Predicted values after running a Tobit model with an endogenous variable

[Mat Log]

Hi all,

I want to estimate a Tobit model with a binary endogenous regressor. As suggested elsewhere on the forum, I use the user-written cmp command.

However, I am not sure on how to use the predict command after using cmp. When analyzing a simple IV Tobit model with a continuous endogenous regressor, I have different expected values when using Stata's command ivtobit and cmp. Please find below the code to compare the two sets of expected values.

I would like to understand where the difference is coming from. Importantly, the linear predictions are the same for the two commands. The difference is only visible for predicted probabilities and expected values.

webuse laborsup, clear
        
        ivtobit fem_inc kids (male_educ = other_inc fem_work), ll first
        predict pr1 if e(sample), e(10,.)
        sum pr1

        
        cmp (fem_inc=kids male_educ) (male_educ=kids other_inc fem_work), ind("cond(fem_inc>10,$cmp_cont,$cmp_left)" $cmp_cont)
        predict pr2 if e(sample), e(10 .)
        sum pr2

[Mat Log]

Please let me know if you need more information or if the example is not sufficient.

Thanks!

[Phil Bromiley]

Before working on the predictions, you should start with the parameters are different. Given that, of course the predictions differ. I don't know what is causing the problem - the only obvious difference is cmp treats the highest observation as censored.

I'm a little confused by your model. I would think you have to include female working in a model of female income and not treat it as an exogenous instrument for male education. I would have thought female working is much more endogenous than male education. All your truncated observations are when females don't work (i.e., 272 fem_work=0, with all the fem_inc values at 10).

I suspect this is not really a tobit situation. You don't have truncated 10's but rather they're in a different situation. If you want to look at the effect of working on income, then why not just look at working women?

[Mat Log]

Thanks for your reply.

Parameters are the same, that's precisely why I am puzzled. What do you mean by:

the only obvious difference is cmp treats the highest observation as censored.

I do not see in the example I wrote why cmp would treat the highest obervation as censored, but I may miss something?

Sorry about the model, I simply took the example given in the help file of cmp, there is no meaning behind this model, I just wanted to compare the two commands.

Thanks again