Doubt about Heckman

[Alejandro Torres]

Dear statalisters,

I am writing you because I have doubts about heckman regressions that I can solve just reading.
I am going to do points in order to try to be clear about my arguments.

1. I was told that I should test a regression for endogeneity (omitted variable) and try to find an instrument, I was told to use Heckman.
2. When I start reading about heckman I found that is used for selection bias, that I understand as a kind of endogeneity (read Green and some papers about it).
3. I found also papers that run heckman for treating endogeneity, not explicitly selection bias.
4. I found papers that explicitly says that run one heckman for selection bias and other heckman for endogeneity bias.
5. I found that some papers that use heckman, use after "," :

   select ((DV=DV!=)=instrument)

   but other use

   select (IV=instrument)

   , similar syntax differences after treat using etregress.
6. I found papers that in the first regression use only the instrument and others use the instrument plus other variables included in second regression.
7. Finally, I did all the combination of analysis and I have of course a mix of results.

So, are there please any possibility from you to give me some help about what is correct? are all correct but depend of the interest? what is the correct sintax?

Thank you so much for any help about it.

Alejandro

[Phil Bromiley]

Wait - it is currently in fashion to label all problems that result in a correlation between rhs variables and the error as endogeneity. But these can reflect very different causes and have somewhat different solutions. Is the problem an endogenous variable, an omitted variable, or sample selection or what? You mention omitted variable - if you really don't observe the omitted variable at all, then there is not a lot you can do. I guess if you could be sure which of your rhs variables correlate with the omitted variable, you could do an endogeneity correlation, but it is hard to be confident that you really know exactly which variables correlate with the omitted variable, etc. You could include variables that you think associate with the omitted variable and hope they're good enough.

The meaning of the first select statement is not very clear, and why DV would be in the first but not the second is not clear. The second format is probably what you should use. While one could use Heckman in some cases of endogeneity, it is really intended for selection. ivreg and eregress are good for endogeneity. For a good estimation, you need at least one variable that is associated with the endogenous variable but does not belong in the primary equation, this goes for both Heckman and ivreg.

[Alejandro Torres]

Dear Phil, I just read your message but it is still useful and clear, I really appreciate it.
Thank you very much for the explanation.
best regards,

Alejandro