Overidentification test after endogenous treatment effects model

[Parul Gupta]

I am using the endogenous treatment effects model -eteffects-. Since I am using two excluded variables to model the selection equation, the reviewer is asking for an overidentification test. From what I understand, this is not possible with -eteffects-.

Can I conduct a Hansen test? If not, what is the workaround, or possible response to the reviewer? I am already reporting the result of the endogeniety test.

[George Ford]

I think the reviewer is a bit off here, but the request is boilerplate.

The eteffects estimator does not admit a Hansen/Sargan test because it is exactly identified (it's a control function approach). In eteffects, the second excluded instrument contributes to identification rather than providing a redundant moment.

If you must, then you might estimate the linear-IV analog of the model instrumenting the endogenous variable with your exclusions (ivreg2 , endog(endovar) robust). Then report the various stats. The effect size may be different, however—this is not a clean alternative. So, at best, you can say the diagnostics are “supportive” of the joint validity of the instruments. There may be other options I'm not aware of.

webuse cattaneo2 , clear
eteffects (bweight i.prenatal1 i.mmarried mage i.fbaby) (mbsmoke i.mmarried mage i.fbaby medu fedu)
ivreg2 bweight i.prenatal1 i.mmarried mage i.fbaby (mbsmoke = medu fedu) , endog(mbsmoke) robust

[Jeff Wooldridge]

One possibility is to include one of the two instruments in the outcome model. If the exclusion restriction is valid then its coefficient should be small and statistically insignificant. So, if your excluded IVs are z1 and z2, include, say, z1 in the model for y.

[Parul Gupta]

George Ford Thanks for the suggestion. I can try to include the IV results, show the difference between eteffects and IVREG and then run the endogeniety test to try and convince the reviewers.

Jeff Wooldridge Are you suggesting the following?

eteffects (bweight i.prenatal1 i.mmarried mage i.fbaby) (mbsmoke i.mmarried mage i.fbaby medu fedu)

eteffects (bweight i.prenatal1 i.mmarried mage i.fbaby fedu) (mbsmoke i.mmarried mage i.fbaby medu)

eteffects (bweight i.prenatal1 i.mmarried mage i.fbaby medu) (mbsmoke i.mmarried mage i.fbaby fedu)

Then show that the coefficient of fedu and medu, when included in the outcome equation respectively is small and insignificant?

[Jeff Wooldridge]

Yes, this is exactly what I was suggesting. It's not perfect because it depends on which variable you leave out, but it is a valid test.

[Parul Gupta]

Thank you for confirming. Can I cite any of your papers to support this?

The reviewer also asked for the Conley test. Can that be done after -eteffects- or after -ivprobit-?