-L-R(8275)-2.png)
a. Show that the OLS estimator is
![Consider the](https://dsd5zvtm8ll6.cloudfront.net/si.question.images/image/images11/909-M-S-L-R(8275)-3.png)
b. Show that the (infeasible) GLS estimator is β0GLS =
![Consider the](https://dsd5zvtm8ll6.cloudfront.net/si.question.images/image/images11/909-M-S-L-R(8275)-4.png)
c. Show that β0GLS can be written as β0GLS =
![Consider the](https://dsd5zvtm8ll6.cloudfront.net/si.question.images/image/images11/909-M-S-L-R(8275)-5.png)
d. Derive the difference β0 - β0GLS and discuss why it is likely to be small when T is large.
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Related Book For
Introduction to Econometrics
ISBN: 978-0133595420
3rd edition
Authors: James H. Stock, Mark W. Watson
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