IV with binary endogenous regressor, 2SLS, 2SRI, Panel IV

[Ale Rengifo]

My question is about what is the best model if I have an endogenous variable and the dependent variable is dichotomous. It can take 0 or 1. I've been reading this article "https://bmcmedresmethodol.biomedcent...18-0513-y#Sec1" where they use GMM and 2SRI to compare the results. But I read in another post that they were using Probit xtivreg lwage exp exp2 (uks = ms), fe.
Now I'm confused about which I should use.
My variables are:
y =stunting (height-for-age for children)
x1=mother's years of education
x2=father's years of education
x3=house wealth (endogenous variable)
I hope someone can help me, thank you.

[Joro Kolev]

I did not quite understand your variables. Or rather you are saying inconsistent things about your variables.

I do not know what is y =stunting, is this binary or continuous variable?

And certainly your x3=house wealth (endogenous variable) sounds to me like a continuous variable, and yet you say "IV with binary endogenous regressor."

You can always do 2SLS. Whether it is the most appropriate thing to do, authorities disagree.

[Ale Rengifo]

Yes, stunting is a binary variable and X3 is a continuous variable.

[Jeff Wooldridge]

Ale: The description in the heading reads backwards to me. It looks like y is binary and your endogenous regressor is continuous. There is no "probit ivreg" command in Stata. What you probably want is ivprobit. If z is your IV for x3:

ivprobit y x1 x2 (x3 = z), twostep
margins, dydx(x3)

You can also try 2SLS estimation of a linear model.

ivregress 2sls y x1 x2 (x3 = z), vce(robust)

Sometimes the coefficient is close to the average marginal effect from ivprobit. Sometimes it isn't.

But now I see that maybe you have panel data?

[Juan Caro]

Prof. Wooldridge, could you extend on the panel data aspect? I have a similar setting, and I would like to account for unobserved heterogeneity. I know that the method proposed in Papke and Wooldrigde (2008) only applies when x3 (in this case) is continuous, so I wonder if there is a similar approach to binary endogenous treatment when the outcome is also binary. Thank you!