Heckma/selection model with categorical variable

[Cristiano Bellavitis]

Hi everyone,

we have some endogeneity risks we would like to address. Our current model is as follows:

probit 1.orgstructurenumericthree $controls
predict phat, xb
gen imr = exp(-.5*phat^2)/(sqrt(2*_pi)*normprob(phat))
reg lnmarketcap $controls i.orgstructurenumericthree imr , vce(robust)

I am using an inverse mills ratio because reviewers raised endogeneity issues for our IV: i.orgstructurenumericthree which is a categorical variable with 3 values (1,2,3).

I wanted to use the above but I believe the selection model needs to be a dummy? Is there a different model we can implement to control for the non-randomness of the variable of i.orgstructurenumericthree? I do need an instrument, right? Or is there a way to not need one?

Any suggestion is welcome, and thank you in advance.

[Jeff Wooldridge]

I have some suggestions if you have an instrument. If you don’t, then adding the IMR is not convincing. One shouldn’t get identification off of a nonlinearity.

[Cristiano Bellavitis]

I have some suggestions if you have an instrument. If you don’t, then adding the IMR is not convincing. One shouldn’t get identification off of a nonlinearity.

Thank you, Jeff. We are in the process of identifying an instrument. Could you please elaborate on your suggestions?