Testing validity of instruments using the cmp command

[Felix Lukowski]

Dear all,

I am estimating an IV-oprobit using the cmp command. How can I test the validity of my instruments? I have already tried different ivregress postestimation commands (e.g. estat firststage) as well as the ivreg2 "first" option. My cmp command is:

cmp (edulevel=patience `controls') (patience=parentsedu `controls') , ind($cmp_oprobit $cmp_cont) nolr

Thank you for your help.

[David Roodman]

Felix, if this were a pure linear regression, a test of validity (exogeneity) would be impossible since the regression is exactly identified--one instrument and one instrumented variable. However, since it is not a linear model, you can try adding the instrument to the second stage. Technically the regression will still be identified (I discuss this in my cmp paper), so if there is a significant coefficient on the added instrument, that is worrisome--especially since this is probably a weak test (as I say, it wouldn't work at all in a linear model). I do something like this in my replication paper with Jonathan Morduch.

As for instrument weakness, I think first-stage diagnostics like those from ivregress or ivreg2 are probably as good as you can get. Whatever theoretical grounding they have doesn't fully carry over to your model, but the test results can still be mentioned as indicative.
--David

[Felix Lukowski]

Thank you, David. I really appreciate your help.