2sls Manual Standard Error Correction

[Mansoor Afzali]

Hi,

I know that this question has been asked before but I still couldn't get anything from reading the other threads. Can you please shed some light on how to correct for standard errors in case we decide to do 2sls manually. Someone told me that including the inverse mills ratio in the second stage will give the same results, is it true?

[FernandoRios]

Hi Mansoor
For your first question. I m also looking into that, but have not done it before. I believe there are a couple of papers by Joseph V. Terza (with publications in Stata Journal), have the procedure explained with a working example.
Regarding your second question. What you are describing is known as control function approach. When your first stage is an OLS, you could include the residuals from that regression into your main regression, and the results would be equivalent to using two stage least squares. The inverse mills ratio is a term more suited to heckman selection models. However, you will find that the Inverse Mills ratio is also referred to as generalized residual.

HTH
Fernando