Why do IV-probit command and CMP probit command yield different results?

[Jeffery Xu]

Hello,

I want to apply instrument variable in my probit model. Initially, I used 'ivprobit' command to estimate my results. Then as a diagnostic test, I used 'cmp' command and re-ran the model. I expected the results yielded by these two techniques would be similar. However, the final results differed significantly. I have attached my commands as well as results below for your review. I will be much appreciated if someone can help me!

In my model, 'obesity' is a binary variable. 'lnwage' is assumed as an endogenous variable while 'emp01esop15' is the instrument variable.

I noticed that the total observations after the execution of these two techniques are different. Is this the reason that why the results are different?

I am sorry for the double post. Since this post presents readable codes and more details concerning my question, please ignore my first post.

The IV-Probit command is:

ivprobit obesity (lnwage=emp01esop15) povertyratio workinghrs hhsize15 newindustry degree maritual sex15 region2015 age2015 age2 workinghr2 emotion ethnicity97 emp01medinsur15

The results after IV-Probit command is:

The CMP command is:

cmp (obesity = lnwage povertyratio workinghrs hhsize15 newindustry degree maritual sex15 region2015 age2015 age2 workinghr2 emotion ethnicity97 emp01medinsur15) (lnwage = povertyratio emp01esop15 workinghrs hhsize15 newindustry degree maritual sex15 region2015 age2015 age2 workinghr2 emotion ethnicity97 emp01medinsur15), ind($cmp_probit $cmp_cont) qui

The CMP result is:

[David Roodman]

Yes, the difference in observations is the key. If the data in one observation are complete for one equation but not the other, cmp will still model the dependent variable in the equation for which the data are complete. You can prevent this with an "if" clause.

[Jeffery Xu]

Yes, the difference in observations is the key. If the data in one observation are complete for one equation but not the other, cmp will still model the dependent variable in the equation for which the data are complete. You can prevent this with an "if" clause.

Thank you, David. Now I am clear why the results yielded by these two techniques are different. Since my endogenous regressor is continuous, I think ivprobit (add if clause to restrict observations) will be much appropriate in this context. But I have another question for you. I want to apply the instrument variable to another ordered probit model. Do you think it’s necessary to add ‘if clause’ to restrict observations under this context? Just as what ivprobit (Heckman theory) do?

[David Roodman]

It depends on what you think causes the missingness. cmp's default greedy approach could better if you think the pattern of missingness is endogenous, so that parameters in the equation with the larger sample will actually be less biased if estimated from that larger sample. Their estimates will not be constructed by that biased selection. Or you can construct a story going the opposite way.