OLS estimators assumptions

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david
Posts: 22
Joined: Thu Apr 07, 2011 10:28 am

OLS estimators assumptions

Postby david » Tue Feb 26, 2013 6:53 pm

Dear Carol,

I hope things are well with you!

After reading sections on I.4.3.4 and I.4.3.5, i have a few questions:

1) "Although the Gauss-Markov theorem has its limitations, OLS estimators will always be consistent provided that the error process is stationary." Does this mean that OLS estimators will always be consistent, even though the explanatory variables are stochastic, when the error process is stationary?

2) What does it mean when you say 'if the explanatory variables are stochastic but satisfy some standard (and not very restrictive) regularity conditions"? i.e. I dont know what the regularity condition means.

3) In I.4.3.5, we use Jarque-Bera to test if the residuals are normal. But the real issue, as i have understood, is whether error process is i.i.d, because if it is i.i.d and our sample is sufficiently large, then asymptotically our OLS estimators would be BLUE and have normal distributions which allow t and F tests to be legitimately used. So why do we bother to check whether residuals are normal, instead of checking if they are i.i.d?

Carol, many thanks for the MRA series. They are absolute gems!!!

Look forward to your reply!

Many thanks and best regards,

David

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: OLS estimators assumptions

Postby coalexander » Sun Mar 10, 2013 11:45 am

Hi David,

Apologies for taking so long to reply. I have been travelling.

1) Yes, even with stochastic regressors, OLS is consistent

2) Regularity conditions refer to behaviour of sample data as sample size increases -- in this simple case we require that the covariance matrix must exist -- more generally regularity conditions require finite moments of higher orders in regularity conditions.

3) Normality is required for inference -- ie. for t-tests etc. to be valid.

Cheers, Carol


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