st: Re: 2sls by hand

[Christopher F Baum <baum@bc.edu>]

--On Friday, December 13, 2002 2:33 -0500 Lee wrote:

> Hi, Listers
>
>      I am puzzled that the IVREG and 2sls give out the following different
> results:
They do not; you're getting essentially the same beta-hats in each case 
(you should do 'predict double' to increase accuracy) and that is all that 
you can expect from doing 2SLS 'by hand'. As any textbook indicates, doing 
2SLS 'by hand' will give you the wrong s^2, var-cov matrix, residuals, and 
summary statistics, since the residuals you want from the second stage are
(y - X betahat) whereas those mindlessly computed by -regress- are (y - Z 
betahat). Likewise, the var-cov for 2SLS will involve both X and Z, whereas 
what you have from -regress- is s^2 (Z'Z)inv, with the wrong s^2. If you 
went to the trouble of calculating the correct statistics 'by hand' after 
the manual second stage -regress-, you would reproduce -ivreg- perfectly.

You _have_ dealt properly with one issue that plagues many users of 
-ivreg-: the fact that the first stage regression should include _all_ of 
the instruments, not merely the excluded instrument. People routinely write 
and ask how to prevent Stata from using all of the included exogeneous 
regressors as instruments in ivreg, which indicates a fundamental 
misunderstanding of the instrumental variables estimator.

Kit
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